Model Predictive Control (MPC) Applied to a Spatial Manipulator Parallel with a 3RRR Kinematic System

Abstract

This paper presents the application of Model Predictive Control (MPC) on a three kinematic 3RRR chains (two revolute joints and one revolute actuator) for a 6-Degree-of-Freedom (6-DOF) spatial manipulator parallel plate mechanism designed similarly to a Stewart platform. The MPC controller is selected for its ability to handle Multi-Input Multi-Output MIMO systems with constraints, instability, and unmeasured disturbances conditions typical in parallel robotic platforms. This study derives a linearized state-space matrices of the nonlinear mechanism by block-level linearization of a Simscape Multibody model imported directly from Solid Works 2016 into MATLAB/Simulink to obtain the continuous time linearized state-space matrices (Ac, Bc, Cc, Dc) to formulate MPC prediction and horizons. Arduino-UNO microcontroller integration scheme is also deployed for hardware implementation. The simulation outcomes demonstrated successful tracking of six motion references three translational (X, Y, Z) and three rotational (α, β, γ) degrees of freedom of position. The results demonstrated that the proposed MPC strategy significantly outperforms traditional controllers in terms of constraint satisfaction, handling of complex nonlinear dynamics, and robustness, while improving tracking precision for the set points and steady-state accuracy.