Learning Barrier Functions for Constrained Motion Planning with Dynamical Systems Stable dynamical systems are a flexible tool to plan robotic motions in realtime. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robotxe2x80x99s workspace. This work presents a novel approach to learn workspace constraints from human demonstrations and to generate motion trajectories for the robot that lie in the constrained workspace. Training data are incrementally clustered into different linear subspaces and used to fit a low dimensional representation of each subspace. By considering the learned constraint subspaces as zeroing barrier functions, we are able to design a control input that keeps the system trajectory within the learned bounds. This control input is effectively combined with the original system dynamics preserving eventual asymptotic properties of the unconstrained system. Simulations and experiments on a real robot show the effectiveness of the proposed approach.

Trajectory Optimization for Unknown Constrained Systems using Reinforcement Learning In this paper, we propose a reinforcement learningbased algorithm for trajectory optimization for constrained dynamical systems. This problem is motivated by the fact that for most robotic systems, the dynamics may not always be known. Generating smooth, dynamically feasible trajectories could be difficult for such systems. Using samplingbased algorithms for motion planning may result in trajectories that are prone to undesirable control jumps. However, they can usually provide a good reference trajectory which a modelfree reinforcement learning algorithm can then exploit by limiting the search domain and quickly finding a dynamically smooth trajectory. We use this idea to train a reinforcement learning agent to learn a dynamically smooth trajectory in a curriculum learning setting. Furthermore, for generalization, we parameterize the policies with goal locations, so that the agent can be trained for multiple goals simultaneously. We show result in both simulated environments as well as real experiments, for a 6DoF manipulator arm operated in positioncontrolled mode to validate the proposed idea. We compare the proposed ideas against a PID controller which is used to track a designed trajectory in configuration space. Our experiments show that our RL agent trained with a reference path outperformed a modelfree PID controller of the type commonly used on many robotic platforms for trajectory tracking.