A comprehensive review on intelligent torque vectoring control for electric vehicle

Abstract

Vehicle dynamic control (VDC) is an important study where the vehicle performance, handling, stability, and statistics of the vehicle can be recorded to improve performance. Torque vectoring controller (TVC) a form of VDC is used to improve vehicle handling and driving in extreme situations by correcting oversteer and understeer conditions, this TVC is used in EV to reduce the consumption of the battery by reducing the general energy use. In TVC, it is broadly classified to classical and intelligent methods where classical methods used a two-stage optimization method via a high and low level controller while intelligent torque vectoring controller (ITVC) methods uses artificial intelligence (AI) based methods like soft computing, machine learning and other AI methods to enhance vehicle performance and efficiency. Each ITVC is reviewed where the advantages, disadvantages and applications of each controller is compared. The study also shows the timeline of ITVC development showing every existing ITVC method being conducted, it also shows the complexity, vehicle stability, braking performance, lateral stability, mechanical energy consumption and energy conversation between the different ITVC methods.

Introduction

Vehicle dynamics (Gillespie, 1992) is the field of study that focuses on understanding how vehicles move and respond to various forces and inputs while in motion. It analyzes the interactions between a vehicle's components, including tires, suspension systems, chassis, and powertrain, along with external forces such as gravity, friction, and aerodynamic drag.

The dynamics of a vehicle can be analyzed in terms of its six degrees of freedom, which encompass longitudinal motion (forward and backward), lateral motion (side to side), and vertical motion (up and down), and rotational movements (yaw, pitch, and roll). Each of these motions is influenced by factors like acceleration, braking, and steering inputs from the driver (Manning and Crolla, 2007).

Key aspects of vehicle dynamics include the study of tire forces (Pacejka, 2002) during acceleration and cornering, the effects of weight distribution on traction and stability, and the role of aerodynamics in shaping vehicle performance. By modeling and simulating these dynamics, this allows engineers to understand how a vehicle will perform under different conditions, supporting the design of safer, more efficient, and better-handling vehicles. Such insights are essential for developing advanced technologies like stability control and active suspension systems, enhancing the overall driving experience.

ITVC methods under vehicle dynamic control technology are especially useful for electric vehicles (EVs) as reduced consumption of electricity from vehicle operation means more uptime of vehicle. One major drawback behind the underutilization of EVs is that their reliability is lower compared to internal combustion engine (ICE) vehicles. With the inevitable shift from fossil fuels to clean energy, driven by environmental or political factors, EVs face significant challenges compared to traditional ICE vehicles, such as limited infrastructure availability, particularly in underdeveloped regions, and high battery storage and maintenance costs, making them less attractive to consumers, which is why techniques this technology reduces the use of battery and increase the general quality of life of EV.

Steering is another crucial aspect of vehicle dynamics. The vehicle's steering system (Bode, 2006; Mammar and Koenig, 2002) must provide precise control over the vehicle's direction of travel, while also being responsive and easy to use. The suspension system contributes to steering by keeping the wheels in contact with the road surface for maximum grip and control. Braking is also a key aspect, requiring reliable, consistent stopping power in various driving conditions. Technologies like anti-lock brake systems (ABS) and electronic stability control (ESC) helps prevent skidding and loss of control during hard braking.

TVC a part of vehicle dynamic control is a means of correcting vehicle oversteer and understeer characteristics during turning and cornering maneuvers. It reduces the vehicle mechanical stress, increases performance and uptime of the vehicle which is especially important as it reduces the battery usage in electric vehicles. EVs play a crucial role in advancing TVC due to their unique powertrain architecture and individual wheel torque control capabilities. Unlike traditional internal combustion engine (ICE) vehicles that rely on mechanical differentials, EV allows precise and independent control of each wheel's torque, significantly enhancing stability, handling, and energy efficiency.

In EVs with multiple motors (e.g., one per wheel or per axle) (Park et al., 2022), TVC can intelligently adjust the torque applied to each wheel based on real-time conditions, improving cornering performance and vehicle stability. Unlike ICE vehicles, which use clutches, differentials, and braking systems to redistribute torque, EV can apply instantaneous torque adjustments electronically, making it faster and more efficient.

EV also allows real-time torque adjustments based on vehicle yaw rate, lateral acceleration, and driver inputs. This improves traction control, reduces understeer and oversteer, and enhances the safety of high-speed maneuvers. EVs can be configured in Front-Wheel Drive (FWD), Rear-Wheel Drive (RWD), or All-Wheel Drive (AWD) setups (Mikle and Bat'a, 2019), making TVC adaptable to different vehicle architectures (Sun et al., 2023). In-wheel motor EVs benefit the most from TVC as they allow for precise control of each wheel independently, eliminating the need for complex mechanical systems.

Numerous technological advancements are being researched to make EVs viable for general use, including regenerative braking, improving wheel dynamics (Koehn and Eckrich, 2004), terrain maneuvers, smart energy limiters, free-wheel driving systems, ABS, suspension control systems (De Bie et al., 2022), ESC, TVC and various methods of traction control like static, rolling (dynamic), and sliding traction control. The combination of these technologies is being implemented more and more in today's EV.

The paper reviews ITVC techniques, evaluates their effectiveness in energy optimization, computational efficiency, efficiency, timeline and compares multiple control strategies to highlight their advantages and limitations. Through already made simulation-based analysis, this paper quantifies and compares the impact of various ITVC methods on key vehicle performance metrics, such as yaw stability, lateral acceleration, and energy consumption (kWh), of vehicle with and without torque vectoring.

By analyzing computational efficiency and real-time feasibility of different ITVC strategies. The computational load associated with Fuzzy Logic (Herath et al., 2024), Model Predictive Control (MPC) (Guo et al., 2024; Hajiloo et al., 2023; Liang et al., 2025), Reinforcement Learning (DDPG) (Deng et al., 2023), and BP Neural Network-based PID controllers is compared to identify their practical applicability in real-time vehicle control systems.

This paper presents a comprehensive review of ITVC systems, a vehicle dynamic control method, offering an overview of available techniques and comparing simulation results to illustrate the advantages and limitations of key strategies. This paper presents a review of ITVC systems, a vehicle dynamic control method, offering an overview of available techniques and comparing simulation results to illustrate the advantages and limitations of key strategies.

Principle of torque vectoring

Torque vectoring control (TVC) (Torque-vectoring.belisso.com, 2009) strategy given in Figure 1 generally consists of:

Reference Generator: Determines the target yaw rate dynamically, factoring in the current steering angle and vehicle speed to achieve a desired optimal understeer behavior.

High-Level Controller: Calculates necessary traction/braking force and yaw moment by referencing pedal inputs and the error between the desired and actual yaw rates.

Low-level controller: A low-level controller aims to distribute torque between the wheels to achieve specific vehicle dynamic responses, such as minimizing yaw rate error and improving handling and stability Figure 2.

Figure 1.

Topology of 4-wheel EV with TVC.

Figure 2.

TVC general scheme.

Reference generator

In TVC, the reference generator (Fujimoto et al., 2004; Hancock et al., 2005) sets the target dynamic behavior of the vehicle. The system calculates the target yaw rate (x) dynamically, drawing on inputs such as steering angle and vehicle speed, and other relevant driver inputs to achieve optimal vehicle behavior, such as improved cornering or stability during maneuvers. Additionally, it generates reference values for key parameters like yaw rate and sideslip angle, which are essential for maintaining vehicle stability and handling. These reference values guide the high-level controller in ensuring the vehicle follows the desired understeer characteristics or meets specific handling performance goals.

In more advanced systems, the reference generator adapts its calculations based on varying conditions, such as the driver's intentions or the vehicle's dynamic state. For instance, it may adjust the understeer gradient to provide more precise control under different driving scenarios, including sporty or energy-efficient modes. Ultimately, the reference generator plays a crucial role in ensuring the vehicle maintains its intended path and stability by providing the high-level controller with the necessary reference values.

In TVC systems, the reference generator calculates a target yaw rate (and sometimes a sideslip angle) using the driver's steering input and the vehicle's speed. The reference for yaw rate is generally based on the steady-state understeer gradient and is mathematically expressed as in equation (1).

$$X_{\mathrm{ref}}={\displaystyle \frac{v_x}{L+K_u{v}_x^2}.\delta }$$

(1)where, $X_{\mathrm{ref}}$ , reference yaw (rad/s) rate; $v_x$ , Longitudinal speed (m/s); L, Distance between front and rear axles/Wheel length (m); $K_u$ , Understeer gradient; $\delta$ , Steering angle (rad).

High-level controller

Receiving driver inputs, vehicle states, and reference generator outputs, the high-level controller (Canale et al., 2007) calculates the total driving torque (T_TOT) and required yaw moment (M_z) for optimal vehicle control. It uses two parallel logics to compute its outputs.

The drivability controller sets the total torque demand, converting accelerator pedal input into a torque reference for the engine or motors via drivability maps, thus meeting driver requirements (Esmailzadeh et al., 2003).

