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 safe guaranteed exploration framework using optimal control, which achieves first-of-its-kind results: guaranteed exploration for non-linear 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 non-linear dynamics and unknown domains. Based on this framework we propose an efficient algorithm, SageMPC, SAfe Guaranteed Exploration using Model Predictive Control. SageMPC improves efficiency by incorporating three techniques: i) exploiting a Lipschitz bound, ii) goal-directed exploration, and iii) receding horizon style re-planning, 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.

翻译：具有先验未知约束的安全环境探索是限制机器人自主性的基本挑战。在确保安全性的同时，保证充分探索对于自主任务完成同样至关重要。为应对这些挑战，我们提出了一种基于最优控制的新型安全保证性探索框架，首次实现了以下成果：在具有有限时间样本复杂度界的前提下，对非线性系统进行保证性探索，同时以任意高概率被证明是安全的。该框架具有普适性，适用于包含复杂非线性动力学和未知域的多种现实场景。基于该框架，我们提出了一种高效算法SageMPC（基于模型预测控制的安全保证性探索）。SageMPC通过融合三项技术提升效率：i）利用Lipschitz界，ii）目标导向探索，及iii）滚动时域风格重规划，同时保持框架所需的样本复杂度、安全性与探索保证。最后，我们使用车辆模型通过SageMPC在具有挑战性的未知环境中展示了安全高效的探索能力。