Inverse kinematics control of redundant planar manipulator with joint constraints using numerical method

In this paper, an efficient numerical scheme is associated with the scheming of the inverse kinematics for a four degrees of freedom redundant planar robotic manipulator. The manipulator under study is an RRPR redundant manipulator with joint angle constraints at each joint. Firstly, using the forward kinematics transformation matrix, a plot of the reachable workspace was obtained. This plot was used to determine equations for the possible end-effector positions. Then the analytic approach was used to determine equations for the inverse kinematic scheme. The inverse kinematics scheme initially sets the first joint angle as a constant at the current position in order to determine the inverse solution. However, if the solution calculated is not within the joint constraints then it uses numerical techniques to determine the least displacement new first joint parameter to determine the next possible solution. This results in a faster and more accurate convergence to the desired solution as compared to the traditional approaches.