A geometric method for kinematics of delta robot and its path tracking control

Abstract

This paper presents a geometric method for solving the inverse and forward kinematics of Delta robot, and then investigated the problem of path tracking control. The forward kinematics is most commonly solved by various iterative methods, which may suffer from slow convergence rate and strict initial value conditions. In this paper, this problem is simplified as solving the intersection point of two circles and then transforming the coordinates system to get the final solution. This method has advantages in its simplicity, accuracy and efficiency. Based on the solution to kinematics and the derivation of Jacobian matrix, the path tracking control is studied from two parts: the superior trajectory planning and the lower control system. Trajectory planning aims to define a temporal motion law along a given geometric path. A method for trajectory planning is presented which is based on a modified trapezoidal velocity profile (TVP) of which initial and final velocities could be nonzero depending on its movement model, whether continuous path (CP) or point to point (PTP). A velocity control method is proposed using a nonlinear PD controller to ensure the end effector tracking the desired path with high precision. At last, a demo trajectory is generated to verify the feasibility of the method experimentally.