Maneuvers of a controlled vehicle, such as a car, traveling at moderate to high speeds are planned by propagating cost waves in a configuration space using two search strategies referred to as budding and differential budding. Control is achieved by monitoring properties of the controlled vehicle and adjusting control parameters to achieve motion relative to a frame of reference. The frame of reference may change before the transformation to configuration space occurs. The method transforms goals, obstacles, and the position of the controlled vehicle in task space to a configuration space based on the position of these objects relative to a moving frame of reference. The method also determines a local neighborhood of possible motions based on the control capabilities of the vehicle. In one embodiment, the controlled parameters are time derivatives of the monitored properties. A variation of the method provides for the parallel computation of the configuration space. In one embodiment of the parallel computation, the case where two processes are used, a first process and configuration space would be used to plan. A second process and configuration space would be used to read the setpoints which are sent as control directives to the vehicle.