gait stability using zmp algo.pdf

TASK ORIENTED STABLE GAIT SYNTHESIS IN BIPED LOCOMOTION By Rachit Kumar Rastogi

MAY, 2005

THESIS

Al l a h a b a d

Date:

I/ W E H EREBY RECOMMEN D TH AT TH E TH ESIS PREPARED U N D ER

MY/ OU R

SU PERVISION

BY

Rachit

Kumar

Rastogi

ENTITLED Task oriented stable gait synthesis in biped locomotion BE ACCEPTED

IN

PARTIAL

REQU IREMEN TS

FOR

TECH N OLOGY

IN

TH E

FU LFILLMEN T D EGREE

OF

IN FORMATION

OF

TH E

MASTER

OF

TECH N OLOGY

(INTELLIGENT SYSTEMS) FOR EXAMINATION

COUNTERSIGNED

( Dr. G. C. Nandi), Dean (Academic), Indian Institute of Information Technology, Allahabad

DEAN (ACADEMIC)

THESIS ADVISOR

Al l a h a b a d

CERTIFICATE OF APPROVAL*

Th e fo re go in g th e s is is h e re by a p p ro ve d as a cre d ita ble s tu d y in th e are a o f In fo rm atio n Te ch n o lo gy ca rrie d o u t an d p re s e n te d in a m an n e r s atis facto ry to w arran t its acce p tan ce as a p re re qu is ite to th e d e gre e fo r w h ich it h as be e n s u bm itte d . It is u n d e rs to o d th at by th is ap p ro val th e u n d e rs ign e d d o n o t n e ce s s a rily e n d o rs e o r ap p ro ve an y s tate m e n t m ad e , o p in io n e xp re s s e d o r co n clu s io n d ra w n th e re in bu t ap p ro ve th e th e s is only for the purpose for which it is submitted. COMMITTEE ON FINAL EXAMINATION FOR EVALUATION OF THE THESIS *Only in case the recommendation is concurred in

Task oriented Stable gait synthesis In biped locomotion A Thesis Submitted In Partial Fulfillment of the Requirements For the Degree of Master of Technology In Information Technology (Intelligent Systems)

by

Rachit Kumar Rastogi under

Dr. G. C. Nandi Dean(Academic) Indian Institute of Information Technology, Allahabad

to the Indian Institute of Information Technology, Allahabad May, 2005

Abstract Stability is the core issue in the robotics systems & it s enduring integration with biomechanics raises the issues like reliability of the reinstated body part e.g. Limb, Safety of the Amputee, capability to learn quickly with the environment & understand the stability in different postures. The problem discussed in the thesis is the stability analysis of a human kind of structure while it is carrying some load (e.g. at back, front, top or any of these situations simultaneously). Trajectories of different Joints are evaluated and stable gait of a person in a particular posture is predicted by selecting the trajectory which gives the maximum distance of Zero Moment Point (ZMP) from the edges of the stability region. The results were compared to kinematics of various subjects captured by video streaming. The locomotion of a 7 Link biped robot was simulated using the standard open dynamics engine which helped in creating, destroying & moving the robot bodies considering the external friction, collision etc. A ZMP control algorithm was evolved which was used for maintaining the stability of amputee during his walking on uneven terrains. Goal is to simulate the motion of a human body while carrying weight, as by taking care of various joint parameters such as velocity, torques etc. Since humans do not base their decisions on precise measurements while walking, a control design was also proposed based on ZMP architecture for generation of angular patterns of gait cycle. In that model reference values were generated using control algorithm & values coming from sensors were verified with that. Finally the patterns were then used for generation of damping signals in active prosthetic knee joints. The results suggest a feasible solution to gait pattern generation and adjustment of damping in prosthetic knee joints to achieve humanoid walking.

Keywords: ZMP, limb, gait, stability region.

"There is only one condition in which we can imagine managers not needing subordinates, and masters not needing slaves. This would be if every machine could work by itself, at the word of command or by intelligent anticipation." - Aristotle, from his justification of slavery in Politics

Acknowledgement Before, I get into thick of things; I would like to add a few heartfelt words for the people who were part of my thesis in numerous ways, people who gave unending support right from the beginning. During this period, the faculty members and my batchmates took keen interest and participated actively. They are very efficient and qualified in their respective disciplines.

I express my sincere gratitude to Dr. G.C.Nandi, Professor & Dean, IIIT Allahabad for his affectionate encouragement and guidance during the entire Thesis. The Brainstorming sessions with him & my group members viz. Hemant Kumar Anand, Khalil Jibran & V Naresh Reddy organized every week worked as the foundation stone for the Thesis work.

I would like to thank Dr. M.D. Tiwari, Hon ble Director, IIIT-Allahabad for the facilities and environment for research.

Not the least I would like to appreciate the support and guidance of all my Teachers specially Dr.U.S.Tiwary, Dr. Sudip Sanyal & Prof. M. Radhakrishnan and my all M.Tech. Friends without whose help and support the thesis could not have been a success.

I am also thankful to Bhaskar Gupta & Hemant for paying special attentions & giving me their valuable time to discuss and clear the doubts in between the Thesis.

Lastly I would like to thank my family for the love, support and encouragement that they have given me through the past months, helping me to persevere in my studies. In addition, wish to thank specially Maa & Pa, for giving me the educational opportunity that allowed me to do my post graduation.

List of Figures Figure 2.1

Walking Cycle

Figure 2.2

Different views of a Human during walking

Figure 3.1

Biped Model and Degree of Freedoms of it s joints

Figure 4.1

Different views of Lower Limb prosthesis

Figure 4.2

Commercially available knee designs

Figure 4.3 (a) Sagittal assembly of C-Leg (b) Sagittal View of C-Leg Figure 4.4 (a) Sagittal view of subject wearing C-Leg (b) Frontal view of subject wearing C-Leg Figure 5.1

Complete Gait Cycle

Figure 5.2

Forces and moments acting on the Foot in Single support phase

Figure 5.3

Moments acting on the Foot & trying to rotate it

Figure 5.4

Position of ZMP point

Figure 5.5

The stabilizing subsystems of the spine.

Figure 5.6

Dysfunction of spinal stability system.

Figure 5.7

The load-deformation behavior of a spinal Segment, showing the neutral and elastic zones that constitute the physiological ROM

Figure 5.8

Depicting the situation during walking and movement of ZMP

Figure 5.10

Walking cycle of experimental biped

Figure 5.11

Sagittal view of 7-Link Biped Model (with weight on back)

Figure 6.1

Posture of Biped model during a complete walking cycle

Figure 6.2

Parameters of walking

Figure 6.3

Walking cycle

Figure 6.4 (a) Biped Model (b) Leg of Biped Model Figure 6.5

Active Knee control using ZMP

Figure 6.6

Design of Biped Model Damping Control System

Figure 7.1

Left Ankle motion curve in a complete cycle

Figure 7.2

Left Ankle motion curve (Xa,Za,Theta) in multiple cycles

Figure.7.3

Right Ankle motion curve (Xa,Za,Thetaa) in single cycle

Figure 7.4

Right Ankle motion curve (Xa,Za,Theta) in multiple cycles

Figure 7.5

Hip motion curve (Xh,Zh,Thetah) in single cycle

Figure 7.6

Hip motion curve (Xa,Za,Theta) in multiple cycles

Figure 7.7

X Position of different joints in the system in multiple cycles

Figure 7.8 (a) Trajectory of Left Knee (b) Trajectory of Right Knee Figure 7.9

Hand motion curve in multiple cycles

Figure 7.10

Velocity of Left Ankle

Figure 7.11

Velocity of Right Ankle

Figure 7.12

Velocity of Left Knee & Velocity of Right Knee in multiple cycles

Figure 7.13

Velocity of (a) Hip (b) Hand in 5 cycles

Figure 7.14

Acceleration of Left Ankle in 3 cycles

Figure 7.15

Acceleration of Right Ankle in multiple cycles

Figure 7.16

Acceleration of Left and Right Knees

Figure 7.17

ZMP Results with varying Load

Figure 7.18

Complete Gait Cycle with Load on Back equivalent to 10% of Subject s Weight

Figure 7.19

Complete Gait Cycle with Load on Back equivalent to 10% of Subject s Weight

Figure 7.20

Comparison plot of Ankle parameters obtained through the video and model

Figure 7.21

Stick diagram for Biped walking (Interval = 0.01 second, cycles = 5)

Figure 7.22

Angular Velocity of Hip & Knee

Figure 7.23

Variation in Trunk inclination angle by varying load

Figure 7.24

Damping in Left Knee

Figure 7.25

Damping in Right Knee

TABLE OF CONTENTS Chapter 1 INTRODUCTION........................................................................................... 1 1.1 Outline of thesis ................................................................................................................... 2 1.2 Analysis of previous research ............................................................................................. 3 1.3 Key issues ............................................................................................................................. 5 1.4 Statement of the Problem ................................................................................................... 5

Chapter 2 HUMAN WALKING...................................................................................... 7 Chapter 3 BIPED LOCOMOTION............................................................................... 10 3.1 Problems in Biped Locomotion Analysis......................................................................... 11 3.2 Basic System Architecture for Biped Locomotion.......................................................... 11 3.3 Possible approaches for Biped Locomotion .................................................................... 12 3.3.1 Sesorimotor Reflexes ................................................................................................................ 13 3.3.2 Central Pattern Generators (CPG) ............................................................................................. 14

Chapter 4 ACTIVE LIMB PROSTHESIS ................................................................... 15 4.1 Prosthetic Knee designs .................................................................................................... 17

Chapter 5 MEHTODOLOGIES ADOPTED ............................................................... 19 5.1 Walking Primitives............................................................................................................ 19 5.1.1 5.1.2 5.1.3 5.1.3

Gait Cycle.................................................................................................................................. 20 Zero Moment Point (ZMP)........................................................................................................ 23 Stability of Physical Structure in walking ................................................................................. 26 Stability using ZMP approach ................................................................................................... 28

5.2 Plan of Work...................................................................................................................... 30 5.3 Formulations...................................................................................................................... 31 5.3.1 On Mathematical base ............................................................................................................... 31 5.3.2 On Logical base......................................................................................................................... 34

Chapter 6 DESIGN AND IMPLEMENTATION ........................................................ 35 6.1 Mathematical model for Trajectory generation ............................................................. 35 6.1.1 Foot Trajectory .......................................................................................................................... 35 6.1.2 Hip Trajectory ........................................................................................................................... 40 6.1.3 Knee Trajectory......................................................................................................................... 42

6.2 Algorithm for planning walking patterns ....................................................................... 45

6.3 Subject Motion Analysis (In real life situations)............................................................. 47 6.3.1 Database of Subject carrying weights in different modes ........................................................ 48 6.3.2 ANOVA (A statistical varaince analysis technique) ................................................................. 49

6.4 Comparison of Trajectories.............................................................................................. 50 6.5 Active Prosthetic Knee Control........................................................................................ 51 6.6 Introducation of damping in Artificial Limb.................................................................. 53 6.7 Simulation Algorithm........................................................................................................ 55

Chapter 7 RESULTS AND DISCUSSIONS ................................................................. 56 7.1 Trajectory of Joints ........................................................................................................... 56 7.2 Velocity of Joints ............................................................................................................... 62 7.3 Acceleration of Joints ........................................................................................................ 64 7.4 Trajectory of ZMP ............................................................................................................ 66 7.5 Subject Motion Database .................................................................................................. 67 7.5.1 Segmented Images Database ..................................................................................................... 68

7.6 Damping Analysis.............................................................................................................. 69

Chapter 8 RECOMMENDATIONS.............................................................................. 73 Chapter 9 CONCLUSION & FUTURE WORK.......................................................... 74 REFERENCES ................................................................................................................ 76

Chapter 1 INTRODUCTION

The conventional Walking Systems are pretty complex & taking lot of time for deciding their next step while Bipedal Robots are comparatively Fast & deciding their movements at Runtime but they are moderately taking care of some factors such as the change of terrain, presence of external forces, uneven walking pace & the presence of obstacles in the path.