Using a range of control strategies (Chong et al., 1996), the TVC determines the desired yaw moment (M_z) for the vehicle to improve stability and handling, as shown in equation (2).

$$M_z=K_p({\phi }_{\mathrm{ref}}-{\phi }_{\mathrm{act}})+K_i\int ({\phi }_{ref}-{\phi }_{act})dt+K_d{\displaystyle \frac{d}{dt}({\phi }_{\mathrm{ref}}-{\phi }_{\mathrm{act}})}$$

(2)where, $M_z$ , Yaw moment demand (Nm); ${\phi }_{\mathrm{ref}}$ , reference yaw (rad/s) rate from the reference generator; ${\phi }_{\mathrm{act}}$ , actual yaw (rad/s)rate measured by sensors; $K_p$ , $K_i$ , $K_d$ , PID gains, which control responsiveness.

Low-level controller

With the total driving torque and yaw moment demand as inputs, the low-level controller (Shin-ichiro et al., 2000) determines the torque demand for each motor ( $T_{m,i}$ ) and, if needed, the braking pressure for each brake caliper $(p_{b,i})$ . This layer is crucial for over-actuated vehicles, ensuring that high-level demands are met through effective allocation of individual actuator efforts.

The low-level torque distributor is generally designed in one of two ways (Chen et al., 2013): a fixed front-to-rear distribution or an optimal torque allocation to each wheel. This optimal strategy can either prioritize balanced tire adherence or enhance energy efficiency. When energy efficiency takes precedence, the high-level and low-level controllers are often designed together, optimizing the yaw moment for energy savings, sometimes at the expense of handling.

Responsible for torque distribution between the left and right wheels, the low-level controller in a TVC system operates based on yaw rate error or other goals required from the controller like longitudinal stability, lateral stability, slip ratio control, path following etc. The control objective for obtaining yaw rate comprises yaw rate error, control law, wheel torque allocation, and actuator dynamics.

Yaw rate error

To obtain the desired yaw rate for adjusting the vehicle corrective yaw in real time ${\psi }_{\mathrm{desired}}$ , the low-level controller regulates the differential torque $T_{\mathrm{diff}}$ between the left and right wheels. The yaw rate error $e_{\psi }$ is given in equation (3) as:

$$e_{\psi }={\psi }_{\mathrm{desired}}-{\psi }_{\mathrm{actual}}$$

(3)where, ${\psi }_{\mathrm{desired}}$ , Desired yaw rate (from higher-level controller or driver input); ${\psi }_{\mathrm{actual}}$ , Actual yaw rate (from sensor data); $e_{\psi }$ , yaw rate error

Control law

The low-level controller typically uses a PID controller to compute the differential torque $T_{\mathrm{diff}}$ that will reduce the yaw rate error given in equation (4). It adjusts the differential torque based on proportional, which accumulates yaw rate error; Integral term which will over time correct the steady-state error, and the derivative term, which monitors the yaw rate error's rate of change, providing damping to avoid oscillations.

$$T_{\mathrm{diff}}(t)=k_p{e}_{\psi }+k_i{\int }_0^t{e}_{\psi }(\tau )d\tau +k_d{\displaystyle \frac{d}{dt}{e}_{\psi }(t)}$$

(4)where, $T_{\mathrm{diff}}(t)$ Indicates the differential torque applied between the left and right wheels at a particular time. $k_p{k}_i{k}_d$ are PID gains; $e_{\psi }(\tau )$ indicates yaw rate error at time (t).

Wheel torque allocation

The differential torque $T_{\mathrm{diff}}$ is distributed between the left and right wheels. Assuming the total torque $T_{\mathrm{total}}$ supplied by the powertrain is evenly split between the two wheels, the torque at the left and right wheels is given in equations (5) and (6) as:

$$T_{\mathrm{left}}(t)={\displaystyle \frac{T_{\mathrm{total}}}{2}+{\displaystyle \frac{T_{\mathrm{diff}}(t)}{2}}}$$

(5)

$$T_{\mathrm{right}}(t)={\displaystyle \frac{T_{\mathrm{total}}}{2}-{\displaystyle \frac{T_{\mathrm{diff}}(t)}{2}}}$$

(6)where, $T_{\mathrm{left}}(t)$ , is the torque applied to the left wheel at time t; $T_{\mathrm{right}}(t)$ , is the torque applied to the right wheel at time t; $T_{\mathrm{total}}$ , is the total torque from the powertrain.

Actuator dynamics

The actual torque applied by the actuators (e.g., electric motors or brakes) typically follows a first-order response due to physical limitations like actuator delay. This can be modeled for both left wheel and right wheel using equations (7) and (8):

$$T_{\mathrm{left}}(t)={\displaystyle \frac{1}{\tau }(T_{\mathrm{left},cmd}(t)-T_{\mathrm{left}}(t))}$$

(7)

$$T_{\mathrm{right}}(t)={\displaystyle \frac{1}{\tau }(T_{\mathrm{right},cmd}(t)-T_{\mathrm{right}}(t))}$$

(8)where, $T_{\mathrm{left},cmd}(t),T_{\mathrm{right},cmd}(t)$ , are the commanded torques from the controller; $T_{\mathrm{left}}(t),T_{\mathrm{right}}(t)$ , are the actual torques applied at the left and right wheels; $\tau$ , is actuator time constant and how quickly the actuator can respond to changes in the commanded torque

Artificial intelligent methods

AI methods consist of diverse techniques as shown in Figure 3 are algorithms that allow systems to carry out tasks usually requiring human intelligence, such as decision-making, learning, problem-solving, and pattern recognition. These methods equip machines to perceive reason, learn, and operate intelligently, and they are classified according to how they replicate aspects of human cognition.

Figure 3.

Artificial intelligence methods.

Soft computing

Soft computing (Karray and de Silva, 2004; Kecman, 2001) is a field within computational intelligence focused on solving complex, real-world problems where traditional, precise methods are inefficient or impractical. Unlike hard computing, which depends on exact, binary logic and deterministic models, soft computing utilizes approximation and reasoning techniques to manage uncertainty, imprecision, and partial truths.

Inspired by human problem-solving methods relying on intuition, learning from experience, and handling incomplete information soft computing excels at providing robust, approximate solutions rather than precise, optimal ones. This makes it particularly effective in areas such as pattern recognition, optimization, and control systems. They contain methods like Fuzzy logic, Evolutionary computation, Genetic algorithm etc.

Machine learning

Machine learning (ML) (IBM, 2021) is a branch of AI that allows computers to learn from data, enabling decision-making and prediction without explicit programming. It focuses on designing algorithms and models that recognize patterns, learn from experience, and improve over time by processing large datasets. The objective is to create adaptable systems that handle new data and evolving situations with minimal human oversight. Common ML techniques include supervised learning, unsupervised learning, reinforcement learning (RL) (Sutton and Barto, 2015), and neural networks (NN) (Haddoun et al., 2008).

Other AI methods

They are methods like Expert systems (Jackson, 1998) where it aims to replicate the decision-making capabilities of human ability to solve complex problems by reasoning through a knowledge or rule based, frame based or Fuzzy based (Bai and Wang, 2006) systems. Natural language processing (Bird et al., 2009) where instructions are written in human language, allowing users to interact with and instruct computers using natural, conversational language instead of precise syntax code. Computer Vision (Morris, 2004) where data are feed to the system through image and videos of people and robotics where the internal working is being continuously updated to achieve perfect autonomy.

ITVC (Broggi et al., 2016; Parra et al., 2018) purpose is to use emerging technologies to correct the advanced driver assistance system (ADAS) systems, the electronic systems in EV that uses advanced technologies (sensors, cameras, radars, and software) to assist drivers in driving tasks and improve vehicle safety. ADAS technologies aim to reduce human error in driving by offering assistance, warnings (Zhang et al., 2021), and even automated interventions to prevent accidents or make driving more comfortable (Bertipaglia et al., 2024). They range from simple features like lane departure warnings to more complex systems like adaptive cruise control and autonomous emergency braking to an optimal balance between computational cost and performance (Lenzo et al., 2024). The TVC uses these computational technologies to increase the efficiency, performance, stability, driving conditions, etc. In this method, they are utilized in either the lateral or longitudinal side or both depending upon the author.

As compared to traditional TVC, ITVCs, shown in Figure 4, are being used less as it is currently an emerging technology and not everyone is used to intelligent methods. Having said that, this exists some ITVC methods, those are:

Figure 4.

Intelligent TVC system.

Adaptive Neuro-Fuzzy Inference System (ANFIS)

ANFIS (Jang, 1993) system provides real-time and accurate estimations of vertical tire forces, which are crucial for torque distribution in electric vehicles. Unlike traditional estimators, this ANFIS-based approach relies exclusively on measurable variables, avoiding the need for complex or hard-to-measure inputs. The system, shown in Figure 5, combines fuzzy logic's interpretability and NN learning capability, enabling the adaptive tuning of fuzzy rules and membership functions. This provides more accurate estimations compared to traditional analytical methods, particularly during transient conditions, and demonstrates a significant improvement in dynamic handling and vehicle stability (Wong and Ao, 2024).

