Distributed Safe Cooperative Vector Field for Trajectory Curvature Constrained Multi-Robot Systems

Technical Summary: Distributed Safe Cooperative Vector Field for Trajectory Curvature Constrained Multi-Robot Systems

Problem Formulation
This paper addresses the challenge of coordinating multi-robot systems (MRS) in planar environments where individual robots are subject to trajectory curvature constraints (i.e., minimum turning radii). While Distributed Vector Field (DVF) approaches have proven effective for cooperative motion and path following, existing methods often assume idealized, omnidirectional robots. In practice, when the guidance rate of a vector field exceeds a robot's maximum curvature capability, the resulting trajectories become dynamically infeasible. This infeasibility can lead to tracking errors, system instability, and increased risks of collisions with obstacles or other robots. The core problem is to design a distributed control strategy that ensures cooperative motion, obstacle avoidance, and inter-robot collision avoidance while strictly adhering to the kinematic curvature limits of heterogeneous robots.

Methodology
The authors propose a Distributed Safe Cooperative Vector Field (DSCVF) approach. The methodology integrates three primary components:

1. Distributed Cooperative Vector Field: Building on prior DVF work, the system treats the path parameter as an additional virtual coordinate. Robots share this virtual coordinate with neighbors to achieve coordination. A consensus-based coordination function drives the difference between neighboring virtual coordinates to converge to desired relative states, enabling formation maintenance and synchronized path following.
2. Safety-Oriented Collision Avoidance with Adaptive Boundaries: To address curvature constraints, the authors introduce a safety-oriented collision avoidance vector field. A key innovation is the definition of "limit circles" tangent to the robot's heading with a radius equal to its minimum turning radius. Based on the intersection of these limit circles with obstacles (or other robots), the system defines an adaptively adjustable reactive boundary.
   • If a limit circle intersects an obstacle, the reactive boundary shifts to guide the robot away.
   • The direction of avoidance (left or right) is determined by which limit circle (left or right) intersects the obstacle, ensuring the avoidance maneuver is physically feasible within the robot's turning capabilities.
   • Smooth "bump functions" are used to blend the cooperative vector field and the collision avoidance vector field, ensuring continuous control inputs.
3. Control Law: The final control input is an angular velocity command derived from the saturation of the difference between the robot's current heading and the desired heading defined by the composite vector field. This ensures the robot aligns with the vector field while respecting angular velocity limits.

Key Contributions
The paper makes two primary technical contributions:

1. Adaptively Adjustable Reactive Boundary: The design of a collision avoidance vector field where the reactive boundary level set values are adjusted online based on the robot's pose and the location of obstacles. This mechanism explicitly accounts for kinematic curvature constraints, ensuring that avoidance maneuvers remain within the robot's physical maneuvering capabilities.
2. DSCVF for Heterogeneous Systems: The construction of a distributed safe cooperative vector field specifically for curvature-constrained heterogeneous robots. By composing the cooperative field with the safety-oriented field, the approach retains the scalability and low communication load of classical DVF methods (requiring only a single virtual variable from neighbors) while extending applicability to scenarios with strict dynamic feasibility requirements.

Results
The effectiveness of the proposed approach was validated through both simulations and real-world experiments:

• Simulation: A scenario with four heterogeneous robots (varying maximum angular velocities) moving along a circular path was simulated. The robots successfully maintained desired relative positions, followed the path, and avoided obstacles. The results demonstrated that the adaptive reactive boundary prevented collisions without causing redundant detours, with errors exhibiting periodic fluctuations consistent with obstacle interactions.
• Real-World Experiment: The algorithm was deployed on a physical multi-robot platform (four robots) tracking a closed Lissajous curve. The robots successfully maintained a serial formation, avoided static obstacles, and avoided inter-robot collisions. The experimental data confirmed low path-tracking errors and successful convergence of coordination errors, validating the approach's ability to handle curvature constraints in a real-world setting.

Significance and Claims
The paper claims that its proposed DSCVF provides a safety-guaranteed control solution for multi-robot cooperation in complex environments where curvature constraints are critical. The significance lies in explicitly integrating kinematic curvature constraints into the vector field design, a step often overlooked in existing distributed control strategies. By replacing fixed boundaries with real-time varying boundaries based on limit circles, the method ensures the physical feasibility of collision avoidance maneuvers. The authors assert that this approach effectively balances cooperative motion objectives with safety requirements, offering a robust solution for heterogeneous multi-robot systems operating under strict dynamic limitations.