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Multi-body Dynamic Modeling of Multi-legged Robots

:	Abhijit Mahapatra, Shibendu Shekhar Roy, Dilip Kumar Pratihar
:	Multi-body Dynamic Modeling of Multi-legged Robots
:	Springer-Verlag
:	9789811529535
:	1
:	CHF 85.50
:

:	Informatik
:	English

:	230
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This book describes the development of an integrated approach for generating the path and gait of realistic hexapod robotic systems. It discusses in detail locomation with straight-ahead, crab and turning motion capabilities in varying terrains, like sloping surfaces, staircases, and various user-defined rough terrains. It also presents computer simulations and validation using Virtual Prototyping (VP) tools and real-world experiments.

The book also explores improving solutions by applying the developed nonlinear, constrained inverse dynamics model of the system formulated as a coupled dynamical problem based on the Newton-Euler (NE) approach and taking into account realistic environmental conditions. The approach is developed on the basis of rigid multi-body modelling&nbs ;and the concept that there is no change in the configuration of the system in the short time span of collisions.

Dr. Abhijit Mahapatra received&n sp; B.E. and M.Tech. degrees in Mechanical Engineering from B.E. College (now, BESU), Shibpur, India, and NIT Durgapur, India, in 2002 and 2008, respectively. He received his Ph.D. from NIT Durgapur, India, in 2018. He is currently working as a Senior Scientist in the Advanced Design and Analysis Group at CSIR- Central Mechanical Engineering Research Institute, Durgapur, India.
Dr. Mahapatra has published a number of research papers in national and international journals and confer nce proceedings and filed several patents in the area of product development. His current research interests include design& analysis, multi-body dynamics, and modelling and simulating legged robots.

Dr. Shibendu Shekhar Roy rec ived B.E. and M.Tech. degrees in Mechanical Engineering from NIT, Durgapur. He also holds a Ph.D. from IIT, Kharagpur, India. He is currently working as a Professor at the Department of Mechanical Engineering and Associate Dean (Alumni Affairs& Outreach) at the National Institute of Technology, Durgapur.
Dr. Roy has published more than 68 papers in national and international journals and confer nce proceedings, as well as 4 book chapters, and has filed a number of patents in the area of product development. His current research interests include modelling and simulating legged robots, soft robotics, rehabilitation robotics, additive manufacturing and 3D printing on macro- and micro-scales.

Dr. Dilip Kumar Pratihar ompleted his B.E. and M. Tech. in Mechanical Engineering at NIT, Durgapur, India, in 1988 and 1995, respectively. He received his Ph.D. from IIT Kanpur in 2000. Dr. Pratihar pursued postdoctoral studies in Japan and then in Germany under the Alexander von Humboldt Fellowship Program. He is currently working as a Professor at IIT Kharagpur, India. His research areas include robotics, soft computing and manufacturing science.
He has made significant contributions in the development of intelligent autonomous systems in various fields, including robotics, and manufacturing science. He has published more than 230 papers, mostly in international journals, and is on the editorial board of 12 international journals. He is a member of the FIE, MASME and SMIEEE. He has completed a number of sponsored (funded by DST, DAE, MHRD, DBT) and consultancy projects and is a member of Expert Committee of Advanced Manufacturing Technology, DST, Government of India.

	Preface	7
	Acknowledgements	8
	Contents	9
	About the Authors	11
	Nomenclature	13
	List of Figures	21
	List of Tables	29
	1 Introduction	30
	1.1 Introduction to Multi-legged Robots	30
	1.2 Legged Robot’s Locomotion	31
	1.2.1 Leg Mechanisms and Comparisons: Multi-legged Robots	33
	1.2.2 Advantages of Multi-legged Robots	34
	1.2.3 Disadvantages of Multi-legged Robots	35
	1.2.4 Applications of Multi-legged Robots	35
	1.3 VP Tools for Modeling and Analysis of Multi-legged Robots	36
	1.4 Summary	37
	References	37
	2 Multi-Legged Robots—A Review	39
	2.1 Gait Planning of Multi-Legged Robots	39
	2.1.1 Kinematics of Multi-Legged Robots	40
	2.1.2 Dynamics of Multi-Legged Robots	41
	2.1.3 Foot-Ground Contact Modeling	42
	2.2 Power Consumption Analysis of Multi-Legged Robots	44
	2.3 Stability Analysis of Multi-Legged Robots	48
	2.4 Summary	52
	References	52
	3 Kinematic Modeling and Analysis of Six-Legged Robots	61
	3.1 Description of the Problem	61
	3.1.1 Description of Proposed Six-Legged Walking Robot	61
	3.1.2 Gait Terminologies and Their Relationships	63
	3.2 Analytical Framework	64
	3.2.1 Reference System in Cartesian Coordinates	64
	3.2.2 Kinematic Constraint Equations	68
	3.2.3 Inverse Kinematic Model of the Six-Legged Robotic System	71
	3.2.4 Terrain Model	73
	3.2.5 Locomotion Planning on Various Terrains	74
	3.2.6 Gait Planning Strategy	86
	3.2.7 Evaluation of Kinematic Parameters	88
	3.2.8 Estimation of Aggregate Center of Mass	92
	3.3 Numerical Simulation: Study of Kinematic Motion Parameters	94
	3.3.1 Case Study 1: Robot Motion in an Uneven Terrain with Straight-Forward Motion (DF = 1/2)	95
	3.3.2 Case Study 2: Crab Motion of the Robot on a Banked Terrain (DF = 3/4)	97
	3.4 Summary	102
	References	104
	4 Multi-body Inverse Dynamic Modeling and Analysis of Six-Legged Robots	105
	4.1 Analytical Framework	105
	4.1.1 Implicit Constrained Inverse Dynamic Model	106
	4.1.2 Newtonian Mechanics with Explicit Constraints	108
	4.1.3 Three-Dimensional Contact Force Model	110
	4.1.4 Static Equilibrium Moment Equation	120
	4.1.5 Actuator Torque Limits	121
	4.1.6 Optimal Feet Forces’ Distributions	121
	4.1.7 Energy Consumption of a Six-Legged Robot	123
	4.1.8 Stability Measures of Six-Legged Robots	124
	4.2 Numerical Illustrations	132
	4.2.1 Study of Optimal Feet Forces’ Distribution	132
	4.2.2 Study of Performance Indices—Power Consumption and Stability Measure	141
	4.3 Summary	160
	References	161
	5 Validation Using Virtual Prototyping Tools and Experiments	164
	5.1 Modeling Using Virtual Prototyping Tools	164
	5.2 Numerical Simulation and Validation Using VP Tools and Experiments	165
	5.2.1 Validation of Kinematic Motion Parameters	165
	5.2.2 Validation of Dynamic Motion Parameters	176
	5.3 Summary	188
	References	191
	Appendix	192
	Appendix A.1 Matrix Projectors	192
	Appendix A.2 Loop Equations w.r.t Frame G	192
	Appendix A.3 Important Transformation Matrices	197
	Appendix A.4 Trajectory Planning of Swing Leg	198
	Appendix A.5 Time Calculations for Gait Planning	206
	Appendix A.6 Kinematic Velocity and Acceleration	208
	Calculation of Angular Velocities	208
	Appendix A.7 Jacobian Matrices	210
	Appendix A.8 Parameters Affecting the Dynamics of the Six-Legged Robot	212
	Appendix A.9 Kinematic constraints with respect to G0	215
	Appendix A.10 Geometrical Interpretation of the Interaction Region	219
	Appendix A.11 Objective Function and Evaluation of the Constraints	223
	Index	228