Paper Title
A New Way Points Tracking Controller for Industrial Manipulators

Robotics is a very active field that crosses the traditional boundaries of engineering. A robot manipulator is widely used in many industrial applications. Robotics manipulators present a complex area of study related to kinematics, dynamics, computer vision and control. The paper presents a mathematical model of a 2-DOF degrees-of-freedom robot manipulator using the Lagrangian equation of motion for controlling the motion of a robot, whose end-effector has to move along a given trajectory; the calculation procedure requires the user to define in analytical form or by waypoints the trajectory to be followed.Two-link robot manipulators are a very basic classical and simple example of robot followed in understanding of basics fundamentals of robotic manipulator. The 2-DOF robotic arm is a highly dynamic nonlinear system that requires complex methods of control. Control of robot manipulator for industrial applications is considered as one of the challenging tasks.In thiswork, presents a method for a control algorithm with dynamics for waypoint tracking of robot manipulators, whose end-effector has to move along a given trajectory; dealt with the problem of a waypoints tacking of a two degrees-of-freedom robot manipulator.The control design is applied to the waypoints tracking control of a robot manipulator. It is difficult to control worked robot manipulators because of changing many factors which effect on the system are especially such as the inertia moment of links in the robot manipulator. On the basis of the geometrical characteristics of the robot, a specifically developed program determines the motion laws of the actuators that enable the robot to generate the required movement; this software can be used in all industrial applications for which a robot has to be frequently reprogrammed, in order to generate various types of trajectories with different motion times. For generating command to the actuators, some steps are used. First, the dynamics model of a two-dimension 2-D joint is formulated is described. Second, controller is designed to track a time-varying trajectory with the tracking error and its derivatives and the commanded trajectory.An interpolation-based algorithm between the waypoints is used for generating a real-time and smoothed path, with known ideal target velocity. The velocity and acceleration of the virtual target are produced by first and second time derivatives of the interpolated path. Furthermore, the commands of velocity control system are generated such that minimum distance be stable in all conditions. Then, the combination of command velocity for minimizing the distance as well as the virtual target velocity was projected to the reference frame, and was consequently, sent as commands for the control system. Finally, the simulation study performance of control system was tested for some waypoints. The simulations show that the controller has a good performance and could track the waypoints efficiently, but when the waypoints had a maximum curvature minimum radius; the robot reduces its velocity for giving minimum tracking errors. According to the results analysis, the robot arm was satisfactorily controlled to reach and stay within a desired joint angle position through implementation and simulation of controllers using MATLAB. This proposed method is very simple which can be used for trajectory tracking, and not necessarily to use high acceleration magnitude. Keywords - Robot Manipulators, Robot Dynamics, Velocity Control, Waypoints Tracking, Trajectory Tracking, Motion Robot Control.