Contingency Model-based Control (CMC) for Communicationless Cooperative Collision Avoidance in Robot Swarms

TL;DR

This paper tackles the challenge of collision avoidance in robot swarms operating without inter-agent communication. It introduces Contingency Model-based Control (CMC), which leverages offline consensual rules and contingency trajectories to enforce collision constraints and ensure recursive feasibility in a decentralized setting. The approach embeds contingency-based collision avoidance into a per-agent Finite-time Optimal Control Problem, solved in a receding-horizon manner with adaptive contingency horizons. Theoretical guarantees are provided for recursive feasibility and collision avoidance, and two 2D numerical examples validate the method under realistic swarm scenarios with no communication.

Abstract

Cooperative collision avoidance between robots in swarm operations remains an open challenge. Assuming a decentralized architecture, each robot is responsible for making its own control decisions, including motion planning. To this end, most existing approaches mostly rely some form of (wireless) communication between the agents of the swarm. In reality, however, communication is brittle. It may be affected by latency, further delays and packet losses, transmission faults, and is subject to adversarial attacks, such as jamming or spoofing. This paper proposes Contingency Model-based Control (CMC) as a communicationless alternative. It follows the implicit cooperation paradigm, under which the design of the robots is based on consensual (offline) rules, similar to traffic rules. They include the definition of a contingency trajectory for each robot, and a method for construction of mutual collision avoidance constraints. The setup is shown to guarantee the recursive feasibility and collision avoidance between all swarm members in closed-loop operation. Moreover, CMC naturally satisfies the Plug \& Play paradigm, i.e., for new robots entering the swarm. Two numerical examples demonstrate that the collision avoidance guarantee is intact and that the robot swarm operates smoothly under the CMC regime.

Figures (8)

• Figure 1: Illustration of the acceleration profile (left) and the velocity profile (right) of the contingency trajectory for agent $m$ in step $k$.
• Figure 2: Construction of the collision avoidance constraint for agent $m$, with respect to agent $j$, in the prediction step $i$.
• Figure 3: Composition of the initial velocity $\mathbf{v}_{1|k}^{(m)}$ for the new contingency trajectory. Since it is the sum of $\mathbf{v}_{k}^{(m)}$ (fixed) and $\mathbf{a}_{0|k}^{(m)}\Delta t$ (decision variable), it must lie inside the bold dotted circle.
• Figure 4: Illustration of mutual collision avoidance.
• Figure 5: RTP example: Overview of agent trajectories. The timeline of the plots is top left ($0\,\mathrm{s}\;\text{to}\;20\,\mathrm{s}$), top right ($20\,\mathrm{s}\;\text{to}\;40\,\mathrm{s}$), bottom left ($40\,\mathrm{s}\;\text{to}\;60\,\mathrm{s}$), bottom right ($60\,\mathrm{s}\;\text{to}\;80\,\mathrm{s}$). Agents are shown as dark circles, target points as dark crosses, trajectories as light lines, and initial conditions as small light circles.

Theorems & Definitions (12)

• Remark 5: Contingency horizon
• Remark 6: Contingency plan
• Remark 7: Collision avoidance constraints
• Proposition 8: Change of the contingency horizon
• proof
• Proposition 9: Convexity of the FTOCP
• Remark 10: Limited sensor range
• Lemma 11: Collision avoidance
• proof
• Theorem 12: Recursive feasibility