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

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra where flatness- and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of plane curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from non-linear physics. A high frequency control strategy is proposed such that the averaged systems become flat.

/pdf/flatness-and-defect-of-non-linear-systems-introductory-42ot9eoqmh.pdf

Flatness and defect of non-linear systems: introductory theory and examples

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

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Higher-order sliding modes, differentiation and output-feedback control

In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI) whose optimal solution can be characterized exactly. This family corresponds to the case where the associated linear operator maps the cone of positive semidefinite matrices onto itself. In this case, the optimal value equals the spectral radius of the operator. It is shown that some rank minimization problems, as well as generalizations of the structured singular value ($mu$) LMIs, have exactly this property.

In the same spirit of exploiting structure to achieve computational efficiency, an algorithm for the numerical solution of a special class of frequency-dependent LMIs is presented. These optimization problems arise from robustness analysis questions, via the Kalman-Yakubovich-Popov lemma. The procedure is an outer approximation method based on the algorithms used in the computation of hinf norms for linear, time invariant systems. The result is especially useful for systems with large state dimension.

The other main contribution in this thesis is the formulation of a convex optimization framework for semialgebraic problems, i.e., those that can be expressed by polynomial equalities and inequalities. The key element is the interaction of concepts in real algebraic geometry (Positivstellensatz) and semidefinite programming.

To this end, an LMI formulation for the sums of squares decomposition for multivariable polynomials is presented. Based on this, it is shown how to construct sufficient Positivstellensatz-based convex tests to prove that certain sets are empty. Among other applications, this leads to a nonlinear extension of many LMI based results in uncertain linear system analysis.

Within the same framework, we develop stronger criteria for matrix copositivity, and generalizations of the well-known standard semidefinite relaxations for quadratic programming.

Some applications to new and previously studied problems are presented. A few examples are Lyapunov function computation, robust bifurcation analysis, structured singular values, etc. It is shown that the proposed methods allow for improved solutions for very diverse questions in continuous and combinatorial optimization.

Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization

: The principal goal of this three years research effort was to enhance the research base which would support efforts to systematically control, or take advantage of, dominant nonlinear or distributed parameter effects in the evolution of complex dynamical systems. Such an enhancement is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft and missiles. The principal investigating team has succeeded in the development of a systematic methodology for designing feedback control laws solving the problems of asymptotic tracking and disturbance rejection for nonlinear systems with unknown, or uncertain, real parameters. Another successful research project was the development of a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems. The technical details which needed to be overcome are discussed more fully in this final report.

https://apps.dtic.mil/sti/pdfs/ADA391461.pdf

Nonlinear Control Systems

From the Publisher:
Adaptive Control provides techniques for automatic adjustment in real time of controller parameters to achieve or maintain a desired level of system performance when the process parameters are unknown or variable. The book deals coherently with many aspects of the field, starting with the problems posed and moving onto the presentation of the solutions and their practical significance. As well as presenting recent trends, the book also looks at: Synthesis and Analysis of Parameter Adaptation Algorithms, Recursive Plant Model Identification in Open and Close Loop, Robust Digital Control for Adaptive Control, Robust Parameter Adaptation Algorithms, Direct and Indirect Adaptive Control, and Practical Aspects and Applications. To reflect the importance of digital computers for the application of adaptive control techniques, discrete-time aspects are emphasized. To guide the reader, the book contains various applications of adaptive control techniques.

