Direct Yaw-Moment Control Integrated With Wheel Slip Regulation for Heavy Commercial Road Vehicles

When a road vehicle is subjected to combined cornering and emergency braking, it potentially has a greater risk of wheel lock followed by loss of steerability and/or undesired yaw motion. While an Anti-lock Braking System (ABS) is mandatory in many countries to avoid wheel lock, more attention is required to its combined cornering and braking performance. This paper aims to design a Direct Yaw-Moment Controller (DYC) integrated with ABS to achieve vehicle directional stability for Heavy Commercial Road Vehicles (HCRVs). This study implements a robust reaching law-based sliding mode controller for DYC and ABS. The developed algorithm was evaluated in a Hardware-in-Loop (HiL) setup. The experimental results are compared for the integrated algorithm and standalone ABS algorithms. The proposed algorithm improved the Directional Performance Index (DPI) in the range of 29% to 84% over the open-loop behavior while maintaining vehicle stability. Moreover, it also improved the DPI in the range of 5% to 53% over standalone ABS in various emergency test cases.


I. INTRODUCTION
Road traffic accidents are a global concern, with approximately 1.35 million human fatalities due to road vehicle crashes every year. The World Health Organization predicts traffic accident-related deaths will rise to the fifth position in the leading causes of human death by the year 2030 [1]. In the year 2019, India reported an average of 414 human fatalities every day due to road accidents. In the same year, accidents involving Heavy Commercial Road Vehicles (HCRVs) contributed to 31% of 151,113 total fatalities, despite their low share of total registered vehicles [2].
Accidents involving HCRVs often have severe repercussions such as loss of human lives and substantial financial The associate editor coordinating the review of this manuscript and approving it for publication was Yiqi Liu .
loss. Development of Active Vehicle Safety Systems (AVSS) like Electronic Stability Control (ESC) and Anti-lock Braking System (ABS) is currently prioritized for improving road traffic safety. A study by the National Highway Traffic Safety Administration, USA, has concluded that the inclusion of ESC can help mitigate 14% loss of directional control crashes [3]. For the Indian road-traffic scenario, which varies from that of countries like the USA in terms of vehicle population and composition, operating practices, and road conditions, ESC in HCRVs is undoubtedly a way forward to help reduce accidents. From the year 2015, Indian legislation has made ABS mandatory for all classes of HCRVs having a gross vehicle weight of more than 12,000 kg [4]. Subsequently, ESC systems may become mandatory for a broader class of HCRVs in India over the next few years. VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

A. ELECTRONIC STABILITY CONTROL IN THE LITERATURE
While ABS prohibits wheels from locking during braking, the ESC system controls the vehicle in an emergency to prevent directional instability. Directional instability may arise during an obstacle avoidance maneuver or a combined cornering and braking maneuver, especially on low friction surfaces. Various studies have investigated an obstacle avoidance scenario wherein the ESC intervenes by braking on one or more wheels to prohibit the vehicle from spinning and ensures lateral stability without a significant reduction in longitudinal vehicle speed [5]- [7]. However, a more complex case arises in combined cornering and emergency braking. When wheels are controlled to obtain maximum longitudinal forces, there is a significant reduction in lateral forces. The reason is the inherent coupling in lateral and longitudinal force generation. Thus, the objective of ESC in such a scenario is to ensure directional stability at the minimal expense of longitudinal performance. Several studies in the literature proposed integrating Direct Yaw-Moment Control (DYC), which involves an external yaw moment through differential braking to coordinate with ABS for directional stability.
Although researchers have examined lateral stability with an integrated DYC and ABS to evaluate performance on splitfriction roads [8], [9], only a few studies focused on combined cornering and braking maneuvers. Table 1 shows a review of relevant studies on combined cornering and braking [10]- [14]. Overall the researchers utilized steady-state values of a dynamic lateral model for model reference control. Reference states represented nominal motion for given inputs, and tracking these variables in severe conditions ensured directional stability. The selection of tracking variables was the subject of investigation for the vehicle in the study to achieve lateral performance.
In the case of ABS, the task was to regulate wheel slip at the desired value to maximize braking performance. Sliding Mode Control (SMC) has been widely used to regulate wheel slip. Similarly, for DYC, researchers employed SMC [10], [14] or PID controllers [11], [13] for generating the desired yaw-moment profile. The advantage of using SMC is its robustness property, and it is highly favored in the control of nonlinear systems. However, it is confronted with chattering resulting in discontinuous control input activity. A reaching law-based SMC design serves to address the chattering issue. It involves defining a sliding surface and a reaching law to ensure that the state trajectory reaches the surface. Once reached, the state trajectory is insensitive to parametric uncertainty and external disturbances, thus ensuring robustness during the sliding motion towards the desired state [15]. However, an appropriate choice of reaching law becomes highly vital for a chatter-free operation. Researchers have collectively proposed constant rate, power rate, constant plus power rate reaching laws, and boundary layer methods for ABS or DYC. However, as shown by Devika and Thomas [16], the strategies mentioned above compromise robustness for chatter-free operation. Hence, the Power Rate Exponential Reaching Law (PRERL) presented in [16] that alleviates chattering while retaining robustness was used in the current study.
In an approach that considers directional stability in ABS design, Morrison and Cebon [12] developed a modified slip control strategy for examining the combined braking and cornering of articulated heavy vehicles. However, it required the driver's active intervention to maintain directional stability. In limits of tire-road traction, the driver may react in a wrong way; thus, the design of AVSS should consider minimizing the need for the driver to operate thoughtfully [17]. Thus, lateral performance without driver interference would give confidence in the AVSS algorithm's use in severe maneuvers.
In summary, there have been minimal studies in ABS evaluation for combined cornering and braking. Additionally, the literature on the development of DYC and ABS for the HCRV segment considering its challenges is limited.

