Formation-Preserving Control for Multi-Robot Systems: Experimental Validation

Artificial potential fields (APFs) are widely used for collision avoidance in robotic systems due to their simplicity and real-time performance. However, in cooperative environments, robots may undergo unnecessary displacements caused by repulsive forces from neighboring robots, even after reaching their target positions. This paper presents a formation-preserving control strategy that suppresses such unnecessary motion while retaining the standard APF behavior when robots are far from their desired positions. The stability of the proposed controller is proven through Lyapunov stability analysis. Furthermore, the theoretical analysis establishes local exponential stability and positive invariance of a neighborhood of the desired configuration. A formal proof of collision avoidance is also provided, ensuring that inter-robot safety constraints are preserved. The approach is validated through two simulations and two experiments: the first illustrates APF-induced fluctuations, whereas the second demonstrates that the proposed controller enables robots to maintain their desired target positions.