基于深度神经网络逆动力学补偿与在线自适应的机械臂高精度轨迹跟踪控制

High-Precision Trajectory Tracking Control of Robotic Manipulators Based on Inverse Dynamics Compensation with Online Adaptation of Deep Neural Network

摘要: 机械臂动力学模型中的摩擦、负载变化等不确定因素是制约其轨迹跟踪精度的核心瓶颈。针对该问题，本文提出一种“离线深度学习逆动力学前馈补偿 + 在线递推最小二乘(RLS)末层自适应”的复合控制框架。首先，通过多正弦持续激励轨迹在闭环条件下采集约15.6万组状态–力矩样本，训练多层感知机(MLP)逆动力学模型；随后，将学习得到的前馈力矩与低增益PD反馈复合，构成NN-FF控制器；进一步利用RLS在线更新网络末层权重，形成对负载突变具有自适应能力的ANN-FF控制器。在二自由度机械臂高保真数值仿真平台上的系统实验表明：学习模型的力矩预测均方根误差为0.087 ± 0.004 N·m，较名义刚体模型(1.00 N·m)降低约91%~92% (R² > 0.998)；在六种测试轨迹上，NN-FF的平均任务空间跟踪RMSE为0.49 mm，较PID (14.86 mm)与计算力矩法(7.85 mm)分别提升约30.5倍与16.1倍；面对1.0 kg负载突变，ANN-FF在约3~4 s内完成末层权重的主要重新整定，稳态误差降至1.01 mm，较冻结模型(5.49 mm)降低约82%。ANN-FF单步摊销计算耗时约160 μs，满足1 kHz实时控制要求。研究结果为数据驱动的机械臂高精度控制提供了一条兼顾精度、鲁棒性与实时性的可行途径。

Abstract: Uncertainties such as friction and payload variation in the dynamic model of a robotic manipulator are the core bottleneck limiting its trajectory-tracking accuracy. To address this problem, this paper proposes a composite control framework combining “offline deep-learning inverse-dynamics feedforward compensation + online recursive least-squares (RLS) output-layer adaptation”. First, approximately 156,000 state-torque sample pairs were collected under closed-loop conditions using multi-sine persistently exciting trajectories, and a multilayer perceptron (MLP) inverse-dynamics model was trained on these data. The learned feedforward torque was then combined with a low-gain PD feedback loop to form the NN-FF controller. RLS was further employed to update the network’s output-layer weights online, yielding an ANN-FF controller capable of adapting to sudden payload changes. Systematic experiments on a high-fidelity numerical simulation platform of a 2-DOF manipulator show that the learned model achieves a torque-prediction RMSE of 0.087 ± 0.004 N·m, a reduction of approximately 91%~92% relative to the nominal rigid-body model (1.00 N·m), with R² > 0.998. Across six test trajectories, NN-FF achieves a mean task-space tracking RMSE of 0.49 mm, representing improvements of approximately 30.5-fold and 16.1-fold over PID (14.86 mm) and computed-torque control (7.85 mm), respectively. Under a sudden 1.0 kg payload change, ANN-FF completes the main readjustment of its output-layer weights within approximately 3~4 s, with the steady-state error settling at 1.01 mm—a reduction of about 82% compared with the frozen model (5.49 mm). The amortized per-step computation time of ANN-FF is approximately 160 μs, satisfying the requirements of 1 kHz real-time control. These results provide a feasible pathway for data-driven high-precision manipulator control that balances accuracy, robustness, and real-time performance.