A New Method to Solve the Kinematic Problems of Parallel Robots Using Generalized Reduced Gradient Algorithm

Abstract

This paper proposes a new method of solving the kinematic problems for parallel robots. The paper content aims to solve nonlinear optimization problems with constraints rather than to directly solve high-order nonlinear systems of equations. The nonlinear optimization problems shall be efficiently solved by applying the Generalized Reduced Gradient algorithm and appropriate downgrade techniques. This new method can be able to find exact kinematic solutions by assigning constraints onto the parameters. The procedure can be done without filtering control results from mathematical solution, from which the control time of manipulators can be reduced. The numerical simulation results in this paper shall prove that the method can be applied to solve kinematic problems for a variety of parallel robots regardless of its structures and degree of freedom (DOF). There are several advantages of the proposed method including its simplicity leading to a shorter computing time as well as achieving high accuracy, high reliability, and quick convergence in final results. Hence, the applicability of this method in solving kinematic problems for parallel manipulators is remarkably high.