A hybrid strategy to solve the forward kinematics problem in parallel manipulators

A parallel manipulator is a closed kinematic structure with the necessary rigidity to provide a high payload to self-weight ratio suitable for many applications in manufacturing, flight simulation systems, and medical robotics. Because of its closed structure, the kinematic control of such a mechanism is difficult. The inverse kinematics problem for such manipulators hag a mathematical solution; however, the forward kinematics problem (FKP) is mathematically intractable. This paper addresses the FKP and proposes a neural-network-based hybrid strategy that solves the problem to a desired level of accuracy, and can achieve the solution in real time. Two neural-network concepts using a modified form of multilayered perceptrons with backpropagation learning were implemented. The better performing concept was then combined with a standard Newton-Raphson numerical technique to yield a hybrid solution strategy. Simulation studies were carried out on a flight simulation system to check the validity of the. approach. Accuracy of close to 0.01 mm and 0.01 degrees in the position and orientation parameters was achieved in less than two iterations and 0.02 s of execution time for the proposed strategy.