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Visibility-Aware RRT* for Safety-Critical Navigation of Perception-Limited Robots in Unknown Environments

Taekyung Kim, Dimitra Panagou

TL;DR

This work tackles safe navigation for perception-limited robots in unknown environments by recognizing that traditional safety guarantees require full observability. It introduces Visibility-Aware RRT*, a global planner that integrates a collision-avoidance CBF and a novel visibility CBF within an LQR-based steering framework to produce paths that are both collision-free and observable by the robot’s local controller. The method is proven to yield visibility-aware trajectories when paired with a tracking controller that bounds timing and tracking error, and it is validated through extensive simulations and hardware experiments showing improved safety and reduced replanning compared to baselines. The approach advances practical autonomous navigation by explicitly accounting for sensing limitations and unknown obstacles, enabling safer operation in real-world, perception-constrained settings.

Abstract

Safe autonomous navigation in unknown environments remains a critical challenge for robots with limited sensing capabilities. While safety-critical control techniques, such as Control Barrier Functions (CBFs), have been proposed to ensure safety, their effectiveness relies on the assumption that the robot has complete knowledge of its surroundings. In reality, robots often operate with restricted field-of-view and finite sensing range, which can lead to collisions with unknown obstacles if the planner is agnostic to these limitations. To address this issue, we introduce the Visibility-Aware RRT* algorithm that combines sampling-based planning with CBFs to generate safe and efficient global reference paths in partially unknown environments. The algorithm incorporates a collision avoidance CBF and a novel visibility CBF, which guarantees that the robot remains within locally collision-free regions, enabling timely detection and avoidance of unknown obstacles. We conduct extensive experiments interfacing the path planners with two different safety-critical controllers, wherein our method outperforms all other compared baselines across both safety and efficiency aspects.

Visibility-Aware RRT* for Safety-Critical Navigation of Perception-Limited Robots in Unknown Environments

TL;DR

This work tackles safe navigation for perception-limited robots in unknown environments by recognizing that traditional safety guarantees require full observability. It introduces Visibility-Aware RRT*, a global planner that integrates a collision-avoidance CBF and a novel visibility CBF within an LQR-based steering framework to produce paths that are both collision-free and observable by the robot’s local controller. The method is proven to yield visibility-aware trajectories when paired with a tracking controller that bounds timing and tracking error, and it is validated through extensive simulations and hardware experiments showing improved safety and reduced replanning compared to baselines. The approach advances practical autonomous navigation by explicitly accounting for sensing limitations and unknown obstacles, enabling safer operation in real-world, perception-constrained settings.

Abstract

Safe autonomous navigation in unknown environments remains a critical challenge for robots with limited sensing capabilities. While safety-critical control techniques, such as Control Barrier Functions (CBFs), have been proposed to ensure safety, their effectiveness relies on the assumption that the robot has complete knowledge of its surroundings. In reality, robots often operate with restricted field-of-view and finite sensing range, which can lead to collisions with unknown obstacles if the planner is agnostic to these limitations. To address this issue, we introduce the Visibility-Aware RRT* algorithm that combines sampling-based planning with CBFs to generate safe and efficient global reference paths in partially unknown environments. The algorithm incorporates a collision avoidance CBF and a novel visibility CBF, which guarantees that the robot remains within locally collision-free regions, enabling timely detection and avoidance of unknown obstacles. We conduct extensive experiments interfacing the path planners with two different safety-critical controllers, wherein our method outperforms all other compared baselines across both safety and efficiency aspects.
Paper Structure (16 sections, 3 theorems, 22 equations, 5 figures, 1 table, 4 algorithms)

This paper contains 16 sections, 3 theorems, 22 equations, 5 figures, 1 table, 4 algorithms.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. System Description
  4. Control Barrier Functions
  5. High Order CBF
  6. PROBLEM FORMULATION
  7. GLOBAL PATH PLANNER
  8. Visibility-Aware RRT*
  9. HOCBF for Collision Avoidance
  10. Incorporating Visibility Constraint into CBF
  11. Time-to-Reach
  12. Time-to-Rotate
  13. Visibility CBF
  14. LOCAL TRACKING CONTROLLER
  15. RESULTS
  16. ...and 1 more sections

