On nonholonomic mobile robots and optimal maneuvering

The authors consider the robot path planning problem in the presence of nonintegrable kinematic constraints, known as nonholonomic constraints. Such constraints are generally caused by one or several rolling contacts between rigid bodies and express that the relative velocity of two points in contact is zero. They make the dimension of the space of achievable velocities smaller than the dimension of the robot´s configuration space. Using standard results in differential geometry (Frobenius integrability theorem) and nonlinear control theory, the authors first give a formal characterization of holonomy (and nonholonomy) for robot systems subject to linear differential constraints and state some related results about their controllability. They then apply these results to `car-like´ and `trailer-like´ robots. Finally, they present an implemented planner, which generates collision-free paths with a minimal number of maneuvers for car-like and trailer-like robots among obstacles