Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems

Learning-based control algorithms require collection of abundant supervision for training. Safe exploration algorithms enable this data collection to proceed safely even when only partial knowledge is available. In this paper, we present a new episodic framework to design a sub-optimal pool of motion plans that aid exploration for learning unknown residual dynamics under safety constraints. We derive an iterative convex optimization algorithm that solves an information-cost Stochastic Nonlinear Optimal Control problem (Info-SNOC), subject to chance constraints and approximated dynamics to compute a safe trajectory. The optimization objective encodes both performance and exploration, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust learning model. We prove the safety of rollouts from our exploration method and reduction in uncertainty over epochs ensuring consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot.