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.

使用最优控制提出新的安全保证的探索框架，其中包括对于非线性系统的有限时间样本复杂度边界下的保证的探索，具有任意高概率的可靠性和安全性，在复杂的非线性动态和未知领域的许多实际情景中具备一般性和适用性。

非线性系统的安全保证探索