Simulation of joint position response of 60 kg payload 4-Axes SCARA configuration manipulator taking dynamical effects into consideration

The method of conventional control of a manipulator, without considering varying effects of robot dynamics, results in degraded response with unnecessary vibrations thus limiting the precision and speed of the end effector. As the column joint is subjected to worst dynamic conditions when all the axes are in motion, simulation of position response of column joint of a 60-Kg payload 4-axes SCARA type manipulator is presented by taking dynamical effect into consideration. The paper analyses dynamical effect on the basic control system by comparing the position response of the column joint, with and without considering the effects of robot dynamics, with PID controllers in the position as well as velocity loops as basic compensators. It has been found that dynamical effects on a SCARA type manipulator with a 60-Kg payload is very small and is suitable for pick and place type industrial applications. 1.0 Introduction The conventional approach of using only robot kinematics for trajectory path planning renders inadequate control of manipulator especially if the manipulator payload is high. Treating each joint of the robot arm as a simple joint servomechanism of a manipulator results in degraded response with unnecessary vibrations, limiting the precision and speed of the end-effector.[1] A method of dynamic compensation of the joint torque is presented along with a comparison of the position response of the system with and without considering dynamic model. The analysis is carried out by designing the control scheme of a 60 Kg payload SCARA type robot having 4 Degrees of Freedoms (DOFs). The robot can be controlled manually through control console / teach pendant or through the use of customised GUI in a supervisory computer. MATLAB’s SIMULINK is used as the simulation tool for designing the control scheme and for analysis of positional response of joint. 2.0 The Robot System: The photograph of the 4-axes robot manipulator with control console with specification given in Table 1 is shown in Fig. 1. Fig. 1 Manipulator with control console 3.0 Dynamic modeling: The well known dynamical equations of a manipulator is given in eq.(1).[1] For the sake of simplicity of analysis, the rotation i.e orientation of end-effector, is neglected because this joint does not contribute much to the overall dynamic effect on the column joint. From this relation, the dynamic torque equation for column or base axis of the manipulator, is given by eq.(2). In the equations, Jijk, for i = 1,..,4 ; j = 1,..,4 ; k = 1,..,4 represent elements of 4x4 pseudo-inertial matrices where the numbers 1,2,3 and 4 represents column, arm1, arm2 & end-effector respectively with sub-script notation representing correlation between two axes. Elements of inertia matrices are calculated using manipulator geometric configuration. In the analysis, the end-effector rotation θ4 is neglected. Elements of D matrix, h matrix and c matrix are calculated at each sample instant, corresponding to a defined straight-line path of end-effector by taking the reduction ratio into account, in order to reflect the dynamical torque on the column motor shaft. The schematic configuration of the manipulator is shown in Fig. 2. 2 D (t) = J1 + J2 + J3 + J3 l + J3 l + J3 l 11 11 44 11 413 143 4 4 3 + (J3 +J3 l )l S S + (J3 +J3 l )l C C 41 4 4 3 2 1 13 41 443 2 1 13 + J4 + {J4 (l S +l S ) + J4 (l S +l S )}S 11 11 3 13 2 1 14 3 13 2 1 134 + {J4 (l C +l C ) 11 3 13 2 1 where