{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T08:47:19Z","timestamp":1778316439085,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T00:00:00Z","timestamp":1709078400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014013","name":"Innovate UK","doi-asserted-by":"publisher","award":["104277"],"award-info":[{"award-number":["104277"]}],"id":[{"id":"10.13039\/100014013","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents the development of path-tracking control strategies for an over-actuated autonomous electric vehicle. The vehicle platform is equipped with four-wheel steering (4WS) as well as torque vectoring (TV) capabilities, which enable the control of vehicle dynamics to be enhanced. A nonlinear model predictive controller is proposed taking into account the nonlinearities in vehicle dynamics at the limits of handling as well as the crucial actuator constraints. Controllers with different actuation formulations are presented and compared to study the path-tracking performance of the vehicle with different levels of actuation. The controllers are implemented in a high-fidelity simulation environment considering scenarios of vehicle handling limits. According to the simulation results, the vehicle achieves the best overall path-tracking performance with combined 4WS and TV, which illustrates that the over-actuation topology can enhance the path-tracking performance during conditions under the limits of handling. In addition, the performance of the over-actuation controller is further assessed with different sampling times as well as prediction horizons in order to investigate the effect of such parameters on the control performance, and its capability for real-time execution. In the end, the over-actuation control strategy is implemented on a target machine for real-time validation. The control formulation proposed in this paper is proven to be compatible with different levels of actuation, and it is also demonstrated in this work that it is possible to include the particular over-actuation formulation and specific nonlinear vehicle dynamics in real-time operation, with the sampling time and prediction time providing a compromise between path-tracking performance and computational time.<\/jats:p>","DOI":"10.3390\/s24051566","type":"journal-article","created":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T10:37:36Z","timestamp":1709116656000},"page":"1566","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Predictive Path-Tracking Control of an Autonomous Electric Vehicle with Various Multi-Actuation Topologies"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6686-5160","authenticated-orcid":false,"given":"Chenhui","family":"Lin","sequence":"first","affiliation":[{"name":"Advanced Vehicle Engineering Centre, Cranfield University, Bedford MK43 0AL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1812-7101","authenticated-orcid":false,"given":"Boyuan","family":"Li","sequence":"additional","affiliation":[{"name":"Advanced Vehicle Engineering Centre, Cranfield University, Bedford MK43 0AL, UK"},{"name":"Research Center for Intelligent Transportation, Zhejiang Lab, Hangzhou 311121, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2727-8339","authenticated-orcid":false,"given":"Efstathios","family":"Siampis","sequence":"additional","affiliation":[{"name":"Advanced Vehicle Engineering Centre, Cranfield University, Bedford MK43 0AL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7874-4526","authenticated-orcid":false,"given":"Stefano","family":"Longo","sequence":"additional","affiliation":[{"name":"Advanced Vehicle Engineering Centre, Cranfield University, Bedford MK43 0AL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0152-3730","authenticated-orcid":false,"given":"Efstathios","family":"Velenis","sequence":"additional","affiliation":[{"name":"Advanced Vehicle Engineering Centre, Cranfield University, Bedford MK43 0AL, UK"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/j.trc.2015.09.011","article-title":"Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions","volume":"60","author":"Katrakazas","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Schwesinger, U., Rufli, M., Furgale, P., and Siegwart, R. (2013, January 23). A sampling-based partial motion planning framework for system-compliant navigation along a reference path. Proceedings of the 2013 IEEE Intelligent Vehicles Symposium (IV), Gold Coast, Australia.","DOI":"10.1109\/IVS.2013.6629500"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bonab, S.A., and Emadi, A. (2019, January 14\u201317). Optimization-based Path Planning for an Autonomous Vehicle in a Racing Track. Proceedings of the IECON 