I am a master’s student at Chongqing Jiaotong University, and my research focuses on the lateral–longitudinal integrated control of chassis-by-wire electric vehicles for motion sickness mitigation. With the rapid promotion of new energy vehicles worldwide, the penetration rate of electric vehicles has increased dramatically. In 2025, the national vehicle population in China reached 469 million, of which new energy vehicles accounted for 43.97 million units, representing 12.01% of the total vehicle population. Compared with conventional internal combustion engine vehicles, electric vehicles exhibit more pronounced transient characteristics in both vehicle dynamic response and chassis actuation. Under typical driving conditions, such as turning, acceleration, and deceleration, the vehicle motion state responds more directly to control commands, making motion state changes more significant. This high-response characteristic, while improving vehicle dynamic performance and control precision, simultaneously makes occupants more sensitive to vehicle motion changes. When there is inconsistency or delay between vehicle motion information and occupant visual or vestibular perception, the balance system and spatial perception of occupants may be disturbed, leading to continuous stimulation of the vestibular system, which increases the likelihood of motion sickness among occupants. According to a cross-national survey conducted by the University of Michigan Transportation Research Institute, over 40.25% of respondents experienced motion sickness of varying degrees while riding intelligent electric vehicles, with the overall incidence being 17.24% higher than that of conventional vehicles.
Occupant motion sickness has a significant impact on the riding experience and the popularization of electric vehicles. During driving, occupants may experience symptoms such as inattention, sweating, pale complexion, stomach discomfort, and even vomiting. These symptoms not only directly cause physiological discomfort during travel but also affect the psychological feelings and travel experience of occupants. Frequent or persistent motion sickness prevents occupants from reading, working, or engaging in other activities normally during vehicle travel, reduces travel efficiency, and increases potential safety risks during driving or riding. Moreover, long-term occurrence of such physiological discomfort weakens user trust in vehicle performance and quality, reduces satisfaction, and thus limits the popularization and promotion of electric vehicles in practical use. Therefore, research on the prevention and mitigation of motion sickness among electric vehicle occupants, thereby improving ride comfort, is of great significance.
From the perspectives of motion sickness mechanism, existing mitigation methods, and chassis subsystem control methods, I conducted a comprehensive literature review. Research on motion sickness mechanisms has formed multiple explanatory frameworks including sensory conflict theory, postural instability theory, and expectation theory, along with evaluation systems based on various rating scales and the Motion Sickness Dose Value (MSDV). However, different theories focus on different core variables and causal chains, making it difficult to provide a unified and verifiable explanation for the motion sickness mechanisms and individual differences of vehicle occupants in complex scenarios involving non-driving task participation. Existing motion sickness mitigation research mainly focuses on occupant-side interventions, external auxiliary means, and vehicle-side regulation. Occupant-side pharmacological treatments are effective but often accompanied by side effects such as drowsiness. Psychological and visual guidance interventions mostly produce trend-level improvements with insufficient stability. Olfactory and musical external auxiliary means can enhance subjective experience but mostly depend on small samples and virtual scenarios, and their repeatability and quantitative mechanisms under real vehicle complex conditions remain to be improved. Vehicle-side research tends to focus more on autonomous driving motion planning and velocity profile optimization, while research on vehicle chassis dynamics control for motion sickness mitigation is relatively scarce. Therefore, vehicle chassis dynamics control for motion sickness mitigation, thereby improving vehicle anti-motion-sickness performance and enhancing occupant ride comfort, has become a research priority.
From the perspective of chassis control, Active Front Steering (AFS) improves vehicle steering response characteristics by adjusting the front wheel angle, while Direct Yaw Moment Control (DYC) generates additional yaw moment through differential braking or driving force distribution to regulate vehicle yaw motion. Since AFS and DYC have good complementarity in control mechanisms and action modes, coordinating the two can improve vehicle handling stability while suppressing adverse motion stimuli, providing a technical basis for the anti-motion-sickness chassis coordinated control research. In previous studies, the coordinated control of AFS and DYC has been extensively investigated for vehicle handling stability. However, most studies have focused on stability and handling performance improvement, with insufficient attention to the impact of vehicle motion state changes on occupant motion sickness responses and ride comfort. With the development of electric vehicles and intelligent driving technology, occupant motion sickness has gradually become an important factor affecting the riding experience. Therefore, exploring chassis-by-wire multi-actuator coordinated control methods to suppress adverse motion stimuli and improve ride comfort while ensuring vehicle stability, to reduce occupant motion sickness, has important research significance.
My research is supported by the Chongqing Graduate Scientific Research and Innovation Foundation under the project “Research on Test Evaluation and Active Mitigation Technologies for Motion Sickness in Electric Vehicle Occupants”. The overall research framework encompasses three main aspects: identification of motion-sickness-sensitive motion parameters based on real-vehicle tests, vehicle dynamics modeling considering motion-sickness-sensitive motion parameters, and lateral–longitudinal coordinated control of chassis-by-wire systems for motion sickness mitigation.
Identification of Motion-Sickness-Sensitive Motion Parameters Based on Real-Vehicle Tests
To reveal the relationship between vehicle motion stimuli and occupant motion sickness responses during electric vehicle driving, and to provide a basis for the identification of motion-sickness-sensitive vehicle motion parameters and the construction of evaluation methods, I conducted real-vehicle motion sickness tests. According to the sensory conflict theory, motion sickness essentially arises from the sustained mismatch between multi-sensory inputs caused by actual vehicle motion and the motion expectations or internal model outputs formed by the central nervous system based on past experience, thereby inducing a series of autonomic nerve reactions and manifesting as nausea, sweating, dizziness, and even vomiting. Vehicle acceleration, deceleration, steering, and road excitation are transmitted through the seat and body to the head, forming acceleration stimuli. Among these, the vestibular otolith organs are particularly sensitive to acceleration. The visual system and proprioception jointly participate in spatial orientation and self-motion perception. When the motion perceived by the otoliths is inconsistent with the self-motion cues provided by vision, or inconsistent with the internal model’s prediction of future motion, significant neural mismatch and perceptual conflict will form, thereby inducing motion sickness.
Based on the motion sickness mechanism, the electric vehicle occupant motion sickness test needed to collect two types of key data: occupant subjective motion sickness responses and vehicle acceleration motion parameters, ensuring time synchronization between the two. For the test vehicle, I systematically configured and managed the cabin environment, chassis key parameters, and drive/brake actuation systems of a certain brand of 7-seat intelligent pure electric SUV to construct repeatable, controllable, and standardized test conditions. The electric drive system had a total power of 390 kW and a peak total torque of 673 N·m. I established clear and consistent control requirements for key factors such as chassis system status, drive and brake system response characteristics, occupant behavior constraints, and occupant seating posture and visual boundary conditions, to minimize non-target interference and improve consistency among trials.
