Trajectory Optimization in Discrete Mechanics

Trajectory optimization involves both the optimization of inputs and the feedback regulation of the resulting trajectories. This article covers the main points of adapting trajectory optimization to the numerical routines in discrete mechanics. We start with a brief description of discrete mechanics and variational integrators and then move on to linearization, estimation, local projections in discrete function spaces, and iterative methods in trajectory optimization. Throughout, we discuss the results in the context of open-source software trep that implements all of the techniques for interconnected rigid body systems.