Optimization-Based Distributed Flocking Control for Multiple Rigid Bodies

This letter considers distributed flocking control on the Special Euclidean group for networked rigid bodies. The method captures the three flocking rules proposed by Reynolds: cohesion; alignment; and separation. The proposed controller is based only on relative pose (position and attitude) information with respect to neighboring rigid bodies so that it can be implemented in a fully distributed manner using only local sensors. The flocking algorithm is moreover based on pose synchronization methods for the cohesion/alignment rules and achieves safe separation distances through the application of control barrier functions. The control input for each rigid body is chosen by solving a distributed optimization problem with constraints for pose synchronization and collision avoidance. Here, the inherent conflict between cohesion and separation is explicitly handled by relaxing the position synchronization constraint. The effectiveness of the proposed flocking algorithm is demonstrated via simulation and hardware experiments.

I. Introduction

Flocking, swarming, and schooling are common emergent collective motion behaviors exhibited in nature [1], [2]. These natural collective behaviors can be leveraged in multi-robot systems to safely transport large cohesive groups of robots within a workspace. To capture these effects, Reynolds introduced three heuristic rules: cohesion; alignment; and separation, to reproduce flocking motions in computer graphics in 1987 [3]. These rules have been applied by researchers in various fields including physics, biology, social science, and computer science [4]–[8]. The scope and flexibility of this motion coordination strategy have also caused it to be widely leveraged by robotics and control engineering communities to develop motion coordination control methods for multi-robot systems [9]–[19].