Gradient-based bearing-only formation control: an elevation angle approach

Abstract

This paper proposes an elevation angle rigidity theory in both 2D and 3D spaces, and applies it to solve multi-agent formation control with only inter-agent bearing/direction measurements in agents’ local coordinate frames. Motivated by the sensor technology in measuring elevation angle and angular diameter, we develop elevation angle rigidity by attaching each agent in a multi-agent framework with a rod in 2D and a ball in 3D, respectively. By defining the elevation angle rigidity matrix, conditions for infinitesimal elevation angle rigidity are derived. Compared to previously developed angle rigidity-based and bearing rigidity-based formation control laws, the proposed elevation angle rigidity-based control law can maintain the gradient-based control property. Compared to distance-based formation control laws, less sensor measurements are required. The formation maneuvering with desired translation and rotation is also realized by using only local bearing measurements. Simulation examples illustrate the advantages and effectiveness of the proposed approach.