Motion Control of Three Links Robot Manipulator (Open Chain) with Spherical Wrist - Alwan, Hassan Mohammad; Rashid, Zaid Hikmat (Al-Khwarizmi Engineering Journal, 2019)
Robot manipulator is a multi-input multi-output system with high complex nonlinear dynamics, requiring an advanced controller in order to track a specific trajectory. In this work, forward and inverse kinematics are presented based on Denavit Hartenberg notation to convert the end effector planned path from cartesian space to joint space and vice versa where a cubic spline interpolation is used for trajectory segments to ensure the continuity in velocity and acceleration.  Also, the derived mathematical dynamic model is based on Eular Lagrange energy method to contain the effect of friction and disturbance torques beside the inertia and Coriolis effect. Two types of controller are applied ; the nonlinear computed torque control (CTC) and the simpler form of its Proportional Derivative plus Gravity (PD+G)  where they are designed to reduce the tracking trajectory errors which tend to zero where the used Kp and Kv gains are 900,60. Also, the RMS errors for tracking a step input of CTC were equal to  [2.5E-14, 4.4E-14, 5.0E-14, -4.7E-14, -3.9E-14, -4.6E-14] (deg) and of PD+G were equal to [-1.77E-5, -1.22E-6, -4.28E-6, -8.97E-6, -1.32E-5, 1.05E-5] (deg)  for joints one to six, respectively. The results show that CTC is more accurate but requires additional acceleration input and is more computationally extensive and PD+G controller is performed with acceptable tracking errors in manipulator position control applications.