Spherical Formation Tracking Control of Nonlinear Second-Order Agents With Adaptive Neural Flow Estimate

This article addresses the spherical formation tracking control problem of nonlinear second-order vehicles moving in flowfields under both undirected networks and directed, strongly connected networks. Different from the previous adaptive estimate of the time-invariant parameters of flowfields, the flowfields under our consideration are spatial and absolutely unknown dynamics. Adaptive neural networks (ANNs) with the novel cooperative adaptive algorithms are proposed to approximate the flowfield acting on the channel of each vehicle’s velocity (i.e., the mismatched flowfield) and the flowfield pushing the acceleration (i.e., the matched flowfield), respectively. For the purpose of avoiding the complex derivation derived from backstepping, the novel first-order filters are generated by dynamic surface based on barrier functions and relative positions of neighbors. The proposed control algorithms and adaptive upgrade law are fully distributed without using any global information of the graph. The uniform boundedness is analyzed in the Lyapunov sense. Simulation results are given to verify the theoretical analysis.

I. Introduction

Contemporarily, an increasing phenomenon has appeared in formation cruise [1], oceanic and planetary explorations [2], [3] by a fleet of sensor-equipped vehicles formation moving along a set of given orbits. This scenario derives a novel coordinated control problem named as the formation tracking control problem, especially for the spherical formation tracking problem in three dimensions (3D). In the past few years, most results focus on the flow-free motion. The details can be found in the cases of leader-following [4]–[6], virtual structure [7], [8], and geometric extension [9]–[11].