Artificial Potential Functions (APFs) enable effective real-time collision avoidance in robotics but degrade formation integrity in dense multi-robot environments by displacing converged robots via repulsive fields from moving agents. This paper proposes a set-point controller augmented with APFbased collision avoidance, in which the repulsive field is spatially modulated to progressively stiffen the formation response as each agent approaches its target. The stiffness profile is governed by tunable design parameters that provide independent control over two key properties: the degree of disturbance rejection applied to settled agents, and the spatial extent of the neighborhood around each set-point within which that rejection is active. The stability of the closed-loop system is established through a Lyapunov analysis. The proposed approach is evaluated by comparing its ability to keep each robot in its desired position in the presence of disturbance-generating neighbors with that of a conventional APF controller.
Wojciech Kowalczyk, Arpit Joon, Shivam Goyal· International Conference on...· 0 citations
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.
Wojciech Kowalczyk, Arpit Joon, P. Herman· Applied Sciences· 0 citations
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