Figure 5.

ANFIS structure (Haddoun et al., 2008).

The system outperforms traditional methods, such as PID-based controllers (Abdolrasol et al., 2022; Wang et al., 2007) by effectively reducing understeer and enhancing cornering abilities through better torque distribution. The approach not only enhances vehicle dynamics but also contributes to a 10% increase in energy efficiency, demonstrating the system's potential for ADAS in EV.

An elementary Sugeno first order ANFIS model (Al-Hmouz et al., 2012) with two inputs, x and y, incorporating two fuzzy if-then rules outlined in equations (9) and (10):

$$\mathrm{Rule}1:x\mathrm{is}{A}_1\mathrm{and}y\mathrm{is}{B}_1,\mathrm{then}{f}_1=p_{1}x+q_{1}y+r_1$$

(9)

$$\mathrm{Rule}2:x\mathrm{is}{A}_2\mathrm{and}y\mathrm{is}{B}_2,\mathrm{then}{f}_2=p_{2}x+q_{2}y+r_2$$

(10)where $A_1,A_2$ are fuzzy set for input x; where $B_1,B_2$ are fuzzy set for input y; $p_1{q}_1{r}_1$ and $p_2{r}_2{q}_2$ are parameters for linear output $f_1$ and $f_2$ taken from equations (9) and (10).

Layer 1 is shown by equation (11) is the input layer $O_1^i$ ,

$$O_1^i={\mu }_{Ai}(x),O_1^j={\mu }_{Bj}(y),i=1,2$$

(11)where $O_1^i$ , $O_1^j$ are output membership functions for input x and y; where ${\mu }_{Ai}(x),{\mu }_{Bi}(\mathrm{y})$ are membership degrees

Layer 2 is the rule layer $O_2^i$ , given by equation (12)

$$O_2^i=w_i={\mu }_{Ai}(x).{\mu }_{Bi}(x),i=1,2$$

(12)where $w_i$ is the firing rule strength

Layer 3 is the layer of normalization $O_3^i$ , given by equation (13)

$$O_3^i=\overline{w_i}={\displaystyle \frac{w_i}{w_1+w_2},i=1,2}$$

(13)where $\overline{w_i}$ is the strength of normalized firing for each rule.

Layer 4 is the output layer $O_4^i$ , is given in equation (14)

$$O_4^i=\overline{w_i}.f_i=\overline{w_i}.(p_{i}x+q_{i}y+r_i),i=1,2$$

(14)where $f_i$ is the output of the linear equation for each rule.

Layer 5 is the summation layer $O_5$ is given in equation (16)

$$O_5=\sum _i{O}_4^i=\sum _i\overline{w_i}.f_i,i=1,2$$

(15)

This gives the final ANFIS formula equation (16) where,

$$O={\displaystyle \frac{w_1}{w_1+w_2}.f_1+{\displaystyle \frac{w_2}{w_1+w_2}.f_2,i=1,2}}$$

(16)where $w_1,w_2$ are firing strengths of the fuzzy rules and $f_1,f_2$ are output functions linked to each rule.

Fuzzy logic controller

A fuzzy logic controller (FLC) (Abdolrasol et al., 2023; Kahveci et al., 2013), controls lateral torque distribution by determining the torque needed on each side of the vehicle, based on yaw rate and sideslip angle, and adjusts it with fuzzy rules for enhanced stability. Steps for FLC include:

Fuzzification: Translates crisp inputs into fuzzy values by assigning them a degree of membership within fuzzy sets. For an input variable xxx, the degree of membership in fuzzy set A is denoted by ${\mu }_A(x):X\to [0,1]$ , where ${\mu }_A(x):X\to [0,1]$ is the membership function, mapping values to degrees between 0 and 1.

Inference: Applies fuzzy rules to the fuzzified inputs. The rules are usually shown as ‘if-then’ statements, such as:

Rule 1: If $x_1$ is $A_1$ and $x_2$ is $B_1$ , output becomes $C_1$

Rule 2: If $x_1$ is $A_2$ and $x_2$ is $B_2$ , output becomes $C_2$

Firing strength rule of each is given in equations (17) and (18) calculated using a logical operation such as the min (AND) operator:

$$w_1=\min ({\mu }_{A1}(x_1),{\mu }_{B1}(x_2))$$

(17)

$$w_2=\min ({\mu }_{A2}(x_1),{\mu }_{B2}(x_2))$$

(18)where $w_1,w_2$ represent the firing strengths of the rules.

Aggregation: The fuzzy sets from each rule’s output are aggregated into a single fuzzy set, as given in Equation (19). Each rule output is scaled according to its firing strength. For example, if $C_1$ is the output membership function, the scaled version is:

$${\mu }_{C1}(y)=w_1.{\mu }_{C1}(y)$$

(19)

Defuzzification: Changes the fuzzy output set back into a crisp value. The centroid method is the preferred approach, where the crisp output y is determined in equation (20) as:

$$y={\displaystyle \frac{{\int }_{\mathrm{domain}}y.{\mu }_C(y)dy}{{\int }_{\mathrm{domain}}{\mu }_C(y)dy}}$$

(20)where ${\mu }_C(y)$ corresponds to the aggregated membership function over the output domain.

Back Propagation Neural Network (BPNN)

In BPNN (Geng et al., 2018), the difference from a NNis that during training process the backpropagation algorithm for supervised learning. It automatically adjusts the weights of the network by propagating the error backward from the output layer to the input layer during training, enabling the network to learn and reduce error over time and during error minimization it systematically reduces the error by calculating the gradient of the error function with respect to the network's weights and adjusting them using gradient descent. This allows for iterative learning and improvement. The BPNN uses gradient descent to minimize the loss function and continuously update the weights.

The primary equation for backpropagation is below (21) where it consists of updating the weights in the NN. The update rule for weight wbetween neuron i and neuron j is:

$${w^{(t+1)}}_{ij}={w^t}_{ij}-\eta {\displaystyle \frac{\mathrm{\partial }E}{{\mathrm{\partial }}_{w_{ij}}}}$$

(21)where, $w_{ij}$ , is the weight connecting neuron i to j; $\eta$ , is the learning state; $E$ is the error function; $\eta (\mathrm{\partial }E/{\mathrm{\partial }}_{w_{ij}})$ , is the gradient of the error wrt $w_{ij}$ , t is the time

Genetic Fuzzy Yaw Movement Controller (GFYMC)

The controller uses genetic algorithms (GA) to automatically optimize the FLC (Jalali et al., 2013a). The GA searches for the optimal membership function and fuzzy rules by evaluating performances from different configurations and adjusting them over multiple generations. This allows for better adaptation to changing conditions and enhances the controller's performance. It also continuously adapts its fuzzy rules and membership functions based on real-time performance feedback. This results in a more flexible and adaptive control strategy, which is especially useful for complex, dynamic systems like vehicle yaw movement.

By optimizing the parameters using genetic algorithms, the GFYMC provides improved performance in terms of stability, precision, and response to dynamic changes in the vehicle's movement, especially in critical driving situations like cornering and sudden maneuvers.

$$\mathrm{Fuzzification}:{\mu }_A(x)={\displaystyle \frac{1}{1+{(x-c/\sigma )}^2}}$$

(22)where, x stands for the input variable; c is the center point of the membership function; σ represents membership function width.

$$\mathrm{Fuzzy}\mathrm{Rule}\mathrm{Evaluation}:w_i=\min ({\mu }_A(x_1),{\mu }_B(x_2))$$

(23) $w_i$ , is the firing strength.

$$\mathrm{Defuzzification}:y={\displaystyle \frac{\sum w_i.f_i}{\sum w_i}}$$

(24)where $f_i$ are the rule output values, and $w_i$ are the firing strengths.

In GFYMC, GA optimizes the parameters (e.g., c, σ and fuzzy rule set). It evolves a population of candidate solutions over several generations, using operators like:

Selection; chooses the best-performing fuzzy rule configurations. Crossover; combines parts of two fuzzy rule sets to create a new solution. Mutation; randomly modifies parts of a fuzzy rule set to explore new possibilities.

The GA minimizes the yaw error $e_{\phi }$ by optimizing the fuzzy rule set given in equation (25):

$${\min }_{\mathrm{rules}}\sum ({e^2}_{\psi })=\sum ({\psi }_{\mathrm{desired}}-{\psi }_{\mathrm{actual}}{)}^2$$

(25)where, $e_{\phi }$ indicates yaw error; ${\psi }_{\mathrm{desired}}$ shows requested yaw rate; ${\psi }_{\mathrm{actual}}$ shows the current yaw rate.

Through GA, the controller finds the best fuzzy rules and membership functions to minimize this error, providing more accurate and adaptive yaw control.

Neuro-fuzzy controller

A neuro-fuzzy controller (Ulutas et al., 2020) enhances a generic fuzzy controller by introducing learning capabilities, allowing it to automatically tune its rules and membership functions through training. This makes it more adaptive and able to handle dynamic environments while maintaining the interpretability of a FLC.