In daily routine life Human beings are walking along-with some load possibly at their back or in hands. The load can be constant as the time is increasing and the person is walking or it can be varied depending upon the task the person is doing. Normally the person is carrying bucket of water or some load in bag and he is providing the necessary stimulus with the help of his trunk to support the load at back and with hands to support it at left or right side. Various joints attached in the system are having their respective torques and maximum load bearing capacity therefore once a load is been applied over the system then the joints readjust themselves to follow a smooth and stable trajectory in walking.

It s also been observed that in the walking Cycle of a subject (e.g. A Biped Robot) there are several possible Gaits for the next Step and Stability is the Major Issue to all these probable Gaits. Now out of all the available gaits some gaits are reachable but termed as highly unstable. Therefore in driving a biped robot the major task is to choose the most stable and reachable gait sequence within the shortest time. In case of Biped robot the stability is also dynamically analyzed by Hirai [1] in Honda s ASIMO; he had proposed methods of walking pattern synthesis based on zero moment point (ZMP) [2]. The ZMP is defined as the point on the ground about which the sum of all the moments of the active forces equals zero or that means the point onto which the forces acting from up 1

Chapter-1 Introduction

M.Tech.Thesis

side equals the forces generated by the down side. Now for stable biped walking ZMP is ought to be in the region made after joining all contact points. The hypothesis is that if ZMP is within the convex hull or region between the feet and the ground, then the biped robot is possible to walk. Basically, these analysis first design a desired ZMP trajectory, then derive the hip motion or upper body motion required to achieve that ZMP trajectory. The advantage of this method is that the stability margin can be large if the desired ZMP is designed near the center of the stable region.

The Thesis describes a proposed method for deriving the stable trajectory of various joints present in the biped system; in the presence of an external Load. It includes the ground conditions and dynamic stability constraint too. The sequence of work can be categorized as follows.

1.1 Outline of thesis: Chapter 2 reviews the basic idea behind the human walking, the joints and units necessary to produce the desired stimulus. Motion and co-ordination in between two different joints is discussed.

Chapter 3 discusses the evolution of Biped locomotion, how does it happen in the Robots and what are the basic control architecture for the same.

Chapter 4 gives the feel of Active Limb Prosthesis. It describes the way one has to go for adopting the Below Knee Amputation (BKA). Reliability of artificial prosthesis limb is enhanced by mixing the desired path concept.

Chapter 5 provides the entire description of the methodologies adopted in the thesis work.

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M.Tech.Thesis

Chapter 6 confers the development phase of the Thesis; which covers the mathematical model for the assumed biped model and ZMP Control algorithm along-with the modifications.

Results are discussed in chapter 7. The section covers the variation in position, velocity and acceleration of Body joints by varying the weights along the body & obtains the stable trajectory of ZMP in weighted condition.

Conclusion is given in the last section and scope of future integration is also incorporated.

Materials (e.g. URLs, books and research papers) used & studied are given in Reference.

1.2 Analysis of previous research: A well know fact is that biped robots are supposedly more mobile then the conventional wheeled robots, especially when we are considering the case of walking or running on rough terrain, climbing up the staircases & crossing the unevenly distributed obstacles of different-2 heights. In the past many related issues such as stability criterion, actual robot design and application [3], and dynamics analysis have been studied.

A focus of many studies has been walking pattern synthesis. Previously the prediction of the walking patterns was done by reading the data from human movements. McGeer [4] described a natural walking pattern generated by the passive interaction of gravity and inertia on a downhill slope. To extend the minimum-energy walking method [17] to level ground and uphill slopes, Rostami et al. [5] have proposed methods of gait generation by minimizing the cost function of energy consumption. Silva et al. [6] have investigated the required actuator power and energy by adjusting walking parameters. Since a biped robot tends to tip over easily, it is necessary to take stability into account when determining a

3


M.Tech.Thesis

walking pattern. Zheng et al. [7] have proposed a method of gait synthesis for static stability.

To ensure the dynamic stability of a biped robot, Shih et al. [8], and Dasgupta et al. [9] have proposed methods of walking pattern synthesis based on zero moment point (ZMP) [2]. As ZMP movement is depend upon the Hip motion and Hip movement is limited so it is not possible to achieve all desired trajectories. Furthermore, to achieve a desired ZMP trajectory, the hip acceleration may need to be large. In this case, since the upper body is relatively massive, energy consumption increases, and control for task execution of the upper limbs becomes difficult. Therefore, it is desirable to obtain hip motion without first designing the desired ZMP trajectory.

For a biped robot to be able to walk in various ground conditions, such as on level ground, over rough terrain, and in obstacle- filled environments, the robot must be capable of various types of foot motion. For example, a biped robot should be able to lift its feet high enough to negotiate obstacles, or have support feet with suitable angles to match the roughness of the terrain. Most previous literature has described foot trajectories generated by polynomial interpolation. When there are various constraints such as ground conditions and various foot motions, the order of the polynomial is too high and its computation is difficult, and the trajectory may oscillate.

The actuator s size and weight are restricted in developing a human-size biped robot or humanoid robot. Therefore, the power of actuators, the pick-torque, and pick-velocity of joints are limited. When the stability constraint and the ground conditions are satisfied, it is additionally desirable to select a walking pattern that requires small torque and velocity of the joint actuators. To reach this goal, it is necessary to clarify the relationship between the actuator specifications and the walking patterns. This relationship is also important to select suitable actuators and speed reduction devices such as gears and pulley-belts when designing the actual biped robot. However, this issue has not been sufficiently discussed before.

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M.Tech.Thesis

1.3 Key Issues: There can be any no. of additions into the present theory of Biped Locomotion but in general all Theories converge in case of:

Uneven terrain

Presence of external forces

Uneven or varying height obstacle avoidance

Variable mass system

Uneven walking pace (as usual we do analyze a Rhythmic Pace)

Wrong or un-optimized initial conditions

1.4 Statement of the Problem: Problem raised in the Thesis work is the generation of a unique gait sequence out of all available gait patterns in a particular posture of human being. The evolution had taken shape primarily in the form of Bipedal walking on the even terrain by maintaining the constant velocity. The systems were designed easily by applying the logic of forward kinematics and evaluating the positions of various joints present in the system with the help of joint angles (e.g. n-Link manipulator). Later on the systems developed were more advanced and used the concept of Inverse kinematics and then evaluate the joint angles for a desired position. Presently the world belongs to the study of dynamics which deals with the presence of external force in the system and the torque generated by them. The thesis work is the prediction of the reference trajectory (or standard trajectory) to be used

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M.Tech.Thesis

in the control module of an artificial prosthetic knee. The trajectory has to be derived in the way such that it gives the maximum stability for the humanoid in the presence of an external force or mass. As the problem can be enhanced further by considering the case of walking with load on both sides and variating the mass around the subject s body. It basically results in the generation of torques on every individual link and that torque causes the change in trajectory of ZMP therefore the system has to re-compute the ZMP while loading or unloading the weight. Problem can be molded further as by doing the analysis for un-even terrains and subject motion is analyzed on the sloppy surface. A method is also being proposed for planning walking patterns, which includes the ground conditions, dynamic stability constraint, and relationship between walking patterns and actuator specifications. Some values ought to be fixed up in control design as when sensor senses the values of parameters viz. knee, hip and ankle angles and after preprocessing these values has to be passed into the system. Therefore those values have to be compared and verified with some reference values, which can be generated using CPG or ZMP approach.

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Chapter 2 HUMAN WALKING Human walking is an inherently complex phenomenon. Broadly it can be divided in two phases during a complete walking cycle: Double Support Phase Single Support Phase (very minute interval) It can be termed as a process of "continuous and controlled falling." Every time for taking a step, one has to lean forward and fall slightly, and caught by the outstretched foot. If one failed to put the foot forward, he would fall flat on his face. After the foot touches the ground, the body s weight is transferred to it and knee bends to absorb the shock. The front leg then lifts the body and propels it forward as the rear leg swings up to catch you again, and the cycle repeats.

Fig.2.1 Walking Cycle

Walking is complex. Not only do the feet have to move across the ground, but the hips, spine, arms, shoulders, and head all move in sync to keep the system in balance. Although these movements are complex, if one break them down joint by joint, the mechanics of walking becomes clear. 7

Chapter-2 Human Walking

M.Tech. Thesis

The body parts actively taking part in the walking cycle are given as: The feet and legs - The feet and legs propel the body forward. To keep the character looking natural, one should always keep the joints bent slightly, even at full leg extension. The hips, spine, and shoulders - The body s center of gravity is at the hips; all balance starts there, as does the rest of the body s motion. During a walk, it s best to think of the hips motion as two separate, overlapping rotations. First, the hips rotate along the axis of the spine, forward and back with the legs. If the right leg is forward, the right hip is rotated forward. Second, at the passing position, the free leg pulls the hip out of center, forcing the hips to rock from side to side. These two motions are then transmitted through the spine to the shoulders, which mirror the hips to maintain balance. The arms - Unless the character is holding something or gesturing, its arms hang loose at the sides. When walking, they act like pendulums, dragging a few frames behind the motion of the hips and shoulders. Even at full extension, try keeping the arms slightly bent at the elbows, to make them look natural. The head and spine from the side - If you look at a character s spine from the side, you can see its general posture, which may be very stiff or slouched over, depending on the character s attitude. The spine also absorbs some of the shock transmitted to the hips from the legs, making it flex from front to back a bit. In a standard walk, the head tries to stay level, with the eyes pointing in the direction of the walk, but it bobs around slightly to stay balanced. If a character is excited, this bobbing will be more pronounced. The head may also hang low for a sad character, or may look around if the scene requires it. A model is drawn on the next page which has the humanoid structure and it s view from the Sagittal plane and frontal plane are pictured up.

