Orthogonal vector field-based control for a multi-robot system circumnavigating a moving target in 3D

We address the problem of multiple networked robots circumnavigating a dynamic target in a three-dimensional setting. A distributed cooperative control strategy is proposed that guarantees convergence of the robots to a circular formation with prescribed radius and inter-agent distances around a moving target. The circular formation is constrained to evolve on a plane of motion that is fixed in orientation but translates along the target trajectory. The control design is carried out using three potential functions, each of which defines a control objective, with gradient fields that are orthogonal to each other. The novelty in this approach lies in the orthogonality of the vector fields, which decouples the control objectives and ensures asymptotic convergence to the desired formation, subject to some mild initial condition constraints. The convergence properties are analyzed using Lyapunov-based methods, and the control strategy is demonstrated through numerical simulations and experiments on a robotic test bed.