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

TL;DR

This paper introduces a model predictive control framework that safely explores unknown constraints and escapes local minima, ensuring convergence and safety in partially unknown environments, demonstrated through autonomous vehicle simulations.

Contribution

A novel MPC scheme that balances exploration and safety, with formal guarantees and practical validation in autonomous driving scenarios.

Findings

Successfully explores unknown constraints safely

Escapes local minima caused by obstacles

Provides formal convergence and safety guarantees

Abstract

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