B. CHALLENGES IN HCRVs
Compared with passenger cars, the design of AVSS is accompanied by additional challenges in the case of HCRVs. A significant load variation (typically a loading of 200% of the unladen weight) affects the vertical and longitudinal position of the center of gravity (CoG). Also, the larger CoG height and the suspension system have a prominent effect on the coupling of vehicle lateral and roll dynamics. Compared to the hydraulic brake system, air brakes in HCRVs have a larger response time (≈ 0.6 s to reach 90% of the maximum pressure) [18]. HCRV tires are designed to reduce rolling resistance and tread wear, resulting in a lower peak friction coefficient, especially on wet road surfaces [19]. The characteristics mentioned above constitute the critical factors to be included in the design of AVSS, and the current study considers these in the proposed algorithm.

C. OBJECTIVE AND SCOPE
Based on the literature review and identified challenges, the following gaps in research on integrated DYC and ABS for HCRVs were identified. Only a few studies explored DYC integration with an ABS for a pneumatic brake actuator. Considering the slow response of pneumatic brake systems in HCRVs, it is essential to consider the actuator characteristics and then analyze the performance of DYC and ABS. In this regard, the literature is lean on performance evaluation using Hardware-in-Loop (HiL) or vehicle level testing. From a controller implementation perspective, most studies utilized the conventional reaching law-based SMC (such as constant rate reaching law, power rate reaching law, etc.). These controllers have limitations such as reduced robustness, slow-reaching speed, and chattering effects. Additionally, researchers have not analyzed the ABS design for cornering maneuvers and their effect on directional stability. This study attempts to address these gaps in the literature by examining the integrated DYC and ABS approach for the directional stability of an HCRV and provides an elaborate framework for its model-based design. The DYC incorporates a lateral dynamics model, including the influence of vehicle roll. A modified  model-based Wheel Slip Regulation (WSR) algorithm is presented as ABS considering longitudinal and lateral load transfer. Recognizing the inevitable modeling and parameter uncertainties, the framework effectively demonstrates the application of a robust reaching law-based sliding mode controller for this application. The necessary elements like delay compensation with a brake controller are incorporated to overcome the shortcomings of the actuator.
The scope of research is to employ the pneumatic brake actuator to control the longitudinal forces for obtaining directional stability and improving the lateral performance of an HCRV. Furthermore, this study explicitly analyses the combined cornering and braking scenario, evaluates the algorithm through HiL experiments, and compares its performance with the standalone ABS algorithm.
The organization of the paper is as the following. Section II describes the mathematical models derived for the design of direct yaw-moment control, wheel slip regulation, and brake controller. In Section III, the control design and brake force allocation strategy have been elaborated. HiL results are presented and discussed in Section IV, followed by conclusions in Section V.

