Safe circumnavigation of an agent along irregular orbit using bearing-only information

This brief studies the challenge of safely circumnavigating a stationary target along an irregular orbit using only bearing measurements. A scalar estimator and a controller are proposed, which simultaneously achieve target localisation and orbit tracking while guaranteeing that the agent never enters a prescribed safe-circle area around the target. Notably, the proposed circumnavigation pattern accommodates irregular orbits, thereby removing the restrictive regular orbital assumption prevalent in existing bearing-only circumnavigation literature. Several existing estimators can be viewed as special cases of the proposed estimator. Rigorous analysis establishes the asymptotic convergence of both the estimation and orbit-tracking errors, as well as full-time safety. For practical implementation, the derivative of the estimated target position in the estimator is approximated by a finite difference, and sufficient conditions are derived to guarantee safety and ultimate boundedness, with the resulting bounds proportional to the sampling period. Numerical simulations validate the theoretical results.