INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises

http://www.cds.caltech.edu/%7Emurray/books/MLS/pdf/mls94-complete.pdf

A Mathematical Introduction to Robotic Manipulation

By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.

Basic problems in stability and design of switched systems

This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

This paper introduces the concept of a hybrid system and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.

Perspectives and results on the stability and stabilizability of hybrid systems

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

The 3-D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom; it is acted on by gravity and it is fully actuated by control forces. The 3-D pendulum has two disjoint equilibrium manifolds, namely a hanging equilibrium manifold and an inverted equilibrium manifold. The contribution of this paper is that two fundamental stabilization problems for the inverted 3-D pendulum are posed and solved. The first problem, asymptotic stabilization of a specified equilibrium in the inverted equilibrium manifold, is solved using smooth and globally defined feedback of angular velocity and attitude of the 3-D pendulum. The second problem, asymptotic stabilization of the inverted equilibrium manifold, is solved using smooth and globally defined feedback of angular velocity and a reduced attitude vector of the 3-D pendulum. These control problems for the 3-D pendulum exemplify attitude stabilization problems on the configuration manifold SO(3) in the presence of potential forces. Lyapunov analysis and nonlinear geometric methods are used to assess global closed-loop properties, yielding a characterization of the almost global domain of attraction for each case.

Asymptotic Smooth Stabilization of the Inverted 3-D Pendulum

A design procedure for simultaneous position and force control is developed, using Lyapunov's direct method, for manipulators in contact with a rigid environment that can be described by holonomic constraints. Many manipulators that interact with their environment require taking into account the effects of these constraints in the control design. The forces of constraint play a critical role in constrained motion and are, along with displacements and velocities, to be regulated at specified values. Lyapunov's direct method is used to develop a class of position and force feedback controllers. The conditions for gain selection demonstrate the importance of the constraints. Force feedback has been shown not to be mandatory for closed-loop stabilization, but it is useful in improving certain closed-loop robustness properties. >

Position and force control for constrained manipulator motion: Lyapunov's direct method

In this paper a reorientation maneuvering strategy for an interconnection of planar rigid bodies in space is developed. It is assumed that there are no exogeneous torques, and torques generated by joint motors are used as means of control so that the total angular momentum of the multibody system is a constant, assumed to be zero in this paper. The maneuver strategy uses the nonintegrability of the expression for the angular momentum. We demonstrate that large-angle maneuvers can be designed to achieve an arbitrary reorientation of the multibody system with respect to an inertial frame. The theoretical background for carrying out the required maneuvers is briefly summarized. Specifications and computer simulations of a specific reorientation maneuver, and the corresponding control strategies, are described. I. Introduction I N this paper we develop a reorientation strategy for a system of N planar rigid bodies in space that are interconnected by ideal frictionless pin joints in the form of an open kinematic chain. Angular momentum preserving controls, e.g., torques generated by joint motors, are considered. The TV-body system is assumed to have zero initial angular momentum. Our earlier work1'2 demonstrated that reorientation of a planar multibody system with three or more interconnected bodies using only joint torque inputs is an inherently nonlinear control problem that is not amenable to classical methods of nonlinear control. The goal of this study is to indicate how control strategies can be explicitly constructed to achieve the desired absolute reorientation of the TV-body system. There are many physical advantages in using internal controls, e.g., joint torque controls, to carry out the desired multibody reorientation maneuvers. First of all, this control approach does not modify the total angular momentum of the multibody system. In addition, internal controls have obvious advantages in terms of energy conservation. Moreover, they can be implemented using standard electrical servo motors, a simple and reliable control actuator technology. The formal development in this paper is concerned with control of a multibody interconnection in space that has zero angular momentum. Although these results are formulated in a general setting, we have been motivated by several classes of specific problems. Several potential applications of our general results are now described. Manipulators mounted on space vehicles and space robots have been envisioned to carry out construction, maintenance, and repair tasks in an external space environment. These space systems are essentially multibody systems satisfying the assumptions of this paper. To carry out the desired tasks, they must be capable of performing a variety of reorientation maneuvers. Previous research on maneuvering of such space multibody systems has mainly focused on maneuvers that achieve desired orientation of some of the bodies, e.g., an end effector, whereas the orientation of some of the remaining bodies cannot be specified, at least using the methodologies employed.3"8 Using the approach suggested in this paper, maneuvers that achieve any desired reorientation for all of the

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/77104/AIAA-11411-971.pdf;sequence=1

Planar reorientation maneuvers of space multibody systems using internal controls

An efficient and accurate computational approach is proposed for a nonconvex optimal attitude control for a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete time necessary conditions for optimality are derived, and an efficient computational approach is proposed to solve the resulting two-point boundary-value problem. This formulation wherein the optimal control problem is solved based on discretization of the attitude dynamics and derivation of discrete time necessary conditions, rather than development and discretization of continuous time necessary conditions, is shown to have significant advantages. In particular, the use of geometrically exact computations on SO(3) guarantees that this optimal control approach has excellent convergence properties even for highly nonlinear large angle attitude maneuvers.

Optimal Attitude Control of a Rigid Body Using Geometrically Exact Computations on SO(3)

Three-dimensional attitude and shape control problems are studied for a class of spacecraft with articulated appendages and reaction wheels. A number of special cases of such attitude control problems have been studied previously. We provide a unified formulation and a comprehensive set of results for planning of attitude and shape maneuvers of a spacecraft, assuming that joint actuators and reaction wheels provide a sufficiently rich set of inputs. The development is based on a nonlinear, drift-free, control model that characterizes the attitude and shape change dynamics, assuming zero angular momentum of the system. Controllability results are presented for the general case, and specialized results are identified for interesting multibody spacecraft configurations. These results are made explicit by providing computable formulas for the Lie brackets in terms of the spacecraft geometry, mass properties, and shape. Constructive motion planning approaches are described to achieve spacecraft attitude and shape change maneuvers. A distinct feature of these approaches is that they require only simple computations, as is desirable for online implementation. Emphasis is given to the interplay between the shape change dynamics and the attitude change dynamics in achieving the maneuver planning objectives.

N.H. McClamroch

Papers

Asymptotic Smooth Stabilization of the Inverted 3-D Pendulum

Position and force control for constrained manipulator motion: Lyapunov's direct method

Planar reorientation maneuvers of space multibody systems using internal controls

Optimal Attitude Control of a Rigid Body Using Geometrically Exact Computations on SO(3)

Nonlinear attitude and shape control of spacecraft with articulated appendages and reaction wheels