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 triaxial attitude control testbed has been developed as part of a research program on spacecraft multibody rotational dynamics and control. In this paper, equations of motion are derived and presented in various forms. Actuation mechanisms are incorporated into the models including: moment actuators that are fixed to the triaxial base body, as well as reaction wheel actuators and proof mass actuators that are fixed to the triaxial base body. The models also allow incorporation of unactuated auxiliary bodies that are constrained to move relative to the triaxial base body. The models expose the dynamic coupling between the rotational motion of the triaxial base body, the relative or shape motion of the auxiliary degrees of freedom, and dynamics associated with actuation mechanisms.

http://ieeexplore.ieee.org/iel5/7709/21120/00980388.pdf

Equations of motion for the triaxial attitude control testbed

Presents a hybrid feedback control approach for stabilizing a class of cascade nonlinear systems to an equilibrium. The control architecture is a combination of nonlinear analog feedback and switched (sampled data) feedback, that, in a certain sense, feedback linearizes the closed loop at the analog time scale and at the time scale induced by the switching. Conditions for local asymptotic stability and global asymptotic stability of the equilibrium of the closed loop hybrid system are developed. The results are applied to the construction of hybrid controllers that stabilize a class of underactuated mechanical systems and a class of nonlinear nonminimum phase systems. In particular, a hybrid controller is developed and studied for the model of a rotational and translational actuator.

Hybrid control for stabilization of a class of cascade nonlinear systems

This paper introduces a global uncertainty propagation scheme for the attitude dynamics of a rigid body, through a combination of numerical parametric uncertainty techniques, noncommutative harmonic analysis, and geometric numerical integration. This method is distinguished from prior approaches, as it allows one to consider probability densities that are global, and are not supported on only a single coordinate chart on the manifold. It propagates a global probability density through the full attitude dynamics, instead of replacing angular velocity dynamics with a gyro bias model. The use of Lie group variational integrators, that are symplectic and remain on the Lie group, as the underlying numerical propagator ensures that the advected probability densities respect the geometric properties of uncertainty propagation in Hamiltonian systems, which arise as consequence of the Gromov nonsqueezing theorem from symplectic geometry. We also describe how the global uncertainty propagation scheme can be applied to the problem of global attitude estimation.

/pdf/global-symplectic-uncertainty-propagation-on-so-3-24eh61w0ei.pdf

Global symplectic uncertainty propagation on SO(3)

A design procedure for simultaneous position/force control is developed, using Lyapunov's direct method for mechanical systems with holonomic constraints. Many mechanical systems which interact with their environment require the effects of these constraints to be taken into account in the control design. The force applied by the constraint plays a critical role in constrained motion and is, along with displacements and velocities, to be regulated at specified values. Lyapunov's direct method is used to develop a class of decentralized position/force controllers. The approach avoids coordinate transformation and does not require force feedback. The conditions for gain selection demonstrate the importance of the constraints. An example is used to demonstrate this control design method; closed-loop characteristics are indicated by computer simulations. >

http://ieeexplore.ieee.org/iel2/796/2456/00070431.pdf

Position/force control design for constrained mechanical systems: Lyapunov's direct method

A deterministic attitude estimator for a rigid body under an attitude dependent potential is studied using small error assumptions. This estimator requires only a single direction measurement to a known reference point at each measurement instant. The measurement cannot completely determine the attitude, but an attitude estimation scheme based on this measurement is developed; a feasible set compatible with the measurement is described and it is combined with an attitude dynamics model to obtain an attitude estimate. The attitude is globally represented by a rotation matrix, and the uncertainties are described by ellipsoidal sets. A numerical example for a spacecraft in a circular orbit is presented.

http://www.math.ucsd.edu/~mleok/pdf/LeLeMcSa2006_gaesdm.pdf

N.H. McClamroch

Papers

Equations of motion for the triaxial attitude control testbed

Hybrid control for stabilization of a class of cascade nonlinear systems

Global symplectic uncertainty propagation on SO(3)

Position/force control design for constrained mechanical systems: Lyapunov's direct method

Global Attitude Estimation using Single Direction Measurements