Real-time state estimation for spatial six-degree-of-freedom linearly actuated parallel robots

This paper presents a novel numerical method, Global Newton–Raphson with Monotonic Descent algorithms (GNRMD), to solve the effectively real-time spatial 6-DOF states of parallel robots in practice. Based on geometrical frame of parallel robots, the highly nonlinear equations of system states estimation are obtained using analytical approach. GNRMD algorithms modified from Global Newton–Raphson method are developed to solve the nonlinear equations in real-time application. The procedure of GNRMD algorithms are programmed in MATLAB/Simulink, and then compiled to a real-time PC with Microsoft Visual Studio .NET for implementation. Applying the proposed algorithms, the real-time spatial 6-DOF states of the parallel robots are estimated. In addition, the performances, accuracy, convergence, property of real-time and effectiveness, of the proposed method are analyzed and verified in experiment and theory. Furthermore, the presented algorithms are used in a DOF control scheme of parallel robots. Simulation and experimental results show the proposed algorithms are effective and feasible for spatial states estimation of parallel robots, and are suitable for a real-time control system required accurate feedback of system states.