Securing Isosceles Triangular Formations under Heterogeneous Sensing and Mixed Constraints

TL;DR

This paper develops a control strategy for three heterogeneous robots to achieve and maintain an isosceles triangular formation using local sensing and gradient-based control laws, with conditions ensuring shape convergence.

Contribution

It introduces a gain ratio condition for shape control in heterogeneous multi-robot systems with mixed sensing constraints, extending previous formation control methods.

Findings

Derived a sufficient gain ratio condition for shape convergence.

Validated theoretical results with numerical simulations.

Achieved formation control under heterogeneous sensing and mixed constraints.

Abstract

This paper focuses on securing a triangular shape (up to translation) for a team of three mobile robots that uses heterogeneous sensing mechanism. Based on the available local information, each robot employs the popular gradient-based control law to attain the assigned individual task(s). In the current work, robots are assigned either distance and signed area task(s) or bearing task(s). We provide a sufficient condition on the gain ratio $R_{\text{Ad}}$ between the signed area and the distance control term such that the desired formation shape, an isosceles triangle, is reached from all feasible starting positions. Numerical simulations are provided to support the theoretical analyses.