Geometry and control of the nonholonomic integrator: An electrodynamics\n analogy

2020/07/26 by Pragada Shivaramakrishna, Shivaramakrishna, Pragada, A. Sanand Amita Dilip +1
Engineering · Mathematics · #Control and Dynamics of Mobile Robots #Control and Stability of Dynamical Systems #Dynamics and Control of Mechanical Systems #FOS: Electrical engineering #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2007.13074

openalex publication_date 2020/07/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider some generalizations of the classical nonholonomic integrator and\ngive a geometric approach to characterize controllability for these systems. We\nuse Stokes' theorem and results from complex analysis to obtain necessary and\nsufficient conditions for controllability. Furthermore, we show that optimal\ntrajectories of certain minimum energy optimal control problems defined on\nthese systems can be identified with the trajectory of a charged particle in an\nelectromagnetic field.\n

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