In order to enable the multi-agents to elliptically circumnavigate the multi-targets in more complex environment, we propose a geometric center estimator and an elliptical circumnavigation controller in two-dimensional space by only employing bearing measurements without knowing the target's position and velocity. The stability of the algorithm is proved for both stationary targets and dynamic targets. Finally, a series of numerical simulations is presented to verify the correctness of the algorithm both in ideal networks and in networks with communication delays. K E Y W O R D S bearing measurements, circumnavigation, multi-agents system, target localization 1 3250 /journal/rnc Int J Robust Nonlinear Control. 2020;30:3250-3268. CHUN and TIAN 3251 F I G U R E 1 Planning of the trajectory when targets are surrounded by obstacles [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 2 Circular circumnavigation and elliptical circumnavigation [Colour figure can be viewed at wileyonlinelibrary.com] target agentIt is found that all the above algorithms can only make a single agent or a group of agents move on a circle centered at the target or the geometric center of multi-targets. However, in practical applications, some agents often need to change the type of the circumnavigation trajectory according to the work scene and the geographical environment. For example, in military reconnaissance, a more general circumnavigation trajectory needs to be designed to avoid exposure to the detection range of the hostile target in some cases. Figure 1 shows the planning of the trajectory when the hostile targets are surrounded by some obstacles, where the red circle is the detection boundary of the hostile targets. If the agent is still moving on a circle at this time, it has to be close enough to the targets under the influence of the obstacles. This can make the agent completely within the detection range of the hostile targets, greatly increasing the probability of being captured by the targets. However, if an elliptical circumnavigation trajectory is used, the probability of being captured can be eliminated. Figure 2 shows the circular circumnavigation and the elliptical circumnavigation. When targets are distributed in a strip shape, compared to elliptical circumnavigation, the circular circumnavigation is not the optimal solution to energy consumption, cost or circumnavigation efficiency. In addition, the circular circumnavigation is a special case of the elliptical circumnavigation which can accomplish whatever circular circumnavigation can.Nevertheless, extending the circumnavigation controller from the circle case to the elliptical case may cause some nontrivial problems both in the controller design and stability analysis. For the circular circumnavigation, the axial velocity and the tangential velocity are always orthogonal. Therefore, the controller design in the axial direction and in the tangential direction can be accomplished separately. Actually, in most literature on the circular circumnavigation...
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