具有模型不确定性的冗余机器人数据驱动模型预测控制

唐进福; 金龙

doi:10.12263/DZXB.20260604

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具有模型不确定性的冗余机器人数据驱动模型预测控制

更新时间：2026-07-29

- 具有模型不确定性的冗余机器人数据驱动模型预测控制
- Data-Driven Predictive Control of Redundant Robots Under Model Uncertainty
- 电子学报 2026年页码：1-10
- 作者机构：
  
  1.兰州大学信息科学与工程学院，甘肃兰州 730000
  2.兰州理工大学自动化与电气工程学院，甘肃兰州 730050
- 作者简介：
  
  唐进福男，2002年出生于江西省赣州市。现为兰州大学硕士研究生。主要研究方向为机器人与模型预测控制。 E-mail: tangjf2024@lzu.edu.cn
  金龙男，1988年12月出生于甘肃省兰州市。现为兰州大学人工智能学院教授。主要研究方向为智能计算与机器人。 Email: jinlong@lzu.edu.cn
- 基金信息：
  
  国家自然科学基金(62476115)
- DOI：10.12263/DZXB.20260604
  中图分类号： TP399;
- 收稿：2026-06-16，
  
  录用：2026-07-13，
  
  网络首发：2026-07-29，
- 稿件说明：
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唐进福, 金龙. 具有模型不确定性的冗余机器人数据驱动模型预测控制[J/OL]. 电子学报, 2026,1-10.

TANG Jinfu, JIN Long. Data-Driven Predictive Control of Redundant Robots Under Model Uncertainty[J/OL]. ACTA ELECTRONICA SINICA, 2026, 1-10.
唐进福, 金龙. 具有模型不确定性的冗余机器人数据驱动模型预测控制[J/OL]. 电子学报, 2026,1-10. DOI： 10.12263/DZXB.20260604.

TANG Jinfu, JIN Long. Data-Driven Predictive Control of Redundant Robots Under Model Uncertainty[J/OL]. ACTA ELECTRONICA SINICA, 2026, 1-10. DOI： 10.12263/DZXB.20260604.

摘要

针对具有运动学模型不确定性以及关节角度、速度和加速度等多重物理约束的冗余机器人轨迹跟踪问题，本文提出一种数据驱动模型预测控制（Model Predictive Control，MPC）方法。现有速度级或加速度级控制方法通常依赖精确解析模型，并将不同层级的约束保守地转换到同一决策层，容易引入额外参数并压缩机器人实际可行域。为此，本文基于冗余机器人的速度级运动学关系构建滚动预测模型，在MPC优化问题中直接施加关节位置、速度和加速度边界，使各类约束按照其原始物理含义参与求解。针对制造装配误差、机械磨损和末端工具变化造成的雅可比矩阵未知或时变问题，设计完全由实时关节速度与末端速度数据驱动的雅可比矩阵在线学习律，并通过有界随机激励增强输入数据的方向丰富性，使估计矩阵在缺少精确几何参数和离线标定模型时仍能持续更新。进一步地，将MPC方案转化为带线性不等式约束的二次规划（Quadratic Programming，QP）问题，根据Karush-Kuhn-Tucker最优性条件构造神经动力学（Neural Dynamics，ND）求解器，以连续状态演化在线获得最优控制信号。该求解器主要由向量运算构成，并可利用上一采样时刻的系统状态作为当前求解初值，适合参数连续变化的滚动优化过程。理论分析给出了雅可比矩阵学习误差的收敛性，并基于李雅普诺夫方法证明ND求解器误差系统的全局渐近稳定性和指数收敛特性。本文在7自由度Franka Emika Panda机器人上开展仿真、同条件对比和实机绘图实验。结果表明：在初始雅可比矩阵设为零的情况下，所提方法仍能使估计误差快速趋近于零，机器人稳定跟踪期望轨迹，关节角度、速度与加速度始终满足各自的物理边界；与现有数据驱动学习方法相比，该方法能够更有效地抑制关节速度抖振并提高轨迹跟踪精度。以1 kHz频率执行的实机实验进一步验证了所提方法在未知结构参数条件下的实时性和工程可行性。

Abstract

To address the trajectory-tracking problem of redundant robots subject to kinematic model uncertainty and multiple physical constraints on joint angles

velocities

and accelerations

this paper proposes a data-driven model predictive control (MPC) method. Existing velocity-level or acceleration-level control methods generally rely on accurate analytical models and conservatively convert constraints at different levels to a single decision level

which can introduce additional parameters and reduce the actual feasible region of the robot. To overcome these limitations

a receding-horizon prediction model is constructed based on the velocity-level kinematic relationship of the redundant robot. The bounds on joint positions

velocities

and accelerations are directly imposed in the MPC optimization problem

allowing each type of constraint to participate in the optimization according to its original physical meaning. To handle an unknown or time-varying Jacobian matrix caused by manufacturing and assembly errors

mechanical wear

and changes in end tools

an online Jacobian learning law fully driven by real-time joint-velocity and end-effector-velocity data is designed. Bounded random excitation is introduced to enhance the directional richness of the input data

enabling the estimated Jacobian matrix to be continuously updated without accurate geometric parameters or an offline calibration model. Furthermore

the MPC formulation is transformed into a quadratic programming (QP) problem with linear inequality constraints. Based on the Karush-Kuhn-Tucker optimality conditions

a neural dynamics (ND) solver is constructed to obtain the optimal control signal online through continuous state evolution. The solver mainly consists of vector operations and can use the state at the previous sampling instant as the initial state of the current solution

making it suitable for receding-horizon optimization with continuously varying parameters. Theoretical analysis establishes the convergence of the Jacobian learning error. The global asymptotic stability and exponential convergence of the error system of the ND solver are also proved using the Lyapunov method. Simulations

comparative simulations under identical conditions

and real-robot drawing experiments are conducted on a seven-degree-of-freedom Franka Emika Panda robot. The results show that

even when the initial Jacobian estimate is set to zero

the proposed method can rapidly drive the estimation error toward zero

enable the robot to stably track the desired trajectory

and keep the joint angles

velocities

and accelerations within their respective physical bounds throughout the task. Compared with an existing data-driven learning method

the proposed method more effectively suppresses joint-velocity chattering and improves trajectory-tracking accuracy. The real-robot experiment performed at a frequency of 1 kHz further verifies the real-time performance and engineering feasibility of the proposed method under unknown structural parameters.

关键词

Keywords

references

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