Securing Isosceles Triangular Formations under Heterogeneous Sensing and Mixed Constraints
This work provides a theoretical condition for robust formation control for robotic systems, which is relevant for multi-robot coordination in various applications.
This paper addresses the problem of maintaining an isosceles triangular formation among three mobile robots using heterogeneous sensing. The authors derive a sufficient condition on the gain ratio between signed area and distance control terms to ensure the desired isosceles triangle formation is achieved from all feasible starting positions.
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.