Safe Guaranteed Exploration for Nonlinear Systems

Abstract

Safely exploring environments with a-priori unknown constraints is a fundamental challenge that restricts the autonomy of robots. While safety is paramount, guarantees on sufficient exploration are also crucial for ensuring autonomous task completion. To address these challenges, we propose a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">safe guaranteed exploration</i> framework using optimal control, which achieves first-of-its-kind results: guaranteed exploration for nonlinear systems with finite-time sample complexity bounds, while being provably safe with arbitrarily high probability. The framework is general and applicable to many real-world scenarios with complex nonlinear dynamics and unknown domains. We improve the efficiency of this general framework by proposing an algorithm, SAfe Guaranteed Exploration using Model Predictive Control (SageMPC). SageMPC leverages three key techniques: first, exploiting a Lipschitz bound; second, goal-directed exploration; and third, receding horizon style replanning, all while maintaining the desired sample complexity, safety, and exploration guarantees of the framework. Lastly, we demonstrate safe efficient exploration in challenging unknown environments using SageMPC with a car model.