Regarding subject screening, since individual health conditions, gender, age, motion sickness susceptibility, and other physiological characteristics as well as external conditions can significantly influence motion responses, I established strict screening criteria. I used the Motion Sickness Susceptibility Questionnaire (MSSQ-Short) to assess and screen the motion sickness susceptibility of subjects. The MSSQ-Short score was calculated by summing item scores:
$$MSSQ = \sum_{i=1}^{k} m_i$$
where k is the number of transportation modes and amusement facilities experienced by a subject, and m is the score for experiencing a particular transportation mode or amusement facility. A total of 100 subjects aged 13-60 completed the physical condition questionnaire and MSSQ-Short survey. After screening according to the above standards, 59 subjects were ultimately included in the subsequent motion sickness testing phase. All subjects were healthy, had no vestibular dysfunction, and had MSSQ-Short scores not lower than 7 points. The average age of the subjects was 37.68 years, with a male-to-female ratio of 1.2:1. All subjects were clearly informed before the test began that they could terminate and withdraw from the experiment at any time if they felt any discomfort, to safeguard the rights and interests of the subjects.
To reduce the impact of driving operation differences on vehicle motion stimulus consistency, I selected two experienced drivers to perform the test tasks to ensure that they could successfully complete various test conditions under different road environments. The subjective motion sickness responses of occupants were recorded using the Motion Illness Severity Classification (MISC) scale. The MISC scale grades motion sickness levels with discrete levels from 0 to 10, enabling rapid scoring without significantly interrupting the riding task. For efficient and low-interference collection of subjective motion sickness scores and unified time synchronization with vehicle motion data in real-vehicle tests, I developed a timer and voice announcer based on Python. The system automatically counted down at preset intervals, prompted test personnel to quickly record MISC scores by voice at the appropriate time, and automatically recorded the score values and corresponding timestamps to a file. This approach replaced frequent manual inquiry with program-triggered reminders, reducing interference with occupant attention and subjective feelings, while also mitigating errors caused by manual timing, thereby improving the accuracy and repeatability of subjective scores.
For vehicle motion stimulus measurement, I used a WIT HWT-605 sensor with acceleration measurement accuracy of 0.01 g and a sampling frequency of 10 Hz. The sensor was installed on the rigid structure beneath the passenger seat to approximate the actual motion stimulus input to which occupants were exposed, while reducing the secondary filtering effect of seat cushion elastic deformation. To further enhance the consistency and scientificity of subjective evaluation and reduce uncertainty in subjective scoring, I introduced the Car Sickness Rating (CSR) on the basis of the MISC scale. The MISC 0-10 levels were mapped to four categories of motion sickness severity. A total of 956 subjective motion sickness response samples were finally obtained. After the classification, 190 samples corresponded to no motion sickness (CSR=0), 454 samples corresponded to mild motion sickness (CSR=1), 246 samples corresponded to moderate motion sickness (CSR=2), and 66 samples corresponded to severe motion sickness (CSR=3). I designed a closed-loop test route with a total mileage of about 45 km and a single test duration of about 60 minutes. The route was composed of multiple types of road sections, including urban main roads, urban streets, and mountainous roads, providing composite stimuli such as continuous curvature changes, significant longitudinal slope changes, and local bumpy excitation.
After completing all real-vehicle motion sickness tests, I performed statistical summarization of subjective motion sickness responses based on a fixed-interval sampling strategy. In the data organization process, invalid records caused by acquisition pollution and signal loss were excluded, and 404 valid vehicle motion parameter samples at 120-second intervals were obtained. According to the time synchronization principle, subjective motion sickness samples were matched with vehicle motion parameter samples, forming 404 groups of combined data samples. For the analysis of motion sickness-sensitive parameters, I processed both acceleration and jerk signals. Since this study focused on the amplitude levels and fluctuation degrees of motion stimuli rather than differences in positive and negative directions, subsequent calculations and statistical analyses were based on the absolute values of acceleration and jerk. Table 1 presents the statistical results of vehicle acceleration parameters across different road sections.
| Parameter | Segment 1 | Segment 2 | Segment 3 | Segment 4 |
|---|---|---|---|---|
| Mean |lateral acceleration| (g) | 0.074 | 0.081 | 0.063 | 0.054 |
| Mean |longitudinal acceleration| (g) | 0.065 | 0.035 | 0.077 | 0.048 |
| Mean |vertical acceleration| (g) | 0.002 | 0.001 | 0.001 | 0.002 |
| Max |lateral acceleration| (g) | 0.524 | 0.519 | 0.537 | 0.526 |
| Max |longitudinal acceleration| (g) | 0.443 | 0.421 | 0.428 | 0.265 |
| Max |vertical acceleration| (g) | 0.671 | 0.409 | 0.334 | 0.267 |
| Std lateral acceleration (g) | 0.097 | 0.111 | 0.101 | 0.081 |
| Std longitudinal acceleration (g) | 0.080 | 0.087 | 0.087 | 0.058 |
| Std vertical acceleration (g) | 0.037 | 0.041 | 0.039 | 0.019 |
To compensate for the limitation that pure peak-type indicators cannot characterize the cumulative effect of motion stimuli, I further incorporated the cumulative effect of ride time on occupant motion sickness. Based on the vehicle motion data obtained from the real-vehicle road tests, I standardized the derivation of motion-sickness-related indicator calculations according to the basic framework of human vibration evaluation in British Standard BS6841-1987 and International Standard ISO2631-1:1997. Combined with relevant experimental findings, I extended the motion sickness dose value calculation concept, which was centered on vertical vibration in the standard, to the horizontal direction, thereby establishing a unified calculation method for evaluating the impact of horizontal vibration on occupant motion sickness responses.
The band-limiting filter expression is:
$$\frac{a_{m1}(s)}{a_{m0}(s)} = H_b(s) = H_l(s) \cdot H_h(s) = \frac{s^2 \omega_2^2}{s^2 + \frac{\omega_2}{Q_1} s + \omega_2^2} \cdot \frac{s^2}{s^2 + \frac{\omega_1}{Q_1} s + \omega_1^2}$$
After band-limiting filtering, the frequency-weighted filter can be expressed as:
$$\frac{a_{m2}(s)}{a_{m1}(s)} = H_{\omega}(s) = H_t(s) \cdot H_s(s)$$
The weighted acceleration can be derived accordingly. According to the calculation relationship specified in ISO2631-1:1997, the MSDV is:
$$MSDV_m = \left[ \int_{0}^{T} a_{m2}^2(t) dt \right]^{1/2}$$
Using the vehicle acceleration signals collected from real-vehicle tests, I calculated the MSDV values in different axes. The results showed that as MSDV increased, the occupant motion sickness level generally exhibited an increasing trend, indicating that this indicator can effectively characterize the cumulative effect of vehicle vibration or acceleration stimuli over time and exhibits good same-direction variation characteristics with occupant subjective motion sickness responses. Since MSDV not only reflects instantaneous stimulus intensity but also captures the mechanism of discomfort enhancement caused by cumulative sustained stimuli, I treated MSDV as a key quantitative indicator for motion sickness evaluation.
