2000/04/19 by William Pasillas-Lépine, William Pasillas-Lepine, Pasillas-Lepine, William +2
Computer Science · Engineering · Mathematics · #58A30 (Secondary) #93B29 (Primary) #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Control (math.OC) #Robotic Path Planning Algorithms #math.DG #math.OC #msc:58A30 #msc:93B29
paper · pdf · doi:10.48550/arxiv.math/0004125
LaTeX2e, 23 pages, 4 figures, submitted to International journal of control
arxiv created 2000/04/19 · openalex publication_date 2000/04/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an algebraic problem (the resolution of a system of polynomial equations), which we illustrate by steering the two-trailer system in a neighborhood of singular configurations. We show also that the n-trailer system is a universal local model for all Goursat structures and that all Goursat structures are locally nilpotentizable.