An Optimization Approach to Solve the Inverse Kinematics of Redundant Manipulator

A robot arm is the combination of links and joints in the form of a chain with one end is fixed while the other end is free. The joints are either prismatic or revolute, driven by actuators. In order to move the free end, also called the end effector, along a certain path, most, if not all, of the joints are to be moved. In doing so it is necessary to solve the inverse kinematics equation. In the case of redundant manipulator, inverse kinematics is much more difficult when compared to a non redundant manipulator whose kinematics is not so complicated. Let r(t) = f(q(t)) be the direct kinematics equation of a given manipulator where q(t) is n × 1 vector containing n-joint variables and r(t) is m × 1 vector in R representing the position and orientation of the end-effector and f is a continuous nonlinear function whose structure and parameters are known for a given manipulator. The inverse kinematics problem [3] is to find the joint variables given the desired positions and orientations of the end-effector through the inverse mapping