Tight autonomous circumnavigation of unpredictably moving targets by an underactuated nonholonomic robot

Abstract An underactuated nonholonomic autonomous robot with a Dubins car kinematics navigates through a planar environment that hosts an unpredictably moving rigid formation of point-wise targets. Both the number of the targets and their geometric configuration are unknown. The robot measures the relative positions of the targets within a limited sensing range but has no access to their velocities or other kinematic parameters. The robot has to approach the formation, and to subsequently move so that first, all targets are surrounded by the robot’s path, and second, a predefined distance to the currently nearest target is maintained. However, a lower bound on the turning radius of the robot typically makes perfect achievement of the second objective impossible since different targets become the nearest to the robot in the course of its movement. So a scheme for on-the-fly synthesis of a feasible and somewhat optimal approximation of the ideal circumnavigation path is offered. Based on this development, the paper presents a computationally efficient control law that accomplishes the mission as much as possible. The effectiveness of the advocated approach is justified by mathematically rigorous proofs of nonlocal convergence and is confirmed by simulation tests and experiments with real robots.