# Neural Approximation Enhanced Predictive Tracking Control of a Novel Designed Four-Wheeled Rollator
## 4 Results and Discussion  
In order to demonstrate the effectiveness of the proposed position tracking controller, path tracking experiments, compared with previous work [35; 58; 59], are carried out on the developed four-wheeled elderly rollator using simulation [51; 60]. Two groups of comparative experiments are discussed as follows:  
1. Trajectory tracking co-simulation of the elderly rollator, including straight lines, curves, and obstacles, is intended to illustrate the position accuracy and robustness of the proposed NMPC algorithm. 2. To further demonstrate the advantage of NMPC in uncertain disturbances for the assistive elderly walker, including internal mechanical friction and external rollator and human interaction forces, a contrast experiment using NMPC and MPC related to previous work [35], is discussed for the circular path. The main experiment parameter setting are as follows: robot speed \(v=1\) m/s, prediction horizon \(N_{p}=25\), control horizon \(N_{e}=15\), weight coefficient \(\sigma=9.5\), MPC sample time \(T=0.025\) s, interference signal of sine curve \(d=0.025\) and period \(t=2.5\) s.  
The tracking performance of task 1 is shown in Figure 12. The desired trajectory is mainly composed of the straight path with 7.12 m, the circular arc with a radius of 5.05 m, and three obstacles with narrow aisles. The width of the obstacle is only 4 cm wider than the rollator body, so as to demonstrate the accuracy of the NMPC control method. Set the elderly rollator to advance at a uniform speed of 1 m/s, and pass the trajectory of straight, arcs, and obstacles in sequence. It can be inferred from the tracking events displayed in Figure 13 that the elderly rollator using the proposed NMPC method can follow the mentioning path properly, and the elderly rollator responds smoothly with a lateral error around \(\pm 0.08\) meters and a longitudinal error within \(\pm 0.2\). Both the lateral position and the longitudinal position are capable of tracking the reference way, whether in straight or curve sections. Furthermore, the pitch angle is constrained in a reasonable range, and the rollator  
Figure 11: Controller framework of NMPC. velocity is constant, revealing that the rollator reply of accuracy and frequency matches the fast real-time in an assistant rollator system. In addition, the developed NMPC algorithm can accurately pass through the uncertain disturbances of narrow aisles (7.5 s, 15.8 s, 24.2 s), and the proposed control scheme can achieve a satisfactory performance with high accuracy and respond quickly in trajectory tracking performances, indicating that the NMPC algorithm can achieve a satisfactory performance with high accuracy and respond quickly in tracking performances. Figure 12: The tracking results of NMPC. Figure 13: The tracking performances of the NMPC approach in lateral position, yaw angle, longitudinal position, rollator speed, lateral error, yaw error, longitudinal error, and pitch angle. Moreover, to demonstrate the advantage of the NMPC approach in uncertain physical interaction, and compared with previous work [35], a circular tracking simulation is implemented with the method of MPC and NMPC. The tracking performance under the dynamic disturbance with sinusoid input is displayed in Figure 14, and the comparative results of NMPC and MPC in a longitudinal position, lateral position, roll angle, rollator speed, and the position error of longitude and lateral. It can be gathered that both the rollator using NMPC and MPC approach can basically follow the desired trajectory in the lateral position and longitudinal position as displayed in Figure 15. However, from the speed respond of the rollator, there is some fluctuation in the tracking process using the MPC method, obviously, while the NMPC approach can effectively maintain the stable speed.