三自由度机械臂运动学分析与轨迹规划算法研究

Study on Kinematics Analysis and Trajectory Planning Algorithm of Three Degrees of Freedom Manipulator

为实现三自由度机械臂运动控制,采用D-H参数法建立运动学模型,运用机械臂的齐次变换矩阵,求得运动学正解;对比代数法和几何法求运动学逆解的优劣,采用一种三自由度机械臂逆运动学求解的几何法,避开多解性问题。运用Bresenham插补算法,在笛卡尔空间坐标系中对机械臂进行轨迹规划,最后通过Matlab Robotic Tool仿真分析,得到各关节的位移、速度和加速度随时间变化曲线,并验证算法的准确性。该方法可为其他多关节机器人动力学和轨迹规划等研究提供理论分析和依据。

In order to realize the three-degree-of-freedom manipulator motion control,a kinematics model was established using the DH parameter method,and the kinematics positive solution was obtained by using the homogeneous transformation matrix of the manipulator;the advantages and disadvantages of the inverse kinematics solution were compared by the algebraic method and the geometric method.A geometric method for inverse kinematics of a three-degree-of-freedom manipulator solves the problem of multiple solutions.The Bresenham interpolation algorithm was used to traject the trajectory of the manipulator in the Cartesian space coordinate system.Finally,the displacement,velocity and acceleration curves of each joint were obtained by Matlab Robotic Tool simulation,and the accuracy of the algorithm was verified.This method can provide theoretical analysis and basis for other multi-joint robot dynamics and trajectory planning research.