Controllability of Mobile Robots with Kinematic Constraints.

Abstract

Abstract : This report addresses the controllability problem for robot systems subject to kinematic constraints on the velocity and its application to path planning. It is shown that the well-known Controllability Rank Condition Theorem is applicable to these systems when there are inequality constraints on the velocity in addition to equality constraints, and/or when the constraints are nonlinear instead of linear. This allows us to infer a whole set of new results on the controllability of robotic systems subject to nonintegrable kinematic constraints (called nonholonomic systems). A car with limited steering angle is one example of such a system. For example, we show that: (1) An n body car system, which consists of a car towing n - 1 trailers, is controllable for n < 4 even if the steering angle is limited; (2) An n-body car (n < 4) that can only turn left is still maneuverable on the right; (3) If there is a path for an n body car system (n < 4) with limited steering angle in a given environment then there is another path that uses only the extremal values of the steering angle. It is conjectured that these results are true for all n.