Collision Risk Quantification and Conflict Resolution in Trajectory Tracking for Acceleration-Actuated Multi-Robot Systems

TL;DR

The paper tackles collision risk and deadlock in arbitrarily large teams of wheeled mobile robots by introducing AA-SOATT, an acceleration-actuated, CBF-based framework for simultaneous obstacle avoidance and trajectory tracking. It achieves nonconservative safety without inter-robot communication, leveraging a QP at the acceleration level and two deadlock-resolution strategies, including an auxiliary velocity in the TT error that preserves global convergence. Theoretical guarantees are provided: forward invariance of safety sets and global asymptotic convergence to the desired trajectories under specified conditions, along with a unique equilibrium for the closed-loop system. Comprehensive simulations and real-world TurtleBot3 experiments demonstrate reduced invasiveness, smooth CA trajectories, and robust performance as the swarm scales, outperforming existing methods in large-scale scenarios.

Abstract

One of the pivotal challenges in a multi-robot system is how to give attention to accuracy and efficiency while ensuring safety. Prior arts cannot strictly guarantee collision-free for an arbitrarily large number of robots or the results are considerably conservative. Smoothness of the avoidance trajectory also needs to be further optimized. This paper proposes an accelerationactuated simultaneous obstacle avoidance and trajectory tracking method for arbitrarily large teams of robots, that provides a nonconservative collision avoidance strategy and gives approaches for deadlock avoidance. We propose two ways of deadlock resolution, one involves incorporating an auxiliary velocity vector into the error function of the trajectory tracking module, which is proven to have no influence on global convergence of the tracking error. Furthermore, unlike the traditional methods that they address conflicts after a deadlock occurs, our decision-making mechanism avoids the near-zero velocity, which is much more safer and efficient in crowed environments. Extensive comparison show that the proposed method is superior to the existing studies when deployed in a large-scale robot system, with minimal invasiveness.

Figures (7)

• Figure 1: Schematic of the AA-SOATT-based control method. WMRs obtain states information of the neighboring WMRs and obstacles relying on the onboard sensors. These data, along with preferred states and physical constraints, are fed into the system, and as a result, a QP formulation is synthetized. By solving this equation recursively, the optimal control inputs are derived and then employed in conjunction with the WMR's kinematics model to actuate WMRs.
• Figure 2: An illustration of the trajectories generated by Eq. (\ref{['eqn.n4']}), Eq. (\ref{['eqn.n5']}), Eq. (\ref{['eqn.n7']}), Eq. (\ref{['eqn.nn5']}) and our method, respectively.
• Figure 3: Distance profiles generated by Eq. (\ref{['eqn.n4']}) when the number of WMRs is $35$ and $39$, respectively. The safety threshold is $0.96$. Obviously, the safety constraint is violated in these two examples.
• Figure 4: Velocity profiles synthesized by four deadlock detection methods, respectively, where deadlock decisions on near-zero velocity in Safety2017TROhe2024simultaneous, colored by the green and blue lines respectively, lead to a slow-reacting system.
• Figure 5: 100 WMRs SOATT illustration achieved by: (a) Eq. (\ref{['eqn.12a']}), (b) Eq. (\ref{['eqn.12b']}), (c): Eq. (\ref{['eqn.13']}), respectively.