Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space  

作　　者：Xiaodong He Zhiyong Sun Zhiyong Geng Anders Robertsson 

机构地区：[1]State Key Laboratory for Turbulence and Complex Systems,Department of Mechanics and Engineering Science,College of Engineering,Peking University,Beijing 100871,China [2]IEEE [3]Department of Electrical Engineering,Eindhoven University of Technology(TU/e),5600 MB Eindhoven,the Netherlands [4]Department of Automatic Control,LTH,Lund University,22100 Lund,Sweden

出　　处：《IEEE/CAA Journal of Automatica Sinica》2022年第2期270-282,共13页自动化学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(61773024,62073002);the Eindhoven Artificial Intelligence Systems Institute(EAISI),and the ELLIIT Excellence Center and the Swedish Foundation for Strategic Research,Sweden(RIT150038)。

摘　　要：This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space.The vehicle’s model is established on the matrix Lie group SE(3),which describes the configuration of rigid bodies globally and uniquely.We focus on the kinematic model of the underactuated vehicle,which features an underactuation form that has no sway and heave velocity.To compensate for the lack of these two velocities,we construct additional rotation matrices to generate a motion of rotation coupled with translation.Then,the state feedback is designed with the help of the logarithmic map,and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction.Later,the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance.Finally,simulation examples are provided to verify the effectiveness of the stabilization controller.

关 键 词：Exponential stabilization logarithmic feedback matrix Lie group underactuated vehicle 

分 类 号：U664.82[交通运输工程—船舶及航道工程] TP273[交通运输工程—船舶与海洋工程]