基于Twistor的航天器领航-跟随编队有限时间姿轨耦合控制

Finite-Time Orbit-Attitude Coupled Control for Leader-Follower Spacecraft Formation Based on Twistors

针对双航天器六自由度领航-跟随编队的姿轨耦合控制问题,为了简化六自由度控制器的设计,采用twistor对双航天器的相对姿轨运动进行统一描述,提出了有限时间收敛的六自由度姿轨耦合控制律。首先,定义合理的坐标系,给出twistor描述的双航天器相对姿轨运动方程;其次,提出twistor框架下的终端滑模面,为有限时间收敛控制律的设计提供基础;然后,应用滑模控制理论,基于所提出的终端滑模面,设计有限时间收敛的六自由度姿轨耦合控制律,并证明其在有限时间收敛。最后,通过数值仿真,验证所提出算法的有效性。基于twistor的六自由度姿轨耦合编队控制律设计比传统设计方法更为简洁,比基于对偶四元数的控制律计算量小,更适合于计算资源有限航天器的六自由度编队控制。

For the coupled orbit-attitude control problem of six-degree-of-freedom(6-DOF)leader-follower spacecraft formation,the relative orbit and attitude motion between the spacecraft is described by twistors in a unified form,which can simplify 6-DOF controller design for the formation.Then a finite-time controller is proposed for the twistor dynamic system.Firstly,some coordinate systems are defined,and the relative orbit-attitude coupled motion equations of the formation spacecraft described by twistors are given.Secondly,a terminal sliding surface under the twistor framework is proposed,which provides the basis for the design of the finite-time control law.Thirdly,based on the proposed terminal sliding surface,a finite-time 6-DOF orbit-attitude coupled control law is developed,and the finitetime convergence of which is proved via Lyapunov analysis.Finally,the effectiveness of the proposed algorithm is demonstrated by numerical simulations.The development of twistor based orbit-attitude coupling formation control laws is much more straightforward than conventional design,and the control law bears less computation burden than the dual quaternion-based control law.