In an advance for autonomous vehicle trajectory design, engineering researchers have demonstrated that directly embedding standardized frequency-shaping filters into a vehicle’s spatial path planner substantially reduces simulated passenger motion sickness compared to standard optimization methods. The computational investigation, conducted by researchers Ishu Jaiswal, Somnath Buriuly, and Arpita Sinha in Discover Vehicles, addresses a key technological barrier to the widespread public acceptance of autonomous transportation. By formulating a space-domain optimal control problem that incorporates state-space realizations of standardized motion sickness sensitivity filters, the authors demonstrated that trajectory generation can systematically suppress sickness-inducing frequency components. Numerical evaluations across diverse road geometries revealed that trajectory planners driven by standardized frequency-weighted costs consistently achieve lower motion sickness dose values than raw energy-minimizing formulations or simplified high-pass filtering approximations.
Motion sickness presents a persistent challenge to the deployment of automated passenger vehicles, with transportation statistics indicating that the condition affects nearly half of adult road transit passengers. Conversely, occupants of autonomous vehicles relinquish operational control and often engage in secondary non-driving activities, such as reading, utilizing mobile digital devices, resting, or listening to music. Research cited by the authors demonstrates that passive postures, coupled with reduced alertness and inclined body positions, significantly heighten individual vulnerability to nausea, lightheadedness, and fatigue. Because occupants cannot instinctively anticipate sudden vehicle motions, automated planners must intrinsically eliminate the low-frequency lateral and longitudinal oscillations that provoke somatic discomfort.
To establish an effective mitigation framework, the authors examined established human vibration standards, notably International Standard ISO 2631-1 and British Standard BS 6841-1987, which quantify whole-body vibration and motion sickness dose values. Human physiological susceptibility to motion sickness is highly frequency-dependent, exhibiting pronounced sensitivity to horizontal and vertical translational oscillations within the low-frequency band spanning 0.0315 Hz to 0.25 Hz. Prior investigations established that lateral accelerations resulting from turning techniques represent a primary driver of motion sickness, with lateral sensitivity behaving independently of frequency from 0.0315 Hz to 0.25 Hz before diminishing at twelve decibels per octave between 0.25 Hz and 0.8 Hz. Although early autonomous vehicle optimization efforts attempted to enhance passenger comfort by penalizing pure squared accelerations or employing second-order high-pass filters, the authors identified critical deficiencies in existing literature. Previous approaches relied on continuous-time formulations without standardized filter states or failed to integrate full filter dynamics into computationally efficient spatial-domain collocation frameworks.
Addressing these structural gaps, the research team formulated a road-vehicle trajectory planner using a continuous unicycle kinematic model cast within a spatial curvilinear coordinate frame. Rather than parameterizing vehicle motion strictly across continuous time, the curvilinear framework maps system behavior along the road centerline arc length, denoted by the spatial coordinate s. Under this mathematical mapping, road geometry is comprehensively defined through a continuous curvature profile, allowing the vehicle’s longitudinal progress, lateral deviation, and relative heading angle to be tracked relative to road boundaries. The unicycle model incorporates seven core state variables: longitudinal velocity, road-relative arc length, lateral displacement, relative heading angle, inertial coordinates, and yaw angle. Forward vehicle velocity is bounded between 0.1 meters per second and 30 meters per second, ensuring uninterrupted forward progress while constraining lateral offsets within four meters of the centerline. Transforming system differential equations into the spatial s-domain links trajectory optimization directly to geometric road profiles while preserving kinematic consistency through algebraic differential relations.
The central theoretical contribution of the study lies in augmenting the vehicle’s dynamic state equations with the differential state-space realization of frequency-weighting filters. In the absence of an officially standardized horizontal motion sickness filter, the researchers adapted the standardized ISO 2631-1 vertical weighting filter, designated Wf, applying its empirical transfer dynamics to both longitudinal and lateral vehicle acceleration channels. Realizing this standardized filter in canonical state-space form required introducing sixteen auxiliary state variables—eight tracking longitudinal acceleration dynamics and eight dedicated to lateral acceleration dynamics. For rigorous comparative analysis, the authors formulated three distinct optimization cost functions: a baseline energy-minimization cost penalizing raw squared accelerations, an approximate motion sickness cost employing a second-order high-pass filter with four state variables and a tuned cutoff frequency of 0.08 Hz, and the sixteen-state standardized Wf filter formulation. Each cost functional integrated filtered acceleration components across the spatial trajectory, directly penalizing vehicle motions falling within the frequency spectrum most disruptive to human passengers.
To compute optimal trajectories across these complex augmented models, the authors employed direct collocation, discretizing the continuous spatial optimal control problem into a finite-dimensional nonlinear programming problem. The spatial planning horizon was partitioned into uniform one-meter intervals, utilizing the trapezoidal collocation method to enforce vehicle kinematics, path constraints, and differential filter equations at each collocation node. The mathematical problem was modeled within the CasADi symbolic optimization framework and solved using the IPOPT interior-point nonlinear programming solver running under MATLAB on an Intel Core i7-9750H processor with eight gigabytes of memory. Because the nonlinear coupling between vehicle kinematics and high-order filter dynamics can provoke solver convergence failures, the team developed a robust warm-start initialization strategy. A reduced-order vehicle model tracked a nominal path using a proportional-integral controller configured with proportional gain of 1.1 and integral gain of 0.5 under constant velocity, generating a kinematically feasible initial guess that ensured reliable numerical convergence across all tested scenarios.
