二阶非完整平面3R欠驱动机械臂位置控制

Position control for planar 3R underactuated manipulator with second-order non-holonomic constraints

为解决中间关节是欠驱动的平面3R机械臂末端点位置控制问题,提出了一种基于轨迹规划与跟踪控制方法.根据系统数学模型、几何关系和期望位置,利用差分进化算法求解所有连杆的目标角度.首先,构造Lyapunov函数设计控制器使得第一、第三连杆到达目标角度;然后,根据系统约束关系,对第一连杆进行轨迹规划,并利用差分进化算法优化轨迹参数;当第一连杆跟踪轨迹后,第二连杆被间接控制到目标角度.最后,基于Lyapunov函数设计控制器使第一连杆跟踪规划轨迹,并维持第三连杆状态不变,使系统末端点从给定初始位置到给定期望位置.仿真实验表明,在33.94 s时,系统末端点能够稳定到目标位置(0.2,0.8) m,对于不同的初始位置和期望位置,轨迹规划与跟踪控制方法同样有效.

A method based on trajectory planning and tracking control was proposed to solve the end-point position control problem of a planar 3 R manipulator with a middle underactuated joint. According to the mathematical model of the system, the geometry relationships and the desired position, the target angles of all links were calculated by a differential evolution algorithm. Firstly, the controller designed by a Lyapunov function achieved the first and third links to the target angles. Then, according to the constraint of the system, a parametric trajectory was planned for the first link, and the suitable parameters of the trajectory were optimized by the differential evolution algorithm. After the first link tracked the trajectory, the second link was indirectly controlled to its target angle. Finally, based on the Lyapunov function, the controller was designed to make the first link track the planned trajectory and maintain the state of the third link unchanged, so that the end-point of the system is from the given initial position to the given desired position. The simulation experiments show that at 33.94 s, the end-point of the system can be stabilized to the target position(0.2, 0.8) m, and the trajectory planning and tracking control method is equally effective at different initial position and the desired position.