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REVIEW 3 major objections 6 minor 48 references

A diffusion residual re-sizes the yaw reference and tightens the handling envelope so limit-handling MPC anticipates model error instead of reacting after side-slip grows.

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2026-07-14 13:15 UTC pith:BZSAC3F7

load-bearing objection Clean systems paper: diffusion residual moments on reference + envelope, not the law; low-μ recovery is real but in-mix mean correction, not grip transfer. the 3 major comments →

arxiv 2607.10243 v1 pith:BZSAC3F7 submitted 2026-07-11 cs.RO cs.SYeess.SY

Diffusion-Residual Model Predictive Steering Control for Vehicle Stabilization at the Limit of Handling under Model Uncertainty

Bongsob Song This is my paper
classification cs.RO cs.SYeess.SY
keywords model predictive controldiffusion modelsvehicle stability controllimits of handlingchance-constrained controlreal-time controluncertainty quantificationactive front steering
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

At the limit of handling, a stabilizing model-predictive steering controller lives or dies by two settings it cannot know in advance: the yaw-rate target it tracks and the margin of the stable-handling envelope it enforces. Fixed or worst-case choices are either too timid or unsafe once tires saturate and the simple bicycle model drifts from the real car. This paper trains a small conditional diffusion model on the residual between that bicycle model and higher-fidelity behavior, conditioned only on speed and the driver's steering command. From the residual it extracts two numbers: a mean that re-sizes the tracked yaw reference to what is actually achievable, and a predictive spread that is propagated over the prediction horizon to back off the envelope with a one-sided chance constraint. The resulting controller, D-res, therefore anticipates caution before tracking error appears rather than correcting it afterward with high gain. Because only those two moments are needed, the generator is tabulated offline; online the controller adds a single table lookup to a standard linear time-varying MPC, meets a 100 Hz budget on an embedded automotive processor, and, across vehicle, tire, road, and maneuver diversity in both a 7-DOF model and high-fidelity co-simulation, lowers peak side-slip and recovers directional stability on low-friction maneuvers where the fixed reference over-commands available grip.

Core claim

Learning the operating-point residual of the nominal bicycle model with a command-conditioned diffusion generator, then feeding only its mean into the yaw reference and its spread into a one-sided chance back-off on the Beal–Gerdes stable-handling envelope, yields a real-time stabilizing MPC that reduces peak side-slip and restores low-friction directional stability across vehicle, tire, road, and maneuver diversity without changing the control law or running diffusion online.

What carries the argument

Diffusion-residual MPC (D-res): a shared conditional diffusion residual generator that, for each command, returns the mean of a reference residual (used to re-size the tracked yaw rate) and the spread of a state residual (propagated over the horizon to tighten the envelope via a one-sided chance back-off).

Load-bearing premise

The residual learned from command alone, tabulated offline and pooled across dry and low-friction training surfaces without online road-friction input, stays accurate enough for closed-loop reference re-sizing and envelope tightening when the real car, tire, load, or driver differ from the training setup.

What would settle it

On a vehicle, tire, load, or road surface outside the training distribution, if closed-loop peak side-slip under D-res no longer improves on the fixed-reference baseline—or if low-friction step and lane-change maneuvers still diverge—then the command-only tabulated residual fails to transfer.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes diffusion-residual MPC (D-res) for active-front-steering stabilization at the limit of handling. A command-conditioned diffusion model learns two residuals of a nominal bicycle model and supplies only their mean and spread: the mean re-sizes the tracked yaw-rate reference (D-ref), while the spread is propagated over the prediction horizon and used as a one-sided chance back-off on the Beal–Gerdes stable-handling envelope (D-env). Moments are tabulated offline so the online controller adds a single lookup to a baseline LTV-MPC, with no in-loop diffusion, and is shown to meet a 100 Hz budget on a Jetson AGX Xavier (worst-case 4.08 ms). Evaluation is a controlled five-rung ablation (NOM, D-env, D-ref, GP-ref, D-res) on a 7-DOF plant and high-fidelity CarMaker co-simulation across a four-vehicle fleet, tire/load variants, dry and low-μ surfaces, and ISO/FMVSS maneuvers, with peak side-slip as the primary KPI. The reported result is reduced peak side-slip where the fixed bicycle model is least accurate and recovery of low-μ divergence that the fixed reference over-commands.

Significance. If the claims hold under the paper’s stated scope, the contribution is a practical and well-scoped coupling of a generative residual model to a stabilizing MPC: uncertainty is applied to the reference and constraints rather than the control law, only two moments are needed online, and real-time feasibility on an automotive-grade embedded target is demonstrated with a measured WCET. The five-rung ablation, GP-ref baseline under an identical back-off, path-deviation reporting, load/tire probes, LOVO diagnostic, and closed-loop risk audit are stronger empirical practice than is common in limit-handling MPC papers that fix a single vehicle and maneuver. The novelty claim—first use of a diffusion model’s predictive spread as a chance-constraint back-off for limit-handling stabilization—is plausible given the related-work placement. The work is simulation-scoped and in-domain with per-tier retraining; that is a limitation of impact, not of internal soundness.

