Enhanced MPC for Omnidirectional Robot Motion Tracking Using Laguerre Functions and Non-Iterative Linearization

Abstract

To cope with the computational complexity of the traditional model predictive control, and to reduce the error of the linearization and prediction processes, this paper presents an improved model predictive control algorithm, based on Laguerre functions, for the motion tracking of an omnidirectional mobile robot with non-iterative linearization. To design the controller, the kinematic modeling of the three-wheeled omnidirectional robot was first performed. Next, the model predictive algorithm was developed using Laguerre functions to parametrize the control signals. At each sampling instant of the online optimization, a linearization along the predicted trajectory, based on the duality principle between optimal control and stochastic filtering, was carried out to deal with the nonlinearities of the system. This non-iterative linearization provides better approximation of the nonlinear behavior which improves the prediction process and the tracking performance, with lower computational burden due to the use of the Laguerre functions. The new controller is applied to solve the trajectory-tracking problem of an omnidirectional robot. A comparative study between the proposed controller, the conventional model predictive control, and the nonlinear model predictive approach is made. Simulation results confirm that the new controller outperform the latter ones regarding tracking accuracy with considerably low computational effort. The feasibility of the controller is demonstrated by real-time experiment on the Robotino-Festo omnidirectional mobile robot.

Keywords

• Laguerre functions
• linearization
• model predictive control (MPC)
• omnidirectional mobile robot
• stochastic filtering
• trajectory-following