Distributed Formation Control for Unicycle Agents Using Fourier Descriptors

This paper studies the control of multiagent formations in which the Fourier descriptors of the sequence of agent positions are constrained to be zero outside a selected set of low frequencies. This specification enables the mobile agents to form a low-frequency discretized planar closed curve without sharp variation while accommodating high flexibility of the curve’s shape. We propose a novel approach for controlling this type of formation assuming a motion model with unicycle kinematics and velocity saturation. Our approach uses a distributed estimator to compute the values of the Fourier descriptors at the selected set of low frequencies, and employs these estimates in a gradient-based motion control strategy. We exploit existing techniques to define a convergent gradient-based control law under the considered motion constraints. Compared to prior work in this problem, our approach only requires distributed interactions between agents, and explicitly considers realistic motion constraints. We also study how to combine descriptors from different sets of frequencies, which enhances transient control performance. We present simulation examples to illustrate the properties of the proposed approach.