Algebraic Geometry For Robotics And Control Theory

The 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.

Laura Menini received the Laurea degree in 1993 and her PhD in 1997 from the University of Rome Tor Vergata, where she is currently Full Professor. She co-authored the books Symmetries and Semi-invariants in the Analysis of Nonlinear Systems (Springer, 2011) and Mathematical Methods for System Theory (World Scientific, 1998). She is Chair of the IFAC Coordinating Committee 2 - Design Method and Senior Editor of the IEEE Control Systems Letters. Corrado Possieri received his Bachelor's and Master's degrees in Medical Engineering and his PhD degree in Computer Science, Control and Geoinformation from the University of Rome Tor Vergata, Italy, in 2011, 2013, and 2016, respectively. In 2016, he visited the University of California, Santa Barbara (UCSB). In 2018, he joined the Dipartimento di Elettronica e Telecomunicazioni at the Politecnico di Torino, where he was an Assistant Professor. Subsequently, in 2019, he joined the Istituto di Analisi dei Sistemi ed Informatica "A Ruberti" of the Consiglio Nazionale delle Ricerche (IASI-CNR), where he is currently a Researcher. He is Associate Editor of the IEEE CSS Conference Editorial Board, the EUCA Conference Editorial Board, and the IFAC Conference Editorial Board. Antonio Tornambè is currently Full Professor of Control Theory at the University of Rome Tor Vergata. His research interests are in control theory for linear and nonlinear systems. He is the co-author of Discrete-Event System Theory: An Introduction (World Scientific, 1995), Mathematical Methods for System Theory (World Scientific, 1998) and Symmetries and Semi-invariants in the Analysis of Nonlinear Systems (Springer, 2011).