Nilpotentization of the kinematics of the \(n\)-trailer system at singular points and motion planning through the singular locus. (English) Zbl 1024.93036
Summary: We propose 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 non-holonomic 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 neighbourhood 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.
MSC:
93C85 | Automated systems (robots, etc.) in control theory |
93B29 | Differential-geometric methods in systems theory (MSC2000) |
70Q05 | Control of mechanical systems |