Time optimal steering for a mobile robot along a given path

We present an open loop control design allowing to steer in a minimum time a wheeled robot along a prespecified smooth geometric path, between arbitrary given postures, while satisfying a set of dynamical constraints, such as actuator saturation or maximum admissible accelerations. Using the concept of “differential flatness” the problem is shown to be equivalent to the selection of the optimal time parametrization of the given geometric path. Using the inverse of the time derivative of this parametrization as the decision variable, the problem reduces to a convex minimization problem, which can be solved as a finite parameter optimization problem.