Formation optimization for a fleet of wheeled mobile robots — A geometric approach

Tight formation-based operations are critical in several emerging applications for robot collectives — ranging from cooperative payload transport to synchronized distributed data-collection. In this paper, we investigate the optimal relative layout for members of a team of Differentially-Driven Wheeled Mobile Robots (DD-WMRs) moving in formation for ultimate deployment in cooperative payload transport tasks.Our particular focus is on modeling such formations, developing the motion plans and determining the “best formation” in a differential-geometric setting. Specifically, a preferred team-fixed frame serves as a virtual leader inducing motion plans for the individual DD-WMRs which form the vertices of a virtual structure. The resulting motion plans for the DD-WMRs as well as overall team-performance depend both on the specifiedteam-frame motions as well as their relative-layout within the formation.Emphasis is placed on developing suitable invariant (yet quantitative) measures of formation quality and a systematic optimization-based selection of the formation-layout. The use of relative formation-parameterization with respect to a team-frame serves to decouple the team-level optimal layout selection process. The optimal location of each DD-WMR can now be found with respect to the team-frame individually and the feasibility of distributed implementation facilitates scaling to larger-sized formations. Analytical and numerical results, from case studies of formation optimization of three DD-WMRs maneuvering along certain desired planar paths, are presented to highlight the salient features and benefits.