2019\u201445th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal.","DOI":"10.1109\/IECON.2019.8926856"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Faulwasser, T., Kern, B., and Findeisen, R. (2009, January 15\u201318). Model predictive path-following for constrained nonlinear systems. Proceedings of the 48th IEEE Conference on Decision and Control (CDC) Held Jointly with 2009 28th Chinese Control Conference, Shanghai, China.","DOI":"10.1109\/CDC.2009.5399744"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Laurense, V.A., Goh, J.Y., and Gerdes, J.C. (2017, January 24\u201326). Path-tracking for autonomous vehicles at the limit of friction. Proceedings of the 2017 American Control Conference (ACC), Seattle, WA, USA.","DOI":"10.23919\/ACC.2017.7963824"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Mad\u00e5s, D., Nosratinia, M., Keshavarz, M., Sundstr\u00f6m, P., Philippsen, R., Eidehall, A., and Dahl\u00e9n, K. (2013, January 23\u201326). On path planning methods for automotive collision avoidance. Proceedings of the 2013 IEEE Intelligent Vehicles Symposium (IV), Gold Coast, Australia.","DOI":"10.1109\/IVS.2013.6629586"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1204","DOI":"10.1109\/TCST.2016.2599783","article-title":"Collision Avoidance and Stabilization for Autonomous Vehicles in Emergency Scenarios","volume":"25","author":"Funke","year":"2017","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_8","unstructured":"Coulter, R.C. (1991). Implementation of the Pure Pursuit Path Tracking Algorithm, Carnegie Mellon University. Technical Report CMU-RI-TR-92-01."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Hoffmann, G.M., Tomlin, C.J., Montemerlo, M., and Thrun, S. (2007, January 9\u201313). Autonomous Automobile Trajectory Tracking for Off-Road Driving: Controller Design, Experimental Validation and Racing. Proceedings of the 2007 American Control Conference, New York, NY, USA.","DOI":"10.1109\/ACC.2007.4282788"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Roselli, F., Corno, M., Savaresi, S.M., Giorelli, M., Azzolini, D., Irilli, A., and Panzani, G. (2017, January 27\u201330). H\u221e control with look-ahead for lane keeping in autonomous vehicles. Proceedings of the 2017 IEEE Conference on Control Technology and Applications (CCTA), Kohala Coast, HI, USA.","DOI":"10.1109\/CCTA.2017.8062781"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Tagne, G., Talj, R., and Charara, A. (2013, January 23\u201326). Higher-order sliding mode control for lateral dynamics of autonomous vehicles, with experimental validation. Proceedings of the 2013 IEEE Intelligent Vehicles Symposium (IV), Gold Coast, Australia.","DOI":"10.1109\/IVS.2013.6629545"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"109120","DOI":"10.1109\/ACCESS.2019.2933895","article-title":"Optimal Path Tracking Control of Autonomous Vehicle: Adaptive Full-State Linear Quadratic Gaussian (LQG) Control","volume":"7","author":"Lee","year":"2019","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"K, V., Sheta, M.A., and Gumtapure, V. (2019, January 29\u201330). A Comparative Study of Stanley, LQR and MPC Controllers for Path Tracking Application (ADAS\/AD). Proceedings of the 2019 IEEE International Conference on Intelligent Systems and Green Technology (ICISGT), Visakhapatnam, India.","DOI":"10.1109\/ICISGT44072.2019.00030"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1177\/0954407014566031","article-title":"Comparative study of autonomous path-following vehicle control via model predictive control and linear quadratic control","volume":"229","author":"Yakub","year":"2015","journal-title":"Proc. Inst. Mech. Eng. Part D J. Automob. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1258","DOI":"10.1109\/TCST.2012.2200826","article-title":"Model Predictive Control for Vehicle Stabilization at the Limits of Handling","volume":"21","author":"Beal","year":"2013","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/TITS.2008.2011697","article-title":"A Predictive Controller for Autonomous Vehicle Path Tracking","volume":"10","author":"Raffo","year":"2009","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Alessandretti, A., Aguiar, A.P., and Jones, C.N. (2013, January 17\u201319). Trajectory-tracking and path-following controllers for constrained underactuated vehicles using Model Predictive Control. Proceedings of the 2013 European Control Conference (ECC), Zurich, Switzerland.","DOI":"10.23919\/ECC.2013.6669717"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"98009","DOI":"10.1109\/ACCESS.2020.2981417","article-title":"Path Tracking Control for Active Rear Steering Vehicles Considering Driver Steering Characteristics","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1080\/00423114.2011.597864","article-title":"Development of a path-tracking