Abstract: Due to the diversity of work requirements and environment, the number of degrees of freedom (DOFs) and the complexity of structure of industrial robots are constantly increasing. It is difficult to establish the accurate dynamical model of industrial robots, which greatly hinders the realization of a stable, fast and accurate trajectory tracking control. Therefore, the general expression of the constraint relation in the explicit dynamic equation of the multi-DOF industrial robot is derived on the basis of solving the Jacobian matrix and Hessian matrix by using the kinematic influence coefficients method. Moreover, an explicit dynamic equation with general constraint relation expression is established based on the Udwadia-Kalaba theory. The problem of increasing the time of establishing constraint relationship when the multi-DOF industrial robots complete complex task constraints is solved. With the SCARA robot as the research object, the simulation results show that the proposed method can provide a new idea for industrial robot system modeling with complex constraints.

Key words: industrial robot, constraint relationship, kinematic influence coefficients method, Jacobian matrix, Hessian matrix

摘要： 工作要求和环境的多样性使得工业机器人的自由度数和结构复杂性不断增加，难以建立其精确的动力学模型，对实现稳定、快速、准确的轨迹跟踪控制造成很大的阻碍。因此，在利用运动学影响系数法求解Jacobian矩阵和Hessian矩阵的基础上，推导了多自由度工业机器人解析动力学方程中约束关系的一般表达式，建立了基于Udwadia-Kalaba理论的含一般约束关系表达式的解析动力学方程，从而解决了多自由度工业机器人在完成复杂任务约束时增加约束关系建立时间的问题。以SCARA机器人为研究对象，仿真结果表明：该方法为复杂约束条件下的工业机器人系统建模提供了一种新的思路。

关键词: 工业机器人，约束关系，影响系数法，Jacobian矩阵，Hessian矩阵