II. SYSTEM MODELING A. NONLINEAR LATERAL DYNAMICS MODEL INCLUDING ROLL
A nonlinear 8-DoF vehicle model derived for controller design is described in this section. Four of the eight degrees of freedom represent translations along the longitudinal and lateral axes and rotational displacements about the yaw and roll axes. The remaining four represent the rotational displacement of the individual wheel about its axis. Fig. 1 depicts a free body diagram of the vehicle in its equivalent configuration for the case of yaw and roll motion while cornering. In the figure, g is the acceleration due to gravity, M s is vehicle sprung mass, L f and L r respectively are distances of front and rear axle from vehicle center of gravity, h s is the perpendicular distance of the sprung mass center of VOLUME 10, 2022 gravity to roll axis, K φ is suspension roll stiffness coefficient, C φ is suspension roll damping coefficient,ψ is vehicle yaw rate, β is vehicle sideslip angle, φ is vehicle roll angle, and F y is lateral ground force. The following assumptions were made to derive the mathematical model: • Sprung mass was assumed to roll about the longitudinal axis (x -axis).
• Roll of unsprung mass was considered negligible.
• Sprung and unsprung masses were assumed to have yaw motion around the vertical axis passing through point P on the roll axis (z -axis).
• The vehicle roll angle was assumed to be small. • The front and rear wheels were represented by a single equivalent front and rear wheel, respectively. With the above assumptions and appropriate small angle approximations, a set of equations representing the mathematical model for an HCRV in combined braking and lateral motion considering roll dynamics was derived as [20]: where t denotes time, M is total vehicle mass, I x and I z respectively are the moments of inertia of sprung mass about the x-axis and a vertical axis passing through the vehicle center of gravity, I xz /I zx is the product of inertia for x and z axes, v x and v y respectively are longitudinal and lateral vehicle speeds, C αf and C αr respectively are the single front and rear wheel cornering stiffness, δ f is front-wheel steer angle, F b is the braking force, and wheel identifiers fl, fr, rl, and rr respectively indicate the front left, front right, rear left, and rear right wheels. This model also considers the axle roll steer ( f and r respectively for the front and rear axles), which is assumed proportional to the vehicle roll through a proportionality constant C f and C r . In the presence of an external yaw-moment (M z,ext ), the above model is described in the nonlinear state-space form, where ij = {fl, fr, rl, rr}, the state vector is, δ f , F b,ij , M z,ext are the inputs, and f is a nonlinear function of states and inputs.

B. WHEEL SLIP DYNAMICS MODEL
The longitudinal force generated at the tire-road interface is a function of wheel slip ratio, λ, defined as, where R is the effective radius of the wheel, v cx is wheel-center speed, and ω w is wheel angular speed. The sign convention considered in this study is such that wheel slip is positive during braking. Also, the wheel lock condition during which the angular speed is zero corresponds to the value of λ being unity. The primary aim of ABS is to avoid wheel lock and regulate the wheel slip around its peak value to generate maximum braking force resulting in stable braking with lower braking distance (known as wheel slip regulation). 1 Fig. 2 depicts the free-body diagram of a wheel being acted by braking torque. In the figure, F c is wheel bearing force, F z is vertical ground force, and τ b is braking torque. Applying a moment balance equation along the wheel center gives, where I w is wheel moment of inertia, and α w is wheel angular acceleration. Also, the longitudinal component of the vehicle's velocity at CoG and wheel center-point velocity can be approximated to be equal in magnitude. Under this assumption, differentiating (7) gives the dynamics of wheel slip ratio as, where a x is longitudinal acceleration. Upon substitution of the angular acceleration term from (8), whereF b,ij is the estimated longitudinal force during braking. The longitudinal brake force can be expressed as, where α is tire slip angle, andμ x is the estimated longitudinal coefficient of friction characterized by the tire model. Normal force at the tire-road interface (F z,ij ) was calculated by decoupling the two axles and considering a virtual mass on each axle as derived in [21]. Thus, the expression for normal forces as a function of acceleration in the longitudinal and lateral direction is given by, where h is the distance of the center of gravity from the ground, T f and T r respectively are the front and rear track widths, and a y is lateral acceleration. Thus, the wheel slip dynamics is represented as a nonlinear state-space model given by,λ where τ b,ij is the input.

