Distributed Planning for Rigid Robot Formations with Probabilistic Collision Avoidance

TL;DR

The paper tackles maintaining rigid robot formations under position uncertainty while enforcing probabilistic collision avoidance. It introduces a distributed VRB-based framework that maps local velocity commands into formation parameters, employs consensus to maintain cohesion, and uses a constraint-satisfaction layer to enforce a collision probability upper bound $\bar{p}_{coll}$. Collision guarantees are achieved by linearizing nonconvex quadratic safety conditions into distributed linear constraints via a Rayleigh-quotient bound and projection steps, with validation in both simulation and real teleoperation experiments. The results show the formation can deform safely around obstacles while remaining near consensus, demonstrating a practical approach for autonomous multi-robot coordination with uncertainty considerations, and the authors provide open-source code at GitHub.

Abstract

This paper presents a distributed method for robots moving in rigid formations while ensuring probabilistic collision avoidance between the robots. The formation is parametrised through the transformation of a base configuration. The robots map their desired velocities into a corresponding desired change in the formation parameters and apply a consensus step to reach agreement on the desired formation and a constraint satisfaction step to ensure collision avoidance within the formation. The constraint set is found such that the probability of collision remains below an upper bound. The method was demonstrated in a manual teleoperation scenario both in simulation and a real-world experiment.

Figures (12)

• Figure 1: System architecture: Each robot has a local planner, a formation planner and a control system Mikkelsen2023DistributedConfiguration.
• Figure 2: Transformation of a unit grid swarm configuration with $\varphi=\pi/4$, $s_x=1$, $s_y=2$, $t_x=3$, and $t_y=1$. Black circle: base configuration. Red circle: transformed base configuration Mikkelsen2023DistributedConfiguration.
• Figure 3: Distance vector covariance ellipse, ball region and hyperplane approximation.
• Figure 4: Robots $i$ scaling parameter derivative $\frac{d}{dt}\bm{s_i}$ (red vector) is projected onto a linear approximation (green line) of a quadratic constraint (black ellipse).
• Figure 5: Robot trajectories for simulation of formation of four UAVs passing through a corridor. As the robots approach the corridor the formation starts to shrink until it reaches a stationary size that can pass through the corridor.