Frequency-domain and correlation analyses
To determine the accuracy of the effects of longitudinal, lateral, and vertical acceleration motion quantities on occupant motion sickness responses, I used Fourier transform to convert time-domain acceleration signals to the frequency domain. The spectral analysis of the three-axis acceleration signals of a typical sample with high occupant motion sickness levels showed that lateral acceleration exhibited significant energy distribution in the low-frequency range, which is typically closely related to lateral dynamic behaviors such as vehicle turning. Longitudinal acceleration also showed certain energy concentration in the low-frequency region, but the energy concentration distribution was not as extensive as that of lateral acceleration. In contrast, the vertical acceleration changed relatively smoothly within the sensitive frequency band without obvious energy concentration. The frequency-domain analysis results indicated that vehicle lateral and longitudinal acceleration are important motion stimulus factors affecting occupant motion sickness.
To further quantitatively analyze the correlation between vehicle motion parameters and subjective motion sickness responses, I conducted Pearson correlation analysis on acceleration, jerk, MSDV variation values, and other vehicle motion parameters against the subjective CSR. The Pearson correlation coefficient is:
$$r = \frac{\sum_{i=1}^{n}(x_i – \bar{x})(y_i – \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i – \bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i – \bar{y})^2}}$$
To further verify the statistical validity of the correlations and avoid erroneous judgments caused by sample dispersion and random factors, I used the t-test, whose statistic is expressed as:
$$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$$
The correlation analysis and significance test results are shown in Table 2.
| Parameter | Physical meaning | Correlation coefficient with CSR | Significance |
|---|---|---|---|
| ax,max | Maximum longitudinal acceleration | 0.34 | p < 0.01 |
| ay,max | Maximum lateral acceleration | 0.40 | p < 0.01 |
| az,max | Maximum vertical acceleration | 0.09 | p ≥ 0.05 |
| jx,max | Maximum longitudinal jerk | 0.23 | p < 0.05 |
| jy,max | Maximum lateral jerk | 0.24 | p < 0.01 |
| jz,max | Maximum vertical jerk | 0.20 | p ≥ 0.05 |
| ΔMx | Longitudinal MSDV variation | -0.26 | p < 0.01 |
| ΔMy | Lateral MSDV variation | -0.20 | p < 0.01 |
| ΔMz | Vertical MSDV variation | -0.21 | p ≥ 0.05 |
Combining the above correlation analysis and significance test results, I found that occupant motion sickness showed high sensitivity to vehicle lateral and longitudinal acceleration, jerk, and MSDV variation values, indicating that the amplitude levels and transient variation characteristics of vehicle horizontal motion stimuli are important dynamic factors inducing occupant motion sickness responses. Compared with longitudinal motion stimuli, lateral motion stimuli had a stronger correlation with subjective motion sickness responses, suggesting that lateral dynamic variations play a dominant role in motion sickness formation. Therefore, in the subsequent anti-motion-sickness control, I focused on regulating vehicle lateral motion responses under motion-sickness-prone conditions while considering the coordinated control of longitudinal related motion variables. By suppressing lateral and longitudinal acceleration peaks and their variation rates, the motion stimulus intensity and its abruptness could be alleviated, thereby achieving active mitigation of occupant motion sickness.
Construction of the motion sickness evaluation function
To validate the effectiveness of subsequent anti-motion-sickness control strategies, I constructed an evaluation function based on the identified motion-sickness-sensitive motion parameters. The evaluation function takes the following form:
$$MS_{eval} = \beta_1 j_{x,max} + \beta_2 j_{y,max} + \beta_3 a_{x,max} + \beta_4 a_{y,max} + \beta_5 \Delta M_x + \beta_6 \Delta M_y + \beta_7 Y + \theta$$
where MSeval is the occupant motion sickness evaluation function value, θ is the bias term, and βi (i = 1, 2, …, 7) are the influence weight factors of the corresponding features on occupant motion sickness.
Considering the large number of feature dimensions and the potential significant correlation among variables, direct ordinary least squares estimation could easily lead to unstable parameters and overfitting. Therefore, I employed ridge regression to introduce an L2 regularization term into the loss function to shrink the regression coefficients, thereby alleviating the interference of multicollinearity on estimation results. The ridge regression coefficients are:
$$\beta_i = (A^T A + \lambda I)^{-1} A^T C$$
where A is the independent variable matrix, AT is its transpose, C is the dependent variable vector (the occupant motion sickness grade CSR in this study), λ is the regularization parameter, and I is the identity matrix. Before the ridge regression, I applied Z-score standardization to eliminate the influence of different dimensions. I used K-fold cross-validation with K=10 repeated 10 times to determine the optimal regularization parameter. Figure 2 shows the ridge trace for different feature parameters. When the optimal regularization parameter λ was determined to be 18.5, all feature estimation coefficients became stable. Substituting this into the equation, the motion sickness evaluation function becomes:
$$MS_{eval} = 0.306 j_{x,max} + 0.495 j_{y,max} + 1.098 a_{x,max} + 0.615 a_{y,max} – 0.127 \Delta M_x + 0.026 \Delta M_y – 0.021 Y + 0.044$$
To verify the validity of the established evaluation function, I randomly selected 10 subjects from the 59 subjects for validation, containing 97 CSR samples. I compared the evaluation function prediction values with the subjective motion sickness grades CSR. Since CSR is a discrete grade variable while the evaluation function output is continuous, I used the absolute deviation between predicted values and corresponding subjective motion sickness grades as the validation criterion. The results showed that the evaluation function prediction values generally increased with increasing subjective motion sickness grade, with good hierarchical distribution characteristics across different grades. Most prediction values fell within the tolerance range of their respective grades, demonstrating that the established evaluation function can effectively characterize the variation patterns of occupant motion sickness responses. The evaluation function only requires vehicle motion parameters for evaluation and does not require occupants to be present during testing, making it suitable for evaluating vehicle motion sickness comfort and for assessing the effectiveness of subsequent anti-motion-sickness control.
