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探讨了本体位置与姿态均不受控的漂浮基空间机器人在时间延迟(简称时延)情况下惯性空间轨迹跟踪的控制问题。利用拉格朗日方法并结合系统动量守恒关系,分析、建立了漂浮基空间机器人完全能控形式的系统动力学模型及运动Jacobi关系。以此为基础,针对系统存在时延的情况,利用泰勒级数预测、逼近的方法,建立了适用于时延情况下控制系统设计的数学模型。利用该模型,提出了一种空间机器人在时延情况下的改进非线性反馈控制方案。然后运用Lyapunov第二类方法,结合范数以及图形分析的方法证明了在时延情况下整个闭环控制系统的渐近稳定性。文中提到的控制方案能够有效地克服系统存在时延的影响,控制漂浮基空间机器人末端爪手跟踪惯性空间的期望轨迹。系统数值仿真结果证明了上述控制方案的有效性与精确性。
In this paper, the control of inertial space trajectory tracking in floating base space robot with uncontrolled position and attitude is discussed in time delay (referred to as delay). Based on the Lagrange method and the systematic conservation of momentum, a system dynamics model and a motion Jacobi relation for the fully controllable form of a floating base space robot are established. Based on this, a mathematical model suitable for the design of control system under the condition of delay is established to deal with the delay of the system by using the method of Taylor series prediction and approximation. Using this model, an improved nonlinear feedback control scheme for space robot under delay condition is proposed. Then using Lyapunov second class method, the norm stability and the asymptotic stability of the entire closed-loop control system under the condition of delay are proved by the combination of norm and graph analysis. The control scheme mentioned in this paper can effectively overcome the delay of the system and control the desired trajectory of the inertial space of the fingertip of the floating space robot. The numerical simulation results show that the above control scheme is effective and accurate.