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Turning Circle-based Control Barrier Function for Efficient Collision Avoidance of Nonholonomic Vehicles

Changyu Lee, Kiyong Park, Jinwhan Kim

TL;DR

The paper tackles inefficiencies in collision avoidance for nonholonomic vehicles by replacing Euclidean-distance CBFs with a turning-circle-based CBF (TC-CBF) integrated into discrete-time MPC. TC-CBF assesses obstacle proximity via the vehicle's turning circles, accounting for heading and turning constraints, and uses a smooth-max formulation to enable optimization. Compared against ED-CBF in unicycle simulations and underactuated ASV experiments, TC-CBF consistently delivers smoother trajectories, maintains higher speeds, and reduces mission times, especially in static, head-on, and overtaking scenarios. The work demonstrates practical benefits for real-world nonholonomic platforms by improving safety guarantees while enhancing control efficiency.

Abstract

This paper presents a new control barrier function (CBF) designed to improve the efficiency of collision avoidance for nonholonomic vehicles. Traditional CBFs typically rely on the shortest Euclidean distance to obstacles, overlooking the limited heading change ability of nonholonomic vehicles. This often leads to abrupt maneuvers and excessive speed reductions, which is not desirable and reduces the efficiency of collision avoidance. Our approach addresses these limitations by incorporating the distance to the turning circle, considering the vehicle's limited maneuverability imposed by its nonholonomic constraints. The proposed CBF is integrated with model predictive control (MPC) to generate more efficient trajectories compared to existing methods that rely solely on Euclidean distance-based CBFs. The effectiveness of the proposed method is validated through numerical simulations on unicycle vehicles and experiments with underactuated surface vehicles.

Turning Circle-based Control Barrier Function for Efficient Collision Avoidance of Nonholonomic Vehicles

TL;DR

The paper tackles inefficiencies in collision avoidance for nonholonomic vehicles by replacing Euclidean-distance CBFs with a turning-circle-based CBF (TC-CBF) integrated into discrete-time MPC. TC-CBF assesses obstacle proximity via the vehicle's turning circles, accounting for heading and turning constraints, and uses a smooth-max formulation to enable optimization. Compared against ED-CBF in unicycle simulations and underactuated ASV experiments, TC-CBF consistently delivers smoother trajectories, maintains higher speeds, and reduces mission times, especially in static, head-on, and overtaking scenarios. The work demonstrates practical benefits for real-world nonholonomic platforms by improving safety guarantees while enhancing control efficiency.

Abstract

This paper presents a new control barrier function (CBF) designed to improve the efficiency of collision avoidance for nonholonomic vehicles. Traditional CBFs typically rely on the shortest Euclidean distance to obstacles, overlooking the limited heading change ability of nonholonomic vehicles. This often leads to abrupt maneuvers and excessive speed reductions, which is not desirable and reduces the efficiency of collision avoidance. Our approach addresses these limitations by incorporating the distance to the turning circle, considering the vehicle's limited maneuverability imposed by its nonholonomic constraints. The proposed CBF is integrated with model predictive control (MPC) to generate more efficient trajectories compared to existing methods that rely solely on Euclidean distance-based CBFs. The effectiveness of the proposed method is validated through numerical simulations on unicycle vehicles and experiments with underactuated surface vehicles.

Paper Structure

This paper contains 18 sections, 24 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Control Barrier Functions
  4. Collision Avoidance using ED-CBF
  5. Turning Circle-based Control Barrier Function
  6. Control Barrier Function Design
  7. MPC with TC-CBF
  8. Experimental Validation
  9. Unicycle simulations
  10. Simulation setting
  11. Parameter Settings
  12. Results
  13. Underactuated ASV experiments
  14. Vehicle modeling
  15. TC-CBF for ASVs
  16. ...and 3 more sections

Figures (9)

  • Figure 1: The coordinate systems.
  • Figure 2: Geometrical representation of the ED-CBF constraints.
  • Figure 3: Geometrical representation of the TC-CBF constraints.
  • Figure 4: Comparison of the two CBF functions with parameters $r_{\text{max}} = 0.3$, $\alpha = 0.5$, and $u = 1.5m/s$.
  • Figure 5: Result comparison with different parameter sets in the static obstacle avoidance scenario.
  • ...and 4 more figures

Theorems & Definitions (1)

  • Remark