Multi-Body Dynamic Modeling of Multi-Legged Robots

Preface
Acknowledgements
Contents
About the Authors
Nomenclature
List of Figures
List of Tables
1 Introduction
	1.1 Introduction to Multi-legged Robots
	1.2 Legged Robot’s Locomotion
		1.2.1 Leg Mechanisms and Comparisons: Multi-legged Robots
		1.2.2 Advantages of Multi-legged Robots
		1.2.3 Disadvantages of Multi-legged Robots
		1.2.4 Applications of Multi-legged Robots
	1.3 VP Tools for Modeling and Analysis of Multi-legged Robots
	1.4 Summary
	References
2 Multi-Legged Robots—A Review
	2.1 Gait Planning of Multi-Legged Robots
		2.1.1 Kinematics of Multi-Legged Robots
		2.1.2 Dynamics of Multi-Legged Robots
		2.1.3 Foot-Ground Contact Modeling
	2.2 Power Consumption Analysis of Multi-Legged Robots
	2.3 Stability Analysis of Multi-Legged Robots
	2.4 Summary
	References
3 Kinematic Modeling and Analysis of Six-Legged Robots
	3.1 Description of the Problem
		3.1.1 Description of Proposed Six-Legged Walking Robot
		3.1.2 Gait Terminologies and Their Relationships
	3.2 Analytical Framework
		3.2.1 Reference System in Cartesian Coordinates
		3.2.2 Kinematic Constraint Equations
		3.2.3 Inverse Kinematic Model of the Six-Legged Robotic System
		3.2.4 Terrain Model
		3.2.5 Locomotion Planning on Various Terrains
		3.2.6 Gait Planning Strategy
		3.2.7 Evaluation of Kinematic Parameters
		3.2.8 Estimation of Aggregate Center of Mass
	3.3 Numerical Simulation: Study of Kinematic Motion Parameters
		3.3.1 Case Study 1: Robot Motion in an Uneven Terrain with Straight-Forward Motion (DF = 1/2)
		3.3.2 Case Study 2: Crab Motion of the Robot on a Banked Terrain (DF = 3/4)
	3.4 Summary
	References
4 Multi-body Inverse Dynamic Modeling and Analysis of Six-Legged Robots
	4.1 Analytical Framework
		4.1.1 Implicit Constrained Inverse Dynamic Model
		4.1.2 Newtonian Mechanics with Explicit Constraints
		4.1.3 Three-Dimensional Contact Force Model
		4.1.4 Static Equilibrium Moment Equation
		4.1.5 Actuator Torque Limits
		4.1.6 Optimal Feet Forces’ Distributions
		4.1.7 Energy Consumption of a Six-Legged Robot
		4.1.8 Stability Measures of Six-Legged Robots
	4.2 Numerical Illustrations
		4.2.1 Study of Optimal Feet Forces’ Distribution
		4.2.2 Study of Performance Indices—Power Consumption and Stability Measure
	4.3 Summary
	References
5 Validation Using Virtual Prototyping Tools and Experiments
	5.1 Modeling Using Virtual Prototyping Tools
	5.2 Numerical Simulation and Validation Using VP Tools and Experiments
		5.2.1 Validation of Kinematic Motion Parameters
		5.2.2 Validation of Dynamic Motion Parameters
	5.3 Summary
	References
Appendix
Appendix A.1 Matrix Projectors
Appendix A.2 Loop Equations w.r.t Frame G
Appendix A.3 Important Transformation Matrices
Appendix A.4 Trajectory Planning of Swing Leg
Appendix A.5 Time Calculations for Gait Planning
Appendix A.6 Kinematic Velocity and Acceleration
Calculation of Angular Velocities
Appendix A.7 Jacobian Matrices
Appendix A.8 Parameters Affecting the Dynamics of the Six-Legged Robot
Appendix A.9 Kinematic constraints with respect to G0
Appendix A.10 Geometrical Interpretation of the Interaction Region
Appendix A.11 Objective Function and Evaluation of the Constraints
Index