Validating the performance of the frequency-shaped planner required evaluating three distinct motion sickness dose value metrics to prevent optimization artifacts from skewing conclusions. The first metric, designated MSDV-DS, was obtained directly from the optimal objective value returned by the nonlinear solver, serving as a composite proxy that incorporates both trajectory discomfort and terminal penalty weights. The second metric, designated MSDV-OS, was computed by extracting optimal state and control trajectories from the solver and integrating the frequency-weighted acceleration signals over time in accordance with ISO 2631-1 definitions. The third metric, designated MSDV-FS, utilized forward simulation, feeding the solver’s optimal acceleration and steering control sequences into independent time-domain filter dynamics. The researchers observed tight numerical consistency between the optimal state metric and the forward simulation metric across all evaluated road scenarios. This robust agreement confirmed that trajectories generated within the spatial collocation framework remain dynamically reliable and do not rely on mathematical idealizations or solver discretization discrepancies.
The comparative effectiveness of the three candidate cost functions was systematically investigated across diverse geometric road profiles, including constant-length curved segments, concentric circular roads, S-shaped curves, and a literature-derived realistic road track that incorporates representative highway layouts. Across every evaluated road family, the standardized Wf frequency-weighted cost function consistently produced the lowest motion sickness dose values for any given radius of curvature, demonstrating superior performance in suppressing discomfort-inducing dynamic motions. Formulations utilizing the second-order high-pass filter achieved moderate reductions in motion sickness metrics, outperforming the baseline energy-minimization objective but failing to match the sickness attenuation delivered by the standardized filter. The baseline energy cost, which simply minimized total squared acceleration effort, consistently registered the highest motion sickness dose values. Furthermore, parametric evaluations revealed a fundamental inverse relationship between road radius of curvature and motion sickness severity, particularly under energy-based planning, confirming that sharper roadway turns naturally excite stronger low-frequency lateral accelerations that aggravate occupant motion sickness symptoms.
The investigation yielded critical operational insights regarding the trade-off between passenger ride comfort and terminal state tracking accuracy. When soft terminal cost penalties were incorporated into the objective function to enforce precise vehicle stopping and centerline alignment at the trajectory endpoint, motion sickness dose values increased across all road types. In fixed-length road segments, larger curvature radii paradoxically elevated sickness metrics under terminal-constrained formulations because the numerical optimizer was forced to execute abrupt steering and deceleration adjustments near the finish line to satisfy boundary conditions within restricted spatial distance. Conversely, on road families where track length naturally expanded alongside radius of curvature, motion sickness dose values exhibited pronounced, consistent reductions. The expanded physical distance provided the trajectory planner with greater spatio-temporal freedom to distribute necessary steering and speed modifications gradually, successfully damping the excitation of critical frequency components within the passenger sensitivity range and confirming that sufficient travel distance mitigates the adverse discomfort effects associated with strict endpoint constraints.
Despite the clear performance advantages demonstrated by the standardized frequency-shaping framework, the authors detailed notable engineering limitations and practical computational challenges associated with real-world implementation. Augmenting the vehicle model with sixteen filter states increases the overall state dimension to twenty-three variables, substantially escalating algebraic problem complexity and memory demands within the nonlinear programming solver. Looking toward future autonomous transportation systems, the researchers highlighted several promising development pathways, including extending the spatial optimization formulation to composite road networks, integrating multi-axial human sensory mismatch models, and developing robust control algorithms capable of managing real-time perceptual uncertainties and environmental road variations. Nonetheless, this study provides rigorous computational evidence that embedding standardized frequency-shaping principles directly into spatial trajectory planning represents an essential engineering strategy for conquering motion sickness in autonomous vehicles.
Subject of Research: Frequency-weighted trajectory optimization for autonomous vehicle motion sickness mitigation
Article Title: Effect of frequency shaping cost on trajectory planner for mitigation of motion sickness
Article References: Jaiswal, I., Buriuly, S., & Sinha, A. (2026). Effect of frequency shaping cost on trajectory planner for mitigation of motion sickness. Discover Vehicles, 2(1), Article 17. https://doi.org/10.1007/s44465-026-00018-z
Image Credits: AI Generated
DOI: 10.1007/s44465-026-00018-z
Keywords: autonomous vehicles, motion sickness mitigation, trajectory planning, motion sickness dose value, frequency shaping, ISO 2631-1, direct collocation, curvilinear coordinates, unicycle vehicle model, nonlinear programming, ride comfort, lateral acceleration, sensory conflict, high-pass filter, optimal control problem, IPOPT solver, CasADi framework
News Source: Denise Maddox. (November 15, 2026). Standardized Frequency Filter Optimization Reduces Motion Sickness in Autonomous Vehicle Simulations. Scienmag.
