Learning optimal trajectories for nonholonomic systems

Many advanced robotic systems are subject to non-holonomic constraints, e.g. wheeled mobile robots, space manipulators and multifingered robot hands. Steering these mechanisms between configurations in the presence of perturbations is a difficult problem. In fact, the divide et impera strategy (first plan a trajectory, then track it by feedback) has a fundamental drawback in this case: due to the peculiar control properties of non-holonomic systems, smooth feedback cannot provide tracking of the whole trajectory. As a result, it would be necessary to give up either accuracy in the final positioning or predictability of the actual motion. We pursue here a different approach which does not rely on a separation between planning and control. Based on the learning control paradigm, a robust steering scheme is devised for systems which can be put in chained form, a canonical structure for non-holonomic systems. By overparametrizing the control law, other performance goals can be met, typically expressed as cost functions to be minimized along the trajectory. As a case study, we consider the generation of robust optimal trajectories for a car-like mobile robot, with criteria such as total length, maximum steering angle, distance from workspace obstacles, or error with respect to an offline planned trajectory