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摘要: 为解决机器人动力学模型未知问题并提升系统鲁棒性，本文基于扰动观测器，考虑动力学模型未知的情况，设计了一种自适应神经网络（Neural network，NN）跟踪控制器.首先分析了机器人运动学和动力学模型，针对模型已知的情况，提出了刚体机械臂通用模型跟踪控制策略；在考虑动力学模型未知的情况下，利用径向基函数（Radial basis function，RBF）神经网络设计基于全状态反馈的自适应神经网络跟踪控制器，并通过设计扰动观测器补偿系统中的未知扰动.利用李雅普诺夫理论证明所提出的控制策略可以使闭环系统误差信号半全局一致有界（Semi-globally uniformly bounded，SGUB），并通过选择合适的增益参数可以将跟踪误差收敛到零域.仿真结果证明所提出算法的有效性并且所提出的控制器在Baxter机器人平台上得到了实验验证.Abstract: For solving uncertainties of robotic dynamics and improving system robustness, an adaptive neural network (NN) tracking control is proposed considering uncertainties of robotic dynamics. Firstly, the kinematic model and dynamic model of robots are addressed. When the dynamics of the robots are known, a model-based tracking control strategy is proposed. Then, considering that the robotic dynamics are unknown, an adaptive radial basis function (RBF) neural network tracking control is proposed based on full state feedback to solve uncertainties. Disturbance observer is designed to counteract to unknown disturbance. By utilizing the Lyapunov direct method and the back-stepping method, all error signals are shown to be semi-globally uniformly bounded (SGUB). By choosing proper parameters, the tracking error can converge to a small neighborhood of zero. Simulation results and experiment results on Baxter robot are carried out to show the effectiveness of proposed method.1) 本文责任编委 魏庆来
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图 1 3旋转关节自由度机器人Robotic toolbox中的模型
Fig. 1 Model of 3 revolute joint robot in robotic toolbox
图 6 关节1含扰动观测器和不加扰动观测器角度跟踪控制
Fig. 6 Joint 1 angle tracking control with and without disturbance observer
图 7 关节1含扰动观测器和不加扰动观测器速度跟踪控制
Fig. 7 Joint 1 velocity tracking control with and without disturbance observer
图 8 关节2含扰动观测器和不加扰动观测器角度跟踪控制
Fig. 8 Joint 2 angle tracking control with and without disturbance observer
图 9 关节2含扰动观测器和不加扰动观测器速度跟踪控制
Fig. 9 Joint 2 velocity tracking control with and without disturbance observer
图 10 关节3含扰动观测器和不加扰动观测器角度跟踪控制
Fig. 10 Joint 3 angle tracking control with and without disturbance observer
图 11 关节3含扰动观测器和不加扰动观测器速度跟踪控制
Fig. 11 Joint 3 velocity tracking control with and without disturbance observer
图 16 机器人系统结构: 1.肩$S_0$关节; 2.肩$S_1$关节; 3.肘$E_0$关节; 4.肘$E_1$关节; 5.腕$W_0$关节; 6.腕$W_1$关节; 7.腕$W_2$关节; 8.声纳传感器; 9.面部摄像头; 10.显示屏; 11.末端摄像头; 12.末端抓手; 13.操作旋钮; 14.柔性关节; 15.肩关节支撑弹簧; 16.吸盘
Fig. 16 The system structure of Baxter robot: 1. shoulder joint $S_0$; 2. shoulder joint $S_1$; 3. elbow joint $E_0$; 4. elbow joint $E_1$; 5. wrist joint $W_0$; 6. wrist joint $W_1$; 7. wrist joint $W_2$; 8. sonar sensor; 9. facial camera; 10. screen; 11. end-effector camera; 12. gripper; 13. operating knob; 14. flexible joint; 15. $S_1$ shoulder support spring; 16. sucker
表 1 Baxter机器人D-H参数和连杆质量
Table 1 D-H parameter and link mass of Baxter robot
Link $\theta$ $d$ (m) $a$ (m) $\alpha$ (rad) $m$ (kg) 1 $\theta_1$ 0.2703 0.069 $-\frac{\pi}{2}$ 5.70044 2 $\theta_2$ 0 0 $\frac{\pi}{2}$ 3.22698 3 $\theta_3$ 0.3644 0.069 $-\frac{\pi}{2}$ 4.31272 4 $\theta_4$ 0 0 $\frac{\pi}{2}$ 2.07206 5 $\theta_5$ 0.3743 0.01 $-\frac{\pi}{2}$ 2.24665 6 $\theta_6$ 0 0 $\frac{\pi}{2}$ 1.60979 7 $\theta_7$ 0.2295 0 0 0.54218 
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表 2 Baxter机器人PD控制参数
Table 2 PD control parameter of Baxter robot
Joint P D $S_0$ 50.01 2.5 $S_1$ 60 1.3 $E_0$ 15.1 2.5 $E_1$ 14 3 $W_0$ 25.2 3 $W_1$ 12 10 $W_2$ 12.3 10
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