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

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.