Vehicle Dynamics Modeling Considering Motion-Sickness-Sensitive Motion Parameters
The real-vehicle test and statistical analysis results showed that occupant motion sickness was correlated with vehicle lateral and longitudinal accelerations and their variation rates (jerks), and that the MSDV could effectively characterize the cumulative effect of motion stimuli. To transform these motion-sickness-sensitive vehicle motion parameters from experimental conclusions into model variables that can be precisely calculated and output, I conducted a dynamic analysis of the motion-sickness-sensitive motion parameters. In the vehicle center-of-mass coordinate system, the vehicle lateral and longitudinal accelerations can be expressed as:
$$a_x = \dot{v}_x – v_y \omega_r$$
$$a_y = \dot{v}_y + v_x \omega_r$$
where ax and ay are the vehicle longitudinal and lateral accelerations, vx and vy are the vehicle center-of-mass longitudinal and lateral velocities, and ωr is the vehicle yaw rate. The vehicle acceleration is determined by the resultant forces acting on the vehicle:
$$m a_x = \sum F_X, \quad m a_y = \sum F_Y$$
Taking the derivative of the acceleration expressions gives the jerk:
$$\dot{a}_x = \ddot{v}_x – \dot{v}_y \omega_r – v_y \dot{\omega}_r$$
$$\dot{a}_y = \ddot{v}_y + \dot{v}_x \omega_r + v_x \dot{\omega}_r$$
The above equations show that lateral and longitudinal accelerations depend not only on velocity change rates in their respective directions but are also affected by the coupling effects of yaw motion. Their magnitudes are determined by the longitudinal and lateral forces generated by the tires, which in turn are closely related to tire slip angles, slip ratios, and vertical loads. Jerks are not only related to tire force change rates but also to yaw angular acceleration. Therefore, I needed to establish a vehicle dynamic model that can uniformly describe the planar motion and wheel rotational dynamics of the vehicle body, combined with a nonlinear tire model to describe the tire lateral and longitudinal force characteristics, ensuring that the dynamic responses of motion-sickness-sensitive motion parameters can be accurately represented.
Based on the real-vehicle test analysis results showing that occupant motion sickness responses were most sensitive to lateral motion stimuli, followed by longitudinal motion stimuli, while vertical effects were relatively limited in this study, I made reasonable simplification assumptions for the vehicle model. The assumptions were: neglecting the internal clearance of the steering system and related moments; neglecting the self-aligning torque of tires; neglecting the elastic deformation of the suspension system and its dynamic transmission characteristics; neglecting the effect of road roughness excitation on vehicle vertical motion; neglecting vehicle motion along the z-axis; neglecting the rolling and pitching motions of the vehicle about the x- and y-axes; and treating the vehicle as a rigid body. Based on these assumptions, I created a seven-degree-of-freedom vehicle dynamics model in MATLAB/Simulink that includes the longitudinal, lateral, and yaw motions of the vehicle body, as well as the rotational motions of the four wheels.
The longitudinal motion equation of the vehicle body is:
$$m a_x = (F_{x,fl} + F_{x,fr}) \cos \delta_f – (F_{y,fl} + F_{y,fr}) \sin \delta_f + F_{x,rl} + F_{x,rr}$$
The lateral motion equation is:
$$m a_y = (F_{x,fl} + F_{x,fr}) \sin \delta_f + (F_{y,fl} + F_{y,fr}) \cos \delta_f + F_{y,rl} + F_{y,rr}$$
The yaw motion equation is:
$$I_z \dot{\omega}_r = l_f \left[ (F_{x,fl} + F_{x,fr}) \sin \delta_f + (F_{y,fl} + F_{y,fr}) \cos \delta_f \right] – l_r (F_{y,rl} + F_{y,rr}) + \frac{T_w}{2} \left[ (F_{x,fr} – F_{x,fl}) \cos \delta_f + (F_{y,fl} – F_{y,fr}) \sin \delta_f \right] + \frac{T_w}{2} (F_{x,rr} – F_{x,rl})$$
The wheel rotational dynamics equation is:
$$I_w \dot{\omega}_{ij} = T_{d,ij} – T_{b,ij} – F_{x,ij} R$$
To accurately describe tire force characteristics across the full operating range, I adopted the Magic Formula (MF) tire model, which provides a good balance between accuracy and computational efficiency. In pure cornering conditions, the tire lateral force is expressed as:
$$F_{y0} = -\frac{\mu}{\mu_0} D_y \sin \left[ C_y \arctan \left( B_y \alpha – E_y \left( B_y \alpha – \arctan(B_y \alpha) \right) \right) \right]$$
The tire slip angles for the four wheels are:
$$\alpha_{fl} = \delta_f – \arctan \left( \frac{v_y + l_f \omega_r}{v_x – 0.5 T_w \omega_r} \right), \quad \alpha_{fr} = \delta_f – \arctan \left( \frac{v_y + l_f \omega_r}{v_x + 0.5 T_w \omega_r} \right)$$
$$\alpha_{rl} = -\arctan \left( \frac{v_y – l_r \omega_r}{v_x – 0.5 T_w \omega_r} \right), \quad \alpha_{rr} = -\arctan \left( \frac{v_y – l_r \omega_r}{v_x + 0.5 T_w \omega_r} \right)$$
The vertical tire loads are affected by the dynamic load transfer due to longitudinal and lateral accelerations:
$$F_{z,fl} = \frac{m g l_r}{2(l_f + l_r)} – \frac{m a_x h_g}{2(l_f + l_r)} – \frac{m a_y h_g l_r}{(l_f + l_r) T_w}$$
$$F_{z,fr} = \frac{m g l_r}{2(l_f + l_r)} – \frac{m a_x h_g}{2(l_f + l_r)} + \frac{m a_y h_g l_r}{(l_f + l_r) T_w}$$
$$F_{z,rl} = \frac{m g l_f}{2(l_f + l_r)} + \frac{m a_x h_g}{2(l_f + l_r)} – \frac{m a_y h_g l_f}{(l_f + l_r) T_w}$$
$$F_{z,rr} = \frac{m g l_f}{2(l_f + l_r)} + \frac{m a_x h_g}{2(l_f + l_r)} + \frac{m a_y h_g l_f}{(l_f + l_r) T_w}$$
The pure longitudinal force tire expression is:
$$F_{x0} = D_x \sin \left[ C_x \arctan \left( B_x s – E_x (B_x s – \arctan(B_x s)) \right) \right]$$
The tire slip ratios are:
$$s_{fl} = \frac{R \omega_{fl} – (v_x – 0.5 T_w \omega_r)}{\max \left[ (v_x – 0.5 T_w \omega_r), R \omega_{fl} \right]}, \quad s_{fr} = \frac{R \omega_{fr} – (v_x + 0.5 T_w \omega_r)}{\max \left[ (v_x + 0.5 T_w \omega_r), R \omega_{fr} \right]}$$
$$s_{rl} = \frac{R \omega_{rl} – (v_x – 0.5 T_w \omega_r)}{\max \left[ (v_x – 0.5 T_w \omega_r), R \omega_{rl} \right]}, \quad s_{rr} = \frac{R \omega_{rr} – (v_x + 0.5 T_w \omega_r)}{\max \left[ (v_x + 0.5 T_w \omega_r), R \omega_{rr} \right]}$$
Since steering and acceleration/deceleration often occur simultaneously during actual vehicle operation, causing tires to be in combined operating conditions, I introduced the combined-slip coupling expressions:
$$F_x = \frac{\sigma_x}{\sigma} F_{x0}, \quad F_y = \frac{\sigma_y}{\sigma} F_{y0}$$
$$\sigma_x = \frac{s}{1 + |s|}, \quad \sigma_y = \frac{\tan \alpha}{1 + |s|}, \quad \sigma = \sqrt{\sigma_x^2 + \sigma_y^2}$$
Table 3 presents the main vehicle parameters used in the dynamic model.