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Chapter-2 Human Walking

M.Tech. Thesis

Fig. 2.2 Different views of a Human during walking

The Height of a person s waist remains almost at constant while the person is walking or it keeps on oscillating in between the maximum and minimum values. The maximum value of the Hip height is at the time of first single support phase and minimum value lies in the double support phase.

Height of knee also shows the oscillating behavior in humans as they don t have the walking which is perfectly rhythmic hence the model has to be designed in the way so that it can handle obstacle coming at runtime & also walking speed is not constant.

The stability of human structure in single support phase on a single foot is remarkable and that has to be copied as by the biped system.

"Many other developmental factors, such as cognitive skills, language skills, motor skills, are delayed usually until walking occurs," - Dale Ulrich, professor of movement science and physical education at the University of Michigan

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Chapter 3 BIPED LOCOMOTION Biped Locomotion comes into picture as for simulating the Human kind of Dynamics in the Robots, as it is fairly complex so the Biped Locomotion is taking care of the every point of the motion. Previously in human walking it s been discussed that the analysis is being done at an earlier stage or in a single Cycle the stability is being checked before the person takes up the step. Same concept is to be applied in the Robotics as by doing GAIT analysis of the Motion or in the Robot motion all of the parameters are being calculated, for example-

Hip Angle or Center of Gravity s Rotation

(-35º <

h

< +60º)

Knee Angle or Leg s center part s Rotation

(-85º <

k

< +25º)

Ankle Angle or Feet-side Rotation Angle

(+55º <

a

< +125º)

These movement ranges depend of the actuator positions. The movement ranges calculated for each joint are represented by

h

,

k

&

a.

Following parts are supposed to fix up in prior before starting the Biped Locomotion:

Trunk Length (Spinal cord) & Weight

Femur Length (Thigh Bone) & Weight

Tibia Length (Shin Bone) & Weight

Foot Length & Weight

Linear Motor

Depends upon the Configuration of the Robot. 10

Chapter-3 Biped Locomotion

M.Tech. Thesis

3.1 Problems in Biped Locomotion Analysis: Some of the basic problems in the biped system are given below:

Unstable systems

Multi-Input and Multi-Output (they take a lot of information of the environment and drive a great number of actuators)

The performance of these kind of robots is usually measured in terms of: Biological similitude Efficiency Smoothness of movements Maximum step speed Robustness in rough superficies

3.2 Basic System Architecture for Biped Locomotion: The biped model [27] was a 7-link biped with 8 degrees of freedom, simulated in a realtime, physics-based virtual environment1. The robot had a waist, a trunk, two legs (comprises two links in each leg), and two foot links. Each knee and ankle joint had one degree of freedom in the Sagittal plane. Each hip joint, connecting the trunk to the waist, had two degrees of freedom: one in the Sagittal plane and one in the frontal plane.

These correspond to the pitch and roll motions. The joints were limited in their motion with joint stops. The hip roll joint on each side had a range of motion between

/7 and

/7 degrees with respect to the frontal plane. The hip pitch joint had a range of motion between - /10 and /10 with respect to the Sagittal plane. The knee joint had a range of motion between - /2 and 0 with respect to the axis of the trunk to which it is attached.

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M.Tech. Thesis

Each of the joints is moved by a simulated torsional actuator. The actuator receives position commands from the controller. It uses a relatively low maximum torque ceiling. Velocity of a link will be greater the further it is from the commanded joint angle position, but if the force required to achieve this velocity is too large, it will only apply the maximum force. This mechanism incorporates a measure of compliance into the system, and is in accordance with the capabilities of real World actuators. All the physical parameters of the biped are kept as static in general.

Fig. 3.1 Biped Model and Degree of Freedoms of it s joints Courtesy: Ms.Chandana Paul, AI Lab, University of Zurich

3.3 Possible approaches for Biped Locomotion: Biped walking pattern generation can be classified into two categories.

The first group uses precise knowledge of dynamic parameter of a robot e.g. mass, location of center of mass and inertia of each link to prepare walking patterns. Therefore, it mainly relies on the accuracy of the model data. On the contrary, the second group uses limited Knowledge of dynamics e.g. location of total center of mass, total angular momentum, etc. Since the controller knows little about the system structure, this approach much relies on a feedback control [20].

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M.Tech. Thesis

3.3.1 Sensorimotor Reflexes:

The Sensorimotor network is a bilaterally decoupled neural controller [27], [28]. This means that each half of the controller is a rhythm generator which only receives sensory inputs from the sensors of one leg and global sensors, and controls the joints of the same leg. Thus, there is no explicit contra-lateral communication or coupling between the two halves of the controller. Each rhythm generator receives one sensory input, each of whose values are scaled to the range [-1, 1]. These inputs correspond to left (or right) foot contact information. The input layer also has one bias node which constantly emits a signal of 1.

The output layer consists of moto-neurons which control the left (or right) hip pitch, hip roll, and knee and ankle joints. The activations of the output neurons are computed by n

a

wi j Oi

(1)

i 1

Where O is the output of a neuron in the output layer. Wij are the synaptic weights of the connections between the sensory inputs in the input layer to the moto-neurons of the output layer. The output of a moto-neuron is then given by O

2 1 e

a

1

(2)

The values at the output layer are scaled to fit the range of their corresponding joint s range of motion. Torsion is then applied at each joint to attain the desired joint angle.

3.3.2 Central Pattern Generators (CPG):

CPG s basically works on the basis of the fact that as in Sensorimeter Reflexes we ought to have the Sensory action and then a Stimulus is being associated with it so we are generally not able to manipulate the data or reflex production is predicted using Neural Networks but works in very close proximity of the fact that Data sets must be present in the System before, while if we analyze the Situation then we will find that generally it

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M.Tech. Thesis

doesn t happen e.g. if a Human being is running and if he/she finds an obstacle then there must be some action for avoiding it but in Sensorimeter it might be possible that there will not be any sequence in the Knowledge-Base so in that case how the person can avoid the Obstacle so for that there must be a Pattern generator in the Hip-side (as there is an connection of the Spinal Cord to that).

That Central Pattern Generation Unit produces some flux of Neurons called CPEs central processing elements which causes the Pattern to be associated/generated and then an action is ought to be sent for the movement of the Leg.

In Bipedal walking there has to be a specified co-ordinate system for every movement so that the Robot can possibly track the route. Hence for that we fix up in prior the coordinate systems for world, body and floor [13].

Fig. 3.2 World co-ordinate system for Biped Robot movement

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Chapter 4 ACTIVE LIMB PROSTHESIS

Prosthesis is a medical field into which an artificial substitute is designed to replace, as much as possible, the function or appearance of a missing limb or body part.

Before starting the Prosthesis the level of motivation of the amputee should be assessed. Foremost, prosthesis must be comfortable to wear, easy to don (put on) and doff (take off), light weight and durable, and cosmetically pleasing. Furthermore, prosthesis must function well mechanically and have reasonably low maintenance & energy requirements. Centers for Medicare & Medicaid Services (CMS), formerly known as Health Care Financing Administration (HCFA) had determined the functional level with certificates of medical necessity for prostheses. Level 0: Does not have the ability or potential to ambulate or transfer safely with or without assistance and prosthesis does not enhance his/her quality of life or mobility. Level 1: Has the ability or potential to use a prosthesis for transfers or ambulating on level surfaces at fixed cadence. Typical of the limited and unlimited household ambulator. Level 2: Has the ability or potential for ambulating with the ability to traverse environmental barriers such as curbs, stairs, or uneven surfaces. Typical of the limited community ambulator. Level 3: Has the ability or potential for ambulating with variable cadence. Typical of the community ambulator who has the ability to traverse most environmental barriers and may have vocational, therapeutic, or exercise activity that demands prosthetic utilization beyond simple locomotion.

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Chapter-4 Active Limb Prosthesis

M.Tech. Thesis

Level 4: Has the ability or potential for prosthetic ambulating that exceeds basic ambulating skills, exhibiting high impact, stress, or energy levels. Typical of the prosthetic demands of the child, active adult, or athlete. The major components of lower extremity prosthesis are the socket, a sock or gel liner, a suspension system, an articulating joint (if needed), a pylon, and a terminal device. The terminal device is typically a foot but may take other forms for water or sports activities. For an amputee the prosthetic knee must fill 3 functions: Provide support during the stance phase of ambulation, Produce smooth control during the swing phase, and Maintain unrestricted motion for sitting and kneeling.

The prosthetic knee can have a single axis with a simple hinge and a single pivot point, or it may have a polycentric axis with multiple centers of rotation. Prostheses are described at this stage as either preparatory or definitive. The preparatory prosthesis is fitted while the residual limb is still remolding. This allows the patient to commence the rehabilitation program of donning and doffing, transfer training, building wear tolerance, obtaining balance and ambulating with the prosthesis several weeks earlier in the process. A preparatory prosthesis often allows a better fit in the final prosthesis as the preparatory socket can be used to mold the residual limb into the desired shape. The increase in energy requirements can be the limiting factor in ambulation. An individual who has a lower extremity amputation and requires a walker or crutches to ambulate uses 65% more energy than someone with a normal gait. Increased levels of energy consumption (percentage above normal) by amputation level are as follows: Below knee unilateral amputation - 10-20% Below knee bilateral amputation - 20-40% Above knee unilateral amputation - 60-70% Above knee bilateral amputation - >200%

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M.Tech. Thesis

Different views of the Prosthesis are shown below:

Lower limb prosthetics Below

knee

end

skeletal

prosthesis with patellar tendon bearing socket with Pelite liner, supracondylar

cuff

strap

suspension with SACH foot.

Anterior View

Oblique View

Lateral View

Fig.4.1 Different views of Lower Limb prosthesis

4.1 Prosthetic Knees designs: Some important factors to consider when comparing prostheses depend on what they will be used for. In particular, the weight, maximum flexion angle and classification (weight and activity they can support) should be considered.

Blatchford Endolite

160 Hi-Activity

3R72 Modular Knee Joint

Fig. 4.2 Commercially available knee designs

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M.Tech. Thesis

The active Limb available in the market is Otto Bock s C-Leg [22], [23] which brings to prosthetics a microprocessor controlled knee joint that is significantly different than conventional mechanical joints. It features swing phase and stance phase movements which are controlled by algorithms in an on-board microprocessor. Real-time (50 Hz) analysis of movement is used to provide the amputee with dynamic gait similar to natural walking. It allows for varying speeds on flat terrain and better function on slopes, stairs, and uneven surfaces. Additionally, it has a second mode that can be preprogrammed for another activity besides walking.