Key Result

Theorem 1

ames_control_2019 Given a CBF $h$ with the associated set $\mathcal{C}$, any Lipschitz continuous controller ${\boldsymbol u} \in \mathcal{K}_\textup{cbf}({\boldsymbol x})$, with $\mathcal{K}_\textup{cbf}({\boldsymbol x}) \coloneqq \{{\boldsymbol u} \in \mathcal{U} : L_f h({\boldsymbol x}) + L_g h({

Figures (5)

  • Figure 1: In this paper we develop an RRT*-based planner that accounts for sensing limitations, and in conjunction with a tracking controller, guarantees avoidance of a priori unknown obstacles. This figure shows trajectories generated by baseline (Top) and visibility-aware (Bottom, Ours) planning methods, tracked by the rover using a CBF-QP controller (baselines and results presented in Section \ref{['sec:experiments']}.). Inset: Snapshot of the Signed Distance Field map just before the collision while following the baseline trajectory, showing that the unknown obstacle (which is located in the dashed circle, but not in the FOV of the robot) is not detected in time, leading to collision.
  • Figure 2: Illustration of the CBF constraints in the LQR-CBF-Steer function. The Integrator generates a sequence of intermediate states using the LQR gain $K_\text{lqr}$. At each intermediate state, the CBFConstraints are checked to ensure that the state satisfies the given constraints. If any constraint is violated, the steering process is terminated, and the last satisfied state is returned as the new node. (a) An example demonstrating the collision avoidance HOCBF constraint \ref{['eq:collision-cbf-constraint']}. (b) An example demonstrating the visibility CBF constraint \ref{['eq:visibility-cbf-constraint']}. ${\boldsymbol x}_{\text{next},1}$ is already within the FOV at ${\boldsymbol x}_t$, satisfying the visibility constraint. For ${\boldsymbol x}_{\text{next},2}$, although it is outside the current FOV, it satisfies the visibility constraint. ${\boldsymbol x}_{\text{next},3}$ might satisfy the visibility constraint $h_{\text{vis}}({\boldsymbol x}_t) \geq 0$\ref{['eq:visibility-cbf']}, but it violates the visibility CBF constraint $\psi_{\textup{vis}}({\boldsymbol x}_t) \geq 0$\ref{['eq:visibility-cbf-constraint']}, causing the steering to terminate.
  • Figure 3: Visualization of the global planning results generated by Baseline 3 and the proposed method in two environments. $\texttt{maxIter}$ is set to 2000 and 3000 for Env. 1 and Env. 2, respectively. The blue and yellow squares represent the start and goal position. The black circles represent the known obstacles. The green lines depict the edges of the tree $\mathcal{E}$ appended during the planning process. The red line depict the final reference path. The shaded areas in gray represent the local collision-free set $\mathcal{B}_t$ that the robot will sense while following the reference path.
  • Figure 4: Visualization of the CBF-QP experiments for Env. 1 with a $45^\circ$ FOV. The reference waypoints (green dots) correspond to the paths in Fig. \ref{['fig:env1_baseline']} and Fig. \ref{['fig:env1_visibility']}. The blue shaded areas represent the actual local collision-free set $\mathcal{B}_t$ collected from the onboard sensor. The orange circles are the hidden obstacles $\mathcal{H}$ and the red dots indicate the detection points of these hidden obstacles. (a) The CBF-QP becomes infeasible when it detects the hidden obstacle, as the robot is already within an unsafe distance to perform collision avoidance. (b) Tracking the reference path from our method, the CBF-QP successfully avoids the hidden obstacle and reaches the goal.
  • Figure 5: Visualization of the Gatekeeper experiments for Env. 2. The reference waypoints correspond to the paths in Fig. \ref{['fig:env2_baseline']} and Fig. \ref{['fig:env2_visibility']}. Red shaded areas depict the subsequent nominal trajectories at the robot's position. (a) The Gatekeeper executes a stop command as the nominal trajectory is deemed unsafe, where the trajectory lies outside of the local collision-free set $\mathcal{B}_t$. Consequently, global replanning is required from the current position. (b) By tracking our reference path, the Gatekeeper successfully navigates to the goal without violating visibility constraint.

Theorems & Definitions (10)

  • Definition 1: Control Barrier Function (CBF) ames_control_2019
  • Theorem 1
  • Definition 2: HOCBF xiao_control_2019
  • Theorem 2
  • Definition 3: Collision-Free Path
  • Definition 4: Visibility-Aware Path
  • Definition 5: Critical Point
  • proof
  • Theorem 3
  • proof