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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.