This paper presents the mathematical modeling and optimal trajectory tracking control of a 3-degree-of-freedom parallel manipulator, commonly known as Maryland manipulator. Three unlike sequential trajectories are considered, and the trajectory-tracking control of a manipulator is performed by the LQR-PID controller. The tuning of LQR-PID is done by using the Grey Wolf Optimizer (GWO), a meta-heuristic method. The two other traditional benchmarking algorithms are Particle Swarm Optimizer (PSO) and Genetic Algorithm (GA). The main goal of this work is to calculate the optimum values of LQR gain parameters i.e. Q and R matrices and PID controller’s gains i.e. K_p, K_i and K_d using three different optimization algorithms, and their performance comparisons are highlighted in simulation results and discussion section. According to the obtained simulation results, the proposed GWO methodology is more efficient and more accurate in trajectory tracking control and generates optimal torques to the input links of the manipulator when compared with other evolutionary optimization algorithms such as PSO and GA.

本文介绍了三自由度并联机械臂（俗称马里兰机械臂）的数学建模和最优轨迹跟踪控制。考虑三种不同的顺序轨迹，并由 LQR-PID 控制器执行机械臂的轨迹跟踪控制。LQR-PID 的调整是通过使用灰狼优化器 (GWO)（一种元启发式方法）来完成的。另外两种传统的基准测试算法是粒子群优化器（PSO）和遗传算法（GA）。这项工作的主要目标是计算 LQR 增益参数（即 Q和R矩阵）和 PID 控制器增益（即 K _p、K _i和K _{d ）的最佳值}使用三种不同的优化算法，仿真结果和讨论部分重点介绍了它们的性能比较。根据获得的仿真结果，与PSO和GA等其他进化优化算法相比，所提出的GWO方法在轨迹跟踪控制方面更高效、更准确，并且可以为机械臂的输入链路生成最佳扭矩。