Hybrid Search Method for Solving the Inverse Kinematics of a Multilink Manipulator

Abstract

The solution of the inverse kinematics problem of the manipulator is considered. The inverse kinematics problem of multi-link manipulators is a multi-extremal optimization problem with functional and positional constraints. Global optimization algorithms are commonly used to solve that kind of tasks. In this paper the solution of the inverse kinematics problem using the hybrid search method is considered. This method is a combination of genetic algorithm and simplex search. The genetic algorithm is not able to move quickly towards the optimum, but is able to find a global optimum on a multi-extremal function. Simplex search quickly moves toward a local minimum, but is not able to find a global minimum. This combination uses the strengths of both search algorithms, while covering the weaknesses. At each step of the genetic algorithm, the best individuals are selected to become the centers of simplex searches. Simplex searches improve the population of the genetic algorithm. Thus, a global extremum can be found in several steps of the genetic algorithm. For testing several redundant and non-redundant manipulators was used and for each of them several desired positions was specified. In solving the inverse kinematics problems, the hybrid algorithm showed comparable accuracy with the genetic algorithm with larger number of calls of the objective function. In addition, this algorithm is very easy to implement and there are no issues associated with the gradients of the objective function and functional limitations. This method allows us to find solutions for non-redundant and redundant manipulators.