Time-Varying Soft-Maximum Barrier Functions for Safety in Unmapped and Dynamic Environments

2024-09-02

arXiv.org

AI Summary

Ensuring safe navigation for autonomous systems in unknown, dynamically changing environments remains challenging due to the lack of prior maps and time-varying obstacles. Method: This paper proposes a composite Control Barrier Function (CBF) framework based on a time-varying soft maximum function. Local CBFs are constructed in real time from LiDAR measurements, and the most recent $N$ local CBFs are smoothly and differentiably fused via the time-varying soft maximum to approximate the union of safety sets. A closed-form, analytically solvable time-varying soft maximum CBF is introduced—enabling guaranteed forward invariance of the safety set without prior map knowledge or static obstacle assumptions. The method integrates with a closed-form quadratic program subject to CBF constraints, ensuring computational efficiency. Results: Validated on nonholonomic ground robots and quadrotors, the approach achieves real-time obstacle avoidance, stable convergence to goals, and significantly enhanced robustness and practicality for safe navigation in dynamic environments.

Technology Category

• Natural Language Processing: Safety and Robustness
• Intelligent Robots: Localization, Mapping, and Navigation
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We present a closed-form optimal feedback control method that ensures safety in an a prior unknown and potentially dynamic environment. This article considers the scenario where local perception data (e.g., LiDAR) is obtained periodically, and this data can be used to construct a local control barrier function (CBF) that models a local set that is safe for a period of time into the future. Then, we use a smooth time-varying soft-maximum function to compose the N most recently obtained local CBFs into a single barrier function that models an approximate union of the N most recently obtained local sets. This composite barrier function is used in a constrained quadratic optimization, which is solved in closed form to obtain a safe-and-optimal feedback control. We also apply the time-varying soft-maximum barrier function control to 2 robotic systems (nonholonomic ground robot with nonnegligible inertia, and quadrotor robot), where the objective is to navigate an a priori unknown environment safely and reach a target destination. In these applications, we present a simple approach to generate local CBFs from periodically obtained perception data.

Problem

• Ensures safety in unknown dynamic environments
• Combines local barrier functions for safe control
• Applies method to ground and aerial robots

Innovation

• Closed-form optimal feedback control for safety
• Time-varying soft-maximum function for CBF composition
• Local CBFs from periodic perception data