Bearing-Based Formation Control with Optimal Motion Trajectory

TL;DR

This paper introduces an optimization method for bearing-based formation control that shortens agent trajectories, improves path straightness, and enhances formation efficiency by tuning controller parameters through nonlinear optimization.

Contribution

It proposes a novel parameterization and optimization approach to improve the path efficiency of bearing-based formation controllers, addressing convoluted trajectories.

Findings

Trajectory straightening by around 16% with minimal training samples.

Further straightening by 66% when incorporating range measurements.

Effective optimization with small sample sizes for large random initial conditions.

Abstract

Bearing-based distributed formation control is attractive because it can be implemented using vision-based measurements to achieve a desired formation. Gradient-descent-based controllers using bearing measurements have been shown to have many beneficial characteristics, such as global convergence, applicability to different graph topologies and workspaces of arbitrary dimension, and some flexibility in the choice of the cost. In practice, however, such controllers typically yield convoluted paths from their initial location to the final position in the formation. In this paper we propose a novel procedure to optimize gradient-descent-based bearing-based formation controllers to obtain shorter paths. Our approach is based on the parameterization of the cost function and, by extension, of the controller. We form and solve a nonlinear optimization problem with the sum of path lengths of the agent trajectories as the objective and subject to the original equilibria and global convergence conditions for formation control. Our simulation shows that the parameters can be optimized from a very small number of training samples (1 to 7) to straighten the trajectory by around 16% for a large number of random initial conditions for bearing-only formation. However, in the absence of any range information, the scale of the formation is not fixed and this optimization may lead to an undesired compression of the formation size. Including range measurements avoids this issue and leads to further trajectories straightening by 66%.