A memetic approach to the inverse kinematics problem

Solving the inverse kinematics problem is at the core of the kinematics control of any articulated mechanism. It refers to determine the joint configuration that places the end-effector in an arbitrary position and orientation in the workspace. Kinematic inversion algorithms are generally based on the (pseudo)inverse Jacobian matrix, however, these methods are local and unstable in the vicinity of singular joint configurations. Alternatively, the inverse kinematics can be formulated as a constrained minimization problem in the robot configuration space. In a previous work, Differential Evolution (DE) was used to solve this optimization problem for a non-redundant robot manipulator. Although, the algorithm was successful in finding accurate solutions it showed a low convergence speed rate. In this paper, a memetic approach is proposed to increase the convergence speed of the DE by introducing a local search mechanism, called discarding. The proposed approach is tested in a simulation environment to solve the kinematic inversion problem of a non-redundant 3DOF robot manipulator. Experimental results shows that the proposed algorithm is able to find solutions with high accuracy in less generations than the original DE approach.