Prescribed Performance Control of Redundantly-actuated Cable Driving Parallel Robots Subjected to Output Constraint
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摘要: 提出一种考虑输出约束的冗余驱动绳索并联机器人(Redundantly-actuated cable driving parallel robots, RCDPRs)预设性能有限时间控制算法. 首先, 采用Newton-Euler方程推导系统动力学模型, 并建立绳索拉力优化模型保证系统正常工作; 其次, 将输出约束问题转化为位置跟踪误差的坐标变换问题, 设计给定时间衰减函数与非对称变换函数, 将约束形式的跟踪误差转化为无约束变量, 实现给定时间的输出约束; 然后, 针对滑模控制的抖振问题, 在预设性能控制中采用模型不确定与扰动估计器进行扰动估计, 并通过自适应方法对扰动估计误差进行补偿; 以此为基础, 提出一种基于精度驱动且在分段点处三阶连续的终端滑模面进行控制算法设计; 最后, 采用Lyapunov函数证明算法的有限时间收敛特性, 并以7自由度冗余驱动绳索并联机器人为控制对象进行仿真研究, 对算法进行验证.
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关键词:
- 滑模控制 /
- 有限时间收敛 /
- 输出约束 /
- 给定时间预设性能控制 /
- 冗余驱动绳索并联机器人
Abstract: This paper proposed a prescribed performance finite-time control algorithm of redundantly-actuated cable driving parallel robots (RCDPRs) considering output constraint. Firstly, the Newton-Euler equation is employed to establish the dynamic model of the system, and the optimization model for all cables was constructed to guarantee properly operation. Then, the output constraint problem is transformed into coordinate transformation problem of the position tracking errors, also the appointed time decay function and the asymmetric transformation function are designed to transform the tracking errors into unconstraint variables, thus the output constraint is realized. Meanwhile, aiming at the chattering problem, the uncertainty and disturbance estimator is proposed, and the adaptive algorithm is designed to compensate the estimation error, on the basis of which, the accuracy-driven terminal sliding mode surface with three-order continuity on the segment point is proposed and applied in controller design. Finally, the Lyapunov function is used to prove that the proposed algorithm has finite-time convergence characteristics, and a seven-degrees-of-freedom RCDPR is used as the control object for simulation research to demonstrate the effectiveness of the proposed controller. -
表 1 RCDPR运动学参数(mm)
Table 1 Kinematic parameters of the RCDPR (mm)
参数 数值 参数 数值 b1 [0, 0, 1000] a1 [−150, −100, 50] b2 [100, 0, 1000] a2 [150, −100, 50] b3 [1000, 1000, 1000] a3 [150, 100, 50] b4 [0, 1000, 1000] a4 [−150, 100, 50] b5 [500, 0, 0] a5 [0, −100, −50] b6 [1000, 1000, 0] a6 [150, 100, −50] b7 [0, 1000, 0] a7 [−150, 100, 50] r 20 表 2 RCDPR惯性参数
Table 2 Inertial parameters of the RCDPR
参数 描述 数值 mp 动平台质量 1.67 kg Ip 动平台转动惯量矩阵 diag{2.78×104, 5.56×104, 7.26×104} kg·mm2 Ib 滑轮转动惯量 1.2×104 kg·mm2 表 3 各控制器参数
Table 3 Parameters of all controllers
控制器 参数 值 PPSMC K1, K2, α1, α2, α3, Δ11, Δ12, Δ13, Δ14, Δ15, Δ16, β4, β5, K3, γ0, T, λ1, λ2, Te, ε1i, ε2i, μ0, μ∞, k 100I6, 50I6, 0.5, 1.5, 1.8, 0.01, 0.01, 0.01, 0.001, 0.001, 0.001, 5, 5, 10I6, 10, 0.001 s, 0.001, 0.01, 0.2 s, 0.5, 1, [0.2, 0.2, 0.2, 0.02, 0.02, 0.02]T, 0.002[1, 1, 1, 0.01, 0.01, 0.01]T, 30 ASTUDESMC k1, k2, αi, T, ε, $ {\omega _1}\sqrt {{{{\gamma _1}} \mathord{\left/ {\vphantom {{{\gamma _1}} 2}} \right. } 2}} $, λ+4ε2 100I6, 50I6, 0.5, 0.001 s, 0.5, 500, 10 TDENFTSMC ρ1, ρ2, α1i, α2i, k1, k2, L 100I6, 50I6, 0.5, 1.8, 0.001 s UDESMC c, 1/a, k 160, 0.001 s, 20 -
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