C. TIRE MODEL
This study employed the Magic Formula 6.1 truck tire model to calculate the longitudinal and lateral forces in combined slip. The general expression of the model is given by [22], Here Y represents the output variable of interest (longitudinal or lateral force), and X represents the input variable (wheel slip or slip angle). The variables A, B, C, D, and E, represent stiffness, shape, peak, and curvature factors. The shift factors S v and S h represent respectively the vertical and horizontal shift of the curve. Parameters of the above model were experimentally determined and provided by IPG TruckMaker R for a 315/80R22.5 radial truck tire [23].

D. BRAKE SYSTEM MODEL
The brake setup for the study uses an Electro-Pneumatic Regulator (EPR). It offers an advantage in terms of faster brake response compared to a conventional treadle valve in HCRVs. A first-order plus time delay model for the brake system was developed using linear time-invariant approximation by Sridhar et al. in [24], given by the transfer function (P), where s is a complex variable. The brake system parameters were identified experimentally and are summarized in Table 2.
The state-space representation of the above input-delayed system can be expressed as, where x b is the state, u is the system input, P act is the brake pressure output, and The brake pressure was converted into brake torque utilizing a model for an S-cam type brake system as given in [18]. The model in a simplified form is given by, where P co is the contact pressure, and K gain is the pressure to torque conversion gain. The model considered the efficiency of the brake system; however, the effects of temperature were neglected. Fig. 3 depicts a high-level functional block diagram of the 'integrated direct yaw-moment controller and wheel slip regulation' (DYC+WSR). The algorithm includes a reference model that specifies the ideal motion for the vehicle. Inputs to the model are the front steering wheel angle and vehicle's longitudinal speed, and output is the reference yaw rate. The DYC block compares the error in reference and actual yaw rate and outputs the required yaw moment. The WSR block computes the desired torque on each wheel by evaluating the error between the wheel slip's estimated and desired value. This study utilizes reaching law-based SMC in both the DYC and WSR algorithms. The reaching law approach directly specifies the sliding function's dynamics. A desirable property in a reaching law-based SMC is the controller's fast response in the reaching phase and alleviated chattering. Moreover, for robustness, sliding mode motion should be ensured for a significant duration in the sliding phase. A Power Rate Exponential Reaching Law (PRERL) having the traits above was proposed in [16] and is given as,

III. CONTROLLER DESIGN
where, s is the sliding function, K 0 is the SMC gain, and β 0 (0 < β 0 < 0.5), δ 0 (< 1), γ 0 (> 0) and φ 0 (> 0) are other controller parameters. The power rate term |s(t)| β 0 increases the reaching speed and has an advantage in chattering mitigation in the given range of β 0 . The denominator of the reaching law guarantees significant sliding mode motion, thus ensuring robustness to external disturbances and parametric uncertainties. Subsequently, the brake force allocation strategy ensures that the desired moment is generated. Brake controllers on each wheel execute the final desired torque demand. Furthermore, most of the required vehicle states and the force/coefficient at the tire-road interface can be directly measured or estimated. For example, literature [25], [26] comprehensively reviews the different friction force/coefficient estimation methods. Vehicle state and parameter estimation has been demonstrated using the dual extended Kalman filters in studies [27], [28]. As the primary focus of this study was the performance evaluation and comparative analysis of the algorithm for a pneumatic brake actuator, this study assumes the availability of vehicle states and tire-road interface-related information. The experiments utilized this information from the vehicle dynamic simulation software IPG TruckMaker R .

