Towards Efficient Learning-Based Model Predictive Control via Feedback Linearization and Gaussian Process Regression

Abstract

This paper presents a learning-based Model Predictive Control (MPC) methodology incorporating nonlinear predictions with robotics applications in mind. In particular, MPC is combined with feedback linearization for computational efficiency and Gaussian Process Regression (GPR) is used to model unknown system dynamics and nonlinearities. In this method, MPC predicts future states by leveraging a GPR model and optimizes a sequence of inputs over feedback linearized states. The controller was tested in simulation by using a twolink planar robot in the presence of model uncertainty. With respect to trajectory-tracking error, the proposed controller outperformed a conventional Proportional-Derivative Inverse Dynamics controller and a GPR-augmented version. Although a fully nonlinear MPC formulation achieved slightly better performance, the proposed controller had an average control calculation time that was 82× faster.

Learning‐based model predictive control for improved mobile robot path following using Gaussian processes and feedback linearization

“…Because the FBL technique exactly linearizes the nonlinear system by a suitable state space change of coordinates, MPC methods combing with FBL are different from the standard linear MPC methods that linearize the system model approximately. Combining FBL with MPC in a way that trades the nonlinear optimization for a linear one has been shown via simulations to reduce the computational burden (Caldwell & Marshall, 2021; Greeff & Schoellig, 2020; Wu et al, 2022) and field experiments (Fader, 2020; Greeff et al, 2022; Oriolo et al, 2002). However, implementing FBL requires a precise model (exact knowledge of kinematic and dynamic parameters) of the system to ensure an exact cancellation of all nonlinearities.…”

A Cascaded and Adaptive Visual Predictive Control Approach for Real-Time Dynamic Visual Servoing

“…The other approach proposed in the literature is linearisation through the system Jacobian, where the system model is linearised successively in the proximity of each operation point in each time step [12]. Furthermore, predictive feedback linearisation methods have been proposed to reduce the computational complexity of real-time implementation [13].…”