Distance-based Formation-Motion Control for Unicycle Agents

Abstract

We present a distance-based distributed formation-motion control law for unicycle agents that are required to move together at a constant reference speed. The distributed control law consists of the standard distancebased formation gradient control law, which is projected to the longitudinal and angular velocity inputs of the unicycle, and of a linear term that depends on the reference speed. The main contribution of this paper is to realize the consistency of unicycle agents' orientations without orientation measurement, thereby reducing the possibility of significant orientation measurement errors in real-world applications. We prove and show numerically the local exponential convergence of the unicycle agents to the desired formation, where they eventually move in unison at a constant reference speed. I. INTRODUCTIONDue to the multitude of problem setups in distributed formation control, there has been numerous research works reported in literature for the past decade. Most of them considers only the formation keeping problem for point masses described by single integrator [1], where the graph rigidity framework [2] [3] [4] has been used to define the formation shape and correspondingly to design the distributed gradient-based control laws. By assuming that all agents are equipped with homogeneous sensor systems, the application of distributed gradient-based control leads to the popular distance-based formation control [5] [6], the bearing-only formation control [7], the angle-based formation control [8], the inner-angle based formation control [9] and the elevationangle formation control [10]. For second-order agents, the design of formation control has been studied in [11] [12]. Recently, the distributed formation control for unicycle agents is presented in [13] [14] where the authors focus on the convergence of the agents towards the desired shape without consensus on the orientation and without enabling a group motion. The latter is typically one of the need-to-have tasks required in a group of collaborating agents.In addition to reaching and maintaining a robust formation shape, the group may need to perform other tasks, such as group motion, obstacle avoidance or rendezvous, at the same time. The design of distributed control laws to solve these tasks simultaneously has been studied, for example, in *This work is supported by Center of Expertise Flexible Manufacturing Systems.