Safe convex-circumnavigation of one agent around multiple targets using bearing-only measurements

This paper presents a new circumnavigation pattern — safe convex-circumnavigation, for the agent to enclose the targets closely, which is a pattern with better performance in harsh environments than the traditional circular circumnavigation pattern. With this new pattern, the agent circumnavigates the convex hull of multiple stationary targets with an expected enclosing distance and speed using the agent's known position as well as the bearing-only information of the targets, in addition, no collision with this convex hull happens in the whole time domain. An algorithm containing scalar estimators and a control protocol is proposed to implement this pattern. The estimators are designed to locate the targets. In the control protocol, the velocity of the agent is decomposed to one directly pointing to the convex hull and one orthogonal to its current direction. The agent is forced to circumnavigate the convex hull of the targets’ estimated positions and finally circumnavigate the convex hull of the real targets because the estimators converge to the exact positions of the targets. The corresponding convergence analysis is provided subsequently. Numerical simulation and real time experiment are conducted to verify the proposed method.