This paper presents a general method for the trajectory planning of the redundant planar manipulator. The mathematical relation between joint space and Cartesian space in a two-dimensional space is first derived. The joint classification is employed to obtain the solutions of corresponding joints. It divides joints into class I redundant joints, class II redundant joints, and nonredundant joints. The new application of knot points in the quintic B-spline curve is introduced to generate inverse solutions of class I redundant joints. Examples show that the number and distribution of knot points have a large effect on their solutions. Moreover, the particle swarm optimization algorithm is extended to generate solutions of class II redundant joints. It also optimizes the initial trajectories of joints and end-effector. Finally, solutions of nonredundant joints can be generated by the derived relation between the joint space and Cartesian space. The proposed methodology is confirmed by a case study. Under the same conditions, results show that the solution obtained by the extended method is not only better than that obtained by the particle swarm optimization algorithm but also closer to the global optimal solution.

中文翻译：

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基于联合分类和粒子群算法的冗余平面机械臂轨迹规划

本文提出了一种冗余平面机械臂轨迹规划的通用方法。首先推导了二维空间中关节空间与笛卡尔空间之间的数学关系。关节分类用于获得相应关节的解。它将关节分为I类冗余关节，II类冗余关节和非冗余关节。介绍了五点B样条曲线中结点的新应用，以生成I类冗余关节的反解。实例表明，结点的数量和分布对其解有很大影响。此外，将粒子群优化算法扩展为生成II类冗余关节的解。它还优化了关节和末端执行器的初始轨迹。最后，通过关节空间与笛卡尔空间之间的导出关系，可以生成非冗余关节的解。案例研究证实了所提出的方法。在相同条件下，结果表明，扩展方法得到的解不仅比粒子群优化算法得到的解更好，而且更接近全局最优解。