Controllability of Mobile Robots with Kinematic Constraints.

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.

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