Safe Guaranteed Exploration for Non-linear Systems

2024-02-09

IEEE Transactions on Automatic Control

AI Summary

This paper addresses safe exploration for nonlinear robotic systems under unknown constraints. Method: We propose the first optimal control framework that jointly ensures safety and exploration completeness, integrating model predictive control (MPC), Lipschitz continuity analysis, goal-directed exploration, and receding-horizon replanning to enable online safety verification and proactive constraint avoidance. Contribution/Results: Theoretically, we establish the first finite-time sample complexity bound for general nonlinear systems—guaranteeing satisfaction of safety constraints with arbitrarily high probability and achieving exploration completeness within a finite number of samples. Empirically, we validate the framework in an autonomous driving simulation environment, demonstrating its safety, efficiency, and realizability of theoretical guarantees.

Technology Category

• Natural Language Processing: Safety and Robustness
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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 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.

Problem

• Safe exploration for non-linear systems with unknown constraints
• Guaranteed finite-time exploration with high safety probability
• Efficient algorithm for complex dynamics in unknown domains

Innovation

• Safe exploration via optimal control
• Lipschitz bound for efficiency
• Model Predictive Control algorithm