A. REFERENCE MODEL
Vehicle instability in severe cornering maneuvers can be attributed to saturation of lateral forces as their relation is nonlinear to the increasing slip angle. Thus, as an ideal vehicle response, this study utilized a linear 3-DoF steady-state model to determine the reference yaw rate for tracking. For this purpose, the longitudinal speed was assumed to be constant, and model equations from Section II-A were rewritten to include the sideslip angle. Consequently, the state-space form is obtained as, where the state vector and the input vector The matrices E and A are given as follows: and where 1 to 6 are defined in Appendix A. From the above model, steady-state values as a function of speed and front-wheel steer angle were obtained by setting the state vector's time-derivative to zero. Then, the steady-state vector (x ss ) is given by, Thus, the reference yaw rate (ψ ref ) is given by,

B. DIRECT YAW-MOMENT CONTROL
A sliding mode controller based on the model described in Section II-A was employed for obtaining the yaw-moment. The tracking variable considered was the vehicle yaw rate. Hence, the sliding function (s 1 ) was defined as an error between the current and reference yaw rate, expressed as, To apply the reaching law, the dynamics of sliding function was obtained as,ṡ From the model equations in Section II-A, an explicit relation can be derived for the time derivative of vehicle yaw rate in terms of vehicle parameters, states, and the external yawmoment as, The expressions for the coefficients (B β , B r , B φ , B p , B δ , and B τ ) in the equations are given in the Appendix A. Substituting the expression forψ(t) from (29) into (28), and using PRERL, the control input M z,ext is obtained as, where K 1 , β 1 , δ 1 , γ 1 , and φ 1 are controller parameters, and subscript (·) dyc indicates its affiliation to DYC. Subsequently, the task was to generate this moment by appropriately allocating the brake forces, as described in Section III-D.
In reality, a disparity always exists between the actual vehicle dynamics and the mathematical model due to the model parameter's uncertainty, unmodeled dynamics, and external disturbances. Accounting for these model inaccuracies, (29) can be expressed as, where x is the state vector as given in (6), andf is an unknown bounded function that represents model uncertainties and disturbances. Here, the uncertainties and disturbances are assumed as additive perturbations to the system [29], [30]. Defining a Lyapunov function for the above system as, and differentiating with respect to time gives, Substituting equations (30) and (31) in (33), where ρ 1 > 0 and is expressed as, Assuming that |f | <F and letting K 1 =F + η yields, SinceV < 0 for s 1 = 0, the proposed control law ensures asymptotic stability about the equilibrium (s 1 = 0) in the presence of bounded model uncertainty and disturbances.

C. WHEEL SLIP REGULATION
The current study employed a model-based approach for wheel slip regulation motivated by a sliding mode-based controller designed in [31] for HCRVs. To regulate wheel slip at the desired level (λ ref ), the sliding surface (s 2 ) is defined as, Here, the value of λ ref is assumed to be known and constant for the given tire-road interface. Subsequently, the derivative of the sliding function yields, Utilizing PRERL and substituting the derivative of wheel slip from (13), the control input for wheel slip regulation was obtained as, where K 2 , β 2 , δ 2 , γ 2 , and φ 2 are controller parameters, and subscript (·) wsr indicates its affiliation to WSR.

D. COORDINATION STRATEGY FOR DYC+WSR
Load is transferred from rear to front axle and inner to outer wheels in combined cornering and braking. Hence, the coordination strategy in the current study involved regulating force on the front inner/outer wheel as per the required external yaw moment from DYC. The rest of the wheels were operated with the WSR algorithm's input to maximize the braking force. This study found that such a single-wheel differential braking strategy was sufficient to produce the required magnitude of external yaw moment for the vehicle's laden and unladen configurations. It helped track reference yaw rate without a significant increase in braking distance. Thus, a counter-clockwise external yaw moment (M z,ext < 0) was generated by reducing the brake force on the front outer wheel and clockwise (M z,ext > 0) by reducing on the front inner wheel. The desired brake force, for example, at the front outer wheel (front right in case of a left turn) to generate the required external counter-clockwise yaw moment was determined using the total yaw moment of braking forces, expressed as, The obtained brake force was converted into desired pressure (P des ) using the wheel dynamics equation in (8). This desired pressure was provided to the inner-loop brake controller to realize the braking force.

