###### Abstract  
This paper investigates the cooperative control problem for a group of autonomous nonholonomic mobile robots, in which the robots are required to collaboratively enclose and track a stationary or moving target in a circular formation. In order to solve the challenging problem that the robots with speed constraints move uniformly to the exact position on the circles centered on the target while avoiding obstacles encountered, a distributed coupling controller scheme consisting of target encircling, phase positioning and spacing assignment, and the avoidance of obstacles is proposed. First, a novel circular motion control law based on the feedback control idea of trajectory tracking is proposed, which guides all robots move to the target-centered circles and maintains the expected distances between the robots and the target. Second, a phase positioning and spacing assignment control law by introducing a nonlinear function is proposed, which can be coupled into the circular motion controller to implement the robots converge to the specified position on the circles. Finally, the obstacles avoidance control law based on artificial potential field only with repulsive force is adopted to ensure each robot effectively avoids obstacles. The rigorous theoretical analysis of the convergence of the proposed controller is given, and then the simulations and experiments are provided to validate the effectiveness and applicability of the proposed control scheme. c 2022 2022 2022 2022 2022 2022 2022  
unmanned aerial vehicle (UAV) swarm systems that form a circular formation can more efficiently observe the specified target from different angles to ensure the comprehensiveness and integrity of the sampling process. According to whether a multi-agent system needs to rotate around the target, we usually divide the circular formation into two categories: cooperative circumnavigation and cooperative following. For the former, cooperative circumnavigation is that a group of autonomous robots circumnavigate the stationary or moving target with prescribed radius, circular velocity, and inter-robot angular spacing [17]. Currently, many circumnavigation-control strategies have been devoted in the most of literature to a single or a team of agents. In [18], a nonlinear periodic continuous time control law based on distance measurement was proposed, which achieved the objective for an agent rotating around a target. In [19], the same circumnavigation problem has been considered by bearing-only measurements to address a surveillance problem, in which a nonholonomic robot achieved a circular motion around a target. However, the forward speed of the agent is required to be a constant, which is easily limited in the practical application. Likewise, a novel bearing-only measurement control scheme was proposed for a single and a group of autonomous nonholonomic mobile robots to enclose around a target of interest [20]. Since the preset target is assumed to be static, this control scheme cannot be applied to the dynamic target situation. To solve this problem, a cooperative controller in Frenet-Serret coordinate system was developed for multiple nonholonomic vehicles via local measurements [21]. However, this controller can only ensure that all robots are evenly distributed on a common circle around a target with time-varying velocity. In [22], a cooperative circumnavigation control methodology based on graph theory and backstepping method was proposed to achieve multiple nonholonomic robots revolving around a moving target. However, the target's speed was only considered in the case of constant speed. In [23], a spacing-adjustment-control strategy was studied, which can make all agents converge to prescribed angular spacing. However, the limitation of the proposed control strategy is that all agents are constrained to move in the one-dimensional space of a circle, i.e., it is completely based on the assumption that the agents are pre-placed on a common circle.