SO(3)上航天器自适应反步姿态跟踪控制

Adaptive Backstepping Attitude Tracking Control for Spacecraft on SO(3)

针对刚体航天器姿态跟踪控制问题,提出了一种自适应反步控制方法。首先,考虑模型不确定性和外部干扰影响,通过引入一个非负定的势函数来描述姿态跟踪误差,在特殊正交李群SO(3)上建立描述航天器姿态运动的相对动力学方程,所建立的动力学模型有效地避免了用修正罗德里格参数或四元数描述航天器姿态时引起的奇异和退绕等问题;其次,设计的自适应反步控制器可保证闭环控制系统最终一致有界收敛,并用李亚普诺夫理论严格证明了闭环系统的稳定性;此外,设计的自适应控制律可以有效地处理系统总干扰;最后,针对航天器姿态跟踪控制场景进行数值仿真分析。结果表明:与传统PD控制器相比,所设计的控制器可以有效地提高控制性能。

An adaptive backstepping control scheme is proposed to address the problem of attitude tracking control of rigid spacecraft.First,considering model uncertainties and external disturbances,a non-negative potential function is introduced to describe the attitude tracking error,and the relative attitude dynamics equations are developed on the special orthogonal Lie group SO(3),where singularities and unwinding problems associated with other attitude representations such as modified Rodriguez parameters(MRPs)or quaternions are avoided.By designing an adaptive law to deal with the system total disturbance,the proposed controller can guarantee the ultimately uniformly bounded convergence of the closed-loop system,whose stability is proved strictly by using the Lyapunov theory.In addition,the designed adaptive control law can effectively deal with the total disturbance of the system.Finally,numerical simulations are carried out on spacecraft attitude tracking scenarios.The results demonstrate that,compared with the traditional proportion-derivative(PD)controller,the designed controller can effectively improve the control performance.