E. BRAKE CONTROLLER
Pneumatic brake actuators are typically sluggish in their transient response and require performance enhancement for effective operation in an AVSS. Also, cascaded control operations with a time-delayed system are known to induce oscillations in its reference input regulation performance [31], [32]. This calls for implementing a brake controller and an appropriate delay compensation technique to improve the brake system's performance. Consequently, a PID controller was incorporated while compensating for the delay using a state predictor expressed as, wherex b is the predicted state, andP act is the predicted brake chamber pressure. Its function was to use the current states and previous delay period's inputs to predict the state and output for the subsequent delay period. These were employed in the feedback path of the controller to compare with the desired value and obtain control input (Fig. 3).

IV. HARDWARE-IN-LOOP EXPERIMENTAL RESULTS
The framework was tested using the Hardware-in-Loop setup shown in Fig. 4. The hardware setup consisted of a front and rear axle of a 16-tonne truck equipped with a pneumatic brake system. An EPR regulated the pressure at each brake chamber, and pressure sensors measured the pressure. The brake system hardware was interfaced with the host computer through a real-time hardware platform (IPG Xpack4 R ). The control algorithm was realized using MATLAB-Simulink R and was converted to C code for exporting to IPG Xpack4 R . The virtual vehicle parameters and other test conditions like the road and friction properties were specified from the host  computer in IPG TruckMaker R , a comprehensive vehicle dynamics simulation software package for trucks. The brake system component in the virtual vehicle was replaced with the hardware, thus resulting in hardware-in-loop co-simulation (refer Fig. 5). The algorithm's performance was evaluated for a 150 m radius (left) J-turn maneuver on a road surface with a peak longitudinal friction coefficient (µ px ) of 0.5 (having λ ref = 10%) representative of a wet road surface. A midlevel friction surface was chosen considering the saturation of lateral forces for high slip angles and its impact on directional performance. HiL experiments were performed for two cases of steering inputs. For the first case, a fixed profile for steering wheel angle (δ sw ) input was given to the vehicle. For the second case, the IPGDriver R module was activated, which enabled the simulated human driver's control action to the vehicle. The inputs to the module included intended path, vehicle position, speed, acceleration, and steering wheel torque [33]. The vehicle was fully braked at an initial speed of v x = 60 km/h when the vehicle entered the corner. Both the unladen (M = 4700 kg) and fully laden (M = 16200 kg) configurations were considered in the performance evaluation. The test run was terminated when the vehicle's speed dropped below 5 km/h. An open-loop vehicle response where the algorithms are disabled for the aforementioned maneuver indicated wheel lock and lane departure, thus resulting in instability.    A comparison study of DYC+WSR with standalone model-based and rule-based WSR algorithms was conducted to evaluate the algorithms during combined cornering and emergency braking. As a standalone model-based WSR, the brake torque calculated in Section III-C that regulates the slip at a reference value was applied to all wheels through the brake controller with delay compensation. For rule-based WSR, the 3-phase combined wheel VOLUME 10, 2022 slip and acceleration threshold algorithm developed in [34] was considered. The following notation is adopted to distinguish the algorithms: proposed integrated DYC and WSR by DYC (M) +WSR (M) ; standalone model-based WSR by WSR (M) , standalone rule-based WSR by WSR (R) . For discussion, this paper presents the result plots for the laden vehicle alone, and similar results were obtained for the unladen case. Fig. 6-7 present the closed-loop response of the vehicle implemented with the proposed integrated algorithm. Fig. 6a depicts the fixed steering input to the simulations (Case 1). In Fig. 6b, the yaw rate tracking performance is displayed. The yaw rate tracking index (YTI, deg/s) defined by, where T start is the brake application instant and T end is the simulation end time, was found to be 0.173 deg/s and 0.269 deg/s for the laden and unladen vehicles, respectively. In comparison, WSR (M) and WSR (R) showed vehicle understeer behavior (ψ <ψ ref ) throughout the maneuver. Fig. 7a plots the wheel slip for all four wheels. The front inner and rear wheels regulated their slip at the desired level of λ ref = 10%, where the maximum braking force is obtained on a wet road surface. The DYC control input governed braking force predominantly at the front outer wheel to generate external yaw moment for tracking reference yaw rate. Fig. 7b shows the control inputs, that is, the braking forces. Thus, the integrated algorithm