  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.
