Tutorial on the generation of ergodic trajectories with projection-based gradient descent

A vehicle trajectory is ergodic with respect to some spatial distribution if the time spent in a region is proportional to the region's integrated density. One method of generating ergodic trajectories is projection-based trajectory optimisation, a gradient descent method that supports non-linear dynamics and balances trajectory ergodicity with control effort. In this study, the authors survey the existing literature on projection-based trajectory generation, focusing on implementation. They introduce an easy-to-use, open-source software package that generates ergodic trajectories orders of magnitude faster than previously reported. The authors' goal is to simplify the implementation of projection-based ergodic control so it can be applied widely across disciplines.