Coordinate-free Circumnavigation of a Moving Target via a PD-like Controller

Abstract: This paper proposes a coordinate-free controller for a nonholonomic vehicle to circumnavigate a fully-actuated moving target by using range-only measurements. If the range rate is available, our Proportional Derivative (PD)-like controller has a simple structure as the standard PD controller, except the design of an additive constant bias and a saturation function in the error feedback. We show that if the target is stationary, the vehicle asymptotically encloses the target with a predefined radius at an exponential convergence rate, i.e., an exact circumnavigation pattern can be completed. For a moving target, the circumnavigation error converges to a small region whose size is shown proportional to the maneuverability of the target, e.g., the maximum linear speed and acceleration. Moreover, we design a second-order sliding mode (SOSM) filter to estimate the range rate and show that the SOSM filter can recover the range rate in a finite time. Finally, the effectiveness and advantages of our controller are validated via both numerical simulations and real experiments.