Energy-Optimized Longitudinal–Steering Coordinated Torque Vectoring for an In-Wheel-Motor-Driven Electric Vehicle

Li, Huichen; Jin, Liqiang; Li, Yingzhuang; Li, Jianhua; Xiao, Feng; Xie, Fangxi; Wang, Zhongshu

doi:10.3390/act15070392

Open AccessArticle

Energy-Optimized Longitudinal–Steering Coordinated Torque Vectoring for an In-Wheel-Motor-Driven Electric Vehicle

by

Huichen Li

,

Liqiang Jin

,

Yingzhuang Li

,

Jianhua Li

^*,

Feng Xiao

,

Fangxi Xie

and

Zhongshu Wang

School of Vehicle Engineering, Jilin University, Changchun 130025, China

^*

Author to whom correspondence should be addressed.

Actuators 2026, 15(7), 392; https://doi.org/10.3390/act15070392

Submission received: 11 May 2026 / Revised: 8 July 2026 / Accepted: 10 July 2026 / Published: 12 July 2026

(This article belongs to the Special Issue Integrated Intelligent Vehicle Dynamics and Control—2nd Edition)

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Abstract

Four-wheel-drive electric vehicles equipped with independently controllable driving, braking, and steering actuators provide additional degrees of freedom for reducing electric-machine and tire-loss energy. This paper presents a real-time longitudinal–steering coordinated torque-vectoring framework for a vehicle driven by four in-wheel motors. A model-predictive active-front-steering controller coordinates the front-wheel steering angle and external yaw moment to reduce steering resistance and lateral tire-slip loss. A reduced inter-axle propulsion problem is analyzed using the Karush–Kuhn–Tucker conditions, and its speed-dependent switching threshold is calibrated offline by particle swarm optimization. Regenerative braking is allocated by an Energy-Optimized Distribution curve subject to ideal-distribution and regulatory constraints. For general positive-torque operation, sequential quadratic programming distributes the four wheel torques by considering motor input power, tire-slip energy, total torque, yaw-moment demand, and actuator limits. Hardware-in-the-loop results under the United States high-acceleration driving cycle and a double-lane-change maneuver show that the proposed strategy reduces energy consumption relative to uniform and tire-utilization-based torque-vectoring strategies.

Keywords: in-wheel-motor-driven electric vehicle; energy-optimized torque vectoring; tire slip energy; longitudinal–steering coordination; regenerative braking; real-time optimization

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MDPI and ACS Style

Li, H.; Jin, L.; Li, Y.; Li, J.; Xiao, F.; Xie, F.; Wang, Z. Energy-Optimized Longitudinal–Steering Coordinated Torque Vectoring for an In-Wheel-Motor-Driven Electric Vehicle. Actuators 2026, 15, 392. https://doi.org/10.3390/act15070392

AMA Style

Li H, Jin L, Li Y, Li J, Xiao F, Xie F, Wang Z. Energy-Optimized Longitudinal–Steering Coordinated Torque Vectoring for an In-Wheel-Motor-Driven Electric Vehicle. Actuators. 2026; 15(7):392. https://doi.org/10.3390/act15070392

Chicago/Turabian Style

Li, Huichen, Liqiang Jin, Yingzhuang Li, Jianhua Li, Feng Xiao, Fangxi Xie, and Zhongshu Wang. 2026. "Energy-Optimized Longitudinal–Steering Coordinated Torque Vectoring for an In-Wheel-Motor-Driven Electric Vehicle" Actuators 15, no. 7: 392. https://doi.org/10.3390/act15070392

APA Style

Li, H., Jin, L., Li, Y., Li, J., Xiao, F., Xie, F., & Wang, Z. (2026). Energy-Optimized Longitudinal–Steering Coordinated Torque Vectoring for an In-Wheel-Motor-Driven Electric Vehicle. Actuators, 15(7), 392. https://doi.org/10.3390/act15070392

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Energy-Optimized Longitudinal–Steering Coordinated Torque Vectoring for an In-Wheel-Motor-Driven Electric Vehicle

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