| Symbol | Parameter | Value |
|---|---|---|
| m | Vehicle mass (kg) | 1530 |
| hg | Center of gravity height (m) | 0.52 |
| Iz | Yaw moment of inertia (kg·m²) | 2315 |
| Tw | Track width (m) | 1.55 |
| lf | Distance from CG to front axle (m) | 1.11 |
| lr | Distance from CG to rear axle (m) | 1.67 |
| Iw | Wheel moment of inertia (kg·m²) | 1.5 |
| R | Wheel rolling radius (m) | 0.325 |
To verify the accuracy of the seven-degree-of-freedom model, I used the CarSim vehicle dynamics model as a reference and validated the Simulink model under sine-wave steering and double-lane-change conditions. The vehicle speed was set to 60 km/h and the road adhesion coefficient was 0.85. The validation results showed that the established seven-degree-of-freedom vehicle model could reproduce the yaw rate, sideslip angle, lateral acceleration, and lateral jerk responses of the CarSim model well under both conditions. Due to the simplifications made before establishing the model, small errors existed in the transient peaks under both conditions, but the overall trends and phase matching were good, indicating that the model can effectively characterize the dynamic variation patterns of motion-sickness-sensitive motion parameters. This model thus provides a reliable modeling basis for the design and simulation verification of anti-motion-sickness control strategies.
Lateral–Longitudinal Coordinated Control of Chassis-by-Wire Systems for Motion Sickness Suppression
Based on the identified motion-sickness-sensitive motion parameters and their relationships with vehicle state variables, I constructed a coordinated control framework combining AFS and DYC for motion sickness suppression in an electric vehicle endowed with a chassis-by-wire actuation architecture. The overall architecture is shown conceptually in Figure 3 (omitted here). The architecture uses a two-degree-of-freedom vehicle reference model to generate the ideal response. AFS and DYC bottom-level controllers are designed separately, and the weights of the two controllers are reasonably distributed to suppress the motion stimuli that induce occupant motion discomfort while ensuring vehicle stability.
For the reference model, in the linear tire cornering range, the front and rear axle lateral forces can be expressed as:
$$F_{y1} = -C_1 \alpha_1, \quad F_{y2} = -C_2 \alpha_2$$
The state equation of the two-degree-of-freedom reference model is:
$$\dot{\beta} = -\frac{C_1 + C_2}{m v_x} \beta – \left( 1 + \frac{C_1 l_f – C_2 l_r}{m v_x^2} \right) \omega_r + \frac{C_1}{m v_x} \delta_f$$
$$\dot{\omega}_r = \frac{C_2 l_r – C_1 l_f}{I_z} \beta – \frac{C_1 l_f^2 + C_2 l_r^2}{I_z v_x} \omega_r + \frac{C_1 l_f}{I_z} \delta_f$$
Defining the state vector xr = [β, ωr]T and the control input ur = δf, the reference model can be written as:
$$\dot{x}_r = A_r x_r + B_r u_r$$
Since lateral acceleration can be expressed as a linear combination of system states and control inputs, and considering that lateral acceleration, yaw rate, and sideslip angle are all dynamic response quantities closely related to occupant motion discomfort, I included lateral acceleration in the reference model output:
$$a_y = C_r x_r + D_r u_r$$
The reference two-degree-of-freedom model can simultaneously characterize the yaw rate, sideslip angle, and lateral acceleration responses, providing a reference basis for the design of both the AFS controller and the DYC controller.
Model predictive control-based AFS controller design
For the AFS controller design, I needed to simultaneously consider path tracking performance, steering smoothness, vehicle lateral stability, and motion-sickness-sensitive motion parameter suppression, which is a typical multi-objective constrained optimization problem. Considering that Model Predictive Control (MPC) can perform online optimization of control inputs within a receding time horizon while explicitly handling constraints on front wheel angle, angle increment, and lateral acceleration, I adopted MPC to design the AFS anti-motion-sickness controller.
Considering that the accumulation and correction of lateral errors during path tracking can both cause lateral acceleration fluctuations, in the path coordinate system I defined the lateral position error ey and the heading error eψ as error states of the prediction model:
$$\dot{e}_y = v_x (\beta + e_{\psi})$$
$$\dot{e}_{\psi} = \omega_r – \omega_{rd}$$
where ωrd is the reference yaw rate, which is computed from the reference path curvature and the vehicle longitudinal velocity. Combined with the two-degree-of-freedom vehicle dynamics equations, the continuous-time error state vector is:
$$x(t) = \left[ e_y, e_{\psi}, \beta, \omega_r \right]^T$$
$$\dot{x}(t) = A_c x(t) + B_c \delta_f(t) + E_c \omega_{rd}(t)$$
Using the zero-order hold method to discretize the continuous-time error model, the discrete form is obtained. To incorporate the front wheel angle change rate constraint into the MPC optimization, I defined the control increment Δδf(k) = δf(k) – δf(k-1) and constructed an augmented state vector. The resulting augmented prediction model is:
$$\xi(k+1) = \tilde{A} \xi(k) + \tilde{B} \Delta \delta_f(k) + \tilde{E} \omega_{rd}(k)$$
In the output vector, I selected the lateral error and the lateral acceleration as outputs:
$$y(k) = C \xi(k) + D \Delta \delta_f(k)$$
Within the prediction horizon Np and control horizon Nc, the MPC obtains the optimal front wheel angle control input by rolling optimization. On the basis of the traditional path tracking cost function, I explicitly incorporated the lateral acceleration penalty term to construct the following performance index:
$$J = \sum_{i=1}^{N_p} \left( q_y e_{y,k+i|k}^2 + q_{\psi} e_{\psi,k+i|k}^2 + q_a a_{y,k+i|k}^2 \right) + \sum_{i=0}^{N_c-1} r_{\delta} \Delta \delta_{f,k+i|k}^2 + \rho \varepsilon^2$$
where qy and qψ are the lateral error and heading error weights for ensuring path tracking accuracy, qa is the lateral acceleration weight for suppressing lateral motion stimuli closely related to motion sickness, rδ is the control increment weight for constraining the front wheel angle change rate, and ε is the slack variable for soft constraints with ρ as its penalty weight.