Fig 4.3 (a) Sagittal assembly of C-Leg

(b) Sagittal View of C-Leg

Snapshot of subject wearing C-Leg (in the situation that Heel of right leg strikes to the ground 1st or the Stance of left leg is going on) is shown below:

Fig 4.4 (a) Sagittal view of subject wearing C-Leg

(b) Frontal view of subject wearing C-Leg

18

Chapter 5 METHODOLOGIES ADOPTED

5.1 Walking primitives: Walking is previously been described as controlled falling. Now the way we push our body forward and in the meantime balance the entire body segment onto a single foot is really the toughest task to handle.

Several theories have been proposed and also been introduced into the previous work section; the class to which humanoid robots resembles to the human is human kind of walking. Therefore the robot decides the smooth and continuous trajectory prior to the walking and on the runtime if it finds an obstacle into it s way then it has to take up the step in the way to avoid it or just make a crossover. Primarily different persons pursue the different-2 gait patterns, which ought to be most stable and chosen on the run time. The same thing can be applied by analyzing the gait cycle into the form of two phases, stance and swing and then supply the desired torques and velocities to the biped.

During walking the person takes up his foot to a certain height (in swing) and then strike the heel to the ground. At that time for the stability of the person his body should lie in the support polygon and his foot should cover the largest stability margin.

The stability term was also coined as the generation of low energy reference trajectory or a rhythmic cycle therefore ZMP concept was evolved mainly for devising the most stable trajectory out of all available gait sequences during the walking.

19

Chapter-5 Methodologies Adopted

M.Tech. Thesis

5.1.1 Gait Cycle: Gait Cycle of a person is normally comprises of the following steps: Initial Contact in Stance Phase Loading Response in Stance Phase Terminal Stance in Stance Phase Pre swing in Swing Phase Mid swing in Swing Phase Terminal swing in Swing Phase

Fig. 5.1 Complete Gait Cycle

The detailed diagram of the subject walking with normal pace which is categorized in the form of different-2 steps is given on the next page.

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M.Tech. Thesis

Images of Gait Cycle

Initial Contact in Stance Phase

The walk usually starts with the feet at the "extended position," where the feet are farthest apart and the character s weight shifts to the forward foot.

Loading Response in Stance Phase As the weight of the body is transferred to the forward foot, the forward knee bends to absorb the shock. This is called the "recoil position," and is the lowest point in the walk.

Terminal Stance in Stance Phase

As the knee is bending and the foot is coming forward so the heel strikes on the surface and swing of the other foot is started.

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M.Tech. Thesis

Pre swing in Swing Phase

The free leg makes contact with the ground, completing half the cycle. The second half is an exact mirror of the first. If it differs, the character may appear to limp.

Mid Swing in Swing Phase

Halfway through the first step, the forward knee straightens out and lifts the body to it s highest point. In this "passing position," the free foot passes the supporting leg.

Terminal Swing in Swing Phase

As the character moves forward, the weight-bearing foot lifts off the ground at the heel, transmitting the force to the ball of the foot. The body starts to fall forward. The free foot swings forward like a pendulum to meet the ground and catch the body s weight.

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M.Tech. Thesis

5.1.2 Zero Moment Point: During walking, the person keeps on oscillating between the two sequences: the doublesupport phase into which the body is supported on both feets, and single-support phase, when only one foot is in contact with the ground while the other is being transferred from the back to front. Thus, the biped locomotion mechanism changes its structure during a single walking cycle from an open to a closed kinematic chain. All of the biped model joints are powered and directly controllable except for the contact between the foot and the ground, where the interaction of the mechanism and environment only takes place.

We can control the motion of the Foot by considering the dynamics associated with it s upper part. If the influence of all forces acting on the biped model can be replaced by the single force then that point is termed as Zero-Moment Point (ZMP). Vukobratovi ć and Juri cić. proposed the semi inverse method for gait synthesis.

It should be noted that despite of the limitation that the motion can be synthesized only for as many joints as the zero-moment conditions can be preset, this method has remained for a long time the only procedure for biped gait synthesis. The ZMP is also indispensable in biped control, for establishing the practically unavoidable feedback with respect to dynamic ground reaction forces.

Representation of ZMP:

For deriving ZMP notion we are considering the Single support phase of Biped model. In that we can think of the part of the system above than ankle of the foot can be replaced by the force FA and the moment MA. and the weight of the foot is acting on it s center of gravity (CoG). The foot also experiences the ground reaction at point P, whose action keeps the whole mechanism in equilibrium.

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M.Tech. Thesis

Fig.5.2 Forces and moments acting on the Foot in Single support phase

Ground reaction can be divided in three components of the force R (Rx, Ry, Rz) and moment M (Mx, My and Mz). Since the friction force acts at the point of contact of the foot with the ground, and the foot on the ground is at rest, those components of the force R and moment M that act in the horizontal plane will be balanced by friction. Therefore, the horizontal reaction force (Rx, Ry) represents the friction force that is balancing the horizontal component of the force FA, whereas the vertical reaction moment Mz represents the moment of friction reaction forces.

Fig.5.3 moments acting on the Foot & trying to rotate it.

that balances the vertical component of the moment MA and the moment induced by the force FA. Thus, if we assume the foot-floor contact is without sliding, the static friction will compensate for the horizontal force components (Rx, Ry) and vertical reaction torque (Mz). The vertical reaction force Rz represents the ground reaction that balances vertical forces. It remains to consider the balancing of the horizontal component of the foot load moment. Horizontal components of all active moments can be compensated for only by changing position of the reaction force R within the support polygon. Therefore, the

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M.Tech. Thesis

horizontal component of the moment MA will shift the reaction force to the corresponding position, to balance the additional load.

Vectorial representation of ZMP:

ZMP can be think of as the point onto which we can replace all the active moments or forces by single force or the net is zero and the system is in stable state. So accordingly if ground reaction acting on the foot is R, the Force on ankle is FA and the force due to gravity is msg then R + F A + ms g = 0

(for the stability of the system)

OP x R + OG x msg + MA +MZ + OA x FA = 0

Mathematical representation of ZMP:

ZMP can be computed with the help of following formula:

(3)

(4)

Fig 5.4 Position of ZMP point (XZMP, YZMP,0)

Where, (Xzmp,Yzmp) are the co-ordinates of ZMP position, Linear & Angular Acceleration in Z and X are measured as a parameter in ZMP which gives a stable trajectory for locomotion [16].

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M.Tech. Thesis

5.1.3 Stability of physical structure in walking: Biological Perspective: The spine is meant to carry loads, allow movement of the different body parts, and provide protection to the spinal cord. Therefore it needs both rigidity and flexibility which are achieved by its unique structure. The spinal stabilizing system consists of three subsystems (Figure 5.5): Passive subsystem

vertebrae, intervertebral discs, spinal ligaments, joint

capsules, and the passive properties of the muscles; Active subsystem

active properties of muscles and tendons;

Neural subsystem

propioceptors and other neural control components.

The three subsystems complement each other and work together to achieve stability. The passive subsystem provides stability at the end of ROM while acting as monitoring transducers at mid range. The neural subsystem receives data from the passive subsystem and other transducers in the spine, integrates it, and activates the active subsystem to stabilize the spine.

Fig. 5.5. The stabilizing subsystems of the spine.

Dysfunction of one or more of the stabilizing components results in an attempt to compensate by one of the other components in order to keep the spine stabilized. Dysfunction of the passive subsystem may be due to mechanical injury or degenerative disease. Compensation will follow in the active subsystem. Dysfunction of the active 26


M.Tech. Thesis

subsystem may be due to disuse, injury or disease and may compromise the system s ability to respond when needed. A dysfunction of the neural subsystem may result from damage to transducers or CNS. This leads to problematic function of the active subsystem (Fig 5.6).

Fig. 5.6. Dysfunction of spinal stability system.

A few definitions help to understand the function of the three subsystems, their injury, and spinal instability (Figure 5.7): Range of motion (ROM) Neutral zone

The physiologic range of the spine.

Part of the ROM (mid range) in which movement is produced with

minimal resistance from the surrounding tissue. Elastic zone

The part of ROM from the end of the neutral zone to the end of ROM. The

neutral zone has been shown to increase with spinal injuries or muscle weakness, and result in spinal instability. It may also decrease due to muscle strengthening or spinal surgery.

Figure 5.7. The load-deformation behavior of a spinal Segment, showing the neutral and elastic zones that constitute the physiological ROM

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M.Tech. Thesis

5.1.4 Stability using ZMP approach: Stability and ZMP [24] are the terms dual to each other so if one is able to successfully evaluate the ZMP trajectory for stable walking or of ZMP lies inside the support polygon then we can say that walking is stable.

For evaluating ZMP the pressure between the foot and the ground can always be replaced by force acting at the center of pressure (CoP). If this force balances all active forces acting on the mechanism during the motion (inertia, gravitation, Coriolis and centrifugal forces and moments) its acting point is ZMP. Thus, in the case of a dynamically balanced gait (Fig 5.8), CoP and ZMP coincide. When the gait is not dynamically balanced (Fig 5.8), ZMP does not exist and the mechanism collapses about the foot edge.

In a balanced gait, the ZMP coincides with CoP. In the case of a disturbance that brings the acting point of the ground reaction force to the foot edge, the perturbation moment will cause rotation of the biped system about the foot edge and its overturning. In that case fictitious ZMP comes in the picture whose distance from the foot edge represents the intensity of the perturbation moment However, on the toe tips we can realize the biped locomotion (Fig. 5.8) by accompanying a pinpoint area (balletic motion) and keeping the ZMP position within the pinpoint area.

Fig. 5.8 depicting the situation during walking and movement of ZMP

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M.Tech. Thesis

Stability is primarily been depending upon the following factors:

Stability margin of foot Support polygon of body ZMP location during walking Posture

Therefore these parameters can be handled individually by computing each one of them in sequence as:

1) Stability margin of the biped model can be determined accordingly as per the phases:

Stability_margin_Single_Support_Phase Stability_margin_Double_Support_Phase

2) Support Polygon of the body has to be computed before the start of walking and it depends upon the posture of the humanoid.

3) Location of ZMP can be computed by evaluating the torques generated in different -2 joints in the system and for stability it s distance from the stability margin has to be maximized.

4) Posture plays an important role in evaluating the stability as for every posture there will be a possible set of trajectories of various joints attached in the system hence all the parameters for stability are primarily depending upon the posture.