It is a hybrid system that combines the principles of FLC and NN to improve the adaptability and learning capabilities. It adjusts its fuzzy rules and membership functions automatically based on input-output data using learning algorithms via hybrid method that involves gradient descent or backpropagation.

Structured similarly to a FLC with rules and membership functions, but with the added ability to learn. The NN aspect of the controller tunes the parameters of fuzzy sets and the rules, making it adaptive but retains the interpretability of a fuzzy controller. It adjusts its fuzzy rules and membership functions based on the data it encounters, offering both learning capability and human-readable rule-based decision making. Retains the interpretability of fuzzy logic while incorporating the learning ability of neural networks. The fuzzy rules can be interpreted, but they are adjusted by the NN. The steps for neuro fuzzy controller are given from equations (26)–(28).

$$\mathrm{Fuzzification}:({\mu }_A(x),{\mu }_B(y)$$

(26)

$$\mathrm{Firing}\mathrm{strength}:w_1=({\mu }_{A1}(x),{\mu }_{B1}(y),w_2=({\mu }_{A2}(x),{\mu }_{B2}(y)$$

(27)

$$\mathrm{Normalization}:\overline{w_1}={\displaystyle \frac{w_1}{w_1+w_2},\overline{w_2}={\displaystyle \frac{w_2}{w_1+w_2}}}$$

(28)

$$\mathrm{Rule}\mathrm{outputs}:f_1=p_{1}x+q_{1}y+r_1,f_2=p_{2}x+q_{2}y+r_2$$

(29)

$$\mathrm{Overall}\mathrm{output}:y=\overline{w_1}.f_1+\overline{w_2}.f_2$$

Learning: $p_i{r}_i{q}_i$ are adjusted using backpropagation to minimize error between the actual and desired outputs.

Deep Deterministic Policy Gradient (DDPG)

Designed for continuous action spaces, this reinforcement learning algorithm uses an actor-critic structure with deep neural networks to approximate the policy (actor) and value function (critic). DDPG is a model-free (Silver et al., 2014) off-policy approach that benefits from experience replay and target networks to make training more stable and efficient. The DDPG Reinforce Learning method is shown in Figure 6.

Figure 6.

DDPG reinforce learning method (Guo et al., 2020).

Actor: The actor ( $a_t$ ) given in equation (30) network maps the state to an action deterministically

$$a_t=\pi (s_t|{\theta }^{\pi })$$

(30)where $\pi (s_t|{\theta }^{\pi })$ is the actor network parameterized by ${\theta }^{\pi }$ and $s_t$ is current state

Critic: The role of the critic ( $y_t$ ) given in equation (31) is to estimate the action-value function

$$y_t=r_t+\gamma Q^{\mathrm{\prime }}(s_{t+1},{\pi }^{\mathrm{\prime }}(s_{t+1}|{\theta }^{{\pi }^{\mathrm{\prime }}})|{\theta }^{Q^{\mathrm{\prime }}}$$

(31)where $r_t$ is the reward, $\gamma$ is the discount factor and Q′ and π′ are the target critic and actor networks, respectively.

Critic Loss function: Training of the critic network given in equation (31) involves minimizing the mean squared error between its predicted Q-values and the target values.

$$L({\theta }^Q)={\displaystyle \frac{1}{N}\sum _t(y_t-Q(s_t,a_t|{\theta }^Q{)}^2}$$

(32)

Actor update: The actor is adjusted based on the gradient of the critic's value function with respect to actions, pushing the actor toward actions that maximize the Q-value, the adjusted value is given in equation (33) as ${\theta }_{{\theta }^{\pi }}J$ where

$${\theta }_{{\theta }^{\pi }}J\approx {\displaystyle \frac{1}{N}\sum _t{\mathrm{\nabla }}_{a}Q(s,a|{\theta }^Q){|}_{a=\pi (s|{\theta }^{\pi })}{\mathrm{\nabla }}_{{\theta }^{\pi }}\pi (s|{\theta }^{\pi })}$$

(33)

Target network update: The target networks are updated softly using ${\theta }^{Q^{\mathrm{\prime }}}$ and ${\theta }^{{\pi }^{\mathrm{\prime }}}$ given by equations (34) and (35)

$${\theta }^{Q^{\mathrm{\prime }}}\leftarrow {\theta }^Q(1-\tau ){\theta }^{Q^{\mathrm{\prime }}}$$

(34)

$${\theta }^{{\pi }^{\mathrm{\prime }}}\leftarrow {\theta }^{\pi }(1-\tau ){\theta }^{{\pi }^{\mathrm{\prime }}}$$

(35)

where, $\tau \in [0,1]$ controls how fast the target networks are updated.

${\theta }^{Q^{\mathrm{\prime }}}$ is the target Q-function network parameters.

${\theta }^Q$ is the current Q-function network parameters.

${\theta }^{{\pi }^{\mathrm{\prime }}}$ is the target policy (actor) network parameters.

${\theta }^{\pi }$ is the current policy (actor) network parameters.

$\tau$ is the soft update factor (or interpolation constant) and it controls the speed of updates between the main network and the target network, typically a small value (e.g., 0.001).

Neural network

Neural networks (NNs) (Dendaluce Jahnke et al., 2019) are increasingly being used in torque vectoring control systems due to their ability to model complex nonlinear dynamics and adapt to real-time conditions. In a vehicle with torque vectoring, the distribution of torque between the wheels is crucial for optimizing handling, stability, and traction (Gao et al., 2024). Traditional control methods such as Proportional-Integral-Derivative (PID) or rule-based controllers may not fully adapt to varying road conditions, driving styles, and vehicle dynamics. Neural networks offer a powerful alternative by learning optimal control strategies from data and making real-time adjustments based on sensor inputs. The general figure for NN is given in Figure 7.

Figure 7.

Neural network.

Weighted sum: Each input $x_i$ is associated with a weight $w_i$ , and all the inputs are combined linearly with the bias b.

$$z=w_1.x_1+w_2.x_2+w_3.x_3+w_4.x_4+b$$

(36)

Activation function: The weighted sum z is passed through an activation function f(z) to introduce non-linearity.

$$a=f(z)=f(w_1.x_1+w_2.x_2+w_3.x_3+w_4.x_4+b)$$

(37)

Output: The result a from the activation function is the final output y of the NN:

$$y=a=f(w_1.x_1+w_2.x_2+w_3.x_3+w_4.x_4+b)$$

(38)where, $x_1,x_2,x_3,x_4$ are inputs; $w_1,w_2,w_3,w_4$ are the weights of each input; b is the bias; $f(z)$ is the activation function; y is the output of the network.

The list of intelligent TVC methods using AI methods is listed under Table 1 and the method of implementation differs from author to author as shown:

Table 1.

