Error compensation of collaborative robot dynamics based on deep recurrent neural network
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摘要: 由于協作機器人的結構比普通工業機器人更為輕巧，一般動力學模型所忽略的復雜特性占比較大，導致協作機器人的計算預測力矩誤差較大。據此提出在考慮重力、科里奧利力、慣性力和摩擦力等的基礎上，采用深度循環神經網絡中的長短期記憶模型對自主研發的六自由度協作機器人動力學模型進行誤差補償。在實驗中采用優化后的基于傅里葉級數的激勵軌跡驅動機器人運動，以電機電流估算關節力矩，獲取的原始數據用來訓練長短期記憶模型(LSTM)補償網絡。網絡的訓練結果和評價指標為預測力矩相比實際力矩的均方根誤差。計算與實驗結果表明，補償后的協作機器人動力學模型對實際力矩具有更好的預測效果，各軸預測力矩與實際力矩的均方根誤差相比于未補償的傳統模型降低了61.8%至78.9%不等，表明了文中所提出補償方法的有效性。Abstract: Establishing the dynamics model of robot and its parameters is significant for simulation analysis, control algorithm verification, and implementation of human–machine interaction. Especially under various working conditions, the errors of the calculated predicted torque of each axis have the most direct negative effect. The general robot dynamics model rarely takes the minor and complex characteristics into consideration, such as the reducer flexibility, inertia force of motor rotors, and friction. However, as the structure of collaborative robots is lighter and smaller than the ordinary industrial robots, the characteristics neglected by general dynamics models account for a relatively large amount. The above facts result in a large error in the calculation and prediction of collaborative robots analysis. To address the short comings of general robot dynamics model, a network based on long short-term memory (LSTM) in deep recurrent neural network was proposed. The network compensates the general dynamics model of a self-developed six-degree-of-freedom collaborative robot based on the consideration of gravity, Coriolis force, inertial force, and friction force. In the experiment, the nondisassembly experimental measurement combined with least-squares method was used to identify the parameters. The motor current was used to evaluate the joint torque instead of mounting an expensive and inconvenient torque sensor. The excitation trajectory based on the Fourier series was optimized. The raw experimental data were used to train the proposed LSTM network. About the accuracy of the dynamic model and the compensation method for the collaborative robot, the root-mean-square error of the calculated torque relative to the actual measured torque was used to train the network and evaluate the proposed method. The analysis and the results of the experiment show that the compensated collaborative robot dynamics model based on LSTM network displays a good prediction on the actual torque, and the root-mean-square error between predicted and actual torques is reduced from 61.8% to 78.9% compared to the traditional model, the effectiveness of the proposed error compensation policy is verified.
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圖 3 參數辨識所用激勵軌跡。（a）位移；（b）速度；（c）加速度
Figure 3. Excitation trajectory for parameter identification: (a) position; (b) velocity; (c) acceleration
圖 6 測試集的激勵軌跡。（a）位移；（b）速度；（c）加速度
Figure 6. Excitation trajectory of test set: (a) position; (b) velocity; (c) acceleration
圖 8 軸5計算力矩（未經補償）、實際力矩和誤差
Figure 8. Calculated torque (uncompensated), real toruqe, and errors of axis-5
圖 9 軸5經過LSTM網絡補償后的計算力矩、實際力矩和誤差
Figure 9. Calculated torque with LSTM compensation, real torque, and errors of axis-5
表 1 網絡主要超參數值
Table 1. Hyperparameters of the net
Parameter Value Time step 100 Batch size 50 Input size 12 Output size 3 Cell size 60 Total layer 3 Learning rate 0.05 
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表 2 各關節計算力矩相對實際力矩的均方根誤差
Table 2. RMS error of calculated torque between real value
Axis Uncompensated/(N·m) Compensated/(N·m) 4 3.61 1.21 5 4.84 1.02 6 6.10 2.33
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