Abstract
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.
Highlights
The precise dynamic model of a robot is an important step to achieve high performance robot control [1]
AL-Dois et al [7] presented a comprehensive study of dynamic performance of serial robot manipulator where they presented a numerical example for PUMA 560 as an illustrative case, the kinematic manipulability and dynamic manipulability as end effector performance are measured
In this work; motion control of a three link robot arm with spherical wrist as shown in Figure (1) is done by two stage the first one is a trajectory planning by specifying the cartesian positon and orientation of the end effector and transform this via points to joint space by application of inverse dynamic the cubic polynomials are generated for each interval of time by using cubic spline interpolation, the second stage is the trajectory tracking by applying two type of controller computed torque control (CTC) and the simpler form of its PD +G using MATLAB Simulink where the resulted joint response was inverted to cartesian space again by the forward kinematic transformation matrix
Summary
The precise dynamic model of a robot is an important step to achieve high performance robot control [1]. In this work; motion control of a three link robot arm with spherical wrist (six DOF) as shown in Figure (1) is done by two stage the first one is a trajectory planning by specifying the cartesian positon and orientation of the end effector and transform this via points to joint space by application of inverse dynamic the cubic polynomials are generated for each interval of time by using cubic spline interpolation, the second stage is the trajectory tracking by applying two type of controller CTC and the simpler form of its PD +G using MATLAB Simulink where the resulted joint response was inverted to cartesian space again by the forward kinematic transformation matrix. The paper is organized sequentially as follow: manipulator forward and inverse kinematic, dynamic modelling, trajectory planning, controller design, result and discussion and conclusions
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