Constrained Probabilistic Movement Primitives for Robot Trajectory Adaptation

Versatile movement representations allow robots to learn new tasks and rapidly adapt them to environmental changes, e.g. introduction of obstacles, placing additional robots in the workspace, modification of the joint range due to faults or range of motion constraints due to tool manipulation. Probabilistic movement primitives (ProMP) model robot movements as a distribution over trajectories and they are an important tool due to their analytical tractability and ability to learn and generalise from a small number of demonstrations. Current approaches solve specific adaptation problems, e.g. obstacle avoidance, however, a generic probabilistic approach to adaptation has not yet been developed. In this paper we propose a generic probabilistic framework for adapting ProMPs. We formulate adaptation as a constrained optimisation problem where we minimise the Kullback-Leibler divergence between the adapted distribution and the distribution of the original primitive and we constrain the probability mass associated with undesired trajectories to be low. We derive several types of constraints that can be added depending on the task, such us joint limiting, various types of obstacle avoidance, via-points, and mutual avoidance, under a common framework. We demonstrate our approach on several adaptation problems on simulated planar robot arms and 7-DOF Franka-Emika robots in single and dual robot arm settings.