# Predictive Control for Small Unmanned Ground Vehicles via a Multi-Dimensional Taylor Network
## 4 MTN Predictive Control Scheme with the Differential Term
### Scheme of Predictive Control with the Differential Term Based on the MTN Model
For the D-MTNC control law parameters, the control effort weighting factor was set to \(1/\varepsilon=0.1\) and the differential term weighting factor was set to \(\gamma=0.005\). For the MTNC control law parameters, the control effort weighting factor was set to \(1/\varepsilon=0.1\). Figure 3: Block diagram of the improved MTN predictive control system. schemes. These results verify that the improved predictive control scheme has a good control effect and good robustness. ### Discussion

For tracking control of SUGVs, the above results show that the proposed method has good performance and tracks the reference signal quickly and accurately. To verify the robustness of the proposed scheme, sharp noise was added. The results of the experiment in terms of tracking, robustness, and real-time performance all show that the proposed scheme has better performance than MTNC and RBFC. Regarding the choice of model structure, what needs illustration is that the MTN predictive model adopted a 4-15-1 structure and the RBF predictive model adopted a 4-18-1 structure in this paper. The MTN structure depends on the middle layer's nodes when the input and output layer are confirmed. The middle layer's nodes rely on the input layer's nodes and the power item. The MTN predictive model's structure is shown in Figure 1. From Figure 1, when the input layer had four nodes and the number of power items was 2, the number of product items was 15. The RBF hidden layer's nodes depend on the history of multiple experiments, and we chose 18 nodes for the hidden layer here. The proposed scheme showed good performance in tracking control of the SUGV. However, SUGVs have a wide range of applications, such as delivery, sanitation, and mining. When facing these practical scenarios, the proposed method needs to be experimentally validated and the appropriate parameters need to be selected according to the actual situation. Figure 6: The tracking trajectory with noise. Figure 7: The tracking error with noise. ## 6 Conclusions

An improved predictive control scheme based on the MTN was proposed for tracking control of SUGVs. The traditional objective function was improved to obtain a predictive objective function with the differential term. The optimal control quantity was given in real time through iterative optimization. A tracking control experiment on a SUGV was carried out to verify the effectiveness of the proposed scheme. The results show that the proposed scheme is effective and has good real-time, robustness, and convergence performance, which ensure that the vehicle can quickly and accurately track the desired yaw velocity signal, and is superior to the traditional MTN and RBF predictive control schemes. The proposed improved MTN predictive control scheme developed in the present paper shows great promise but requires further study. For example, the proposed scheme could be applied to different complex driving scenarios, and some complicated conditions could be considered, such as an actuator failure or input constraints. Writing--original draft preparation, Y.W. ; methodology, C.L. ; writing--review and editing, C.Y. ; validation, M.L. ; formal analysis, H.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors thank the Editor-in-Chief, the Associate Editor, and the anonymous reviewers for their valuable comments and suggestions. The authors declare no conflict of interest. ## References

* _[PERSON] et al. (2021)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Model-free adaptive control of steady-state drift of unmanned vehicles. _Control Theory Appl._**2021**, _38_, 23-32. (In Chinese)
* _[PERSON] et al. (2015)_ [PERSON]; [PERSON]; [PERSON] In the passenger seat: Investigating ride comfort measures in autonomous cars. _IEEE Intel. Transp. Syst. Mag._**2015**, \(7\), 4-17. [CrossRef]
* _[PERSON] et al. (2017)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; et al.