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

Learning-based control algorithms require data collection with abundant\nsupervision for training. Safe exploration algorithms ensure the safety of this\ndata collection process even when only partial knowledge is available. We\npresent a new approach for optimal motion planning with safe exploration that\nintegrates chance-constrained stochastic optimal control with dynamics learning\nand feedback control. We derive an iterative convex optimization algorithm that\nsolves an \\underline{Info}rmation-cost \\underline{S}tochastic\n\\underline{N}onlinear \\underline{O}ptimal \\underline{C}ontrol problem\n(Info-SNOC). The optimization objective encodes control cost for performance\nand exploration cost for learning, and the safety is incorporated as\ndistributionally robust chance constraints. The dynamics are predicted from a\nrobust regression model that is learned from data. The Info-SNOC algorithm is\nused to compute a sub-optimal pool of safe motion plans that aid in exploration\nfor learning unknown residual dynamics under safety constraints. A stable\nfeedback controller is used to execute the motion plan and collect data for\nmodel learning. We prove the safety of rollout from our exploration method and\nreduction in uncertainty over epochs, thereby guaranteeing the consistency of\nour learning method. We validate the effectiveness of Info-SNOC by designing\nand implementing a pool of safe trajectories for a planar robot. We demonstrate\nthat our approach has higher success rate in ensuring safety when compared to a\ndeterministic trajectory optimization approach.\n