# A New Path Tracking Method Based on Multilayer Model Predictive Control
## 4 Conclusions  
In our previous work [5] we found that switching model predictive control (MPC), nonlinear MPC, and most other control methods can operate at different longitudinal velocities but cannot actively adjust the longitudinal velocity according to the given path information. However, when tracking the same reference path, the tracking accuracy can be significantly improved by reducing the longitudinal velocity. To solve this problem, we propose a new MPC control method and name it multilayer MPC.  
From the perspective of science, our contribution is to propose an MPC control framework that can actively adjust the longitudinal velocity according to the path information when path tracking. This is an exploration and development of MPC. We think that this framework can be applied to the control of other automated equipment.  
From an engineering perspective we present many contributions. Firstly, we have demonstrated that the accuracy of path tracking can be improved by adjusting the longitudinal velocity. Compared with the nonlinear MPC controller, the multilayer MPC controller, which can actively adjust the longitudinal velocity, reduces the maximum displacement error by 92.92% and reduces the maximum heading error by 77.02%. Secondly, the real-time performance of multilayer MPC is very good. Moreover, compared with sequential computation, multilayer MPC with parallel computation has better real-time performance and its maximum calculation time is 0.0090 s. Thirdly, the multilayer MPC controller can still perform the path tracking task under the impact of positioning error.  
Of course, there are still some shortcomings in our work. Firstly, limited by the lack of equipment, multilayer MPC has not been verified by real vehicles. We are deeply sorry about this issue, but the problem of acquiring or developing experimental equipment is difficult to solve quickly. We will work hard and try our best to provide the experiment as soon as possible. In addition, for positioning errors, the robustness of linear MPC in multilayer MPC does not satisfy us. We will solve this problem in our future work.  
Conceptualization, G.B., Q.G., and Y.M.; Methodology, G.B. and Q.G.; Software, G.B., Validation, G.B., and K.L.; Investigation, G.B.; Writing-original draft preparation, G.B.; Writing-review and editing, Y.M., L.L., W.L., and Q.G.; Supervision, L.L. and W.L.; Project administration, L.L. and W.L.; Funding acquisition, L.L., W.L., Y.M., and Q.G.  
This research was funded by the National Key Research and Development Program of China, grant number 2018 YFC0604403 and 2016 YFC0802905, the National High Technology Research and Development Program of China (863 program), grant number 2011 AA060408 and the Fundamental Research Funds for the Central Universities, grant number FRF-TP-17-010A2.  
The authors declare no conflict of interest. The funders had no role in the design of the study, in the collection, analyses, or interpretation of data, in the writing of the manuscript, or in the decision to publish the results.  
Figure 24: The computation time of the simulation with positioning errors.