The controller also considers the following constraints:
$$\delta_{f,min} \leq \delta_{f,k+i|k} \leq \delta_{f,max}$$
$$\Delta \delta_{f,min} \leq \Delta \delta_{f,k+i|k} \leq \Delta \delta_{f,max}$$
$$-a_{y,max} – \varepsilon \leq a_{y,k+i|k} \leq a_{y,max} + \varepsilon$$
To transform the optimization problem into a standard quadratic programming form, I constructed the prediction output sequence Y(k), the control increment sequence ΔU(k), and derived:
$$Y(k) = \Psi \xi(k) + \Theta \Delta U(k) + \Gamma W(k)$$
The objective function can then be written in quadratic form:
$$J = \frac{1}{2} z^T \tilde{H} z + \tilde{g}^T z$$
where z = [ΔUT, ε]T. At each sampling instant, the MPC controller solves the quadratic programming problem and applies only the first control input of the optimal control increment sequence. The MPC-based AFS controller can handle path tracking errors, lateral acceleration constraints, and control input constraints in a unified rolling horizon framework, actively suppressing the lateral motion stimuli closely related to motion sickness while ensuring path tracking performance.
Adaptive sliding mode control-based DYC controller design
Considering that when the vehicle approaches the stability boundary, tire lateral forces gradually tend toward saturation, and relying solely on front wheel steering adjustment is no longer sufficient to suppress the increase of yaw rate and the accumulation of sideslip angle in a timely manner, I further introduced Direct Yaw Moment Control to quickly apply additional yaw moment through differential braking, achieving vehicle attitude correction and lateral stability recovery. To handle the parameter perturbations, road adhesion variations, and unmodeled disturbances near the stability boundary while ensuring smooth braking output, I employed adaptive sliding mode control to design the DYC controller. With the introduction of the additional yaw moment, the vehicle dynamics equations become:
$$m v_x (\dot{\beta} + \omega_r) = C_1 \left( \delta_f – \beta – \frac{l_f \omega_r}{v_x} \right) + C_2 \left( -\beta + \frac{l_r \omega_r}{v_x} \right)$$
$$I_z \dot{\omega}_r = l_f C_1 \left( \delta_f – \beta – \frac{l_f \omega_r}{v_x} \right) – l_r C_2 \left( -\beta + \frac{l_r \omega_r}{v_x} \right) + \Delta M_z$$
I defined the error states between the actual and desired states, and constructed a sliding surface that simultaneously constrains both yaw rate error and sideslip angle error:
$$s = e_{\omega_r} + c e_{\beta}$$
where c > 0 is the sliding surface coefficient. The derivative of the sliding surface can be expressed as:
$$\dot{s} = f(x,t) + b \Delta M_z + d$$
To attenuate the high-frequency chattering of conventional sliding mode control, I used a saturation function within a boundary layer to replace the sign function:
$$\operatorname{sat}(s/\phi) = \begin{cases} \operatorname{sign}(s/\phi), & |s| > \phi \\ s/\phi, & |s| \leq \phi \end{cases}$$
where φ is the boundary layer thickness. The adaptive sliding mode control law was constructed as:
$$\Delta M_z = -\frac{1}{b} \left[ f(x,t) + k_1 s + \hat{\xi} \operatorname{sat}(s/\phi) + k_2 s \right]$$
where k1 > 0 and k2 > 0 are the approach gains, and ξ is the online estimate of the disturbance upper bound. The adaptive law is:
$$\dot{\hat{\xi}} = \gamma |s|$$
For stability analysis, I defined the disturbance estimation error ξ̃ = ξ – ξ̂ and selected the Lyapunov function:
$$V = \frac{1}{2} s^2 + \frac{1}{2\gamma} \tilde{\xi}^2$$
Differentiating and substituting the control law yields:
$$\dot{V} \leq -k_1 s^2 – k_2 |s| \leq 0$$
This confirms that the closed-loop system is stable and robust under bounded disturbances. After the upper-layer adaptive sliding mode controller outputs the desired additional yaw moment ΔMz, the lower-layer braking torque distribution converts it into executable wheel braking torques. The additional yaw moment formed by the left-right wheel longitudinal force difference is:
$$\Delta M_z = \frac{T_w}{2R} \left[ (T_{fr} – T_{fl}) + (T_{rr} – T_{rl}) \right]$$
The braking torque demands are first distributed between the front and rear axles according to the axle load ratios, and the final four-wheel target braking torques are determined based on the sign of the desired additional yaw moment. To ensure the executability of the wheel-end braking torque distribution, each wheel should satisfy the friction circle constraint:
$$F_{xi}^2 + F_{yi}^2 \leq (\mu F_{zi})^2$$
The designed adaptive sliding mode control-based DYC can achieve joint robust regulation of yaw rate and sideslip angle through differential braking, quickly correcting vehicle attitude when the vehicle approaches the stability boundary, and weakening the motion response deterioration caused by attitude instability.
AFS and DYC coordinated control strategy design
Considering that DYC braking interventions may introduce additional longitudinal deceleration and switching disturbances, if the two systems lack reasonable coordination, although vehicle stability can be ensured, the premature or unnecessary intervention of DYC could increase lateral and longitudinal motion stimuli, thereby weakening occupant comfort and undermining the anti-motion-sickness objective. Therefore, I designed an AFS and DYC coordinated control strategy for motion sickness mitigation based on phase-plane analysis and clustering-based motion sickness risk region division.
Considering the dimensional differences among different state variables, I defined the normalized quantities of yaw rate and sideslip angle and constructed a phase-plane motion sickness risk index:
$$\gamma_p = \left( \frac{\omega_r}{\omega_{r,ref}} \right)^2 + \left( \frac{\beta}{\beta_{ref}} \right)^2$$
where the reference values are defined as:
$$\omega_{r,ref} = k_g k_r \frac{g}{v_x}, \quad \beta_{ref} = k_{\beta} \frac{g l_r}{v_x^2}$$
Adopting the K-means clustering algorithm to identify the motion sickness risk regions, I considered representative operating conditions covering vehicle speeds of {15, 20, 25, 30} m/s and road adhesion coefficients of {0.4, 0.6, 0.8}. Under different speed and adhesion coefficient combinations, I performed numerical integration of the two-degree-of-freedom state equations with nonlinear tire characteristics under different initial conditions to obtain phase trajectories covering different motion response intensities. From each phase trajectory, I extracted the trajectory risk characteristic value, ultimately obtaining 747 trajectory risk characteristic samples. The clustering objective function was:
$$J_{km} = \sum_{j=1}^{3} \sum_{\bar{\gamma}_p^{(i)} \in S_j} \left\| \bar{\gamma}_p^{(i)} – c_j \right\|^2$$
After convergence, the three cluster centers satisfied c1 < c2 < c3, corresponding to representative γ̄p values under lower, medium, and higher motion sickness risk levels. Taking the midpoints between adjacent cluster centers as the region division boundary thresholds yielded the low motion sickness risk region upper boundary γs = 1.377 and the high motion sickness risk region lower boundary γu = 3.420. The phase-plane motion sickness risk boundary mapping results under selected operating conditions showed that, despite differences in phase trajectory distributions and region boundary shapes under different operating conditions, the phase-plane partitions based on clustering thresholds had consistent risk characterization significance across all operating conditions.
