The joint deflection of robots in machining degrades product accuracy. Compliance error compensation has been investigated to reduce the static deflection of robotic machining. The challenge in compliance error compensation is accurately measuring the deflection or cutting force. External sensors have been used to measure them in robotic machining, but it is not practical. The authors proposed a nonlinear disturbance observer to indirectly measure the cutting force online in robotic machining in the previous study. The observer, however, needs to utilize the robot model that includes characteristics of high nonlinearity, uncertainty, and high dynamic variation for different robot postures. After investigating these challenges of modeling, this paper proposes a hybrid modeling approach combining a physics-based model with a new empirical friction model, and a data-driven model to accurately estimate the cutting force while minimizing the error of the robot's mathematical model. The joint torque calculated from the hybrid model can cover the effect of joints' postures and speeds on the varying dynamic in its workspace. Real-time optimization just before cutting is also proposed to adapt to the real-time joint's motion conditions. The experimental results from aluminum multi-axis cutting show that the estimated cutting force via the nonlinear disturbance observer based on the proposed hybrid modeling approach can improve its accuracy up to 45% and 74% in the x and y directions respectively, compared to the physics-based modeling approach. The deflection of the tool center point can be compensated by using a compliance error compensation method up to 79.1% and 75.4% in the x and y directions, respectively, at 0.5 mm/s feed rate, and up to 77.2% and 78.9% at 3 mm/s feed rate. Consequently, the approaches developed in this paper can solve the problems of conventional robot modeling and improve the accuracy of robot machining.

中文翻译：

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非线性干扰观测器中的混合模型，用于改进机器人加工的柔度误差补偿


机械加工中机器人的关节偏转会降低产品精度。已经研究了柔度误差补偿以减少机器人加工的静态偏转。柔度误差补偿的挑战是准确测量偏转或切削力。在机器人加工中，外部传感器已被用于测量它们，但这并不实用。在之前的研究中，作者提出了一种非线性干扰观测器来间接在线测量机器人加工中的切削力。然而，观察者需要利用机器人模型，该模型包括不同机器人姿势的高非线性、不确定性和高动态变化的特性。在研究了建模的这些挑战之后，本文提出了一种混合建模方法，将基于物理的模型与新的经验摩擦模型和数据驱动模型相结合，以准确估计切削力，同时最大限度地减少机器人数学模型的误差。从混合模型计算的关节扭矩可以涵盖关节姿势和速度对其工作空间中变化动态的影响。还提出了切割前的实时优化，以适应实时接头的运动条件。铝多轴切割的实验结果表明，与基于物理的建模方法相比，基于混合建模方法的非线性扰动观测器估计的切削力可以将其在 x 和 y 方向上的精度分别提高 45% 和 74%。通过使用柔度误差补偿方法，可以补偿刀具中心点的偏斜，在 0.5 mm/s 进给速率下，x 和 y 方向上分别高达 79.1% 和 75.4%，在 3 mm/s 进给速率下高达 77.2% 和 78.9%。 因此，本文开发的方法可以解决传统机器人建模的问题，提高机器人加工的精度。