A memetic approach to the inverse kinematics problem

Abstract

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.

A Multi-objective Differential Evolution Algorithm for Robot Inverse Kinematics

“…Gonzalez and Blanco [9] demonstrated that a memetic approach increases the converge of the differential evolution algorithm for the inverse kinematic problem. They introduced a local search mechanism called discarding.…”

“…Existing numerical methods on evolutionary algorithms, to name a few genetic algorithm [7], [8] and differential evolution [9], [10] provide solutions for the problems of exhaustive search with acceptable accuracy. In practice, usually manually designed look-up tables based approximate inverse kinematics based solutions are used for controlling a robotic manipulator [11].…”

Inverse Kinematics: An Alternative Solution Approach Applying Metaheuristics

“…In other cases, in addition to obtaining a solution close to the optimum, it is necessary to generate it in a given time, which, in turn, implies the fast convergence of the algorithm. For this reason, the authors in [11] proposed a modification to DE in order to reduce the required time for finding the IK of a robot with 3-DOF, introducing a local search mechanism that they called discarding. Memetic algorithms [12][13][14], are hybrid methods that take advantage of the synergy from the combination of the global search capacity of some technique and the power of the local search of another mechanism.…”