Circumnavigation of Multiple Drones Under Intermittent Observation: An Integration of Guidance, Control, and Estimation

Abstract

This paper discusses the circumnavigation of multiple drones around a moving target in an urban area and proposes an integrated solution accounting for estimation, guidance and control. For performing this circumnavigation task, three objectives must be achieved at a steady state: (1) The target and the drones must be on the same plane; (2) The drones must rotate around the target while maintaining a constant distance to the target; and (3) Each drone must be able to avoid collisions with the other drones. To achieve these three objectives, a vector-field-based guidance law can be designed to generate the velocity command which is then integrated to be the position command for each drone. However, in the course of implementing this guidance law, the target's position and velocity information is continuously required, which is unlikely to be the case in an urban environment. To address this issue, a probability function modeling the intermittent or discontinuous observation can be added to the typical Kalman filter, so that the target position is continuously estimated. In addition, when there is a bias in the observation of drone, the bias has to be eliminated by adding a consensus logic (information exchange between neighboring drones) to the correction step of the Kalman filter, resulting in so-called Kalman Consensus Filter (KCF). However, KCF only guarantees the asymptotic convergence to an estimate of the target state which adversely affects the control performance, and so a novel consensus logic, so-called Kalman Finite-time Consensus Filter (KFCF), is proposed for the finite-time convergence and the control performance improvement. The guidance law combined with the estimation scheme (KFCF) is then tracked by each drone being equipped with the Integral Sliding Mode Control (I-SMC) law yielding the finite-time convergence to a prescribed sliding surface in the presence of bounded disturbances. Integrated numerical simulations show the merit of the proposed method.