Nonholonomic Robot Systems. Part 2. Motion Planning under Kinematic Nonholonomic Constraints.

Nonholonomic kinematic constraints in elasticity

A geometrically exact model of a Cosserat rod with nonholonomic constraints is outlined. The constraint forces are derived from the framework of nonholonomic mechanics by using arguments from Cauchy analysis, and a thorough discussion is given concerning the nature of these constraints. By making an additional assumption on the magnitude of the deflections, a simplified model similar to the Eul...

Guidelines in Nonholonomic Motion Planning

Optimal Transportation under Nonholonomic Constraints

We study Monge’s optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures with respect to Lebesgue, and most importantly the absence of sharp abnormal minimizers. In particular, this result is applicable in the case of subriem...

Optimal, Smooth, Nonholonomic Mobile Robot Motion Planning in State Lattices

We present an approach to the problem of mobile robot motion planning in arbitrary cost fields subject to differential constraints. Given a model of vehicle maneuverability, a trajectory generator solves the two point boundary value problem of connecting two points in state space with a feasible motion. We use this capacity to compute a control set which connects any state to its reachable neig...

Formation Compound Control for Nonholonomic Mobile Robots under Motion Constraints

The formation keeping characteristics for nonholonomic autonomous mobile robots are investigated in this paper. A novel approach of compound control is presented, which deals with the formation task based on two different algorithms: a flexible feedback linearization control algorithm and an optimal approximate target algorithm. And the algorithms are selected according to robot’s expected loca...