Adaptive Sliding Mode Control of Mobile Manipulators with Markovian Switching Joints

The hybrid joints of manipulators can be switched to either active (actuated) or passive (underactuated) mode as needed. Consider the property of hybrid joints, the system switches stochastically between active and passive systems, and the dynamics of the jump system cannot stay on each trajectory errors region of subsystems forever; therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this paper, we consider stochastic stability and sliding mode control for mobile manipulators using stochastic jumps switching joints. Adaptive parameter techniques are adopted to cope with the effect of Markovian switching and nonlinear dynamics uncertainty and follow the desired trajectory for wheeled mobile manipulators. The resulting closed-loop system is bounded in probability and the effect due to the external disturbance on the tracking errors can be attenuated to any preassigned level. It has been shown that the adaptive control problem for the Markovian jump nonlinear systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. Finally, a numerical example is given to show the potential of the proposed techniques

Single wheel robot: gyroscopical stabilization on ground and on incline.

by Loi-Wah Sun.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 77-81).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiContents --- p.vList of Figures --- p.viiList of Tables --- p.viiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.1.1 --- Literature review --- p.2Chapter 1.1.2 --- Gyroscopic precession --- p.5Chapter 1.2 --- Thesis overview --- p.7Chapter 2 --- Dynamics of the robot on ground --- p.9Chapter 2.1 --- System model re-derivation --- p.10Chapter 2.1.1 --- Linearized model --- p.15Chapter 2.2 --- A state feedback control --- p.16Chapter 2.3 --- Dynamic characteristics of the system --- p.18Chapter 2.4 --- Simulation study --- p.19Chapter 2.4.1 --- The self-stabilizing dynamics effect of the single wheel robot --- p.21Chapter 2.4.2 --- The Tilting effect of flywheel on the robot --- p.23Chapter 2.5 --- Dynamic parameters analysis --- p.25Chapter 2.5.1 --- Swinging pendulum --- p.25Chapter 2.5.2 --- Analysis of radius ratios --- p.27Chapter 2.5.3 --- Analysis of mass ratios --- p.30Chapter 3 --- Dynamics of the robot on incline --- p.33Chapter 3.1 --- Modeling of rolling disk on incline --- p.33Chapter 3.1.1 --- Disk rolls up on an inclined plane --- p.37Chapter 3.2 --- Modeling of single wheel robot on incline --- p.39Chapter 3.2.1 --- Kinematic constraints --- p.40Chapter 3.2.2 --- Equations of motion --- p.41Chapter 3.2.3 --- Model simplification --- p.43Chapter 3.2.4 --- Linearized model --- p.46Chapter 4 --- Control of the robot on incline --- p.47Chapter 4.1 --- A state feedback control --- p.47Chapter 4.1.1 --- Simulation study --- p.49Chapter 4.2 --- Backstepping-based control --- p.51Chapter 4.2.1 --- Simulation study --- p.53Chapter 4.2.2 --- The effect of the spinning rate of flywheel --- p.56Chapter 4.2.3 --- Simulation study --- p.58Chapter 4.2.4 --- Roll up case --- p.58Chapter 4.2.5 --- Roll down case --- p.58Chapter 5 --- Motion planning --- p.61Chapter 5.1 --- Performance index --- p.61Chapter 5.2 --- Condition of rolling up --- p.62Chapter 5.3 --- Motion planning of rolling Up --- p.65Chapter 5.3.1 --- Method I : Orientation change --- p.65Chapter 5.3.2 --- Method II : Change the initial velocities --- p.69Chapter 5.4 --- Wheel rolls Down --- p.70Chapter 5.4.1 --- Terminal velocity of rolling body down --- p.73Chapter 6 --- Summary --- p.75Chapter 6.1 --- Contributions --- p.75Chapter 6.2 --- Future Works --- p.76Bibliography --- p.7

A Dynamic Coupling Index For Underactuated Manipulators

In recent years, researchers have been dedicated to the study of underactuated manipulators which have more joints than control actuators. In previous works, one always assumes that there is enough dynamic coupling between the active and the passive joints of the manipulator, for it to be possible to control the position of the passive joints via the dynamic coupling. In this work, the authors aim to develop an index to measure the dynamic coupling, so as to address when control of the underactuated system is possible, and how the motion and robot configuration can be designed. We discuss extensively the nature of the dynamic coupling and of the proposed coupling index, and their applications in the analysis and design of underactuated systems, through a detailed mathematical analysis and several illustrative examples. 1 1 Introduction In recent years, researchers have been turning their attention to the so called underactuated systems, where the term underactuated refers to the fac..