Meanshift Shape Formation Control Using Discrete Mass Distribution

TL;DR

This paper introduces a decentralized control strategy for swarm shape formation using a discrete mass-distribution model, enabling complex shape formation and adaptability to swarm size variations without requiring continuous density functions.

Contribution

It develops a fully decentralized, discrete mass-distribution approach and a meanshift control law for complex shape formation in swarms, overcoming limitations of continuous density methods.

Findings

Effective formation of complex shapes demonstrated in simulations.

Swarm size variations are accommodated through adaptive mass estimation.

Decentralized mass estimation converges asymptotically to true values.

Abstract

The density-distribution method has recently become a promising paradigm owing to its adaptability to variations in swarm size. However, existing studies face practical challenges in achieving complex shape representation and decentralized implementation. This motivates us to develop a fully decentralized, distribution-based control strategy with the dual capability of forming complex shapes and adapting to swarm-size variations. Specifically, we first propose a discrete mass-distribution function defined over a set of sample points to model swarm formation. In contrast to the continuous density-distribution method, our model eliminates the requirement for defining continuous density functions-a task that is difficult for complex shapes. Second, we design a decentralized meanshift control law to coordinate the swarm's global distribution to fit the sample-point distribution by feeding back mass estimates. The mass estimates for all sample points are achieved by the robots in a decentralized manner via the designed mass estimator. It is shown that the mass estimates of the sample points can asymptotically converge to the true global values. To validate the proposed strategy, we conduct comprehensive simulations and real-world experiments to evaluate the efficiency of complex shape formation and adaptability to swarm-size variations.