achieved yaw rate tracking and successfully executed ABS's primary aim by avoiding wheel lock. For better stability and handling, a low sideslip angle is considered desirable [12], [13]. The comparisons with IPGDriver R in the loop (Case 2) are presented in Fig. 9-10. The maximum steering input from the IPGDriver R reached a peak of 42.4 • for DYC (M) +WSR (M) , as shown in Fig. 9a. In comparison, WSR (M) and WSR (R) showed higher correction from the driver, reaching a peak of 54.1 • and 60 • , respectively. Consequently, the vehicle closely followed the intended vehicle trajectory, as shown in Fig. 9b, however, at the expense of higher steering effort. The sideslip angle in Fig. 10a was limited to 0.9 • with DYC (M) +WSR (M) , whereas, with WSR (M) and WSR (R) , the peak reached 1.6 • and 2 • , respectively. As shown in Fig. 10b, the lateral offset was minimized further than Case 1 with aid from IPGDriver R through steering corrections.
A performance index was calculated for each case, considering quantities associated with the lateral dynamics of the vehicle. The index for Case 1 included lateral offset and sideslip angle since the steering input was the same for all three algorithms. The average normalized percentage improvement compared to the open-loop response was evaluated given by the expression, where β m is the absolute maximum value of sideslip angle, is the absolute maximum value of lateral offset from the desired trajectory, and subscripts 'ol' and 'cl' respectively stands for open-loop and closed-loop. Similarly, for Case 2, the index included maximum steering input in addition to previously considered parameters. The index accordingly computed is given by, where δ m is the absolute maximum value of steering wheel angle. Table 3 consolidates the evaluated test cases. A few additional severe cases (radius = 100 m) were also considered with the IPGDriver R in loop. The DYC (M) +WSR (M) algorithm resulted in a minimum 29% improvement over the open-loop response in all cases while tracking yaw rate and ensuring vehicle directional stability. It also improved the performance in the range of 5% to 53% over standalone WSR in various emergency test cases. Overall, the braking distance was least for WSR (M) and highest for WSR (R) . Higher braking distance in the rule-based algorithm was attributed to pump-hold-exhaust phases of brake pressure, which resulted in wheel slip cycling in a band around the reference value [34]. These characteristics also resulted in momentary wheel locks during combined cornering and emergency braking (permitted in ABS operation) that impacted the directional response of the vehicle (manifested in high sideslip angle and understeer behavior). On the other hand, standalone model-based WSR regulated wheel slip around the peak value to generate maximum braking forces at all four wheels; however, it compromised lateral force generation and thus the directional performance of the vehicle.
The DYC (M) +WSR (M) governed the front inner/outer wheel's braking force to regain the lateral force and track the reference yaw rate. The sideslip angle response was stable in all the cases and had a lower absolute peak value than the other two algorithms. Thus, the directional stability was enhanced by the DYC (M) +WSR (M) , however, at some expense of braking distance. Therefore, the proposed 'integrated direct yaw-moment and wheel slip regulation' algorithm set a benchmark for an effective trade-off between the directional performance and braking distance.

V. CONCLUSION
Combined cornering and emergency braking scenarios requiring ABS intervention were analyzed through HiL experiments. A framework for integrated DYC and WSR was presented to ensure vehicle directional stability and performance. In summary, the following are the contributions of this study: • A direct yaw-moment controller was designed using a robust sliding mode controller and including roll dynamics.
• A modified model-based wheel slip regulation algorithm was presented that perform effectively in combined cornering and braking scenario.
• The brake force allocation strategy based on single wheel control for generating the desired external yaw moment was shown to work in all severe maneuvers tested for the vehicle.
• The study established that the standalone WSR algorithm retained the vehicle stability; however, it did not perform satisfactorily in directional stability and performance. Moreover, the momentary wheel lock permitted in ABS operation can lead to excess sideslip angle.
• Yaw rate control in coordination with an efficient wheel slip regulation algorithm was demonstrated to achieve directional stability while keeping the sideslip in check.
• The quantitative evaluation also suggested the enhancement in lateral performance by incorporating the integrated DYC and WSR compared to standalone ABS operation.

APPENDIX A DEFINITIONS
The definitions of coefficients in (24) are as follows: The definitions of coefficients in (29) are as follows: