Multi Time Scale Behaviour of The Formation of Multiple Groups of Nonholonomic Wheeled Mobile Robots

TL;DR

This paper presents a multi-time scale control approach for nonholonomic wheeled mobile robots to achieve complex formations and collision avoidance, using a centroid-based transformation and singular perturbation analysis.

Contribution

It introduces a novel multi-time scale formation control method with a centroid-based transformation and collision avoidance for nonholonomic robots.

Findings

Effective formation control demonstrated through simulations

Multi-time scale convergence achieved for different subsystems

Collision avoidance integrated into the control design

Abstract

Different geometric patterns and shapes are generated using groups of agents, and this needs formation control. In this paper, Centroid Based Transformation (CBT), has been applied to decompose the combined dynamics of nonholonomic Wheeled Mobile Robots (WMRs) into three subsystems: intra and inter group shape dynamics, and the dynamics of the centroid. The intra group shape dynamics can further be partitioned into the shape dynamics of each group, giving the notion of multiple group. Thus separate controllers have been designed for each subsystem. The gains of the controllers are such chosen that the overall system becomes singularly perturbed system, and different subsystems converge to their desired values at different times. Then multi-time scale convergence analysis has been carried out in this paper. Negative gradient of a potential based function has been added to the controller to ensure collision avoidance among the robots. Simulation results have been provided to demonstrate the effectiveness of the proposed controller.