Cooperative Circumnavigation Based on Composite Vector Fields in Various Scenarios

ABSTRACT This article investigates the cooperative circumnavigation problem for a multi‐agent system in both obstacle‐free environments and environments with obstacles. A semi‐ellipsoid obstacle model, considering both the geometric dimensions of the agent and the obstacle, is constructed to simplify and substitute for a real‐world obstacle. Afterward, for the obstacle‐free scenario, a composite vector field composed of a normal guidance vector field (NGVF), a tangent guidance vector field (TGVF), and a vertical guidance vector field (VGVF) is proposed. Based on this, a finite‐time controller is developed to drive the multi‐agent system to achieve prescribed circumnavigation configurations, including orbit and any pre‐specified angular distributions, in a finite time. For environments containing obstacles, a new composite vector field is created by incorporating repulsive force fields (RVFs), which are constructed based on obstacles, into the aforementioned composite vector field. Additionally, the corresponding obstacle avoidance strategy is devised to ensure agents safely avoid obstacles in the task area while performing circumnavigation. Furthermore, a more general situation of circumnavigation missions with constraints from task requirements on circumnavigation angular velocity and height of agents is considered. Simultaneously, the corresponding stability and convergence are rigorously analyzed. Finally, numerical examples are given to corroborate the effectiveness of the theoretical results.