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推导了具有运动约束的机器人的拉格朗日动力学方程，该方程中包含了广义约束力。广义约束力被表达为机器人系统状态变量和广义输入力的显函数，力信息由此获得，因此无须使用力传感器即可同时控制机器人的力和位置。利用动力学冗余度（广义输入力的数目大于广义约束力的数目），设计了基于广义逆矩阵的力与位置混合控制器。控制仿真结果表明，该控制方法具有较高的精度和较好的稳定性。
The Lagrangian kinetic equation of a robot with motion constraint is deduced, which contains the generalized binding force. Generalized binding is expressed as a explicit function of the state variables of the robot system and the generalized input force from which the force information is derived so that the force and position of the robot can be simultaneously controlled without the use of a force sensor. Utilizing the dynamics redundancy (the number of generalized input forces is larger than the number of generalized binding forces), a force-position hybrid controller based on generalized inverse matrix is designed. Control simulation results show that the control method has higher accuracy and better stability.