[Paper Review] Decentralized Probabilistic Multi-Robot Collision Avoidance Using Buffered Uncertainty-Aware Voronoi Cells

Hai Zhu, Bruno Brito+1 more|arXiv (Cornell University)|Jan 11, 2022

Distributed Control Multi-Agent Systems4 citations

TL;DR

This paper proposes a decentralized, communication-free probabilistic collision avoidance method for multi-robot systems under localization and sensing uncertainty. It introduces buffered uncertainty-aware Voronoi cells (B-UAVC) that enforce chance constraints on collision probability using Gaussian uncertainty models, enabling safe navigation for single-integrator, double-integrator, differential-drive, and nonlinear robots in simulation and real-world experiments with ground vehicles and quadrotors.

ABSTRACT

In this paper, we present a decentralized and communication-free collision avoidance approach for multi-robot systems that accounts for both robot localization and sensing uncertainties. The approach relies on the computation of an uncertainty-aware safe region for each robot to navigate among other robots and static obstacles in the environment, under the assumption of Gaussian-distributed uncertainty. In particular, at each time step, we construct a chance-constrained buffered uncertainty-aware Voronoi cell (B-UAVC) for each robot given a specified collision probability threshold. Probabilistic collision avoidance is achieved by constraining the motion of each robot to be within its corresponding B-UAVC, i.e. the collision probability between the robots and obstacles remains below the specified threshold. The proposed approach is decentralized, communication-free, scalable with the number of robots and robust to robots' localization and sensing uncertainties. We applied the approach to single-integrator, double-integrator, differential-drive robots, and robots with general nonlinear dynamics. Extensive simulations and experiments with a team of ground vehicles, quadrotors, and heterogeneous robot teams are performed to analyze and validate the proposed approach.

Motivation & Objective

• Address the challenge of safe multi-robot navigation in cluttered environments when robot positions and obstacle locations are uncertain due to sensor noise and estimation errors.
• Develop a decentralized, communication-free approach that ensures probabilistic collision avoidance without requiring shared state or trajectory information among robots.
• Extend the buffered Voronoi cell (BVC) framework to handle uncertainty by formalizing chance-constrained buffered uncertainty-aware Voronoi cells (B-UAVC) under Gaussian-distributed uncertainty.
• Ensure scalability and robustness across diverse robot dynamics, including single-integrator, double-integrator, differential-drive, and general nonlinear systems.
• Validate the method across extensive simulations and real-world experiments with heterogeneous robot teams, including ground vehicles and quadrotors.

Proposed method

• Construct a chance-constrained buffered uncertainty-aware Voronoi cell (B-UAVC) for each robot at each time step, given a specified collision probability threshold and Gaussian-distributed localization and sensing uncertainty.
• Formulate the B-UAVC as a minimax optimization problem to compute the optimal separating hyperplane that maximizes the minimum distance to uncertain robot and obstacle positions.
• Solve the resulting optimization problem numerically by iteratively computing the hyperplane normal vector $\mathbf{a}_{ij}$ and offset $b_{ij}$ using a combination of matrix inversion and scalar parameter $t$ that balances uncertainty covariance matrices.
• Constrain each robot’s motion to remain within its B-UAVC, ensuring that the probability of collision with any other robot or obstacle remains below the user-defined threshold.
• Integrate the method with one-step and receding-horizon controllers for different robot dynamics, including single-integrator, double-integrator, differential-drive, and quadrotor models.
• Implement a heuristic deadlock resolution strategy: for one-step controllers, robots move along edges within their B-UAVC if progress stalls; for receding-horizon planners, temporarily rotate the goal by 90° to escape local minima.

Experimental results

Research questions

• RQ1 How can decentralized multi-robot collision avoidance be made robust to localization and sensing uncertainty without requiring communication between robots?
• RQ2 Can the buffered Voronoi cell (BVC) framework be extended to probabilistic scenarios with Gaussian-distributed uncertainty while preserving decentralization and scalability?
• RQ3 What is the impact of uncertainty-aware safe regions (B-UAVC) on the safety and performance of multi-robot systems across diverse robot dynamics?
• RQ4 How effective is the proposed method in preventing collisions under realistic uncertainty levels in both simulation and real-world experiments?
• RQ5 Can heuristic deadlock resolution strategies effectively recover robots from local minima or progress stalls in complex environments?

Key findings

• The proposed B-UAVC method ensures probabilistic collision avoidance by maintaining the collision probability below a user-defined threshold, even under significant localization and sensing uncertainty.
• The method is fully decentralized and communication-free, requiring only local knowledge of neighboring robot positions and their uncertainty covariances.
• Extensive simulations and real-world experiments with up to 10 ground robots and 6 quadrotors demonstrate robust performance across diverse dynamics, including single-integrator, double-integrator, differential-drive, and nonlinear quadrotor models.
• The approach successfully prevents collisions in cluttered environments with uncertain obstacle locations, as validated in both simulation and hardware experiments.
• The heuristic deadlock resolution mechanism effectively recovers robots from progress stalls and local minima, with temporary goal rotation enabling escape from trapped configurations.
• System identification from real flight data of Parrot Bebop 2 quadrotors yielded accurate dynamics parameters, enabling realistic simulation and validation of the method.