A Kinematic Model of the Nonholonomic n-bar System: Geometry and Flatness

Shunjie Li (1) , Witold Respondek (1)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

We propose a kinematic model of a system moving in $\mathbb{R}^{m+1}$ and consisting of $n$ rigid bars attached successively to each other and subject to the nonholonomic constraints that the velocity of the source point of each bar is parallel to that bar. We prove that the associated control system is controllable and feedback equivalent to the $m$-chained form around any regular configuration. Hence we deduce that the $n$-bar system is flat and the cartesian position of the source point of the last bar is a flat output. The $n$-bar system is a natural generalization of the $n$-trailer system and we provide a comparison of flatness properties of both systems.

Mots clés: $n$-bar system; $m$-chained form; Cartan distribution; Feedback equivalence; Flatness

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Shunjie Li, Witold Respondek. A Kinematic Model of the Nonholonomic n-bar System: Geometry and Flatness. the 8th IFAC Symposium on Nonlinear Control Systems, Sep 2010, Bologna, Italy. ⟨hal-00586413⟩