Dynamic and Nonlinear Programming for Trajectory Planning in Moving Environments

Trajectory planning on high dimensional systems with respect to obstacle avoidance proposes multiple challenges to traditional techniques from optimization. While gradient based solvers tend to struggle with the non-smooth, non-differentiable structure of geometric collision avoidance constraints, sampling based methods can not handle complex dynamics. Also graph as well as dynamic programming based strategies become impractical facing the curse of dimensionality. Nevertheless, a strategy combining dynamic programming (DP) with nonlinear programming (NLP) into an iterative algorithm recently achieved promising results on a robotic arm scenario within a static environment. In this work, we modify the algorithm, to be able to handle moving environments, including on the one hand collision avoidance with time dependent obstacles, but also time dependent goal constraints. As a proof of concept, we apply the new strategy to a space manipulator, planning its trajectory towards a tumbling piece of space debris.