Safety-assured Fixed-time Control for Space Robot under Asymmetric Output Constraints
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摘要: 针对具有随机扰动和非对称输出约束的空间机器人系统, 提出一种基于二阶滑模的保安全固定时间控制器. 首先, 结合动量守恒定理和拉格朗日方程推导出姿态受控、位置不控的空间机器人系统的动力学模型. 其次, 对包含系统随机扰动和非线性动力项在内的集总扰动上限进行估计, 并引入一种分段正切型障碍Lyapunov函数以解决空间机器人的非对称输出约束问题, 再借助加幂积分法和扰动补偿法设计了一种二阶滑模保安全固定时间控制方案. 最后, 通过Lyapunov准则证明了空间机器人误差跟踪系统的固定时间稳定性, 详细的数值仿真进一步验证了所设计控制方案在时间与空间两个维度上的可行性和安全性.Abstract: For the space robot with stochastic perturbations and asymmetric output constraints, a safety-assured fixed-time controller based on second-order sliding mode is proposed in this research. First, by combining the momentum conservation theorem and the Lagrange equation, the dynamic model of the space robot system, in which the base attitude is controlled while the base position is uncontrolled, is derived. Then, the upper bound of the lumped disturbance which includes the stochastic perturbations and the nonlinear dynamic terms of the system is estimated, and a piecewise tangent-type barrier Lyapunov function is introduced to address the asymmetric output constraint problem of the space robot. Furthermore, by means of the power-addition-integral method and the disturbance compensation approach, a second-order sliding mode safety-assured fixed-time control scheme is designed. The fixed-time stability of the error tracking system of the space robot is proven via the Lyapunov criterion, and the detailed numerical simulations further confirm the feasibility and reliability of the designed control scheme in both time and space dimensions.
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图 1 姿态受控空间机器人平面结构
Fig. 1 Two-dimensional layout of the attitude-controlled space robot
图 2 本文方法的状态变量时间响应(情景一)
Fig. 2 Time responses of the state variables in the proposed method (Scenario 1)
图 5 本文方法的跟踪误差时间响应(情景一)
Fig. 5 Time responses of the tracking errors in the proposed method (Scenario 1)
图 8 本文方法的控制力矩时间响应(情景一)
Fig. 8 Time responses of the control torques in the proposed method (Scenario 1)
图 11 本文方法的状态变量时间响应(情景二)
Fig. 11 Time responses of the state variables in the proposed method (Scenario 2)
图 14 本文方法的跟踪误差时间响应(情景二)
Fig. 14 Time responses of the tracking errors in the proposed method (Scenario 2)
图 17 本文方法的控制力矩时间响应(情景二)
Fig. 17 Time responses of the control torques in the proposed method (Scenario 2)
图 20 本文方法的状态变量时间响应(情景三)
Fig. 20 Time responses of the state variables in the proposed method (Scenario 3)
图 23 本文方法的跟踪误差时间响应(情景三)
Fig. 23 Time responses of the tracking errors in the proposed method (Scenario 3)
图 26 本文方法的控制力矩时间响应(情景三)
Fig. 26 Time responses of the control torques in the proposed method (Scenario 3)
表 1 空间机器人系统的物理参数
Table 1 Physical parameters of the space robot system
物理量 参数值及单位 基座质量$ m_0 $ 4$ \mathrm{kg} $ 机械臂$ B_1/B_2 $质量$ m_1/m_2 $ 0.3$ \mathrm{kg} $ 旋转中心$ O_0 $与$ O_1 $之间的距离$ l_0 $ 0.15$ \mathrm{m} $ 机械臂$ B_1/B_2 $的轴向长度$ l_1/l_2 $ 0.3$ \mathrm{m} $ 基座中心转动惯量$ J_0 $ 3.4$ \mathrm{kg\cdot m^2} $ 机械臂$ B_1/B_2 $中心转动惯量$ J_1/J_2 $ 0.1$ \mathrm{kg\cdot m^2} $ 
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表 2 控制方法的参数选取
Table 2 Parameter selections of the control methods
控制方法 参数选取 本文方法 $ \begin{array}{l}{\eta_{1}=1.00,\; \eta_{2}=0.20,\; \mu=1.00,\;\omega=1.00}\\{ \sigma=-0.40,\; \nu=1.00} \end{array}$ 文献[25] $ \begin{array}{l}{k_1=1.00,\; k_2=1.20,\; \alpha=1.00,\;\beta=0.80}\\{a_1=1.10,\; a_2=0.70,\; \gamma_1=1.30,\; \gamma_2=0.90}\\{k=0.20}\end{array} $ 文献[26] $\begin{array}{l} {k_1=1.00,\; k_2=1.20,\; \alpha_1=1.00,\;\beta_1=0.50}\\{\alpha_2=0.70,\; \beta_2=0.80,\; \gamma_1=1.30,\; \gamma_2=0.90}\\{ k=0.20,\; \eta=0.01} \end{array}$
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表 3 不同控制方法跟踪误差的RMSE值(rad)
Table 3 The RMSE values of the tracking errors of different control methods(rad)
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