## 3 LB-MPC in Path Tracking of Mobile Platforms
### Learning and Optimizing Prediction Model
#### 3.1.2 Data-Driven Prediction Models  
The data-driven prediction models include two parts, i.e., the nominal system model and the dynamic model composed of additional uncertainties. The nominal system model is learned on the basis of the data, and it ensures the security and stability of the closed-loop system. However, due to prior uncertainty, the experimental data does not incorporate the entire state space. Consequently, the prediction accuracy of the model is not satisfactory. The uncertainty in the system arises from unmodeled nonlinearities or external disturbances and are contained in a finite set of dependent states [25]. Therefore, the uncertainty set is obtained from the data by using GP regression [80; 81] or reinforcement learning [82; 83], and then a dynamic model is formed with additional uncertainties. Finally, a data-driven prediction model is formed by combining the nominal system model. The data-driven prediction models perform path tracking in mobile platforms efficiently and improve the path tracking performance in uncertain environments. An accurate vehicle model that covers the entire performance envelope of a vehicle is highly nonlinear, complex, and unrecognized. In order for uncertainties to be dealt with and for safe driving to be achieved [84], GP regression is used to obtain the residual model, which is also applied to the remote-control racing cars [48]. The trained reinforcement learning model is integrated with the controller to efficiently deal with the tracking error [85]. The inaccuracy in the prior model leads to a significant decline in the performance of MPC. The reinforcement learning based on the online model assists in learning the unknown parameters and updating the prediction model, thereby reducing the path error [86]. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Prediction Model**} \\ \cline{2-4}
**Evaluation Contents** & \multicolumn{3}{c}{**Learning-Based Model**} \\ \cline{2-4}  & **Physical Model** & **Deep Learning Model** & **Reinforcement Learning Model** \\ \hline Simulation accuracy & Low & Medium & High \\ Simulation calculation & Low & Medium & High \\ Modeling difficulty & High & Low & Medium \\ Training difficulty & None & Medium & High \\ Adaptability & Low & High & High \\ References & [71] & [29; 30; 66; 67; 68; 69; 74] & [28; 32; 70; 75] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The comparisons between the physical model, deep learning model, and reinforcement learning model under different evaluation parameters (ratings: none, low, medium, and high). In the field of robotics, high precision path tracking forms the basis of robot operations. The GP of offline training is used to estimate the mismatch between the actual model and the estimated model. The extended Kalman filter estimates the mismatches in the residual model online to achieve the robot arm offset-free tracking [87]. The prediction model based on ML methods and MPC is the best solution for path tracking in cooperative autonomous unmanned aerial vehicles in the cases of different formation [88; 89; 90]. In unknown environments, such as the unstructured or off-road terrains, the robot-terrain interaction model usually does not exist. Even if such a model exists, finding the suitable model parameters is very difficult. The prior model is unable to deal with the influence of complex and dynamic terrains. The learning-based nonlinear model predictive control (LB-NMPC) algorithm includes a simple prior model and a learning disturbance model of environmental disturbance [32; 75]. The disturbance is modeled as a GP function based on the system state, input, and other related variables to reduce the path tracking error of repeated traversal along the reference path. On the basis of the existing LB-NMPC algorithm, researchers have proposed a robust min-max learning-based nonlinear model predictive control [91] and a robust constraint learning-based nonlinear model predictive control (RC-LB-NMPC) method [92] to track the path of off-road terrain.