This paper proposes a nonlinear discrete-time sliding mode based tension control for deployment of tethered space robot with only length and angle measurements. The discrete-time dynamics of deployment is uncovered based on discretization of Hamilton's principle. Taking into account the underactuated dynamics, the proposed discrete-time sliding surface can generate a specified reduced-order system, which can be regarded as an uncertain discrete-time system with multiple time delays, which is caused by a considerable sample interval, and the stability of a reduced-order system is well analyzed by combining a linear matrix inequation technique based on robust control theory and nonlinear discrete-time Lyapunov method. A novel input structure with the auxiliary variable sequence is presented to deal with the tension saturation, and the states can converge to the specified reduced-order system although the input saturation occurs. The proposed discrete-time method makes no appeal to velocity terms. It is cost-effective to use the proposed method for the information of length and angle are easily measured rather than that of velocity, and it conduces to low requirements for the measurement ability of sensors. Simulation results verify the stability analyses, and are coincident with the stability analyses.

中文翻译：

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仅长度和角度测量的系留空间机器人部署的离散时间滑模控制

本文提出了一种基于非线性离散时间滑模的张力控制，用于仅具有长度和角度测量的系留空间机器人的部署。基于汉密尔顿原理的离散化揭示了部署的离散时间动态。考虑到欠驱动动力学，所提出的离散时间滑动面可以生成一个指定的降阶系统，可以将其视为具有多个时间延迟的不确定离散时间系统，这是由相当大的采样间隔引起的，并且通过结合基于鲁棒控制理论的线性矩阵不等式技术和非线性离散时间李雅普诺夫方法，可以很好地分析降阶系统的稳定性。提出了一种具有辅助变量序列的新型输入结构来处理张力饱和，尽管出现输入饱和，状态可以收敛到指定的降阶系统。所提出的离散时间方法对速度项没有吸引力。由于长度和角度信息易于测量而不是速度信息，因此使用所提出的方法具有成本效益，并且对传感器的测量能力要求较低。仿真结果验证了稳定性分析，与稳定性分析相吻合。