An Augmented Lagrangian Based Shooting Method for the Trajectory Optimization of Switched Lagrangian Systems
The application range of a shooting method based on Moreau's sweeping process is extended to the class of switching Lagrangian systems. The method finds at least quasi-optimal trajectories based on a non-gradient minimization strategy that utilizes the augmented Lagrangian approach. An augmented Lagrangian based nongradient shooting method is presented that finds the minimum in trajectory optimization problem over all hybrid executions of a switched Lagrangian system. The optimization will be performed by the direct shooting method combined with successive quadratic penalty method. The numerical integrations are performed by applying Moreau's time-stepping discretization scheme to the measure-differential inclusion describing the mechanical dynamics.