研究了基于变形场不同离散方法的柔性机器人动力学建模和仿真问题。针对多杆空间链式柔性机器人系统，采用假设模态法、有限元法、Bezier插值方法和B样条插值方法对柔性杆变形场进行描述，构造统一形式，运用Lagrange方法，结合4×4齐次变换矩阵，在计入柔性杆横向弯曲变形引起的纵向缩短的情况下，推导得到多杆空间柔性机器人动力学方程，并编制基于4种变形场不同离散方法的多杆空间链式柔性机器人仿真软件。通过仿真算例对柔性机器人系统的动力学问题进行研究。仿真结果表明：有限元法的计算效率较低；假设模态法在处理较大变形问题时其精度低于Bezier插值方法和B样条插值方法的精度；作为新的变形体离散方法， Bezier插值方法和B样条插值方法可以有效地描述柔性杆的变形场，并能运用到多杆空间柔性机器人动力学建模中。%Dynamic modeling and simulation of flexible robots based on different discretization methods are investigated in this paper. Firstly, the physical model of flexible robots consisting of n links and n revolute joints is established. Secondly, the assumed mode method, finite element method, Bezier interpolation method and B-spline interpolation method are used to describe the deformation of the flexible link. Then, kinematics of both rotary-joint motion and link deformation is described by 4×4 homogenous transformation matrices, and the Lagrangian equations are used to derive the governing equations of motion of the system. The longitudinal deformation and the transverse deformation of the flexible link are considered, and the coupling term of the deformation which is caused by the transverse deformation is included in the total longitudinal deformation. Then, a software package for the dynamic simulation of the flexible robots based on the different discretization methods is developed, after that, the dynamic analysis for flexible robots are studied by three examples. The simulation results show that the computational efficiency of finite element method is the lowest, and the Bezier interpolation method and B-spline interpolation method are better than the assumed mode method in dealing with the large deformation dynamic problem. As new discretization methods, Bezier interpolation method and B-spline interpolation method can be used to describe the deformation of the flexible link, and they can be extended to the dynamic modeling for spatial flexible robots.
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