Steering a Mobile Robot: Selection of a Velocity Profile Satisfying Dynamical Constraints

We present an open loop control design allowing to steer a wheeled mobile robot along a prespecified smooth geometric path, minimizing a given cost index and satisfying a set of dynamical constraints. Using the concept of “differential flatness,” the problem is equivalent to the selection of the optimal time parametrization of the geometric path. This parametrization is characterized by a differential equation involving a function of the curvilinear coordinate along the path. For the minimum time problem, as well as for another index (such as the maximum value of the centripetal acceleration) to be minimized over a given time interval, the problem then reduces to the optimal choice of this function of the curvilinear coordinate. Using spline functions interpolation, the problem can be recast as a finite parameter optimization problem. Numerical simulation results illustrate the procedure.