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M.Tech. Thesis

5.2 Plan of Work: The plan for solving the problem is organized into the following steps: Fix the Initial parameters of biped

Generate the trajectories of foot,

Generate the trajectories of foot,

hip and knee through

hip and knee by segmenting the

mathematical model

real-life videos of subject motion

Derive the trajectory of ZMP

Choose the trajectory with largest stability margin

Generate the damping in joints for stable movement

In the above written flow chart the sequence of work is starting by fixing up the initial parameter of biped model or the system to which we want to test our algorithm, and then in the next step we ought to generate the trajectories of the joints in the system by using the two possible approaches: Through mathematical model Through real life subject motion videos

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M.Tech. Thesis

For smoothening the curves, interpolation methods like Spline, cubic can be used, finally goal is obtained in the form of the choice for hip trajectory which covers the largest stability margin and damping is to be obtained on the basis of that.

5.3 Formulations: 5.3.1 On Mathematical base:

Fig. 5.9 Sagittal view of 7-Link Biped Model (without any weight on back)

The biped model used for analysis was a 7 Link model with 6 Degrees of Freedom given in fig 3(a); model carrying weight is shown in 3(b). The key specifications of bipedal model are given in Table 3. In case of normal walking subject puts the body in Single & Double support Phase [16] alternatively and by applying the forward force during stance it accelerates forward. The time for Single Support Phase is very less (as compare to the

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M.Tech. Thesis

Double Support Phase). Also, the Single Support phase is inherently unstable hence a small interval of 0.01 Second is chosen during the Walking Cycle. Table 1: Biped Model Parameters Link Parameters

Trunk

Thigh

Shin

Ankle

Foot

43.0

10.0

5.7

-

3.3

0.50

0.30

0.30

0.10

0.23

Mass (In Kg) Length (In meter)

A model based approach was used for deciding the trajectories of different joints. The foot and hip trajectory were calculated mathematically and optimized using algorithmic approach given in Design and implementation chapter. Finally knee trajectory was interpreted from hip and ankle joint positions. Parameters given in Table 4 were used for calculation of foot trajectory through 3rd order Spline Interpolation. Splines were used as cubic polynomial possible causes the oscillations at hip while increasing the polynomial order. Table 2: Parameters for walking cycle

Parameter

Length of Step

Period of Step

Specification

Value

0.5 meter

0.9 second

Height of

Foot Angle

Foot Angle

Obstacle

(Start)

(End)

0.16 meter

0.2 radians

02 radians

As Hip trajectory plays an important role in designing the bipedal walking system and also provides the stability to the amputee wearing an artificial limb. Hence an algorithmic approach was devised to obtain optimized walking with varying load on the back of the subject. Hip oscillates from minimum to maximum height in one step of gait cycle. Velocity and acceleration at start and end of each step are assumed to be zero. Several Hip trajectories were generated in a particular posture by varying hip to ankle distances.

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M.Tech. Thesis

With the help of ZMP control algorithm we select the trajectory which produces ZMP that covers the largest stability margin.

Fig. 5.10 walking cycle of experimental biped

Biped model carrying weight is shown below. After adding the weight to biped model the ZMP trajectory has to be computer again and again out of several trajectories one trajectory is picked up which yields the largest stability margin.

Fig.5.11 Sagittal view of 7-Link Biped Model (with weight on back)

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M.Tech. Thesis

5.3.2 Logical base: An algorithmic sequence depicts the flow of information in every system; same we have done our here as by devising the steps in the form of ZMP Control algorithm. The algorithm is repeatedly running in the system for the generation of stable and unique trajectories of the joints.

Algorithm takes on input the parameters generated through sensors as in the form of angles of joints structure in the biped. It computes the trajectories of the hip using the values from the foot trajectory and then it inputs those values to ZMP trajectory. Now the algorithm takes on input only two parameters which are the distances of the right ankle from the trunk at the start of cycle and left ankle from the trunk at the end of cycle. Hence the ZMP trajectory produced by the algorithm is unique and by varying only two parameters it gives the biped system almost similar movement as subject is having while carrying the weight.

Algorithm also computes the intermediate trajectories which can be stored and verified on the run time with the help of biped model. A very minute precision for the time is drawn so the intermediate points are having a little variance but stability margins for different-2 hip positions ought to be different.

Some of the trajectory values sets generated by the algorithm are not reachable by the biped but still they count as the stable so in the algorithm the term support polygon is also incorporated. It verifies the distance of ZMP from the stability margin and then finally chooses the trajectory which offers the largest margin among these values.

34

Chapter 6 DESIGN AND IMPLEMENTATION

6.1 Mathematical Model for Trajectory generation: A mathematical approach was drawn for calculating the trajectory of foot and hip. A 7Link biped model was taken up for experimental purposes and all the calculations are done by resolving the kinematics and dynamics of it s joints. At the 1st the trajectory of foot was evaluated using the 3rd order spline trajectory for leveling the curve and then we switched over to the hip trajectory where the concept of ZMP was evolved and then the hip trajectory which offers the largest stability margin during stance and swing was chosen up.

6.1.1 Foot Trajectory:

Trajectory of foot was modeled in the way by assuming some of the walking parameters like length of step; period of walking cycle (depends upon the speed of biped). For our analysis we have taken up the assumption as in the start of cycle the robot is standing by stretching it s left foot forward and making the contact of heel with the ground and right foot is at back side in fully relaxed position.

Now for starting the cycle as the stance phase of left leg is going on so the right leg will come forward say in period equal to Tc. Now as the right foot completes it s swing then left foot has to come in swing mode and then it comes forward henceforth the cycle is completed through following sequence:

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Chapter-6 Design and Implementation

0

M.Tech.Thesis

Td

Tc

Tm

Tc+Td Time (In seconds)

Fig 6.1 Posture of Biped model during a complete walking cycle

Trajectory of Foot is evaluated with the help of above mentioned parameters & 3rd order Spline Interpolation is used for generating the Intermediate Points and smoothening the Trajectory. Previously used Cubic Polynomial causes Oscillation at Hip (if taken the

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M.Tech.Thesis

Higher order of it) henceforth 3rd Order Spline is considered. Trajectory of Left Foot is evaluated with the Model, Right foot possess the same with a delay of period equal to Single Step. Most previous studies have defined foot trajectories in which the feet are always level with the ground, that is, the foot angle

a(t)is

always zero. Since the robot cannot touch

the ground first by the heel of the forward foot and leave the ground finally by the toe of the rear foot, these kinds of foot trajectories are not useful for high-speed walking. Additionally, from the viewpoint of natural human locomotion and aesthetics, it is undesirable that the foot slope always be level.

Let s assume the co-ordinate of the Hip Joint as (Xh,Zh, h), Knee Joint as (Xk,Zk, k), Ankle Joint as (Xa,Za, a) & Hand/Shoulder as (Xhnd,Zhnd, h).The walking parameters can be drawn as:

Fig.6.2 Parameters of walking

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M.Tech.Thesis

Mathematical Formulation:

Letting qb and qf be the designated angles of the swing foot as it leaves and lands on the ground (Fig. ) respectively. Assuming that the entire sole surface of the right foot is in contact with the ground at t = kTc and t = (k=1)Tc+Td , we get the following constraints:

a

(t) =

qgs(k),

t = kTc

qb ,

t = kTc + Td

-qf,

t = (k+1)Tc

qge(k),

t = (k+1)Tc + Td

Where Td is the interval of the double-support phase, and qgs (k) and qge(k) are the angles of the ground surface under the support foot, particularly qgs(k) = qge(k) = 0 on level ground.

Over rough terrain or in environments with obstacles, it is necessary to lift the swing foot high enough to negotiate obstacles. Letting (Lao, Hao) be the position of the highest point of the swing foot (Fig. ), from (1) and the kinematic constraints, the following constraints must be satisfied. K*SL

t = K*Tc

K*SL + lan * sin (qb) + laf * (1 - cos(qb)) Xa (t) =

K*SL + Lo (K+2)*SL

Za (t) =

t = K*Tc + Td t = K*Tc + Tm

lan * sin(qf)

lab * (1-cos (qf))

t = K*Tc + Tc

(K+2)*SL

t = K*Tc + Tc + Td

hgs(K) +lan

t = K*Tc

hgs(K) + laf * sin(qb) + lan * cos(qb)

t = K*Tc + Td

Ho

t = K*Tc + Tm

hge(K) + lab * sin(qf) + lan * cos(qf)

t = K*Tc + Tc

hge(K) + lan

t = K*Tc + Tc + Td

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M.Tech.Thesis

Where SL is the length of one step, (kTc+Tm) is the time when the right foot is at its highest point, lan is the height of the foot, laf is the length from the ankle joint to the toe, lab is the length from the ankle joint to the heel, hgs(k) and hge(k) are the heights of the ground surface which is under the support foot, particularly hgs(k) = hge(k) = 0 on level ground.

As the foot is on ground at t=K*Tc and t= K*Tc+ Tc+ Td the following derivative constraints must be satisfied:

VelocityXa

Xa t

AccelerationXa

VelocityYa

0 VXa t

Ya t

AccelerationYa

VelocityTheta_ a AccelerationTheta_ a

0

0 VYa t a

t

(4)

0

0 VTheta_ a t

0

To generate a smooth trajectory, it is necessary that the first derivative (velocity) terms Xa(t),Za(t),

a(t)

and be differential, the second derivative (acceleration) terms

Xa(t),Za(t),

a(t)

and be continuous at all t, including all breakpoints t = k*Tc, kTc+Td,

kTc+Tm, (k+1)Tc, (k+1)Tc+Td. To satisfy above said constraints and the continuity conditions of the first derivative and the second derivative, the order of the polynomial will be too high and its computation is

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M.Tech.Thesis

difficult. Therefore, we obtain the foot trajectory by third-order spline interpolation. In this case Xa(t), Za(t) and

a(t)

are characterized by third order polynomial expressions,

and the second derivatives Xa(t), Za(t) and

a(t)are

always continuous. By varying the

values of constraint parameters qgs(k),qge(k),hgs(k),hge(k), qb, qf, Hao and Lao we can easily produce different foot trajectories.

6.1.2 Hip Trajectory:

From the viewpoint of stability, it is desirable that hip motion parameter is constant when there is no waist joint; in particular on level ground. Hip motion hardly affects the position of the ZMP. We can specify to be constant, or to vary within a fixed range.

Mathematical Formulation: Assuming that the hip is at its highest position at the middle of the single-support phase, and at its lowest position at the middle of the double-support phase during one walking step, has the following constraints:

Zh (t) =

Hhmin

t = K*Tc + Td/2

Hhmax

t = K*Tc + (Tc-Td)/2

Hhmin

t = K*Tc + Tc+Td/2

The trajectory of that satisfies above equation and the second derivative continuity condition also can be obtained by third spline interpolation.