List of intelligent TVC method and implementation

Author	Method
Dendaluce Jahnke (Dendaluce Jahnke et al., 2019)	Here the author uses predictive NN to optimize torque vectoring in multi-motor electric vehicles in real-time (Parra et al., 2021a). The NN predict wheel slip for different torque distributions, enhancing vehicle dynamics, energy efficiency, and thermal management. The approach is implemented on parallel embedded platforms like GPUs and FPGAs to meet real-time computational demands, allowing for faster optimization and improved handling and stability under varying driving conditions.The NN is used to predict wheel slip for a batch of potential future control actions, enabling real-time torque vectoring optimization and serves as a substitute for computationally expensive physical models of vehicle dynamics, making real-time optimization feasible within the stringent timing requirements of automotive applications.EV dynamics features a four-motor topology, with each wheel independently powered and the objective is to reduce slip and improving stability during cornering, enhancing energy efficiency by optimizing motor operations, mitigating thermal loads across the motors and ensuring smoother operations for better vehicle handling and reduced mechanical stress.NN Architecture composes of a feedforward NN with three hidden layers; The input layer contains variables like current wheel slips, steering wheel position, vehicle speed, and inertial sensor data. The hidden layer features 32, 16, and 8 neurons respectively and the output layer provides torque recommendations for each wheel. The NN inference is implemented on two embedded platforms:GPU (Graphics Processing Unit): Used for high-speed batch prediction due to its parallel processing capability and FPGA (Field-Programmable Gate Array) (Guo et al., 2017): Offers low-latency predictions and energy efficiency, suitable for real-time applications. The GPU implementation achieves significant performance improvements, with optimizations like shared memory and constant memory for handling weights and biases efficiently. The NN predictions feed into a torque-vectoring optimization algorithm, which selects the best torque distribution for the current driving conditions. The system adjusts priorities dynamically, focusing on stability under critical conditions and energy efficiency otherwise.It provide real-time predictions for torque distribution to enhance vehicle stability, energy efficiency, and thermal management], demonstrate the feasibility of deploying complex machine learning models on automotive-grade embedded platforms and achieve high-speed inference with low resource utilization, making the solution viable for cost-sensitive automotive applications. The block diagram for predictive NN is given in Figure 8.Advantages: Speed: The GPU and FPGA implementations enable rapid NN inference, critical for real-time applications. Accuracy: The NN provides precise slip predictions, leading to improved stability and handling. Efficiency: Optimized torque distribution reduces energy consumption and balances thermal loads across motors. Scalability: The approach is adaptable to vehicles with different motor configurations and driving scenarios. Disadvantages: Complexity: Designing and training the NN for accurate slip predictions is resource-intensive. Hardware Limitations: The performance of GPU and FPGA implementations depends on the availability of computational and memory resources. Integration: Combining NN-based predictions with traditional control strategies requires careful tuning and validation. Applications: Enhances EV stability and energy efficiency in multi-motor configurations. Supports safety features like stability control and anti-slip mechanisms. Enables precise control of torque distribution for improved cornering and acceleration.
Jalali (Jalali et al., 2013b)	This paper combines a genetic fuzzy active steering controller (GFASC) with ATVC for electric vehicles. The GFASC uses fuzzy logic to manage nonlinear dynamics and uncertainty in vehicle control, while the genetic algorithm optimizes the fuzzy logic parameters for adaptive, real-time control. This hybrid intelligent system distributes control effort between in-wheel motors and active steering to improve vehicle handling, stability, and path-following performance (Jalali, 2004). The integration of these systems ensures enhanced vehicle dynamics by adapting to various driving conditions and making real-time adjustments to optimize stability and control.ATVC is designed to distribute corrective yaw moments between left-to-right and front-to-rear in-wheel motors. It optimally manages torque allocation to improve stability, especially at high-speed or near-limit conditions and reduces yaw rate and sideslip angle errors while enhancing the vehicle's agility during dynamic maneuvers.The GFASC superimposes driver steering inputs with corrective active steering interventions to maintain stability. A GA is used to optimize the parameters of the fuzzy controller, improving its adaptability to diverse scenarios. It is effective in reducing steering effort required during slippery conditions or when the vehicle approaches its handling limits.A Gaussian activation function governs the interplay between the two controllers, ensuring a smooth transition of control efforts based on the severity of the maneuver. Under mild conditions, the GFASC operates independently, reducing the reliance on in-wheel motor interventions, which can induce oscillations. When the corrective steering angle exceeds a threshold (e.g., at 3°), the ATVC is gradually activated to assist in maintaining stability. The integrated system leverages the strengths of both controllers while minimizing their individual limitations, such as oscillations caused by ATVC or actuator constraints in GFASC and is tested using a two-passenger, all-wheel-drive EV model, equipped with four direct-drive in-wheel motors and an active steering system. Here the papers aim to achieve optimal vehicle stability by utilizing complementary control efforts from both steering and TVC. Improve handling and path-following capabilities, particularly during challenging maneuvers like double-lane changes and braking on μ-split surfaces and enhance longitudinal dynamics by minimizing speed losses during critical maneuvers.The paper shows significant improvements in yaw rate and sideslip control by reducing errors and oscillations. By lowering steering effort from driver input requirements. Speed Maintenance by showing minimal speed loss compared to standalone controllers. It also outperformed standalone ATVC and GFASC in all critical parameters. The ITVC method used by this author is given in Figure 9. Advantages: Dynamic Adaptability: The integrated strategy dynamically distributes control efforts based on real-time driving conditions. Enhanced Stability: Demonstrates superior performance compared to standalone ATVC or GFASC systems, especially in critical situations. Driver Perception: Minimizes disruptive interventions, ensuring smoother operation and better driver acceptance. Efficiency: The system balances safety and performance without excessive reliance on individual actuators. Disadvantages: Complexity of Integration: Designing and tuning the activation function for seamless coordination between the ATVC and GFASC requires extensive simulation and testing. Actuator Constraints: Both systems have performance limits, such as actuator saturation in steering or torque generation at high speeds. Computational Demand: Real-time implementation necessitates efficient algorithms and robust hardware. Applications Suited for EV with multiple independent in-wheel motors requiring precise control over torque distribution and steering. Improves safety, especially in adverse road conditions. Enhances path-following, stability, and maneuverability, critical for self-driving scenarios.
Jalali (Jalali, 2012)	Development of a genetic-fuzzy active steering controller for electric vehicles (Jalali et al., 2013b) with in-wheel motors is done. The system combines fuzzy logic, which manages nonlinear dynamics and uncertainty in vehicle control, with genetic algorithms, used to optimize the fuzzy logic controller's membership functions. This hybrid approach allows the system to adaptively determine the optimal corrective steering angle to maintain vehicle stability. The genetic algorithm enhances the system by optimizing the fuzzy control parameters based on multiple criteria, such as minimizing yaw rate, sideslip angle, and trajectory errors, resulting in improved vehicle handling and stability during various driving maneuvers.It is designed to address the nonlinear dynamics of vehicular motion, leveraging expert knowledge to define the fuzzy rule base in linguistic terms. The input variables are the yaw rate error and its derivative, while the output is the corrective steering angle. It is processed inputs using a Mamdani fuzzy inference system and then the outputs are defuzzified to generate precise corrective steering angles.Multi-criteria GA is used to tune the shapes and distributions of fuzzy membership functions, ensuring optimal control performance. The algorithm minimizes trajectory, yaw rate, and sideslip angle errors by optimizing membership function parameters. Chromosome representation includes scaling parameters for input and output variables, with fitness functions based on weighted mean-squared errors for trajectory and dynamic stability metrics. The controller interacts with a reference model to compute desired yaw rate and trajectory based on steering and speed inputs. A scaling function is employed to fine-tune membership functions symmetrically, improving accuracy without manual adjustments.The controller is validated using simulations of double-lane-change maneuvers, braking in turns, and μ-split road conditions. Implemented on an electronic control module for hardware-in-the-loop (HIL) (Dendaluce et al., 2016) and operator-in-the-loop (OIL) driving simulators to assess real-world feasibility. The objective is enhance vehicle stability by minimizing yaw rate and sideslip angle errors. To improve handling during dynamic and emergency maneuvers and provide a robust, adaptive control solution that requires minimal manual tuning.The model is demonstrate superior performance in simulations and driving tests by reducing yaw rate and trajectory errors during double-lane-change and braking scenarios and increasing stability on μ-split roads, mitigating side-pushing effects. The ITVC method used by the author is given in Figure 10.Advantages: Robustness: Handles nonlinear vehicle dynamics effectively. Adaptability: Genetic tuning ensures optimal performance under diverse conditions. Driver-Friendly: Reduces steering effort and improves comfort during maneuvers. Real-Time Feasibility: Implements efficient computational techniques for real-world application. Disadvantages: Optimization Complexity: Genetic algorithm tuning is computationally intensive. Actuator Limits: Steering systems have finite correction capabilities. Scenario-Specific: Performance is tailored to predefined driving conditions, requiring revalidation for broader applications. Applications: Ideal for in-wheel motor setups requiring precise motion control in EV Enhances safety in adverse conditions. Facilitates robust path-following and stability control in autonomous vehicle
Jalali (Jalali et al., 2009)	The intelligent method used in this paper leverages soft computing techniques (Jalali, 2012) involving fuzzy logic combined with a genetic algorithm to develop an advanced torque vectoring controller for an electric vehicle with in-wheel motors. This soft computing approach allows for real-time, adaptive distribution of torque by calculating the corrective yaw moment based on current driving conditions (Jalali et al., 2009).The fuzzy logic manages the uncertainty in the system, while the genetic algorithm optimizes the fuzzy control parameters (Jalali, 2013a), ensuring that the system dynamically adapts to various driving conditions for improved vehicle stability and control. The genetic fuzzy yaw moment controller combines the principles of genetic algorithms and fuzzy logic to develop a high-level supervisory control mechanism for an electric vehicle with in-wheel motors.This system integrates two major soft computing technique using FLC for handling uncertainty and imprecision in determining corrective yaw moments required to stabilize the vehicle. It allows the system to mimic human-like reasoning to address non-linear and dynamic systems and GA to optimize the parameters of the fuzzy logic system, ensuring that the control strategy is fine-tuned for effectiveness across various driving scenarios. The GFYMC calculates the required corrective yaw moment by evaluating errors in yaw rate and sideslip angle and serves as a supervisory module, assigning tasks to lower-level controllers and actuators, which include individual in-wheel motors. The controller's primary objective is to stabilize the vehicle dynamics by distributing torque in a manner that reduces deviations in vehicle trajectory during both normal and emergency driving conditions.The GFYMC is part of the advanced torque vectoring control system for the AUTO21EV, a two-passenger, all-wheel-drive EV where the system employs left-to-right and front-to-rear torque vectoring strategies (Jalali et al., 2012) to distribute corrective yaw moments across in-wheel motors. The GFYMC interacts with a driver model and simulations to assess performance during complex maneuvers such as double-lane changes, step-steer responses, and brake-in-turn situations (Lenzo et al., 2018). The block diagram used by the author is given in Figure 11.Advantages: Optimized Performance: Genetic algorithms ensure the fuzzy logic controller is tailored to the vehicle dynamics. Precise Control: The controller dynamically adjusts torque to individual wheels, maintaining stability even near the vehicle's handling limits. Improved Stability: The GFYMC reduces yaw rate and sideslip errors, enhancing the vehicle's responsiveness during sudden maneuvers. Disadvantages: Oscillations in yaw rate and sideslip responses due to the actuation of in-wheel motors. Computational intensity in optimizing the fuzzy logic system parameters using genetic algorithms. Sensitivity to the hardware capabilities of in-wheel motors and their limitations during high-speed rotations. Applications: Enhances superior path following and tracking for automated EV. Precise tuning of makes it favorable for high precision tuned EV.
