# Dynamic Decoupling and Trajectory Tracking for Automated Vehicles Based on the Inverse System
## 5 Conclusions  
To achieve the high trajectory tracking precision in the dynamic coupling scenarios, a simultaneous trajectory tracking and stability control method for 4 WID automated electric vehicles is present in this paper based on the inverse system theorem. To reveal the coupling mechanism and to prove the reversibility of 4 WID vehicles, the 3 DOF vehicle dynamic model is constructed. The inverse system learned by a BPNN model shows effectiveness to realize dynamic decoupling. The pseudo linear system composed of the inverse system and the controlled object follows the desired vehicle dynamic states to indirectly achieve trajectory tracking. Three typical and common coupled driving conditions are designed to verify the trajectory tracking accuracy under the simultaneous control of vehicles' longitudinal, lateral and yaw motion. Compared with the pure-pursuit algorithm and the MPC algorithm, the proposed method reduces interactions among vehicle motion directions and reveals better tracking performance. Moreover, since the target states of the vehicle have been constrained within a reasonable range, the decoupling method not only maintains the accurate trajectory tracking but also guarantees the stable vehicle driving under low-adhesion road conditions. Even though the proposed method theoretically shows better control performance, further verifications could be implemented on real vehicles to realize the engineering applications. Conceptualization, Y.Y. and Y.L. ([PERSON]); methodology, Y.Y. and Y.L. ([PERSON]); software and validation, Y.Y. and Y.L. ([PERSON]); formal analysis, Y.Y. and W.Y. ; writing--review and editing,  
Figure 12: The tracking performance index: (**a**) the longitudinal direction; (**b**) the lateral direction; (**c**) the yaw direction; (**d**) the planar motion. Y.Y., Y.L. ([PERSON]) and W.Y. ; supervision and funding acquisition, Y.L. ([PERSON]) and L.Z. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by Key Research Program of the Ministry of Science and Technology ([Grant No. 2017 YFB0102603-3, 2016 YFB0100900), Chongqing Science and Technology Program Project Basic Science and Frontier Technology (Grant No. cstc2018 icyjAX0630), Chongqing Technology Innovation and Application Development Major Theme Special Project (Grant No. cstc2019 jscx-zdztzxX0032), Graduate Scientific Research and Innovation Foundation of Chongqing (Grant No. CYB19063). **Conflicts of Interest:** We declare that there is no conflict of interests in connection with the paper submitted. * _[PERSON] et al. (2016)_ [PERSON]; [PERSON]; [PERSON] A Review of some Pure-Pursuit based Path Tracking Techniques for Control of Autonomous Vehicle. _Int. J. Comput. Appl._**2016**, _135_, 35-38. [CrossRef]
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