拖动示教技术操作简便且效率高，更符合现代化的柔性生产，而实现工业机器人的拖动示教需要准确地测量外力与控制由外力所引起的关节运动。为了实现免力矩传感器测量操作者施加的外力，设计一种基于扰动卡尔曼滤波的外力观测器。该观测器通过将关节外力矩作为扰动项，并引入广义动量，建立机器人系统的状态空间方程，进而采用卡尔曼滤波算法得到关节外力矩的最优观测值。其中，为了提高外力的估计精度，提出以刚体动力学模型和深度神经网络相结合的方式建立机器人的动力学模型，该方法不仅避免了关节摩擦力矩的复杂建模过程，而且将模型中未建模的因素通过深度神经网络进行补偿。为了实现机器人在拖动示教过程中的牵引控制，将机器人的关节运动与外力矩之间的动态响应关系等效为一个质量阻尼系统，并提出一种自适应阻尼的导纳控制方法，将观测到的外力矩转换成示教运动的期望关节转角，并根据外力矩的变化趋势自适应地调整系统阻尼参数，以改善机器人的示教效果。实验表明，所建立的动力学模型在预测力矩上具有更低的均方根误差，可减小不少于20%的误差；采用所提出的控制方案在六自由度的工业机器人上实现了免力矩传感器的拖动示教，自适应阻尼调整方法能减少约19%的关节启动力矩，更有利于机器人示教运动的启停。

The dragging teaching method is easy to operate and has high teaching efficiency, which is more in line with modern flexible production. To realize the dragging teaching of industrial robots, it is necessary to accurately measure the external force and control the motion caused by the external force. In order to measure the external force exerted by the operator without torque sensor, an external force observer based on disturbance Kalman filter was designed. The observer takes the external joint torque as the disturbance term, and introduces generalized momentum to establish the state space equation of the robot system, and then uses the Kalman filter algorithm to obtain the optimal observed value of the external torque. Among them, in order to improve the estimation accuracy, the robot dynamic model was established by combining the rigid-body dynamic model and a deep neural network, which not only avoids modeling the complex friction torque but also compensates for the unmodeled factors through the deep neural network. Besides, in order to realize the leading control of the robot in the process of dragging teaching, the dynamic response relationship between the teaching motion and the external torque is equivalent to a mass damping system. An admittance control method with adaptive damping was proposed to convert the observed external torque into the desired joint angle of the teaching motion, and adaptively adjust the system damping parameters according to the change trend of the external torque to improve the teaching effect of the robot. The experiment results show that the proposed dynamic model has a lower mean square root error in the prediction torque, which can reduce the error by no less than 20%. The proposed control scheme can realize the dragging teaching without torque sensors on the six-degree-of-freedom industrial robot, and the adaptive damping method can reduce the torque required to rotate the joint by about 19%, which is more conducive to the start and stop of the teaching motion.