Adaptive Control

1 Introduction.- 1.1 Overview and examples of infinite dimensional systems.- 1.2 Organization and brief summary.- 1.3 Remarks on notation.- 1.4 Notes and references.- 2 Semigroups of Linear Operators.- 2.1 Motivation and definitions.- 2.2 Properties of semigroups.- 2.3 Generation theorems for semigroups.- 2.4 Relation with the Laplace transform.- 2.5 Differentiability and analytic semigroups.- 2.6 Compact semigroups.- 2.7 Abstract Cauchy problem.- 2.7.1 Homogeneous initial value problems.- 2.7.2 Inhomogeneous initial value problems.- 2.7.3 Lipschitz perturbations.- 2.8 Integrated semigroups.- 2.9 Nonlinear semigroups of contractions.- 2.10 Notes and references.- 3 Stability of C0-Semigroups.- 3.1 Spectral mapping theorems.- 3.2 Spectrum-determined growth condition.- 3.3 Weak stability and asymptotic stability.- 3.4 Exponential stability - time domain criteria.- 3.5 Exponential stability - frequency domain criteria.- 3.6 Essential spectrum and compact perturbations.- 3.7 Invariance principle for nonlinear semigroups.- 3.8 Notes and references.- 4 Static Sensor Feedback Stabilization of Euler-Bernoulli Beam Equations.- 4.1 Modeling of a rotating beam with a rigid tip body.- 4.2 Stabilization using strain or shear force feedback.- 4.3 Damped second order systems.- 4.4 Exponential stability and spectral analysis.- 4.4.1 Exponential stability.- 4.4.2 Spectral analysis.- 4.5 Shear force feedback control of a rotating beam.- 4.5.1 Well-posedness and exponential stability.- 4.5.2 Asymptotic behavior of the spectrum.- 4.6 Stability analysis of a hybrid system.- 4.6.1 Well-posedness and exponential stability.- 4.6.2 Spectral analysis.- 4.7 Gain adaptive strain feedback control of Euler-Bernoulli beams.- 4.8 Notes and references.- 5 Dynamic Boundary Control of Vibration Systems Based on Passivity.- 5.1 A general framework for system passivity.- 5.1.1 Uncontrolled case.- 5.1.2 Controlled case.- 5.2 Dynamic boundary control using positive real controllers.- 5.2.1 Positive real controllers and their characterizations.- 5.2.2 Stability analysis of control systems with SPR controllers.- 5.3 Dynamic boundary control of a rotating flexible beam.- 5.3.1 Stabilization problem using SPR controllers.- 5.3.2 Orientation problem using positive real controllers.- 5.4 Stability robustness against small time delays.- 5.5 Notes and references.- 6 Other Applications.- 6.1 A General linear hyperbolic system.- 6.2 Stabilization of serially connected vibrating strings.- 6.3 Two coupled vibrating strings.- 6.4 A vibration cable with a tip mass.- 6.5 Thermoelastic system with Dirichlet - Dirichlet boundary conditions.- 6.6 Thermoelastic system with Dirichlet - Neumann boundary conditions.- 6.7 Renardy's counter-example on spectrum-determined growth condition.- 6.8 Notes and references.

Stability and Stabilization of Infinite Dimensional Systems with Applications

Suitable either as a reference or as a text for a graduate course in adaptive control systems, this book is a self-contained compendium of easily implementable adaptive control algorithms that have been developed and applied by the authors for over 10 years. These algorithms do not require explicit process parameter identification and have been successfully applied to a wide variety of engineering problems including flexible structure control, blood pressure control and robotics. In general, these algorithms are suitable for a wide class of multiple input-output control systems containing significant uncertainty as well as disturbances.

Direct Adaptive Control Algorithms: Theory and Applications

One of the key ideas in control theory is that of viewing a complex dynamical system as an interconnection of simpler subsystems, thus deriving conclusions regarding the complete system from properties of its building blocks. Following this paradigm, and motivated by questions in molecular biology modeling, the authors have recently developed an approach based on components which are monotone systems with respect to partial orders in state and signal spaces. This paper presents a brief exposition of recent results, with an emphasis on small gain theorems for negative feedback, and the emergence of multi-stability and associated hysteresis effects under positive feedback.

Eduardo D. Sontag

Papers

Nonlinear Control Systems

Adaptive Control

Stability and Stabilization of Infinite Dimensional Systems with Applications

Direct Adaptive Control Algorithms: Theory and Applications

Interconnections of Monotone Systems with Steady-State Characteristics