Mark W. Spong - Robot Modeling and Control

12 Chapter 12Figure 12.1 The sphere as a two-dimensional manifold in .Figure 12.2 Integral manifold in .Figure 12.3 Pictorial representation of a vector field on a manifold.Figure 12.4 Inner-loop/outer-loop control architecture for feedback linearization.Figure 12.5 Single-link, flexible joint robot.Figure 12.6 Step response and motor torque of the flexible joint robot. The difference betw...Figure 12.7 Tracking response and motor torque of the flexible joint robot with a cubic pol...Figure 12.8 Tracking response and motor torque of the flexible joint robot with an observer...

13 Chapter 13Figure 13.1 An underactuated serial-link robot.Figure 13.2 Upper-actuated (left) and lower-actuated (right) robots.Figure 13.3 Illustrating common reference angle conventions.Figure 13.4 The inverted pendulum on a cart.Figure 13.5 An overhead crane, a gimballed rocket and bipedal walking as examples of the in...Figure 13.6 The Acrobot as a gymnastic robot.Figure 13.7 The Pendubot.Figure 13.8 The Reaction-Wheel Pendulum.Figure 13.9 The Reaction Wheel Pendulum.Figure 13.10 Equilibrium configurations of the Acrobot and Pendubot under gravity with zero ...Figure 13.11 Local stabilization of the Reaction-Wheel Pendulum at the inverted position q ...Figure 13.12 Equilibrium configurations of the Pendubot for ue nonzero.Figure 13.13 The determinant of the controllability matrix for equilibrium positions (0, π/2...Figure 13.14 Brachiation motion of the Acrobot with virtual holonomic constraint q 1+ 0....Figure 13.15 A simple pendulum with a force F acting at the bob.Figure 13.16 Phase portrait of the simple pendulum. The constant energy curves are solution ...Figure 13.17 Phase portrait of the closed-loop system. Figure generated by pplane, courtesy ...Figure 13.18 The Reaction-Wheel Pendulum as a parallel interconnection of passive systems.Figure 13.19 Swingup and balance of the Reaction-Wheel Pendulum (left) and phase plane traje...Figure 13.20 Reaction-wheel velocity (left) and saturated control input (right).Figure 13.21 Swingup and balance of the Acrobot using switching control

14 Chapter 14Figure 14.1 Mass m connected to a rigid rod.Figure 14.2 The rolling disk.Figure 14.3 The kinematic car.Figure 14.4 A hopping robot.Figure 14.5 The differential drive robot: top view (left), side view (right).Figure 14.6 The car parking problem.Figure 14.7 Illustrating the notion of Lie bracket direction.Figure 14.8 Response of z 1, z 2, and z 3: Note that z 1and z 2return to t...Figure 14.9 Response of z 1, z 2and z 3.Figure 14.10 Trajectory and control inputs of the DDR computed from the flat outputs.Figure 14.11 Sliding-mode control of the DDR in chain form: response of the chain variables ...Figure 14.12 Sliding-mode control of the DDR in chain form: control inputs.Figure 14.13 Modified sliding-mode control of the DDR in chain form: response of the chain v...Figure 14.14 Modified sliding-mode control of the DDR in chain form: control inputs.Figure 14.15 DDR pose regulation.Figure 14.16 Differential drive robot showing the location of the output located d units a...Figure 14.17 Trajectory of the differential drive robot with partial feedback linearization ...

15 Appendix BFigure 1: The right hand rule.

16 Appendix CFigure C.1: Illustrating the definition of stability.

1 Cover

2 Table of Contents

3 Preface

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