الفهرس 
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Abstract
Over the past few years, vast advancements in technology have occurred through- out multiple industrial revolutions. One of the most important advancements is the use of robotic solutions in the industrial field due to the robots’ accuracy and repeatability to be used in various industrial tasks. As the industrial tasks are considered to have a boosting level of complexity that could not be performed by a single robot, multi-robot systems have gained extensive interest for their ability to handle larger workload and accomplish more complex industrial tasks.
Thus, the main focus of the study is to develop a collaborative robot system ar- chitecture that consists of more than one six degrees of freedom (DoF) robotic manipulator coordinating with each other to jointly manipulate a rigid object to a desired position while tracking several designed trajectories. Firstly, the col- laborative robotic system is modeled as the kinematic and dynamic equations of each robotic manipulator are derived. In addition, the collaborative system kine- matic chain constraints are considered taking into account the dimensions of the handled object, the robots grasping locations and the type of grasping. Secondly, the control procedure is performed utilizing two different control algorithms which are then evaluated and compared in terms of the trajectory tracking accuracy of the manipulated object, the joint angles’ convergence errors and the acceptable control effort of the joints’ actuators for each robotic manipulator.
The controllers used are a decentralized linear parallel Proportional-Integral (PI) control and Computed Torque Control (CTC) used to handle the motion of each robotic system solely. The decentralized linear parallel PI control composes of separate PI control block each of which is used to manage each joint separately taking into account the robot’s forward and inverse kinematic equations of mo- tion to control the robot’s end effector’s position leading the center of mass of the manipulated object to track the desirable designed trajectory. The CTC is designed to control the torques of each robot’s actuators taking into account the robot dynamics equations of motion. The performance of the controllers are tested on two different trajectories; the straight line trajectory and the sine wave trajec- tory. It is observed that the PI controller is better in terms of trajectory tracking convergence and joint angles’ error convergence in performing the straight line track compared to the computed torque algorithm. However, using constant PI gains and changing the desirable track, the error in tracking and in joint angles increased significantly. In the contrary, despite the larger errors of the CTC com- pared of that of PI control, when changing the shape of the task space trajectory
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and changing the initial conditions of the robots’ end effectors, the response does not change which means that the error does not increase based on the desirable track.
This gives the CTC an edge over the linear PI controller. The control effort which is represented as the torques of each robot’s joints is considered to be adequate following the actuator and gear system torque limits with a smooth behaviour to avoid damaging the motors. Furthermore, a sensor model is attached to the manipulated object to be able to estimate the position of the center of mass of the object to be used in real system. The sensor used is the Inertial Measurement Unit (IMU) sensor which is decomposed of Gyroscope and Accelerometer sensors. As the sensors are noisy, thus Kalman filter is used to filter and fuse the sensor readings. The results of the sensing element indicated the presence of bias and drift noises which can be removed by fusing other sensor in addition to the IMU or by subtracting the constant and known bias from the sensor for more accurate sensing. Finally, the collaborative system control performance is further visual- ized to verify and validate the algorithms through MATLAB/Simulink Simscape Multibody tool.