Taherian (Taherian et al., 2021)	A self-adaptive TVCwith Reinforcement Learning (RL) with Deep Deterministic Policy Gradient (DDPG) algorithm is used (Taherian et al., 2021). The RL automatically tune the parameters of the torque-vectoring controller. RL allows the system to learn through a trial-and-error mechanism without requiring prior knowledge or ground truth labels, making it ideal for complex, dynamic environments. Here the TVC ensures lateral and yaw stability by adjusting corrective torques on individual wheels based on the vehicle's center of gravity (C.G) forces. The desired forces at the C.G are calculated based on driver inputs (e.g., steering angle and throttle) and actual vehicle states, aiming to minimize the error between desired and actual forces.Integration of DDPG Algorithm using an actor-critic reinforcement learning method is used to adaptively tune the control input weights of the TVC (Bîndac et al., 2022). The actor network predicts the optimal control actions (weights), while the critic network evaluates the predicted actions to ensure maximized long-term rewards. This approach dynamically updates the weighting parameters of the controller, enabling real-time adaptability to changing driving conditions (Kuutti et al., 2019). The system architecture includes a command interpreter module (CIM) to generate desired forces at the vehicle's C.G based on the reference inputs and vehicle states. RL computes the weight adjustments for the control actions to reduce errors between desired and actual forces, ensuring vehicle stability and handling.The controller is tested on a four-wheel vehicle model with nonlinear tire dynamics from Pacejka model (Taherian et al., 2021) in MATLAB/Simulink. Simulations include various driving scenarios, such as different surface frictions (e.g., icy roads with low friction coefficients) and speeds, to validate the system's robustness. The objective of the paper is to improve vehicle stability and handling by dynamically adjusting torque distribution among wheels. To enhance adaptive control capabilities under varying driving conditions (e.g., surface friction, speed) and validate robustness and generalization of the learned policies in scenarios not encountered during training. The block diagram used by the author is given in Figure 12.Advantages: Adaptability: Real-time parameter tuning enables the controller to adjust to changing environments and driving conditions. Improved Stability: Outperforms traditional tuning methods (e.g., manual and genetic algorithm tuning) in maintaining vehicle stability. Energy Efficiency: Optimized torque distribution contributes to better energy management. Generalization: Demonstrates robustness in scenarios beyond the training environment, such as unforeseen surface conditions or driving inputs. Disadvantages: Computational Demand: Reinforcement learning, particularly DDPG, requires substantial computational resources for training and execution. Complexity of Reward Design: The effectiveness of the RL-based controller heavily depends on the design of an appropriate reward function. Limited Direct Control: The approach only considers longitudinal corrective actions, leaving lateral forces uncontrolled, which may lead to suboptimal performance in certain scenarios. Applications: Enhances safety and control in dynamic and unpredictable driving conditions. Ideal for EV requiring precise and adaptive torque management systems. Provides robust stability and handling improvements in real-time, addressing challenges like low-friction surfaces and high-speed maneuvers.
Parra (Parra et al., 2019)	The method proposed in the document focuses on an energy-efficient TVC approach that integrates a fuzzy logic controller (Lu et al., 2016) and a NN-based vertical tire force estimator. This intelligent system aims to optimize torque distribution in electric vehicles with multiple motors, enhancing both vehicle dynamics and energy efficiency. The FLC manages the yaw moment distribution, while the neural network accurately estimates vertical tire forces in real-time, adjusting the torque applied to each wheel for better grip and stability. Additionally, regenerative braking is incorporated to further reduce energy consumption. The system is designed for real-time implementation on automotive hardware, such as FPGAs, ensuring both performance and efficiency.A Fuzzy Yaw Moment Controller is used to manage lateral torque distribution, ensuring optimal yaw moment control for vehicle stability. Inputs to the controller include yaw rate error, yaw rate derivative error and sideslip angle error.Neuro-Fuzzy Vertical Tire Force Estimator (Pacejka and Besselink, 1997) is used to estimate the vertical forces acting on the tires, which are critical for determining wheel grip and optimal torque allocation. The estimator relies on vehicle dynamics variables that are measurable using an Inertial Measurement Unit (IMU), such as acceleration, velocity, and wheel rotation (Chen and Huang, 2004). Outputs from the estimator are used to calculate longitudinal torque percentages ensuring torque is applied to wheels with higher grip.The algorithm is validated using the Dynacar high-fidelity vehicle dynamics simulator where three powertrain topologies are tested: Front-Wheel Drive (FWD), Rear-Wheel Drive (RWD), and All-Wheel Drive (AWD). A skid-pad test is used to evaluate the lateral dynamics and critical speed performance of each topology.The objective is to enhance vehicle stability and handling by optimizing torque distribution among wheels. To demonstrate the adaptability of intelligent control systems across different powertrain configurations and to reduce dependency on detailed physical modeling by leveraging fuzzy and neuro-fuzzy systems.The algorithm achieves significant improvements in vehicle dynamics by increasing critical speed and lateral acceleration for all configurations, with the highest improvement (12%) observed in AWD vehicles. By eliminates understeering in FWD vehicles and oversteering in RWD vehicles, while maintaining neutral handling in AWD vehicles and demonstrating robust adaptability and effectiveness without requiring parameter retuning across different topologies (Parra et al., 2021b). The block diagram for ITVC used by the author is given in Figure 13.Advantages. Flexibility: The same torque vectoring algorithm is applicable to FWD, RWD, and AWD configurations without modification. Reduced Model Dependency: Intelligent control techniques require minimal reliance on precise vehicle dynamic models. Improved Dynamics: Enhanced lateral acceleration and cornering behavior for all powertrain configurations. Scalability: Suitable for a wide range of electric vehicle architectures. Disadvantages: Complexity of Integration: Requires careful tuning of fuzzy membership functions and neuro-fuzzy estimators. Scenario Specificity: Performance heavily depends on the driving conditions and road friction levels. Computational Demands: Real-time implementation on hardware requires efficient algorithms and optimization. Applications: Optimizes torque distribution for vehicles with independent in-wheel motors in EV Enhances safety and handling in dynamic driving scenarios. Provides robust torque control for precise trajectory tracking in autonomous vehicle
Parra (Pacejka and Besselink, 1997)	The method used in intelligent control techniques for TV in EV with different powertrain topologies, including front-wheel drive (FWD), rear-wheel drive (RWD), and all-wheel drive (AWD). The approach utilizes a FLC combined with a neuro-fuzzy vertical tire force estimator (Pacejka and Besselink, 1997). This method calculates optimal torque distribution between the wheels to enhance vehicle stability and dynamics during cornering, using yaw rate, slip angle, and tire forces as inputs. The effectiveness of the proposed method is validated through vehicle under different driving conditions.FLC and SVM (Yue-Lin et al., 2013) is used to manage the lateral torque distribution. It calculates the torque percentage to be applied to each side of the vehicle based on yaw rate error, its derivative, and the sideslip angle error. It effectively adjusts the torque distribution to improve vehicle dynamics during cornering and stability scenarios.Neural Network-Based Vertical Tire Forces Estimator is designed to estimate vertical tire forces in real-time, crucial for accurate torque distribution. It uses a set of 16 measurable variables (e.g., steering angle, accelerations, wheel torques, and angular speeds) and is implemented in an FPGA (Field-Programmable Gate Array) for high computational efficiency, achieving execution speeds significantly faster than traditional approaches.The paper also includes integration with regenerative braking where a subsystem of this technique is used to enhance energy efficiency by during understeering or oversteering scenarios. The sideslip angle determines when regenerative braking is activated, optimizing both energy consumption and vehicle stability. For hardware implementation the entire control system is validated on a hardware-in-the-loop (HiL) setup, using an embedded system (FPGA and ARM microcontroller) for real-time execution. The NN estimator is optimized for FPGA implementation, balancing computational cost and resource utilization.Purpose and Objectives of this paper is to improve vehicle dynamics behavior by optimally distributing torque among wheels. To enhance energy efficiency by reducing power train losses through regenerative braking and precise torque distribution. Ensure real-time implementation feasibility, addressing computational and hardware limitations. The block diagram for ITVC using fuzzy and vertical estimator is given in Figure 14.Advantages: Dynamic Improvement: Enhances vehicle stability and cornering capabilities in varying road conditions. Energy Efficiency: Achieves up to 13% reduction in energy consumption compared to traditional approaches. Real-Time Operation: Utilizes FPGA for fast computation, ensuring real-time control during challenging maneuvers. Reduced Model Dependency: Combines neural networks and fuzzy logic to minimize reliance on detailed physical models. Disadvantages: 1. Complexity: Requires careful design and optimization for FPGA implementation. 2. Hardware Constraints: Balancing accuracy and computational efficiency within limited FPGA resources. 3. Selective Activation: Regenerative braking activation thresholds must be finely tuned to avoid compromising stability. Applications: 1. Ideal for EV with multiple motors, where precise torque vectoring is critical for performance. 2. Enhances safety, stability, and efficiency in automated or semi-automated driving scenarios. 3. Contributes to extending driving range through efficient power distribution and regeneration strategies.
Geng (Geng et al., 2018)	Here the author employs an intelligent torque distribution control strategy for EV with in-wheel motors. The use of a BPNN combined with a PID algorithm to dynamically adjust torque distribution. The system continuously learns and adapts based on two critical parameters: yaw rate and body slip angle, which are optimized through a weighting mechanism (Edelmann and Plochl, 2017). The NN processes real-time feedback to calculate the desired values for these parameters, while also considering variations in tire stiffness and road conditions (Moazenzadeh et al., 2018). This adaptive approach, along with the constraints on motor torque and road adherence, ensures enhanced vehicle stability and performance under varying driving conditions.BP Neural Network PID Algorithm controller combines BPNN and PID control loops. The NN is responsible for adapting the PID parameters (Kp, Ki​, Kd) dynamically, based on the vehicle's real-time operating conditions. The PID controller utilizes these dynamically tuned parameters from the weight factor and yaw rate deviation to compute the corrective yaw moment torque Mz.The system incorporates double-parameter state feedback control, considering both the yaw rate and body slip angle to improve lateral stability and reduces under/oversteer. A state observer (Parra et al., 2019) is constructed to estimate these parameters in real-time, and a weight factor adjusts the emphasis between yaw rate and slip angle control. The controller accounts for motor torque characteristics by limitations based on motor working conditions like voltage, temperature, and rotation speed. The road adherence limits by preventing excessive torque that might lead to tire slippage or loss of lateral adherence, especially on low-friction surfaces. A Linear Quadratic Regulator (LQR) algorithm is incorporated to optimize torque distribution under constraints, balancing performance and stability.The objective is to enhance vehicle stability by controlling yaw rate and body slip angle simultaneously, preventing tire slippage and maintain road adherence under various conditions and dynamically adjust controller parameters to adapt to changing road and driving conditions.The system was validated through simulations of emergency double lane-change maneuvers (Jalali, 2012) on wet roads with a friction coefficient without the constraints of vehicle exhibited instability, diverging from the desired trajectory. It successfully performed lane changes, maintaining yaw rate and body slip angle within safe limits and demonstrated effective torque allocation and reduced speed losses compared to control systems without adherence constraints. The block diagram used by the author based on the paper is given in Figure 15.Advantages: Real-Time Adaptability: Neural network dynamically adjusts PID parameters based on vehicle state. Improved Stability: Combines yaw rate and body slip angle control to reduce understeering and oversteering. Constraint Handling: Ensures torque distribution adheres to motor and road limitations. Flexibility: Applicable to complex driving scenarios like double lane changes on low-friction roads. Disadvantages: Computational Demands: Real-time implementation of NN-based parameter tuning requires efficient processing capabilities. Sensitivity to Model Accuracy: The effectiveness of desired parameter estimation relies on the fidelity of the vehicle dynamic model. Complex Tuning: Designing the neural network and PID controller requires careful optimization for diverse driving conditions. Applications: Particularly suited for EVs with in-wheel motors, offering precise control over individual wheel torque. Enhances safety in critical maneuvers like emergency lane changes or braking on icy roads. Provides robust trajectory and stability control for self-driving systems.
Parra (Parra et al., 2021a)	The intelligent method described in the document focuses on using nonlinear model predictive control (NMPC) (Kaiser et al., 2014) for energy-efficient torque vectoring in electric vehicles. The approach integrates a fuzzy logic-based weight adaptation mechanism to balance energy efficiency and vehicle stability. The NMPC optimizes both the reference yaw rate and wheel torque allocation in real-time. The FLC dynamically adjusts the NMPC cost function (Bîndac et al., 2022) weights based on driving conditions, such as yaw rate error and sideslip angle, enabling the controller to prioritize either energy efficiency or stability as needed. This intelligent system provides improved cornering stability while minimizing energy consumption.Nonlinear Model Predictive Control (NMPC)is used to optimize the torque distribution across the wheels by predicting vehicle dynamics over a future time horizon. It incorporates constraints such as yaw rate, sideslip angle, tire slip ratios, and torque limits, ensuring safe and efficient operation. It combines the direct yaw moment control layer with the torque allocation layer to minimize conflicts and optimize performance. This integration allows simultaneous consideration of yaw rate tracking, energy-efficient cornering response, and actuation constraints. The desired yaw rate is adaptively computed based on the vehicle's energy-efficient understeer characteristics, dynamically adjusting to changes in speed, tire-road friction, and longitudinal acceleration. A FLC is used to prioritize energy efficiency during normal driving and stability in critical maneuvers.The NMPC optimizes a cost function that includes terms for yaw rate tracking, tire slip power loss, power train power loss, and rear axle slip angle reduction and adaptive weight adjustments are implemented using a fuzzy logic system to balance energy efficiency and safety under varying conditions. The system is validated using a high-fidelity simulation model (Dynacar, 2013) for various driving scenarios, including skid pad tests, obstacle avoidance, and driving cycles (ISO, 2011).The objective is to improve vehicle handling and stability by optimizing torque vectoring, to minimize energy consumption by reducing power losses in the powertrain and tires and to ensure real-time adaptability to changing road and driving conditions. The block diagram used by the author is given by Figure 16.Advantages: Energy Efficiency: Demonstrates significant reductions in powertrain and tire slip power losses. Dynamic Adaptability: The fuzzy logic-based weight adaptation ensures optimal performance in diverse driving scenarios. Stability and Handling: Maintains excellent yaw rate tracking and minimizes vehicle understeer during critical maneuvers. Integrated Control: Prevents conflicts between layers of the torque vectoring system. Disadvantages: Computational Complexity: NMPC requires significant computational resources for real-time operation. Sensitivity to Parameters: Performance relies on accurate modeling of vehicle dynamics and powertrain losses. Implementation Complexity: Integration of multiple control layers and adaptive mechanisms requires careful tuning. Applications: Optimizes torque vectoring for vehicles with independent in-wheel motors in EV Enhances safety and efficiency for autonomous systems. Improves the driving range by minimizing energy consumption during standard and dynamic maneuvers.

