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In this paper, we propose a novel model predictive control (MPC) frameworkfor output tracking that deals with partially unknown constraints. The MPCscheme optimizes over a learning and a backup trajectory. The learningtrajectory aims to explore unknown and potentially unsafe areas, if and only ifthis might lead to a potential performance improvement. On the contrary, thebackup trajectory lies in the known space, and is intended to ensure safety andconvergence. The cost function for the learning trajectory is divided into atracking and an offset cost, while the cost function for the backup trajectoryis only marginally considered and only penalizes the offset cost. We show thatthe proposed MPC scheme is not only able to safely explore the unknownconstraints, but also escape from local minima that may arise from the presenceof obstacles. Moreover, we provide formal guarantees for convergence andrecursive feasibility of the MPC scheme, as well as closed-loop constraintsatisfaction. Finally, the proposed MPC scheme is demonstrated in simulationsusing an example of autonomous vehicle driving in a partially unknownenvironment where unknown obstacles are present.

Safe Exploration and Escape Local Minima with Model Predictive Control under Partially Unknown Constraints