Adjustable Stiffness of a Robot Formation Under Set-Point Control with Collision Avoidance Based on Artificial Potential Functions

Abstract

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.