Safe Navigation under Uncertain Obstacle Dynamics using Control Barrier Functions and Constrained Convex Generators

TL;DR

This paper introduces a novel framework combining Control Barrier Functions and Constrained Convex Generators for safe navigation of agents amid uncertain obstacle dynamics, ensuring collision avoidance through convex optimization.

Contribution

It develops a procedure to convert set-valued obstacle estimates into Control Barrier Functions, enabling safe control in uncertain environments with complex obstacle and agent geometries.

Findings

Effective obstacle flow estimation using CCGs

Successful conversion of CCGs to CBFs via convex optimization

Simulation results demonstrate safe navigation performance

Abstract

This paper presents a sampled-data framework for the safe navigation of controlled agents in environments cluttered with obstacles governed by uncertain linear dynamics. Collision-free motion is achieved by combining Control Barrier Function (CBF)-based safety filtering with set-valued state estimation using Constrained Convex Generators (CCGs). At each sampling time, a CCG estimate of each obstacle is obtained using a finite-horizon guaranteed estimation scheme and propagated over the sampling interval to obtain a CCG-valued flow that describes the estimated obstacle evolution. However, since CCGs are defined indirectly - as an affine transformation of a generator set subject to equality constraints, rather than as a sublevel set of a scalar function - converting the estimated obstacle flows into CBFs is a nontrivial task. One of the main contributions of this paper is a procedure to perform this conversion, ultimately yielding a CBF via a convex optimization problem whose validity is established by the Implicit Function Theorem. The resulting obstacle-specific CBFs are then merged into a single CBF that is used to design a safe controller through the standard Quadratic Program (QP)-based approach. Since CCGs support Minkowski sums, the proposed framework also naturally handles rigid-body agents and generalizes existing CBF-based rigid-body navigation designs to arbitrary agent and obstacle geometries. While the main contribution is general, the paper primarily focuses on agents with first-order control-affine dynamics and second-order strict-feedback dynamics. Simulation examples demonstrate the effectiveness of the proposed method.