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

The complexity of computing the permanent

The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to $(m + n)\sqrt n $.

An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs

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 essential features of the branch-and-bound approach to constrained optimization are described, and several specific applications are reviewed. These include integer linear programming Land-Doig and Balas methods, nonlinear programming minimization of nonconvex objective functions, the traveling-salesman problem Eastman and Little, et al. methods, and the quadratic assignment problem Gilmore and Lawler methods. Computational considerations, including trade-offs between length of computation and storage requirements, are discussed and a comparison with dynamic programming is made. Various applications outside the domain of mathematical programming are also mentioned.

https://www.jstor.org/stable/pdfplus/168733.pdf

Branch-and-Bound Methods: A Survey

Introduction Normal subgroups and homomorphisms Elementary theory of abelian groups Sylow theorems Permutation groups Automorphisms Free groups Lattices and composition series A theorem of Frobenius solvable groups Supersolvable and nilpotent groups Basic commutators The theory of $p$-groups regular $p$-groups Further theory of abelian groups Monomial representations and the transfer Group extensions and cohomology of groups Group representation Free and amalgamated products The Burnside problem Lattices of subgroups Group theory and projective planes Bibliography Index Index of special symbols.

The theory of groups

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Coset representations in free groups

/pdf/a-basis-for-free-lie-rings-and-higher-commutators-in-free-4i6fc43jf4.pdf

A basis for free Lie rings and higher commutators in free groups

If we make this assumption it follows that 2JÎ annuls dA/dyir, where r is the order of A in yx. Let s be the order of A in y%. We form the resultant R of A and dA/dyir, considered as algebraic polynomials in y%8. Since A is irreducible, and cannot be a factor of dA/dyir, R is a nonzero polynomial, free of y%9, which is annulled by 9K. Since R is of lower efiective order than A in y%, 5DÎ must be an essential singular manifold of A relative to y^ The proof is now complete.

/pdf/distinct-representatives-of-subsets-38nbr71d8z.pdf

Distinct representatives of subsets

This paper has as its chief aim the establishment of two formulae associated with subgroups of finite index in free groups. The first of these (Theorem 3.1) gives an expression for the total length of the free generators of a subgroup U of the free group F r with r generators. The second (Theorem 5.2) gives a recursion formula for calculating the number of distinct subgroups of index n in F r . Of some independent interest are two theorems used which do not involve any finiteness conditions. These are concerned with ways of determining a subgroup U of F.

Marshall Hall

Papers

The theory of groups

Coset representations in free groups

A basis for free Lie rings and higher commutators in free groups

Distinct representatives of subsets

Subgroups of Finite Index in Free Groups