Based on these region division results, I constructed the reference weights for DYC and AFS by using a cubic Hermite smoothing function:
$$w_{DYC,ref} = \begin{cases} 0, & \gamma_p \leq \gamma_s \\ 3\chi^2 – 2\chi^3, & \gamma_s < \gamma_p < \gamma_u \\ 1, & \gamma_p \geq \gamma_u \end{cases}$$
$$w_{AFS,ref} = 1 – w_{DYC,ref}$$
$$\chi = \frac{\gamma_p – \gamma_s}{\gamma_u – \gamma_s}$$
This weight assignment enables a smooth transition between pure AFS control, coordinated control, and DYC-dominant control. This smooth transition effectively prevents additional dynamic disturbances caused by hard-switching control inputs and suppresses the additional braking intervention caused by premature or excessive DYC intervention, thereby weakening the lateral and longitudinal acceleration and jerk stimuli experienced by occupants. The final coordinated control outputs are:
$$\delta_f^* = w_{AFS} \delta_{f,AFS}$$
$$\Delta M_z^* = w_{DYC} \Delta M_{z,DYC}$$
Deep reinforcement learning-based optimization of the anti-motion-sickness coordinated control strategy
Within the coordinated region, the optimal weight allocation between AFS and DYC must consider not only vehicle yaw stability but also the suppression of lateral acceleration, longitudinal acceleration, and their jerks. Since the optimal weights vary dynamically with vehicle speed, road curvature, road adhesion conditions, and transient vehicle states, exhibiting significant nonlinear and continuous optimization characteristics, I introduced the Deep Deterministic Policy Gradient (DDPG) algorithm to adaptively optimize the coordination weights of AFS and DYC within the coordinated region.
DDPG is a deep reinforcement learning method for continuous action spaces that utilizes the Actor-Critic structure to achieve coordinated iteration of policy learning and value evaluation. The Critic network learns the state-action value function by minimizing the temporal difference error, while the Actor network continuously updates the policy parameters based on the value gradient information provided by the Critic network, guiding the output actions toward improving the long-term cumulative reward. To improve training stability, DDPG introduces an experience replay mechanism to store interaction samples in the experience pool and random sampling to weaken the temporal correlation among samples. Simultaneously, soft updates of the target network parameters suppress the target value fluctuations during training.
For the coordinated control weight optimization of the electric vehicle, the state vector was defined as:
$$s_k = \left[ \gamma_p, e_r, \chi_y, \chi_x \right]^T$$
where:
$$\chi_y = \kappa_{ay} a_y + \kappa_{jy} j_y, \quad \chi_x = \kappa_{ax} a_x + \kappa_{jx} j_x$$
The action is defined as the DYC weight within the coordinated region:
$$a_k = w_{DYC}(k), \quad 0 \leq a_k \leq 1$$
and the AFS weight is determined by the complementary constraint. The actual DYC effective weight is corrected with the motion sickness risk classification:
$$w_{DYC,eff} = \begin{cases} 0, & \gamma_p \leq \gamma_s \\ a_k, & \gamma_s < \gamma_p < \gamma_u \\ 1, & \gamma_p \geq \gamma_u \end{cases}$$
This ensures that the DDPG agent only performs continuous adaptive adjustment within the coordinated region, while the low-risk and high-risk regions retain the established coordinated control strategy boundaries. The reward function was constructed to include both stability penalties and motion stimulus penalties:
$$r_k = – \left( q_{\gamma} \gamma_p^2 + q_r e_r^2 + q_{ay} a_y^2 + q_{ax} a_x^2 + q_{jy} j_y^2 + q_{jx} j_x^2 + q_w \Delta w_{DYC}^2 \right)$$
$$\Delta w_{DYC} = w_{DYC}(k) – w_{DYC}(k-1)$$
In the offline training phase, the Critic network target Q’ value is:
$$y_i = r_i + \gamma Q’\left( s_{i+1}, \mu'(s_{i+1} | \theta^{\mu’}) | \theta^{Q’} \right)$$
The Critic network is updated by minimizing the mean squared error between the predicted Q value and the target Q’ value:
$$L = \frac{1}{N_b} \sum_{i=1}^{N_b} \left( y_i – Q(s_i, a_i | \theta^Q) \right)^2$$
The target network parameters are softly updated as:
$$\theta^{\mu’} \leftarrow \tau \theta^{\mu} + (1-\tau) \theta^{\mu’}, \quad \theta^{Q’} \leftarrow \tau \theta^{Q} + (1-\tau) \theta^{Q’}$$
For the network structure design, the Actor network receives a 4-dimensional state vector as input, passes through two hidden layers each containing 128 neurons with ReLU activation, and outputs a 1-dimensional action value through a Sigmoid activation function, limiting the output to the interval [0, 1] corresponding to the DYC control weight. The Critic network adopts a dual-stream structure in which the state path and action path are separated and subsequently merged. Table 4 lists the DDPG training hyperparameter settings.
| Parameter | Value |
|---|---|
| Actor learning rate | 0.001 |
| Critic learning rate | 0.001 |
| Sampling time (s) | 0.01 |
| Discount factor | 0.99 |
| Soft update coefficient | 0.001 |
| Batch size | 256 |
| Experience replay buffer capacity | 300000 |
| Maximum number of training episodes | 500 |
| Maximum steps per episode | 2000 |
I conducted offline training of the DDPG agent in the MATLAB/Simulink-CarSim co-simulation environment. The average episode reward convergence curve showed that although the single-episode reward fluctuated during the training process, the sliding average reward continuously increased overall and gradually stabilized in the later training phase, indicating that the constructed training framework had good convergence characteristics. As training progressed, the agent was able to progressively learn the coordinated weight allocation rule between AFS and DYC under vehicle stability constraints, achieving integrated regulation of the lateral and longitudinal motion-sickness-sensitive motion parameters.
