Description
Book SynopsisThe development of inexpensive and fast computers, coupled with the discovery of efficient algorithms for dealing with polynomial equations, has enabled exciting new applications of algebraic geometry and commutative algebra. Algebraic Geometry for Robotics and Control Theory shows how tools borrowed from these two fields can be efficiently employed to solve relevant problem arising in robotics and control theory.After a brief introduction to various algebraic objects and techniques, the book first covers a wide variety of topics concerning control theory, robotics, and their applications. Specifically this book shows how these computational and theoretical methods can be coupled with classical control techniques to: solve the inverse kinematics of robotic arms; design observers for nonlinear systems; solve systems of polynomial equalities and inequalities; plan the motion of mobile robots; analyze Boolean networks; solve (possibly, multi-objective) optimization problems; characterize the robustness of linear; time-invariant plants; and certify positivity of polynomials.
Table of ContentsPreface; List of Figures; List of Tables; List of Symbols; Algebraic Geometry Notions; Implementations in Macaulay2; The Inverse Kinematics of Robot Arms; Observer Design; Immersions of Polynomial Systems into Linear Ones Up to an Output Injection; Solving Systems of Equations and Inequalities; Motion Planning for Mobile Robots; Computation of the Largest f-Invariant Set Contained in an Affine Variety; Boolean Networks; Multi-Objective Optimization; Distance to Internal Instability of LTI Systems Under Structured Perturbations; Decomposition in Sum of Squares; Bibliography; Index;
