Inverse Kinematics of a Redundant Manipulator Robot Using Constrained Optimization

Redundant manipulative robots are characterized by greater manipulability improving performance but complicating inverse kinematics, on the other hand, optimization techniques allow solving complex problems in robotics applications with greater efficiency. This paper presents the inverse kinematics of a redundant manipulative robot with four degrees of freedom to track a desired trajectory, and considering constraint in manipulability. The optimization problem is proposed using the quadratic position errors of the operative end and the constraint is established by a manipulability index, for this the kinematic model of the robot is determined. The results show the points of singularity of the robot and the performance of the proposal implemented, observing the positional errors and the manipulability for each point of the trajectory. In addition, the optimization is evaluated for two desired manipulability values. Finally, it is concluded that the implemented method optimizes the inverse kinematics to track the desired path while constraining the manipulability.