## 5 Discussion on Control System Design  
If a nonlinear dynamic system is considered, the implementation limitations of control algorithms should be discussed. The control system design involves aspects related to robot dynamics, actuator behavior, noise characteristics, and an adequate modeling of these aspects is necessary for model-in-the-loop (MITL) or software-in-the-Loop (SITL) testing.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Performance** & **WANARX** & **GP-NARX** \\ \hline RMSE & 1.2955 & 0.7169 \\ FIT\({}_{\text{Total}}\) & 81.344\% & 90.333\% \\ Time on training dataset [s] & 0.047529 & 0.089865 \\ Time on testing dataset [s] & 0.020124 & 0.002090 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance comparison.  
Figure 7: Comparison between measured output (black line) and models predicted output (green line for GP-NARX, red for WANARX).  
The effectiveness of the control system depends strictly on the model on which the testing is carried out.  
The selection of data driven identification techniques ensures that uncertainties in parameters; delays or constructive mechanical imperfections are included in the tuning of the control parameters during the simulation. The advantage lies in the possibility of employing both state-of-the-art techniques [26] and emerging ones (genetic algorithm (GA), particle swarm optimization (PSO) method, and artificial neural network (ANN) [27]) to obtain optimized gain factors on a faithful model of the system.  
Here, we discuss the possibility of employing the model identified by the Gaussian process regression for control algorithm tuning.  
GP models are widely employed together with model predictive control strategies. Advantages are linked to the computation of a prediction variance, which is an effective measure of the uncertainty of the learned model. They are less susceptible to overfitting, and they have, under certain circumstances, universal approximation capabilities for a large number of functions [28]. In [29], a model predictive control (MPC) based on a Gaussian process model was implemented for a pH neutralization process control example. An interesting aspect is the inclusion of variance information in the optimization process as a constraint to controller actions. In [30], a GP-based MPC framework was introduced in an overtaking scenario at highway curves. A GP model was developed to learn the unknown dynamics and to acquire information about the unexplored discrepancy between the nominal vehicle model and the real vehicle dynamics. The combination with a MPC strategy results in safe and stable control under changing friction road conditions. In [31], a learning-based control approach for underactuated balance robots was considered and a GP regression model was incorporated to enhance robustness to modeling errors.  
In the case of an exam, a combination of a guidance and control algorithms, such as an artificial potential field (APF) and a proportional integrative derivative control (PID) have been implemented and tested using the previously introduced GP-NARX model. The performance of the system has been evaluated on the tracking capability of a reference signal generated in real time by the APF algorithm. Control requirements have been formulated in terms of rise time, settling time, overshoot, and steady state errors. The effectiveness of tuning has been demonstrated by the comparison between simulation data and experiments conducted with the robot.