IOSR Journal of Engineering (IOSRJEN) ISSN (e): 2250-3021, ISSN (p): 2278-8719 Vol. 05, Issue 05 (May. 2015), ||V3|| PP 25-31
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Simulation of non-linear computed torque control on Simulink for two link Scara type manipulator Edip OZTURK1,Ibrahim H.GUZELBEY2, Ahmet SUMNU3 1 2
Mechanical Engineering Dept., Gaziantep University, TURKIYE (Undergraduate student Edip OZTURK) Faculty of Aeronautics and Aerospace,Gaziantep University, TURKIYE (Prof.Dr. Ibrahim H. GUZELBEY) 3 Faculty of Aeronautics and Aerospace, Gaziantep University, TURKIYE (Res.AsstAhmet SUMNU)
Abstract:- In this study, inverse kinematic analysis, dynamic analysis and non-linear computed torque control of two link Scara type manipulator are considered. Trajectory is planned in operational space coordinates and transformed into joint space coordinates by inverse kinematic equations. Equations of motion are obtained by solving Lagrange equations. Model is simulated on Simulink/đ?‘€đ??´đ?‘‡đ??żđ??´đ??ľ ÂŽ with a pick and place operation. Key words: Manipulator Dynamics, Simulation, ScaraManipulator, Torque Control I. INTRODUCTION Robotic manipulators copy human arm in industrial applications such as pick and place,carry parts,welding operations,etc. Scara (Selective Compliance Articulated Robotic Arm) was developed by Professor Hiroshi Makino from University of Yamanashi and his team.Scara manipulator is free to move horizontal plane and its vertical motion is restricted[1] and [2]. Since Scara is the direct driven manipulator, joints are needed to be controlled directly by actuators. In order to achieve desired end-effector position,velocity and acceleration, operational space position,velocity and acceleration need to be transform into joint space[3]. This transformation is done with inverse kinematic equation which are presented in section(2). Equations of motion of a robotic manipulators can be obtained by using Lagrange-Euler method or Newton-Euler method. Since those equations identify the physical behavior of robotic manipulator, these equations are used to simulate and analysis manipulator. These equations are also used to solve forward and inverse dynamics problems. In forward dynamics case, applied torques/forces are given and joint accelerations are found. Integrating accelerations joint velocities and positions are found. In inverse dynamic case, joint positions,velocities and accelerations are given and joint torques/forces are found. In section(3), dynamic equations of manipulator which are found using Lagrange-Euler method are presented. Robotic manipulators are designed to do given task. Task planning and due to that task joint trajectory generation is essential in robotics. In section(4), an artificial pick and place task and due to this task joint trajectories are generated. A joint trajectory includes joint position, velocity and acceleration. Task of the controller is sensing information from controlled plant and improving its performance. This plant can be linear or non-linear[4]. While designing control systems stability, good disturbance rejection and tracking trajectories with acceptable errors are indispensable requirements [5]. These requirements can be provided by linear controllers for slow operation in industry such as; laser cutting, welding processes. In this type control system every joint is controlled as a single input,single output system(SISO) and coupling effects are considered as disturbances. But, this method can’t give satisfactory results at high speeds. In this case, computed torque controller(CTC) is a good solution. The principle of CTC is feedback linearization and it uses the non-linear feedback control law to calculate required joint torques. To get good performance by using CTC, all dynamic and physical parameters are needed to be well known[6]. In section(5), CTC for Scara type manipulator is presented.
II.
INVERSE KINEMATICS OF MANIPULATORS
Inverse kinematics analysis can be expressed as, obtaining joint variables by using Cartesian space coordinates of end effector. Generally, trajectory which will be followed by end effector is known and for that trajectory, required joint variables acquired by inverse kinematics. Due to nonlinearities in kinematic equations, solving inverse kinematics problems more difficult and complicated than forward kinematic problems. In addition, there is no general solution method for inverse kinematics as differ than forward kinematics.
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