Error-Tracking Iterative Learning Control for Robot Manipulators With Iteration Varying Lengths
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摘要: 针对任意初始状态下机械臂轨迹跟踪问题, 提出一种变长度误差跟踪迭代学习控制(Iterative learning control, ILC)方法. 首先, 构造不依赖于期望轨迹的双曲余弦型期望误差轨迹, 放宽经典迭代学习控制初始状态要求严格一致的条件. 由于该误差轨迹只需设置一个常数项, 因而能够有效减少计算量, 使得期望误差轨迹的设计更为简单. 其次, 考虑机械臂运行区间随迭代次数变化的问题, 构建虚拟误差变量补偿机制, 通过定义虚拟误差变量对未运行区间进行信息补偿, 放宽经典迭代学习控制的迭代长度不变条件. 在此基础上, 基于Lyapunov-like理论设计迭代学习控制器和全限幅学习律, 实现机械臂关节位置在指定区间上跟踪给定的期望轨迹和保证未知参数估计值的有界性. 最后, 仿真结果验证了所提方法的有效性.Abstract: In this paper, an error-tracking iterative learning control (ILC) scheme with iteration varying length is proposed for the trajectory tracking of robot manipulators with arbitrary initial shifts. Firstly, a hyperbolic cosine-shaped desired error trajectory independent of the desired trajectory is constructed to relax the identical initial condition requirement in traditional iterative learning control. In the presented desired error trajectory, only one constant parameter needs to be set in prior, such that the computation can be reduced, and the design of the desired error trajectory becomes simpler. Then, the problem that the operating range of the robot manipulator varies with the number of iterations is investigated, and an error compensation mechanism is established to compensate for the error information of the non-operation intervals by defining virtual error variables. Consequently, the identical iterative length condition in traditional iterative learning control can be relaxed. Based on the Lyapunov-like theory, an iterative learning controller and a fully saturated learning law are designed to guarantee that the joint position of the robot manipulator could track the given desired trajectory in the specified interval and the boundedness of the estimation of the unknown parameters, respectively. Numerical simulation results are provided to demonstrate the effectiveness of the proposed scheme.
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图 3 关节位置$q_{11,k}$和期望位置信号$q_{d1}$
Fig. 3 Joint position $q_{11,k}$ and desired position signal $q_{d1}$
图 11 关节位置误差$\tilde q_{12,30}$收敛过程对比
Fig. 11 The comparison of the error $\tilde q_{12,30}$ convergence processes
图 4 关节位置$q_{12,k}$和期望位置信号$q_{d2}$
Fig. 4 Joint position $q_{12,k}$ and desired position signal $q_{d2}$
图 5 误差轨迹$\tilde q_{11,k}$ 和期望误差轨迹$\tilde q_{11,k}^*$
Fig. 5 Error trajectory $\tilde q_{11,k}$ and desired error trajectory $\tilde q_{11,k}^*$
图 6 误差轨迹$\tilde q_{12,k}$和期望误差轨迹$\tilde q_{12,k}^*$
Fig. 6 Error trajectory $\tilde q_{12,k}$ and desired error trajectory $\tilde q_{12,k}^*$
图 8 关节位置$q_{11,k}$跟踪性能对比
Fig. 8 The comparison of joint position $q_{11,k}$ tracking performance
图 9 关节位置$q_{12,k}$跟踪性能对比
Fig. 9 The comparison of joint position $q_{12,k}$ tracking performance
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