The change of is the main factor that affects the stability of a biped robot walking in a Sagittal plane [14]. Some of the methods derive the hip trajectory to execute a desired ZMP which is not a correct way as all desired ZMP trajectories can t be attained and the hip acceleration may need to be very large. To solve these problems, we suggested an algorithmic approach:

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M.Tech.Thesis

A complete walking process is composed of three phases: a starting phase in which the walking speed varies from zero to a desired constant velocity [21], a steady phase with a desired constant velocity, and an ending phase in which the walking speed varies from a desired constant velocity to zero.

Fig.6.3 walking cycle

Let HAFD & HABD denote distances along the X-axis from the hip to the ankle of the support foot at the start and end of the single-support phase, respectively (Fig. 2), we get the following equation:

Xh (t) =

K*SL + HABD

t = K*Tc

K*SL +SL-HAFD

t = K*Tc+Td

K*SL +SL+HABD

t = K*Tc+Tc

To obtain a smooth periodic of the steady phase, the following derivative constraints must be satisfied:

.

X h ( K * Tc )

.

X h ( K *T c Tc )

(5) ..

X h ( K * Tc )

..

X h ( K *T c Tc )

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M.Tech.Thesis

Using third-order periodic spline interpolation, we obtain the trajectory which satisfies second derivative continuity conditions. According to our algorithm we are changing the values of HABD and HAFD to vary within a fixed range (< SL/2).

Finally out of all available hip trajectories we choose up the one which offers the largest stability margin:

Maximum_Stability_Margin(HAFD,HABD)

(6)

(0< HAFD < (SL/2), 0< HABD < (SL/2))

Therefore the computation results in the unique and most stable trajectory within a very minute interval (say 0.01 sec).

6.1.3 Knee Trajectory:

Trajectory of Knee can be evaluated by using the simple mathematics in between the Hip & Ankle joints.

Let the co-ordinates of hip& ankle are (Xh,Zh) & (Xa,Za), now considering the biped model & the lengths according to the figure given on next page. For our computation purposes we cut the leg of biped and then applying some triangle fundamentals over there to compute the position of (Xk,Zk)

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M.Tech.Thesis

Fig.6.4 (a) Biped Model (b) Leg of Biped Model

The Equations of Knee trajectory can be solved as by the method given below:

(X k

X a )2

(Z k

Z a )2

l _ sh 2

(X h

X k )2

(Z h

Z k )2

l _ th 2

Subtract t he two equations 2X k (X h

X k (X h

Xk

Xa)

Xa)

2Z k (Z h 1 l _ sh 2 2

1 2*(X h

Xa)

l _ sh 2

Za)

l _ sh 2

l _ th 2

l _ th 2

Xa

l _ th 2

2

Xa

Za

2

2

Za

Xa

Xh

2

2

2

Xh

Za

Zh

2

2

2

Zh

Xh

2

Z k (Z h

2

Zh

2

Za)

Z k (Z h Z a ) (X h X a )

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M.Tech.Thesis

Let : 1

t1

2*(X h (Z h (X h

t2

Xa)

l _ sh 2

l _ th 2

Xa

2

Za

2

Xh

2

Zh

2

Za) Xa)

hence Xk

t1

Z k * t2

Put the value of Xk in the equation Zk t2 )2

(X h - t 1 2

Zk * t2 2

Z k (t 2

2

(Z h - Z k ) 2

(X h - t 1 ) 2 1)

l_th

2

2 * Z k * t 2 * (X h - t 1 )

Z k (2 * t 2 * (X h - t 1 ) - 2 * Z h )

Zh

2

2

Z k - 2Z h Z k

( (X h - t 1 ) 2

2

l_th

Z h - l_th 2 )

2

0

let : 2

t3

(t 2

1)

t4

(2 * t 2 * (X h - t 1 ) - 2 * Z h )

t5

( (X h - t 1 ) 2

2

Z h - l_th 2 )

hence

Zk

- t4

t42 - 4 * t3 * t5 2 * t3

and Xk

t1

Zk * t 2

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M.Tech.Thesis

Therefore a smooth knee trajectory is obtained by using these equations, now the algorithm give in next section is devised for selecting the unique and most stable trajectory.

6.2 Algorithm for planning walking patterns: A ZMP control algorithm was formulated for hip trajectory generation. The algorithm is having dependency on only 2 parameters HAFD & HABD (the distances along the Xaxis from the hip to the ankle of the support foot at the start and end of the single-support phase in walking cycle).

The trajectory chosen up by the algorithm is supposedly the most stable trajectory as it takes in account the maximum marginal gap from the stability region and also it does lie in stability polygon.

The algorithm generates several possible hip trajectories for a particular posture of a human being now the most stable trajectory out of all these can be stored as the reference value curve for a particular posture and also for a particular human being.

The pseudo code can be written as in following steps:

ZMP control algorithm:

I. START

II: Set the biped parameter (e.g. walking speed, obstacle height, step length etc.). III: Generate the foot trajectory using 3rd order spline.

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IV: Set the parameters (Hip_Ankle_Forward_Distance (HAFD) & Hip_Ankle_ Backward_Distance (HABD)).

V: If (HAFD > (Step_length)/2 and HABD > (Step_length)/2) goto step V a: Generate hip trajectory using 3rd order spline.

b: Compute weight based ZMP & Stability Margin.

c: Increase HAFD & HABD.

d: Choose hip trajectory with largest stability margin.

e: exit

VI: EXIT

Therefore algorithm takes in account all possibilities as we are running up a loop which has a variation half of Step_length hence in the walking step of a person the two possible distances are suppose to lie in between (Step_length/2).

Spline interpolation was used for the generation of Foot trajectories as cubic polynomials causes the oscillations at hip side and also the spline produces the smooth trajectory whereas the cubic results in some spikes in the curves.

The motion of subject was also analyzed by shooting the videos and then drawing the trajectories of the various joints from that.

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6.3 Subject motion analysis (in real life situations): The motion of subject was analyzed in different -2 situations and also by varying the load around the subject [11], [15]. The Video Camera used for Shooting was the Sony Handy cam and subject videos were taken up in the following sequence:

1) Walking with normal pace without any load

2) Walking with load carried on:

(a)

Front Side of Body

(b)

Back Side of Body

(c)

Top Side of Body

(d)

Front & Back Side of Body

Total four subjects were involved in the experiment & their data is given in the table:

Person Name

Sex

Age

Weight

Height

Rachit Rastogi

Male

25

73

56

Bhaskar Gupta

Male

21

63

55

Hemant Anand

Male

24

65

59

Khalil Jibran

Male

24

65

55

Behavior of the person when weight is applied also depends upon their ages and their posture, as the aged person have more inclination as compare to the young ones. The next page will show the database of the subject motion while carrying the weight in different-2 modes.

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6.3.1 Database of Subject carrying weights in different modes: A database of subject carrying weight in different -2 modes was made up; some of the snapshots are also available here: Subject carrying weight in his Right Hand During the experiment the subject carried load in his right hand which causes an inclination in the left side due to weight. Hence during walking the subject keeps on changing his inclination in the left side and also the trajectories of both of the feets is different from each other as in case of normal walking it was same.

Subject carrying weight at Front side

In next experiment Subject walked with load at his front side, which causes him to take small steps, lean forward and a peak in torque was observed as to reach the maximum point during the swing of leg.

Subject carrying weight on his Top

It s been observed that while subject was carrying weight on his top he bent both of his knees and the step length becomes small. A small amount of inclination was also observed at Hip side.

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6.3.2 ANOVA (A statistical variance analysis technique): Analysis of variance (ANOVA) between groups is used to test hypotheses about differences between two or more means. The t-test based on the standard error of the difference between two means can only be used to test differences between two means. When there are more than two means, it is possible to compare each mean with each other mean using t-tests. Analysis of variance can be used to test differences among several means for significance without increasing the Type I error rate. Now in the video database as we have group of several videos of same subjects in same situations therefore for analyzing the variance in between these groups we used the ANOVA technique. In the thesis work ANOVA was also used for analyzing the variance between the trajectories generated by the mathematical model and by the one obtained in the real life situation by analyzing the video of subject motion. Analysis of variance assumes normal distributions and homogeneity of variance. Therefore, in a one-factor ANOVA, it is assumed that each of the populations is normally distributed with the same variance ( 2). In between-subjects analyses, it is assumed that each score is sampled randomly and independently. Research has shown that ANOVA is "robust" to violations of its assumptions. This means that the probability values computed in an ANOVA are satisfactorily accurate even if the assumptions are violated. Moreover, ANOVA tends to be conservative when its assumptions are violated. This means that although power is decreased, the probability of a Type I error is as low as or lower than it would be if its assumptions were met. There are exceptions to this rule. For example, a combination of unequal sample sizes and a violation of the assumption of homogeneity of variance can lead to an inflated Type I error rate.

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6.4 Comparison of Trajectories: A trajectory comparison was done by using the ANOVA technique for variance in between the groups of values.

As in experimental setup we captured the subject motion videos and from that we evaluate the trajectory of ankle, hip & knee. After that we calculate the variance in between the values obtained through the model for foot & hip trajectory.

The trajectory of ankle gets a little shift while we draw a plot of X position obtained through model vs the trajectory obtained through real life video segmentation.

The trajectory of ZMP was observed to be almost same in case of subject carrying load and the biped model along with some weight on it s trunk side.

A minute change was also observed in the velocity & acceleration graphs of the joints in the biped system.

The Angular velocity of the Knee joint was changed with certain peaks in between which causes the biped system to have the unstability for a very short duration in the walking.

Finally the trajectory of angular acceleration was drifted a bit down because of torque produced on the joints and the moments caused by them.

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6.5 Active Prosthetic Knee control: Knee damping [18] adjustment in semi active prosthetic knee joints is done by trained prosthetists based on the feedback from the amputee. This process is used in C-Leg. The damping factors once adjusted remain constant without any consideration of walking speed, weight and gait patterns of a person. Manual interference required to adjust knee resistance is error prone and inaccurate. Hence a dynamic controller is proposed here.

Active Prosthetic knee [19] control requires efficient sensing from both global and local sensors which in our design includes knee angle, hip angle and ground reaction forces. These sensed signals are then preprocessed to obtain velocities and accelerations of the knee and hip.

The ground forces are captured using strain gage sensors; although as a simplification of foot model we are using point contact with the ground. The damping given to the knee varies in each phase of the gait cycle depending upon the sensor information. Our CPG model computes the expected angles and velocities depending upon the sensory feedback. Stance phase damping is varied depending upon the position of hip joint with respect to the knee joint.

