Comparison of Different Methods for Computing the Forward Kinematics of a Redundant Parallel Manipulator

In this paper, three numerical methods are presented to solve the forward kinematics of a three DOF actuator-redundant hydraulic parallel manipulator. It is known, that on the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting that the forward kinematics solution is a key element in closed loop position control of parallel manipulators. The proposed methods, namely the Neural Network Estimation, the Quasi-closed Solution, and the Taylor series approximation, are using mainly numerical computations, with different ideas to solve the problem in hand. The latter two methods are proposed for the first time in literature to solve the forward kinematics of a parallel manipulator. These methods are compared in detail and the advantages or the disadvantages of each method in computing the forward kinematic map of the given mechanism is discussed. It is shown that a 4th order Taylor series approximation to the problem provides a good compromise for practical applications compared to that of other methods considered in this paper.