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

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

A text that makes the mathematical underpinnings of robot motion accessible and relates low-level details of implementation to high-level algorithmic concepts. Robot motion planning has become a major focus of robotics. Research findings can be applied not only to robotics but to planning routes on circuit boards, directing digital actors in computer graphics, robot-assisted surgery and medicine, and in novel areas such as drug design and protein folding. This text reflects the great advances that have taken place in the last ten years, including sensor-based planning, probabalistic planning, localization and mapping, and motion planning for dynamic and nonholonomic systems. Its presentation makes the mathematical underpinnings of robot motion accessible to students of computer science and engineering, rleating low-level implementation details to high-level algorithmic concepts.

Principles of Robot Motion: Theory, Algorithms, and Implementations

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

Continuum robotics has rapidly become a rich and diverse area of research, with many designs and applications demonstrated. Despite this diversity in form and purpose, there exists remarkable similarity in the fundamental simplified kinematic models that have been applied to continuum robots. However, this can easily be obscured, especially to a newcomer to the field, by the different applications, coordinate frame choices, and analytical formalisms employed. In this paper we review several modeling approaches in a common frame and notational convention, illustrating that for piecewise constant curvature, they produce identical results. This discussion elucidates what has been articulated in different ways by a number of researchers in the past several years, namely that constant-curvature kinematics can be considered as consisting of two separate submappings: one that is general and applies to all continuum robots, and another that is robot-specific. These mappings are then developed both for the single-section and for the multi-section case. Similarly, we discuss the decomposition of differential kinematics (the robotâ??s Jacobian) into robot-specific and robot-independent portions. The paper concludes with a perspective on several of the themes of current research that are shaping the future of continuum robotics.

/pdf/design-and-kinematic-modeling-of-constant-curvature-4wrx5stlzx.pdf

Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review

https://www.tpbin.com/Uploads/Subjects/b163b255-bf83-4187-a613-13dce5ca61f0.pdf

Dynamics and contouring control of a 3-DoF parallel kinematics machine

In this paper, we propose a unified control system architecture for multifingered manipulation (CoSAM/sup 2/). CoSAM/sup 2/ achieves simultaneously three objectives of multifingered manipulation: (a) Motion trajectory (velocity/force) tracking of a grasped object; (b) Improving the grasp configuration in the course of object manipulation; and (c) Optimizing grasping forces to enforce contact constraint and compensate for external object wrenches. CoSAM/sup 2/ is organized in a modular and hierarchic structure so that each module implements a specified function using inputs from its predecessors and a minimum number of sensory data signals. CoSAM/sup 2/ is also flexible in accommodating addition of new modules. Here, we give the details for the coordinated motion generation module and the grasping force generation module.

/pdf/coordinated-motion-generation-and-real-time-grasping-force-1isf20aw6a.pdf

Coordinated motion generation and real-time grasping force control for multifingered manipulation

This article develops a geometric theory which unifies the formulation and computation of form (straightness, flatness, cylindricity, and circularity), profile and orientation tolerances stipulated in ANSI Y14.5M standard. The theory rests on an important observation that a toleranced feature exhibits a symmetry subgroup G 0 under the action of the Euclidean group, SE (3). Thus, the configuration space of a toleranced (or a symmetric) feature can be identified with the homogeneous space SE (3)/ G 0 of the Euclidean group. Geometric properties of SE (3)/ G 0 , especially its exponential coordinates carried over from that of SE (3), are analyzed. We show that all cases of form, profile and orientation tolerances can be formulated as a minimization or constrained minimization problem on the space SE (3)/ G 0 , with G 0 being the symmetry subgroup of the underlying feature. We develop a simple geometric algorithm, called the Symmetric Minimum Zone (SMZ) algorithm, to unify the computation of form, profile, and orientation tolerances. Finally, we use numerical simulation results comparing the performances of the SMZ algorithm against the best known algorithms in the literature.

A geometric theory of form, profile, and orientation tolerances

The energy-balance method, originally developed for systems whose behaviors are described by a single continuous differential equation, is extended to hopping systems, where the equations of motion are discontinuous from one phase to the other. Specifically, the perturbation and energy-balance methods were combined to study the existence and stability of the limit cycle behavior of a vertical hopper system. Estimated values of the limit cycles obtained using the proposed method are compared with the true (simulated) values for both the linear and the nonlinear models. The results confirm the validity of the proposed method. >

An energy perturbation approach to limit cycle analysis in legged locomotion systems

This paper investigates the synthesis of a spatial stiffness matrix using simple line springs. A new algorithm is developed, which enables the selection of constituent springs based on their positions and directions. The constraining space of the line springs is then investigated. It is shown that an isotropic stiffness matrix, in general, can be split into the sum of two rank-3 stiffness matrices. The three line springs of the first matrix can be selected to pass through any arbitrary points in space, while the three line springs of the second stiffness matrix lie on a quadric surface, which is usually a hyperboloid of one sheet.

Zexiang Li

Papers

Dynamics and contouring control of a 3-DoF parallel kinematics machine

Coordinated motion generation and real-time grasping force control for multifingered manipulation

A geometric theory of form, profile, and orientation tolerances

An energy perturbation approach to limit cycle analysis in legged locomotion systems

Spatial stiffness realization with parallel springs using geometric parameters