In turn, the swing phase damping is proportional to the difference

between maximum flexion angle obtained through CPG and biologically limiting flexion(taken as 70 deg). These computed values are then used to adjust the resistance offered by prosthetic knee joint to achieve biologically realistic gait. The basic design flow of damper controller is given below.

The design flow is categorized in two phases as digital system & analog system; mainly digital system comprises of the units like Microprocessor, ADC/DAC & Control algorithms. While the analog structure covers the Bipedal model with sensing & actuation unit and also the damping module.

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M.Tech.Thesis

Fig. 6.5 Active Knee control using ZMP

Biped model was used to give the inputs in the form of joint angles and ground forces. The term which primarily affects the gait is the variable weight the subject is carrying values were passed to the ADC module which will serve as an entry gate for the Digital System. ADC outputs the bit stream which was given as an input to microprocessor. The ZMP control algorithm mentioned earlier gives the optimized and stabilized trajectory.

Fig. 6.6 Design of Biped Model Damping Control System

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6.6 Introduction of damping in Artificial Limb: The mechanism of damping is well known as in a nutshell it causes the smoothness in the walking and gives the stability to a person while he or she swings the leg.

Damping can be primarily categorized according to the phases:

Stance Flexion Damping

It s basically the damping caused in the Stance phase flexion part or if we are considering the case of knee then it is the amount of damping introduced during the stance phase to bend the knee.

Stance Extension Damping

It can be defined as the damping needed to extend the leg from the bent position to fully stretched position by taking support for the body on both of the legs.

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M.Tech.Thesis

Swing Flexion Damping

It s basically the damping caused in the Swing phase flexion part or if we are considering the case of knee then it is the amount of damping introduced during the swing phase to bend the knee & then take it to the forward side.

Swing Extension Damping

It can be defined as the damping needed to extend the leg from the bent position to fully stretched position by taking support for the body on both of the legs.

For Stance phase damping we are taking the difference between the two consecutive distances (as the case might be of Knee or Ankle etc) and then multiplying it by damping factor to generate the exact amount of damping.

And in Swing phase a little period is been spent for taking the leg to swinging position which is in between 0-2 seconds, so we are dividing that interval to fixed number and then according the pace of walking we are calculating the damping.

54


6.7 Simulation Algorithm:

M.Tech.Thesis

Create the World

Create a collision world

Create bodies in the Dynamic world

Create joints in the dynamics world

Set the state (position, etc.) of all bodies

Set the parameters of all joints

Attach the joints to the bodies

Create a joint group to hold the contact joints

Create collision geometry objects, as necessary

Simulation Loop

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M.Tech.Thesis

1.) Apply forces to the bodies as necessary.

2.) Adjust the joint parameters as necessary.

3.) Call collision detection; create contact joint for every collision point; put these contact joints into the contact joint group.

4.) Take a simulation step.

5.) Remove all joints in the contact group.

6.) Redraw Scene

Destroy the dynamics and collision worlds

The Biped model was simulated using ODE (Open Dynamics Engine) & OpenGL. It is good for simulating ground vehicles, legged creatures, and moving objects in VR environments. It is fast, flexible and robust, and it has built-in collision detection.

56

Chapter 7 RESULTS AND DISCUSSIONS All Simulations were made using MATLAB 6.5. The results were compared to the kinematics of subjects in specific situations. To generate the trajectory from subject s body, the video was captured in Sagittal plain and joint markers shown in fig 7.18 were segmented out through interpolation. For video streaming analysis and for segmentation of frames virtual dub mod was used. ANOVA was used for statistical analysis of variance in Video Data.

7.1 Trajectory of Joints: It s assumed in the model that Left foot was coming forward and the Right foot was at back side. Now as the walking started the Left Foot got down during the 1st double support phase (.15 Sec duration) and the right foot went up. After that the swing of right leg was started and it reached to the maximum height in .5 sec.

Fig. 7.1 Left Ankle motion curve in a complete cycle

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Chapter-7 Results and Discussions

M.Tech.Thesis

For multiple cycles the parameters of the Left

ankle

following

varied curve,

according which

to

the

shows

the

oscillating nature of Z. Theta values of ankle were oscillating between (-5.73 to 10.14 degrees).

Fig. 7.2 Left Ankle motion curve (Xa,Za,Theta) in multiple cycles

The ankle of right foot moved in swing after the 1st double support phase and it remained in it for .75 second till the Heel of right foot strike to the ground.

Fig. 7.3 Right Ankle motion curve (Xa,Za,Thetaa) in single cycle

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We drew the graph for motion of Right ankle and the cycle counter was set to 5 then it was observed that right ankle was also oscillating for values of Z. and it s angle was keep on changing just as the reverse of the left ankle.

Fig. 7.4 Right Ankle motion curve (Xa,Za,Theta) in multiple cycles

Now with the help of model, trajectory of hip was evaluated and the trajectory was one out of all available possibilities. It s been observed that Z point in the trajectory of hip keeps on oscillating between the range .79 to .83 meter and as the foot was in forward direction therefore the trunk was making some angle in the starting which was around 10 degrees.

Fig. 7.5 Hip motion curve (Xh,Zh,Thetah) in single cycle

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The Hip s X position kept on changing as we proceeded further in the walking and in the stance of left foot the hip shifted a bit as due to the swing of right foot.

Fig. 7.6 Hip motion curve (Xa,Za,Theta) in multiple cycles

The change in X position of the Hip and ankle can be seen from the graph itself as X of Ankle was oscillating for both of the foots and position of hip s X also resembled the right ankle.

Fig. 7.7 X Position of different joints in the system in multiple cycles

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Trajectories of both knees were compared as by plotting the (Xk,Zk,Thetak) it was observed that in the start of cycle a small angle of the left knee was there while right knee was totally straight and had no angle. A little drift was also observed in the Z position of the right knee.

Fig. 7.8 (a) Trajectory of Left Knee (b) Trajectory of Right Knee

At last in trajectory evaluation we took up the trajectory of hand which shows the change in the angle opposite that of hip side.

Hand motion was observed during the multiple walking cycles & it was found in rhythm with the hip motion and it changed normally as with the stance and swinging of hip occurred.

Fig. 7.9 Hand motion curve in multiple cycles

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7.2 Velocity of Joints: Later on moving we evaluated the velocities of respective joints in the system and we found that the velocity of left ankle in stance phase was almost near to zero which is as per the standard and the velocity of Right Ankle was having a sharp rise in swing phase.

Fig. 7.10 Velocity of Left Ankle

The velocity of right ankle was exactly opposite to the left ankle hence after the 1st double support phase the right leg moved into swing and it completed the swing with the velocity of around 1 meter/sec.

Fig. 7.11 Velocity of Right Ankle

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The Knee system had the oscillatory values for the x, z and theta. From the graph it s evident that value of x was also oscillating for the knees for a short duration of time. The Right knee shows a little variation from the left knee trajectory.

Fig. 7.12 Velocity of Left Knee & Velocity of Right Knee in multiple cycles

Velocity of the Hip and Hands were having the almost similar patterns in the graphs as rate of change of the x position of the hip resembled with hand. After 1st double support phase the graph turned almost same and during the single support phase certain peaks were observed.

Fig. 7.13 Velocity of (a) Hip (b) Hand in multiple cycles

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7.3 Acceleration of Joints: Further we observed the following graphs for the acceleration of the joints.

Fig. 7.14 Acceleration of Left Ankle in multiple cycles

It was observed that Ankle acceleration was negative in starting or the leg was in decelerating mode but after the 1st double support phase it came up and accelerated with an amount of 5 meters/sec2. Certain spikes were observed during the complete cycle which depicted the strike of heel to the ground.

Fig. 7.15 Acceleration of Right Ankle in multiple cycles

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The acceleration in knee joint was observed to have the certain peaks or rise during the completion of 1st single support or when the leg was in swing then it had to have the acceleration which turned out to be around 2.5 meters/secs2.

Fig. 7.16 Acceleration of Left and Right Knees

Finally once we got the torques and the accelerations of the different -2 joints we proceeded the further computations for ZMP by using the parameters from the table [1]. Table 1: Biped Model Parameters Link Parameters

Trunk

Thigh

Shin

Ankle

Foot

43.0

10.0

5.7

-

3.3

0.50

0.30

0.30

0.10

0.23

Mass (In Kg) Length (In meter)

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7.4 Trajectory of ZMP: The trajectory of ZMP was calculated by using the formula which was mentioned earlier:

Where (Xzmp, Yzmp) are the co-ordinates of ZMP position. The curves obtained for ZMP shows a little drift by increasing the weight around the subject body.

Fig. 7.17 ZMP Results with varying Load

It was observed that while loading the weight on the back of subject the trajectory of ZMP was shifted down and the step length became small as indicated by the plots in fig 7.17. In critical conditions it had been observed that increasing the weights beyond certain level does not cause much change in trunk bending.

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M.Tech.Thesis

7.5 Subject Motion Database: A database of subjects videos with and without carrying weight is being made up, below is the complete Gait cycle of the subject with varying weight.

Initial Contact

Loading Response

Pre Swing

Initial Swing

mid Stance

mid Swing

Terminal Stance

Terminal Swing

Fig. 7.18 Complete Gait Cycle with Load on Back equivalent to 10% of Subject s Weight

The weight on the back of subject was 10% of subject s own weight, hence the computation was done as follows: Subject weight = 73 Kg Backpack load = 73*(10/100) = 7.3 Kg Total Weight = 73+7.3 = 80.3 Kg

It was observed that during the load based walking the inclination of subject s trunk was continuously increasing as we increased the backpack weight. 67


M.Tech.Thesis

7.5.1 Segmented Images Database: Images were segmented out from the frames of the subject videos & taken at the interval according to the time in between the support phases.

Initial Contact

Pre Swing

Loading Response

mid Stance

Terminal Stance

Initial Swing

mid Swing

Terminal Swing

Fig. 7.19 Complete Gait Cycle with Load on Back equivalent to 10% of Subject s Weight

After converting the images from rgb to gray scale thresholding was applied and a global threshold of intensity level =150 was used for segmenting out the markers from the subject s images.

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7.6 Damping analysis: The variance between the values from the multiple images was calculated using ANOVA; finally the trajectories were plotted comparing the ones generated through model and then one which was generated through subject motion videos. A comparison was drawn among the values taken up by segmenting the markers from the subject s motion videos. It s visible that trajectory generated by the biped model is almost similar in case of the height of ankle or the Z position, while a little more bending was observed in the human structure and also it covers less distance as compare to our assumed biped model.

Fig. 7.20 Comparison plot of Ankle parameters obtained through the video and model

Sticky diagram for the Biped Model drawn at an interval of 0.1 second is given in fig 7.21. It s perfectly stable walk with slightly more tilt at hip side which caused the biped model to lean forward a bit every time. The foots were coming front and going back in rhythmic fashion as can be seen from the diagram to have a trajectory into which the maximum height of the obstacle was reached in every cycle. A knee bend was also

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M.Tech.Thesis

observed during the swinging of the backward leg. Hand was also moving in a rhythmic fashion with a little curve observed during the swing phase.

