Optimization-free Smooth Control Barrier Function for Polygonal Collision Avoidance
🤖 AI Summary
Designing control barrier functions (CBFs) for dynamic collision avoidance among polygons is challenging due to nonsmooth obstacle boundaries, leading to non-differentiability and reliance on online numerical optimization.
Method: This paper proposes a smooth, non-conservative CBF construction that avoids online optimization by leveraging a lower bound of the signed distance field (SDF), modeling obstacle geometry via nested Boolean logic, and employing log-sum-exp smoothing for analytical differentiability.
Contribution/Results: The approach provides the first theoretical guarantees of both safety and completeness for polygonal obstacles, eliminating dependence on numerical optimization inherent in conventional SDF-based methods. The resulting safety filter accommodates nonholonomic systems and is validated in two real-world scenarios: distributed collision avoidance for two underactuated vehicles and mobile obstacle avoidance for container cranes. Simulations demonstrate real-time performance, enhanced safety margins, and significantly reduced computational overhead.
Application Category
📝 Abstract
Polygonal collision avoidance (PCA) is short for the problem of collision avoidance between two polygons (i.e., polytopes in planar) that own their dynamic equations. This problem suffers the inherent difficulty in dealing with non-smooth boundaries and recently optimization-defined metrics, such as signed distance field (SDF) and its variants, have been proposed as control barrier functions (CBFs) to tackle PCA problems. In contrast, we propose an optimization-free smooth CBF method in this paper, which is computationally efficient and proved to be nonconservative. It is achieved by three main steps: a lower bound of SDF is expressed as a nested Boolean logic composition first, then its smooth approximation is established by applying the latest log-sum-exp method, after which a specified CBF-based safety filter is proposed to address this class of problems. To illustrate its wide applications, the optimization-free smooth CBF method is extended to solve distributed collision avoidance of two underactuated nonholonomic vehicles and drive an underactuated container crane to avoid a moving obstacle respectively, for which numerical simulations are also performed.
Problem
Research questions and friction points this paper is trying to address.
Develops optimization-free smooth CBF method
Addresses polygonal collision avoidance efficiently
Extends to underactuated systems' collision avoidance
Innovation
Methods, ideas, or system contributions that make the work stand out.
Optimization-free smooth CBF method
Nested Boolean logic composition
Log-sum-exp smooth approximation
🔎 Similar Papers
No similar papers found.
