Ju Zhiyang, Zhang Hui, Tan Ying, Chen Xiang
School of Transportation Science and Technology, Beihang University, Beijing 100191, China.
Ningbo Institute of Technology (NIT), Beihang University, Ningbo 315323, China.
Math Biosci Eng. 2022 Jan 17;19(3):2913-2934. doi: 10.3934/mbe.2022134.
Control design of mobile sensors for coverage problem is addressed in this paper. The mobile sensors have non-linear dynamics and directional sensing properties which mean the sensing performance is also affected by the pointing directions of the sensors. Different from the standard optimal coverage problem where sensors are assumed to be omni-directional ones, orientation angles of the directional sensors should also be controlled, other than the position control, to achieve the coverage purpose. Considering also the non-linear dynamics of the mobile sensors, new control methodology is necessarily developed for the coverage problem with directional sensors. In the approach proposed, an innovative gradient based non-smooth motion controller is designed for the mobile sensors with unicycle dynamics. With the proposed controllers, the states of sensors will always stay in an positive invariant set where the gradient of the performance valuation function is well-defined if they are initialized within this set. Moreover, the sensors' states are proved to converge to some critical point where the gradient is zero. Simulation results are provided to illustrate the performance of the proposed coverage control strategy.