control system based on model predictive control using infrastructure sensors","volume":"50","author":"Kim","year":"2012","journal-title":"Veh. Syst. Dyn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1002\/oca.2123","article-title":"Optimization-based autonomous racing of 1:43 scale RC cars","volume":"36","author":"Liniger","year":"2015","journal-title":"Optim. Control Appl. Methods"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"184697","DOI":"10.1109\/ACCESS.2020.3029635","article-title":"Path Tracking Control Based on Model Predictive Control with Adaptive Preview Characteristics and Speed-Assisted Constraint","volume":"8","author":"Dai","year":"2020","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1109\/TIV.2018.2874529","article-title":"Comparison of Path Tracking and Torque-Vectoring Controllers for Autonomous Electric Vehicles","volume":"3","author":"Chatzikomis","year":"2018","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Siampis, E., Velenis, E., and Longo, S. (2015, January 15\u201317). Model Predictive torque vectoring control for electric vehicles near the limits of handling. Proceedings of the 2015 European Control Conference (ECC), Linz, Austria.","DOI":"10.1109\/ECC.2015.7330922"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Vasiljevic, G., and Bogdan, S. (2016, January 24). Model predictive control based torque vectoring algorithm for electric car with independent drives. Proceedings of the 2016 24th Mediterranean Conference on Control and Automation (MED), Athens, Greece.","DOI":"10.1109\/MED.2016.7536067"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mikul\u00e1\u0161, E., Gulan, M., and Tak\u00e1cs, G. (2018, January 12\u201315). Model Predictive Torque Vectoring Control for a Formula Student Electric Racing Car. Proceedings of the 2018 European Control Conference (ECC), Limassol, Cyprus.","DOI":"10.23919\/ECC.2018.8550124"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2018.07.004","article-title":"Simultaneous path following and lateral stability control of 4WD-4WS autonomous electric vehicles with actuator saturation","volume":"128","author":"Chen","year":"2019","journal-title":"Adv. Eng. Softw."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.ymssp.2017.12.018","article-title":"Coordinated path-following and direct yaw-moment control of autonomous electric vehicles with sideslip angle estimation","volume":"105","author":"Guo","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Acosta, M., Kanarachos, S., and Fitzpatrick, M.E. (2018, January 9\u201311). On full MAGV lateral dynamics exploitation: Autonomous drift control. Proceedings of the 2018 IEEE 15th International Workshop on Advanced Motion Control (AMC), Tokyo, Japan.","DOI":"10.1109\/AMC.2019.8371149"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Lin, C., Siampis, E., and Velenis, E. (2022, January 8\u201310). Real-Time Path-tracking MPC for an Over-Actuated Autonomous Electric Vehicle. Proceedings of the 2022 American Control Conference (ACC), Atlanta, GA, USA.","DOI":"10.23919\/ACC53348.2022.9867858"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zarkadis, K., Velenis, E., Siampis, E., and Longo, S. (2018, January 12\u201315). Predictive Torque Vectoring Control with Active Trail-Braking. Proceedings of the 2018 European Control Conference (ECC), Limassol, Cyprus.","DOI":"10.23919\/ECC.2018.8550061"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00423119208969994","article-title":"The Magic Formula Tyre Model","volume":"21","author":"Pacejka","year":"1992","journal-title":"Veh. Syst. Dyn."},{"key":"ref_32","unstructured":"Domahidi, A., and Jerez, J. (2023, December 15). FORCES Professional. Embotech AG. 2014\u20132019. Available online: https:\/\/embotech.com\/FORCES-Pro."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/00207179.2017.1316017","article-title":"FORCES NLP: An efficient implementation of interior-point methods for multistage nonlinear nonconvex programs","volume":"93","author":"Zanelli","year":"2017","journal-title":"Int. J. Control"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1016\/j.conengprac.2011.07.010","article-title":"Steady-state drifting stabilization of RWD vehicles","volume":"19","author":"Velenis","year":"2011","journal-title":"Control Eng. Pract."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/5\/1566\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:06:41Z","timestamp":1760105201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/5\/1566"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,28]]},"references-count":34,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["s24051566"],"URL":"https:\/\/doi.org\/10.3390\/s24051566","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,28]]}}}