Fig. 7.21 Stick diagram for Biped walking (Interval = 0.01 second, cycles = 5)

Phase plots for hip and knee joint angles are given in Fig.7.22, which demonstrate the stability of angular plots obtained from ZMP approach.

Fig. 7.22 Angular Velocity of Hip & Knee

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The variation in the inclination of trunk was also analyzed as by varying the load around subject.

0% Load on Subject

10% Load on Subject

20% Load on Subject Fig. 7.23 Variation in Trunk inclination angle by varying load

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Finally the damping curves were plotted as by using the logic discussed previously. The damping for the Single support phase was evaluated by taking the difference between the consecutive X positions. For swing phase damping we chose up the angle of the joint and then if it was greater than the maximum angle that joint can reach then we subtract the value from that & calculate the damping.

Fig. 7.24 Damping in Left Knee

Fig. 7.25 Damping in Right Knee

It s been observed that the damping curve in a single cycle possessed some spikes which are due to the change in phase. The damping was also used for providing the stability to the biped robot under the condition of external load. 72

Chapter 8 RECOMMENDATIONS In the present work we calculated the trajectories of different joints in the assumed biped system by varying the parameters such as height of obstacle and internals of the biped like mass or length of link.

It s been observed that our control algorithm can provide the stability to a distorted kind of structure upto an extent but it converges in the case if the length of link increases exponentially.

Damping of the left and right knees were analyzed in a cycle and found to have certain spikes during phase change which is as per, a more detailed technique for the damping can be used by calculating damping in between the intermediate points and use the interpolation to get the smooth damping curve.

In our Biped system sometimes ZMP went beyond the control or graph contain the spikes hence one has to keep an eye on the previous values and then if the next value has a sudden rise then through interpolation and prediction then next value has to be discarded and curve ought to continue with previous value.

For further additions in the present work we recommend to consider the ground forces which can help in more stability during walking and also for another damping strategy.

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Chapter 9 CONCLUSION AND FUTURE WORK

In the Thesis work we proposed a mathematical model for the trajectory of the various joints in the biped. Later on we calculated the velocities and accelerations of the respective joints and found the changes by varying the terrain conditions and mass of the biped links.

Then after that torques & forces along the center of mass of the respective joints were evaluated which helped in evaluating the trajectory of Zero Moment Point. This step supplied the input to the control algorithm which has to run for all values of the distances from the normal of the body and generate the several sets of hip trajectories.

With the help of Control Algorithm we were able to choose up the unique trajectory by varying the load around the subject & that trajectory provides the maximum stability margin in a particular posture of the biped.

Finally we related the trajectory of Knees with the generation of damping during the load on subject s back and identified it s value during the Stance and Swing phase in the walking cycle.

Therefore in the concluding section we can say that we generated the unique gait sequence by applying some weight around the subject and then analyzed the motion of biped after providing that gait sequence.

The Future scope of work in the present thesis is that we analyzed the walking with normal pace along-with some weight on the back of subject, we did a partial analysis for running part.

74

Conclusion & Future Work

M.Tech. Thesis

Hence the future work can be comprised of analysis of running subject with some weight hanging around his hand or on his back.

Another analysis part can be of the generation of low energy reference trajectory coupled up with the ZMP approach and has to remain constant during the entire life cycle. As in the model we took up the maximum and minimum height of obstacle, which can be varied during the walking so some vision has to be incorporated which facilitates the height of obstacle coming in between. Also we didn t consider that much the case of ditch during walking so some control strategy has to be mixed up to avoid or cross that ditch according to it s size.

At last the scope can be in the form of another control strategy for generation of damping in the biped model, as stance damping was almost correctly generated in the model but swing phase damping found to have a continuous rise which should be in the form of continuous spikes.

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REFERENCES [1] Kazuo Hirai, Masato Hirose, Yuji Haikawa, Toru Takenaka, The Development of Honda Humanoid Robot , Proceedings of the 1998 IEEE International Conference on Robotics & Automation Leuven, Belgium May 1998.

[2] Miomir Vukobratović, Branislav Borovac, ZERO-MOMENT POINT - Thirty Five Years of It s Life , International Journal of Humanoid Robotics, Vol. 1, No. 1 (2004) 157 173.

[3] Jessica K. Hodgins, Marc H Raibert, Adjusting step length of rough terrain locomotion , IEEE Transaction on Robotics and Automation, Vol.7, No.3, June 1991.

[4] Tad McGeer, Passive walking with knees , In Proceedings of IEEE Robotics & Automation Conference, Cincinnati, OH, 1990, pp. 1640-1645.

[5] Mostafa Rostami, Guy Bessonnet, Impactless Sagittal gait of a biped robot during the single support phase , Proceedings of the 1998 IEEE , International Conference on Robotics and Automation Iuven, Belgium May 1998.

[6] Filipe M. Silva, J.A. Tenreiro Machado, Energy Analysis During Biped Walking , Proceedings of the 1999 IEEE, International Conference on Robotics & Automation, Detroit, Michigan May 1999.

[7] Y. F. Zheng and J. Shen, Gait synthesis for the SD-2 biped robot toclimb sloping surface , IEEE Transaction on Robotics and Automation, vol. 6, pp. 86 96, Feb. 1990.

[8] C. L. Shih, Y. Z. Li, S. Churng, T. T. Lee, andW. A. Cruver, Trajectory synthesis and physical admissibility for a biped robot during the single support phase , Proc. IEEE Int. Conf. Robotics and Automation, 1990, pp. 1646 1652.

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[9] A. Dasgupta and Y. Nakamura, Making feasible walking motion of humanoid robots from human motion capture data , In Proceedings of IEEE Int. Conf. Robotics and Automation, 1999, pp. 1044 1049.

[10] Qiang Huang, Kazuhito Yokoi & Shuuji Kajita, Planning Walking Patterns for a Biped Robot , IEEE Transactions on Robotics and Automation, Vol. 17, No. 3, June 2001.

[11] Jing Xian Li and Youlian Hong, Age Difference in Trunk Kinematics during walking with different Backpack weights in 6 to 12 years old children , In Proceedings of XXIInd International Symposium on Biomechanics in Sports (pp. 153156), Ottawa, Canada.

[12] ANOVA: Analysis of Variance between groups: http://www.physics.csbsju.edu/stats/anova.html

[13] Ronan Boulic, Nadia Magnenat-Thalmann, Daniel Thalmann, A global Human walking model with real-time kinematics personification , Computer Science Deptt University of Geneva, Switzerland. URL: http://ligwww.epfl.ch/~thalmann/papers.dir/TVC.walk.pdf

[14] Qiang Huang, Yoshihiko Nakamura, and Tetsunari Inamura, Humanoids Walk with Feedforward Dynamic Pattern and Feedback Sensory Reflection , Proceedings of the 2001 IEEE, International Conference on Robotics and Automation , Seoul, Korea, May 21-26 2001.

[15] James M. Ward Michael G. Wittman Patrick J. Flynn, Visual Analysis of the Effects of Load Carriage on Gait , Computer Science and Engineering, University of Notre Dame, Notre Dame, IN. URL: http://www.wvu.edu/~bknc/2004%20Abstracts/Visual%20Analysis%20of%20the%20Effects%20of %20Load%20Carriage%20on%20Gait.pdf

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[16] Shinichiro Nakaoka1, Atsushi Nakazawa2, Kazuhito Yokoi3 and Katsushi Ikeuchi1, Leg Motion Primitives for a Humanoid Robot to Imitate Human Dances , 1The University of Tokyo, Tokyo, 2Osaka University, Osaka, 3National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan. URL: http://www.cvl.iis.u-tokyo.ac.jp/papers/all/0091.pdf

[17] C. Chevallereau, A. Formalsky, B. Perrin,

Low Energy cost reference

Trajectories for a Biped Robot , Proceedings of the IEEE International Conference on Robotics & Automation May 1998.

[18]

Herr H, Wilkenfeld A.

User-Adaptive Control of a Magnetorheological

Prosthetic Knee. Industrial, Robot: An International Journal. 2003; 30: 42-55.

[19] Alberto Rovetta, Marita Canina, Paolo Allara,Giovanni Campa, Sergio Della Santina, Biorobotic Criteria in the Design of a New Limb Prosthesis . URL: http://robotica.mecc.polimi.it/articoli/articoli%20pdf/ICAR_protesi_2001.PDF

[20] Gordon W. Hiebert, Keir G. Pearson, Contribution of Sensory Feedback to the Generation of Extensor Activity During Walking in the Decerebrate Cat , Journal of Neurophysiology 81: 758-770, 1999.

[21] Eishi Hirasaki, Steven T. Moore, Theodore Raphan, Bernard Cohen, Effects of walking velocity on vertical head and body movements during locomotion , Exp Brain Res (1999) 127:117 130, © Springer-Verlag 1999.

[22] T. Schmalz, S. Blumentritt, K. Tsukishiro, L. Köcher, H. Dietl, Energy efficiency of trans-femoral amputees walking on computer-controlled prosthetic knee joint C-LEG , Otto Bock Orthopaedic Industry, Duderstadt, Germany. URL: http://www.ottobockus.com/products/lower_limb_prosthetics/c-leg_energy.pdf

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[23] Josef Kastner, Roman Nimmervoll, Herbert Kristen & Peter Wagner, What are the benefits of the C-Leg? A comparative gait analysis of the C-Leg, the 3R45 and the 3R80 prosthetic knee joints . URL: http://www.ottobockus.com/products/lower_limb_prosthetics/c-leg_benefits.pdf

[24] Pierre-Brice WIEBER,INRIA Rh one-Alpes, ZIRST Montbonnot, St-Ismier Cedex, France, On the stability of walking systems . URL: http://www.inrialpes.fr/bipop/publications/wieber/iarp-2002.pdf

[25] Erik Cuevas, Daniel Zaldívar, Raúl Rojas, Dynamic Control algorithm for a biped robot . URL: http://page.mi.fu-berlin.de/~zaldivar/files/tr-b-04-18.pdf

[26] Ralph E. Goddard, Yuan. F. Zheng, and Hooshang Hemami, Control of the HeelOff to Toe-Off Motion of a Dynamic Biped Gait , IEEE Transactions on Systems, and Cybernetics, Vol. 22, No. 1, Feb. 1992.

[27] W.Thomas, Miller,

Real time Neural network control of a biped walking

robot , IEEE Control Systems, vol. 14, pp. 41-48, Feb., 1994.

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gait stability using zmp algo.pdf

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