Simulation verification of the coordinated control strategy
To verify the effectiveness of the designed coordinated control strategy for motion sickness suppression, I conducted simulation tests using the established MATLAB/Simulink-CarSim co-simulation platform. The simulation tests were conducted under four comparison scenarios: no control, AFS control, DYC control, and the DDPG-optimized AFS and DYC coordinated control. The simulation output parameters included vehicle stability parameters such as yaw rate and sideslip angle, motion-sickness-sensitive motion parameters such as lateral and longitudinal acceleration and jerk, and motion sickness dose values.
Double-lane-change condition
In the double-lane-change condition, the vehicle was set to travel at an initial speed of 90 km/h on a level road with a road adhesion coefficient of 1.0 along the double-lane-change reference path. The simulation results showed that compared with the no-control scenario, AFS control, DYC control, and coordinated control all improved vehicle stability to some extent and suppressed motion-sickness-sensitive motion parameter fluctuations, with the coordinated control achieving the best comprehensive performance. In terms of vehicle stability response indicators, during rapid steering and counter-steering, the peaks of yaw rate and sideslip angle under coordinated control were reduced and the responses exhibited smaller fluctuations. Regarding motion-sickness-sensitive motion parameters, the coordinated control suppressed the lateral acceleration, longitudinal acceleration, and their jerks to different degrees, particularly during the stages of intense vehicle state changes where the peaks and oscillation amplitudes decreased. The lateral and longitudinal motion sickness dose values exhibited lower growth rates under coordinated control, with final cumulative values smaller than those of the no-control, AFS control, and DYC control scenarios. Table 5 summarizes the motion sickness evaluation indicators under the double-lane-change condition.
| Indicator | No control | AFS control | DYC control | Coordinated control |
|---|---|---|---|---|
| MSDV | 1.81 | 0.88 | 1.24 | 0.71 |
| Motion sickness evaluation function MS | 3.20 | 1.59 | 2.24 | 1.33 |
The coordinated control achieved MSDV and MS values of 0.71 and 1.33, respectively, which were the smallest among the four scenarios. Compared with the no-control scenario, these two indicators decreased by 1.10 and 1.87, respectively; compared with AFS control, they decreased by 0.17 and 0.26; and compared with DYC control, they decreased by 0.53 and 0.91.
Slalom condition
In the slalom condition, the vehicle was set to travel at the same initial speed on the level road with an adhesion coefficient of 1.0. Compared to the double-lane-change condition, the slalom condition required the vehicle to complete multiple consecutive direction changes within a shorter time, more readily exciting vehicle transient dynamic responses and motion-sickness-sensitive motion parameter variations. The simulation results showed that the yaw rate and sideslip angle under the no-control scenario exhibited significant fluctuations with large peaks. After the introduction of AFS control and DYC control, the vehicle lateral attitude response was improved to a certain extent. Under the coordinated control scenario, the peaks and oscillation amplitudes of yaw rate and sideslip angle were further reduced, demonstrating the ability of the proposed control strategy to effectively suppress the drastic changes in vehicle lateral attitude during consecutive steering. For the motion-sickness-related indicators, the lateral acceleration and jerk exhibited more frequent alternating fluctuations under the slalom condition. The coordinated control showed the most significant suppression effect on the sensitive motion parameters. Table 6 summarizes the motion sickness evaluation indicators under the slalom condition.
| Indicator | No control | AFS control | DYC control | Coordinated control |
|---|---|---|---|---|
| MSDV | 3.48 | 1.93 | 2.49 | 1.57 |
| Motion sickness evaluation function MS | 4.70 | 1.76 | 2.96 | 1.48 |
Under the coordinated control scenario, the MSDV and MS values were 1.57 and 1.48, respectively, both being the smallest among the four scenarios. Compared with the no-control scenario, the two indicators decreased by 1.91 and 3.22, respectively; compared with AFS control, they decreased by 0.36 and 0.28; and compared with DYC control, they decreased by 0.92 and 1.48. The simulation results under both the double-lane-change and slalom conditions confirmed that the proposed coordinated control strategy can effectively suppress motion-sickness-sensitive motion parameter fluctuations, reduce the motion sickness dose value and the evaluation function value, and thus improve the anti-motion-sickness performance of the electric vehicle.
Conclusion and outlook
In this research, I systematically investigated the identification of motion-sickness-sensitive motion parameters of electric vehicle occupants, vehicle dynamics modeling considering these parameters, and the design of an anti-motion-sickness coordinated control strategy for a chassis-by-wire electric vehicle. The principal contributions of this thesis are as follows.
First, the motion-sickness-sensitive motion parameters were identified based on real-vehicle tests, and evaluation indicators were constructed. Based on the motion sickness mechanism, real-vehicle test schemes were designed, and synchronized data of subjective motion sickness responses and vehicle motion parameters were collected. Through time-domain analysis, Fourier-transform-based frequency-domain analysis, and Pearson correlation analysis, the motion-sickness-sensitive motion parameters were identified as the lateral and longitudinal accelerations and jerks, and the MSDV was introduced to construct an objective evaluation indicator. A motion sickness evaluation function was established using ridge regression combined with K-fold cross-validation. Validation results indicated that the identified parameters and the constructed evaluation function can effectively characterize occupant motion sickness responses.
Second, a seven-degree-of-freedom vehicle dynamics model was established considering the motion-sickness-sensitive motion parameters. The relationships between the sensitive motion parameters and vehicle state variables were analyzed, and a vehicle dynamics model incorporating the Magic Formula nonlinear tire model was developed in MATLAB/Simulink. The model was validated against the CarSim model under sine-wave steering and double-lane-change conditions, demonstrating acceptable accuracy in reproducing the dynamic responses of the motion-sickness-sensitive motion parameters.
Third, an anti-motion-sickness coordinated control strategy for chassis-by-wire electric vehicles was designed. MPC was used for AFS control design and adaptive sliding mode control was used for DYC control. Based on phase-plane analysis with clustering-based motion sickness risk region division, a coordinated control strategy was designed. The DDPG algorithm was employed to further optimize the control weights in the coordinated region. Under double-lane-change and slalom conditions, the coordinated control strategy was shown to effectively suppress motion-sickness-sensitive motion parameter fluctuations, reduce the MSDV and motion sickness evaluation function values, and improve the anti-motion-sickness performance of the electric vehicle.
For future research, several improvements could be considered. In the real-vehicle tests, many measures were taken to minimize the influence of individual differences on subjective motion sickness responses; however, the final sample size was relatively limited. Future work could establish more standardized experimental conditions and increase the sample size to further improve the test accuracy. In addition, the designed anti-motion-sickness coordinated control strategy was only validated in simulation. Future research could validate the optimized control strategy under hardware-in-the-loop conditions to further verify its real-time applicability and robustness in practical implementations.