Figure 8.

ITVC using predictive neural network.

Figure 9.

Genetically tuned fuzzy active steering control ITVC method.

Figure 10.

Genetically tuned fuzzy control for ITVC.

Figure 11.

ITVC with FLC and soft computing.

Figure 12.

ITVC using RL and DDPG algorithm.

Figure 13.

ITVC using fuzzy and NN method with regenerative braking.

Figure 14.

ITVC using fuzzy and vertical tire estimator.

Figure 15.

ITVC using back propagation NN.

Figure 16.

ITVC using NMPC and fuzzy logic based weight adaptation.

By analyzing key dynamic parameters such as maximum sideslip angle $|\beta {|}_{\max }$ , maximum roll angle $|\phi {|}_{\max }$ , braking displacement $\mathrm{\Delta }{x}_{\mathrm{braking}}$ , maximum lateral acceleration $|a_y{|}_{\max }$ and maximum lateral displacement

$|\mathrm{\Delta }y{|}_{\max }$ , we can assess how well each control strategy improves vehicle stability, handling, and safety. Yaw Stability $|\beta {|}_{\max }$ :

Lower values indicate better yaw control and reduced sideslip, meaning the vehicle maintains a more controlled trajectory. The range from 4° to 13° shows that different controllers have varying effectiveness in managing lateral slip.

Vehicle body roll $|\phi {|}_{\max }$ :

A higher roll angle can indicate more lateral weight transfer, which may affect stability. The values range from 9° to 13°, showing differences in how torque vectoring systems influence body roll. Table 2 provides a qualitative comparison of intelligent vectoring methods. One the other hand, Table 3 provides a comparison based on controller response while Table 4 compares their computational speeds and mechanical energy consumptions.

Table 2.

Comparison of intelligent torque vectoring methods.

