Circular Formation Algorithms for Multiple Nonholonomic Mobile Robots: An Optimization-Based Approach

This paper revisits the circular formation control problem proposed in [G. S. Seyboth, J. Wu, J. Qin, C. Yu, and F. Allgower, “Collective circular motion of unicycle type vehicles with nonidentical constant velocities,” IEEE Transactions on Control of Network Systems, vol. 1, no. 2, pp. 167–176, Jun. 2014.] for multiple nonholonomic mobile robots with nonidentical constant forward speeds. Specifically, we study two types of circular formations: First, a circular motion with synchronized/balanced phase configuration; and second, a concentric circular formation with both circular orbits control and phase synchronization/balancing. Existing works on the above problems utilize a fixed-gain control input, which increases the workload of the engineers for selecting favorable algorithm parameters. To reduce this workload, we study the above problems from a new perspective by utilizing optimization methods, based on which two variable-gain control algorithms are proposed such that much greater flexibility on the selection of algorithm parameters is acquired. The global convergence properties of the proposed algorithms are analyzed under some mild assumptions. Both simulations and field experiments are presented to validate the effectiveness of the proposed formation algorithms.