Bearing and Distance Formation Control of Rigid Bodies in SE(3) with Bearing and Distance Constraints

TL;DR

This paper develops a formation control method for rigid bodies in SE(3) using bearing and distance constraints, enabling agents to achieve desired formations without a global reference frame, validated through simulations.

Contribution

It introduces a novel control framework combining bearing and distance constraints in SE(3) for formation control, with conditions ensuring convergence.

Findings

Successful formation achievement in simulations

Control framework handles bearing-only and combined constraints

Agents operate without a global reference frame

Abstract

Rigidity of the interaction graph is a fundamental condition for achieving the desired formation which can be defined in terms of distance or bearing constraints between agents. In this paper, for reaching a unique formation with the same scaling and orientation as the target formation, both distance and bearing constraints are considered for defining the desired formation. Besides, both distance and bearing measurements are also available. Each agent is able to gather the measurements with respect to other agents in its own body frame. So, the agents are coordinated-free concerning a global reference frame. On the other hand, the framework is embedded in SE(3). The control signal is designed based on a gradient descent method by introducing a cost function. Firstly, the formation problem is considered for bearing-only constraints in SE(3) configuration. Then, the formation control is expressed for the general case of both bearing and distance constraints. Furthermore, the essential conditions that guarantee reaching the desired formation are discussed. Finally, the validity of the proposed formation control is verified by numerical simulations.