Leveraging Precomputation with Problem Encoding for Warm-Starting Trajectory Optimization in Complex Environments

Motion planning through optimization is largely based on locally improving the cost of a trajectory until an optimal solution is found. Choosing the initial trajectory has therefore a significant effect on the performance of the motion planner, especially when the cost landscape contains local minima. While multiple heuristics and approximations may be used to efficiently compute an initialization online, they are based on generic assumptions that do not always match the task at hand. In this paper, we exploit the fact that repeated tasks are similar according to some metric. We store solutions of the problem as a library of initial seed trajectories offline and employ a problem encoding to retrieve near-optimal warm-start initializations on-the-fly. We compare how different initialization strategies affect the global convergence and runtime of quasi-Newton and probabilistic inference solvers. Our analysis on the 38-DoF NASA Valkyrie robot shows that efficient and optimal planning in high-dimensional state spaces is possible despite the presence of globally non-smooth and discontinuous constraints, such as the ones imposed by collisions.