Relaxed DAEs in path planning and path following

This paper studies a computationally efficient and robust method for path planning and path following tasks for unmanned systems. The method is based on relaxed differential-algebraic equations (DAEs), which allow to handle deviations from a prescribed path. The relaxation is designed by a suitably formulated optimal control problem with the aim to guide the system back to the desired path in a smooth way. The approach merely requires to solve a higher index DAE numerically. In addition, a parametric sensitivity analysis can be used to obtain Taylor approximations of perturbed solutions at very low computational cost. We demonstrate the method for a path following task with an unmanned ground vehicle (UGV) and a transition to hover maneuver of an unmanned aerial vehicle (UAV).