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

Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given. >

/pdf/nonholonomic-motion-planning-steering-using-sinusoids-3lyefe031n.pdf

Nonholonomic motion planning: steering using sinusoids

Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined. The paper is divided into two parts. The first part introduces and defines concepts such as Nerode realization, multistructural forms and results from differential geometry which are then used to derive a recursive input-output model for multivariable deterministic non-linear systems. The second part introduces several examples, compares the derived model with other representations and extends the results to create prediction error or innovation input-output models for non-linear stochastic systems. These latter models are the generalization of the multivariable ARM AX models for linear systems and are referred to as NARMAX or Non-linear AutoRegressive Moving Average models with exogenous inputs.

/pdf/input-output-parametric-models-for-non-linear-systems-part-44hf73mgve.pdf

Input-output parametric models for non-linear systems Part II: stochastic non-linear systems

This paper presents a novel randomized motion planner for robots that must achieve a specified goal under kinematic and/or dynamic motion constraints while avoiding collision with moving obstacles with known trajectories. The planner encodes the motion constraints on the robot with a control system and samples the robot's state × time space by picking control inputs at random and integrating its equations of motion. The result is a probabilistic roadmap of sampled state ×time points, called milestones, connected by short admissible trajectories. The planner does not precompute the roadmap; instead, for each planning query, it generates a new roadmap to connect an initial and a goal state×time point. The paper presents a detailed analysis of the planner's convergence rate. It shows that, if the state×time space satisfies a geometric property called expansiveness, then a slightly idealized version of our implemented planner is guaranteed to find a trajectory when one exists, with probability quickly converg...

/pdf/randomized-kinodynamic-motion-planning-with-moving-obstacles-u6o55k62ct.pdf

Randomized Kinodynamic Motion Planning with Moving Obstacles

We present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems. A necessary condition for the problem to be solvable is derived in terms of an unobservability distribution, which is computable by means of suitable algorithms. The existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an "observable" quotient subsystem unaffected by all fault signals but one. For this subsystem, a fault detection filter is designed.

A geometric approach to nonlinear fault detection and isolation

The properties of controllability, observability, and the theory of minimal realization for linear systems are well-understood and have been very useful in analyzing such systems. This paper deals with analogous questions for nonlinear systems.

R. Hermann

Papers

Nonlinear controllability and observability