Control Strategies for Pursuit-Evasion Under Occlusion Using Visibility and Safety Barrier Functions

TL;DR

The paper addresses pursuit-evasion under occlusion by encoding evader visibility and obstacle safety as non-smooth time-varying control barrier functions (CBFs) based on the signed distance to the pursuer’s FoV and to obstacle sets. A two-layer approach combines a kinodynamic planner (SST) guided by a Motion Planning Transformer (MPT) to generate non-myopic reference trajectories with a convex optimization controller that enforces CBF constraints, using generalized gradients for nondifferentiable points. The authors provide Lipschitz proofs for the visibility CBF, describe practical gradient estimation via finite differences, and validate the framework in CARLA simulations and real Jackal robot experiments with onboard sensing. Results show robust visibility maintenance and safe obstacle avoidance even under severe occlusion and dynamic evader motion, highlighting the method’s practical viability for autonomous pursuit tasks.

Abstract

This paper develops a control strategy for pursuit-evasion problems in environments with occlusions. We address the challenge of a mobile pursuer keeping a mobile evader within its field of view (FoV) despite line-of-sight obstructions. The signed distance function (SDF) of the FoV is used to formulate visibility as a control barrier function (CBF) constraint on the pursuer's control inputs. Similarly, obstacle avoidance is formulated as a CBF constraint based on the SDF of the obstacle set. While the visibility and safety CBFs are Lipschitz continuous, they are not differentiable everywhere, necessitating the use of generalized gradients. To achieve non-myopic pursuit, we generate reference control trajectories leading to evader visibility using a sampling-based kinodynamic planner. The pursuer then tracks this reference via convex optimization under the CBF constraints. We validate our approach in CARLA simulations and real-world robot experiments, demonstrating successful visibility maintenance using only onboard sensing, even under severe occlusions and dynamic evader movements.

Figures (7)

• Figure 1: A mobile pursuer aims to keep a mobile evader within its field of view despite occlusions and without colliding with obstacles. The inset shows the evader in the pursuer's camera view.
• Figure 2: Illustration of the proof that the visibility CBF is Lipschitz continuous in a 2D environment where the pursuer and evader states are positions and orientations. The triangles show the pursuer's unoccluded FoV, while the dashed polygons inside show the occluded FoV. The distances to the points $\mathbf{z}_1$ and $\mathbf{z}_2$ from $\mathbf{y}(t)$ define the visibility CBF at $\mathbf{x}_1$ and $\mathbf{x}_2$, respectively.
• Figure 3: CARLA simulation trajectory
• Figure 4: Top: Snapshots from pursuer's view along its trajectory. Bottom: The red and blue curves denote the pursuer and evader trajectories, respectively. (a) The instance when the target is first observed by the pursuer; (b) The pursuer loses the evader around a corner; (c) The pursuer relocates the evader after turning the corner.
• Figure 5: Real-world experiments. The pursuer and evader paths are shown in blue and yellow, respectively. The green star indicates the pursuer's starting position. The red region shows the pursuer FoV. Different experiments are shown clockwise from top left: (1) Simple loop around a single obstacle; (2) Evader follows an 'S' shape. The pursuer grazes an obstacle near a sharp turn denoted by the orange circle; (3) The evader charts a long path through a cluttered environment; (4) The pursuer cuts off the evader.

Theorems & Definitions (8)

• Definition 1: garg2021robust
• Lemma 1: garg2021robust
• Definition 2: clarke1990optimization
• Definition 3: clarke1990optimization
• Definition 4
• Definition 5
• Proposition 1
• proof