Method	Description	Advantages	Disadvantages	Applications
FLC	Rule-based system that handles uncertainty and approximate reasoning to make decisions.	Simple to implement, handles imprecision well, intuitive for human reasoning.	Requires detailed rule tuning; may struggle with highly dynamic, real-time adjustments.	Adjusts torque vectoring based on driver inputs and vehicle state, such as yaw rate and sideslip angle, to enhance stability and control in various driving conditions.
RL	Learning-based approach where agents learn optimal actions by receiving feedback from the environment through rewards or penalties.	Adapts to dynamic environments, learns optimal strategies, can handle complex systems.	Requires extensive training data, time-consuming, may not guarantee safety in real-time applications.	Optimizes torque distribution by learning from various driving scenarios, achieving balance between stability and performance in real-time.
NN	A set of algorithms modeled loosely after the human brain that recognizes patterns and can model complex systems based on data.	Learns from data, can model nonlinear systems, handles large datasets well.	Requires a lot of data, prone to overfitting, may lack interpretability in decision-making processes.	Predicts optimal torque split between wheels by analyzing historical driving data, driver behavior, and road conditions, enhancing handling in different scenarios.
DDPG	A model-free reinforcement learning algorithm that operates over continuous action spaces using actor-critic methods.	Suited for continuous control tasks, learns from high-dimensional data, can handle complex dynamics.	Computationally expensive, needs a large amount of exploration data, sensitive to hyperparameter tuning.	Adjusts torque vectoring continuously in real-time for enhanced handling and stability, particularly in high-speed or complex driving environments.
BPNN	A supervised learning method that uses backward propagation of errors to adjust weights in a neural network.	Good for supervised learning tasks, efficient training with gradient descent.	Prone to local minima, requires labeled data, less efficient for very deep or complex networks.	Predicts torque distribution by learning from labeled data on ideal torque outputs for different conditions, ensuring optimal wheel traction and stability.
NMPC	Optimization-based control method that predicts future behavior by solving a dynamic model in real-time to achieve optimal control actions.	Real-time optimization, ensures safety constraints, handles nonlinearities well.	Computationally intensive, requires accurate modeling, may be hard to scale for highly complex systems.	Applies optimal torque distribution to each wheel based on real-time predictions of vehicle motion, managing stability and performance under high-speed or complex maneuvers.

Braking performance $\mathrm{\Delta }{x}_{\mathrm{braking}}$ _g:

This measures the longitudinal displacement during braking. Some strategies significantly reduce braking displacement, meaning they are more effective at stabilizing the vehicle under braking.

Lateral stability $|a_y{|}_{\max }$ & $|\mathrm{\Delta }y{|}_{\max }$ :

Table 3.

Vehicle response to double lane change for various controllers.

Parameter	$|\beta {|}_{max}$	$|\phi {|}_{max}$	$\mathrm{\Delta }{x}_{\mathrm{braking}}$	$|a_y{|}_{max}$	$|\mathrm{\Delta }y{|}_{\max }$
No TVC	26.3°	115.4 °/s	48.4 m	8.2 $m/s^2$	15.9 m
ITVC (GFYMC) (Jalali, 2012)	6.2°	31.2 °/s	44.5 m	8.4 $m/s^2$	0.46 m
ATVC (Jalali, 2012)	6.1°	36.4 °/s	47.3 m	8.4 $m/s^2$	2.70 m
ITVC (GFASC) (Jalali et al., 2013b)	13.6°	60.1 °/s	45.7 m	8.4 $m/s^2$	0.36 m
ITVC(GFASC + ATVC) (Jalali et al., 2013b)	7.5°	31.5 °/s	45.6 m	8.4 $m/s^2$	0.27 m
ITVC (Fuzzy + Regenerative) (Parra et al., 2019)	n/a	n/a	44.5 m	13.33 $m/s^2$	n/a
ITVC (NMPC + Fuzzy) (Kuutti et al., 2019)	7.0°	n/a	n/a	12.5 $m/s^2$	n/a
Predictive NN (Dendaluce Jahnke et al., 2019)	4.0°	10 °/s	n/a	3.5 $m/s^2$	0.9 m
Fuzzy + Neural tire (Pacejka and Besselink, 1997)	4.0°	12 °/s	n/a	3.2 $m/s^2$	0.85 m
ANFIS + Fuzzy (Parra et al., 2018)	4.0°	11 °/s	3.2 m	3.8 $m/s^2$	1.0 m

$|a_y{|}_{\max }$ represents the maximum lateral acceleration, which indicates the vehicle’s ability to handle high-speed cornering without losing traction.

$|\mathrm{\Delta }y{|}_{\max }$ shows lateral deviation, with lower values indicating better path-following ability.

Vehicles with lower $|\beta {|}_{\max }$ , | $|\phi {|}_{\max }$ , and higher $|a_y{|}_{\max }$ offer a safer and more comfortable driving experience, especially in emergency maneuvers.

Table 4.

Comparison of computational speed and mechanical energy consumption between different ITVC.

Control method	Execution time (ms)	Complexity	Energy Consumption (kWh)	Energy Improvement
Fuzzy + NN	2.5 ms	Medium	1.43	3.18
GFASC	4.1 ms	Medium	1.71	0.59
Fuzzy	3.2 ms	Low	1.13	3.93
NMPC	5.6 ms	High	1.1	7.06
DDPG	6.3 ms	Very High	1.07	9.43
BPNN	n/a	Med to High	1.18	24.6

Timeline and summary of ITVC development

The historical timeline of ITVC development is shown in Figure 17. It spans a little less than three decades and it needed contributions from different researchers to be fully constructed. ITVC development is done in six distinct steps. To develop an intelligent TVC, the first step is to determine vehicle characteristics and set performance goals. This can be done by identifying whether the system is for EV, with independent per-wheel motors, all-wheel drive (AWD) systems or other configurations. The next step is to develop a Vehicle Dynamic Model. This requires the selection for the DOF of the vehicle and other characteristics such as weight. Once an appropriate dynamic model is present at hand, the next step is to select the controller. It is possible that an intelligent controller from any AI method be used to optimize the longitudinal or lateral torque distribution. It goes without saying that the operation of this controller must be optimized, which is the next step. Optimization of the controller is used to determine the most efficient and effective distribution of torque between the wheels of a vehicle to improve handling, stability, and energy efficiency. The optimization process ensures that the torque applied to each wheel maximizes vehicle performance under various driving conditions while adhering to constraints like safety and hardware limits. Once the above steps are undertaken, it is possible to simulate the model and study its performance. It is possible to simulate the vehicle using any software such as Dynacar, IPG carmaker (Grüne and Pannek, 2011), CarSimand Matlab (Houska et al., 2011). Once the simulation results are obtained and deemed to be satisfactory, the final step of ITVC Development process is testing and validation. This can be performed in real or simulated conditions (IPG Automotive, 2013). It is very important to use different drive test methods such as forward, reverse, lane change, ramp steer, step steer etc. as well as different drive cycles. The results are compared and contrasted with those of other methods for benchmarking.

Figure 17.

Historical timeline of ITVC development studies.

Result

As compared to traditional methods, ITVC handles the complexity of real-world scenarios, where non-linear, multi-dimensional dynamics can exceed the capacity of traditional control logic defined by the driver. It encompasses several advantages including ability for continuous and dynamic torque adjustments, which improves handling, stability. For the study performed for the controller above, it can be concluded that there are several advantages and disadvantages and utilities. NN and FLC are able to provide smoother control, even under complex, changing conditions, reducing sudden torque changes and improving ride comfort. RL and NMPC are optimized for energy use, enabling torque adjustments that save power in EV or reduce fuel consumption. It also offers adaptability and learning.

RL and NN learn from data and dynamically adjust to conditions without predefined rules while traditional methods are typically rule-based. NMPC and DDPG optimize for multiple objectives, such as energy efficiency and handling, allowing vehicles to maintain performance across a wider range of conditions.

While Traditional methods perform well in predictable environments it lacks adaptability and real-time optimization that ITVC offers in scenarios where the driving environment is dynamic, such as autonomous driving, sports cars, or high-performance off-road vehicles. The integration of EVs with larger electric power system is underway (Honda R&D, 2005; Ikushima and Sawase, 1995) and there are novel approaches that propose using EV and V2G technologies in very different scenarios which range from stabilizing renewable energy intermittency (Aftab et al., 2018; Ustun et al., 2019), stabilizing voltage (Farooq et al., 2022; Safiullah et al., 2022), providing virtual inertia in weak power systems (Mishra et al., 2024) to supplying energy lifeline in emergencies (Hussain et al., 2020). All of these developments, when considered as part of a larger picture, show that EVs will become more important in the energy domain in the near future and ITVC will play a crucial role in this transition.

Conclusion

Using ITVC promotes enhanced vehicle stability and handling higher efficiency and adaptability to complex and dynamic environment, in all of the above stated methods, the computational ability, predictive and anticipatory capability of AI methods allows ITVC to have superior advantages over traditional methods. The main downside of these methods is the computational cost, training and tuning of the parameters which can get very costly and requiring sensitive and precise data which can also be prone to a new subset of problems like cyber-attacks, etc. Other than that it offers superior performance in most parameters. As the automotive industry advances toward autonomous EV, the future scope of ITVC is expansive encompassing AI integration, advanced machine learning, V2 V communication, and personalized driving experiences. It will become an essential technology for the next generation of smart, autonomous, and efficient EV.