major comments (3)
  1. Abstract, §IV-C, and §V-C: the headline claim that D-res “restores directional stability on low-friction maneuvers” is carried almost entirely by the mean re-size E[Δr_ref|c] (Table III: D-ref alone turns M3-low from 99–125° spins to ≤0.63°; D-env alone does not recover and can regress). That mean is tabulated from residuals pooled over dry and low-μ training at the same command c=[v_x, δ_driver], with μ neither a conditioning input nor observed online. The manuscript does not report a dry-only-trained generator evaluated on low-μ, nor intermediate/unseen μ. Please tighten the abstract, contribution list, and conclusion so the low-μ result is explicitly scoped as in-mix residual reference correction with low-μ data in the training pool—not as command-only grip transfer or surface extrapolation. A dry-only→low-μ ablation (even negative) would make the scope falsifiable.
  2. §IV-B Eqs. (14)–(16) and §V-B: the chance back-off uses a Gaussian moment approximation (κ=Φ^{-1}(0.95)=1.645) while the paper reports that the residual is measurably non-Gaussian (skewness −1.34, excess kurtosis −1.81, normality rejected). The closed-loop exit-rate audit (0% under D-res vs. η=5%) is valuable, but the text also states that the margin covering 95% of draws is 1.75σ̂ at the fleet median (up to 3.1σ̂ near the limit), so the Gaussian form attains nominal per-step coverage on only about a quarter of cells. Please state more prominently that the back-off is a data-driven margin-tightening surrogate whose risk is audited in aggregate closed loop, not a per-step probabilistic guarantee, and either (i) report the empirical VaR/quantile table the architecture already supports or (ii) qualify every “chance-constrained” claim accordingly so the Gaussian form is not over-read.
  3. §V-A–V-C and Tables II–III: the generator is retrained per tier and the evaluation is in-domain. That is disclosed, but several summary sentences still read as if a single residual oracle transfers across plant fidelity. Please make the per-tier retraining and in-domain scope visible in the abstract and in the fleet-median claims (e.g., “with the generator retrained on each tier’s residual data”), so the cross-tier agreement is not mistaken for zero-shot transfer of the diffusion model.
minor comments (6)
  1. §IV-B: recursive feasibility and closed-loop stability are left empirical. A short explicit statement that the soft slack gives only persistent QP feasibility (not set invariance) already appears; consider elevating it to the limitations paragraph in §VI so readers do not expect a terminal-set certificate.
  2. Table III, M6-low † cells: excluding the maximum-amplitude low-μ sweep as a maneuver-design limit is reasonable, but the abstract’s “restores directional stability on low-friction maneuvers” should cross-reference that M6-low is excluded from the envelope-pass base so the claim is not over-generalized.
  3. §V-E: on-target timing is profiling of a fixed-iteration Hildreth QP, not closed-loop HIL and not a static WCET certificate. The paper already flags this as future work; a one-sentence reminder in the abstract’s real-time sentence would prevent over-reading “runs within the 100 Hz budget” as vehicle-validated.
  4. Fig. 4(a) oracle vs. command-only fidelity: the 3.1% oracle match vs. the deployed command-only error (+46%/−25% on the two channels) is important; consider a small table or callout so readers see that reported closed-loop gains already use the weaker online conditioning.
  5. Notation: β is used both for vehicle side-slip and for the diffusion noise schedule β_t; the paper notes the distinction once, but a consistent subscript (e.g., β_side vs. β_t) would reduce ambiguity in §IV-A.
  6. Companion code is promised upon acceptance; if available during revision, pointing reviewers to the moment-table generation and the five-rung ablation scripts would strengthen reproducibility claims.

Circularity Check

0 steps flagged

No derivation circularity: residual moments are learned from open-loop mismatch and applied to reference/constraints; closed-loop β_peak is an independent plant KPI, not forced by the fit.

full rationale

The paper does not present a first-principles derivation whose conclusion equals its inputs. It defines open-loop residuals H = ẋ_m − ẋ_nom and Δr_ref = r − r_lin, fits a conditional diffusion generator to those residuals, and feeds only the resulting mean and spread into a standard LTV-MPC reference and chance back-off (Eqs. 10–27). Closed-loop KPIs (β_peak, spins, path deviation) are measured on the 7-DOF and CarMaker plants against NOM, D-env, D-ref, and GP-ref ablations that share the same MPC weights and back-off form; those outcomes are not algebraically identical to the residual tables. In-domain, per-tier retraining and pooling of dry/low-μ residual mass are disclosed scope choices (abstract; IV-C; V-A), not a self-definitional reduction of the stability claim. Chance-constraint risk is audited empirically in closed loop rather than asserted by construction. Citations for bicycle MPC, Beal–Gerdes envelopes, chance tightening, and DDPM are external; there is no load-bearing self-citation uniqueness chain. Mild generalization concerns (command-only conditioning, in-mix low-μ recovery) are correctness/transfer issues, not circularity of the derivation chain.

Axiom & Free-Parameter Ledger

7 free parameters · 6 axioms · 2 invented entities

The method rests on standard bicycle/LTV-MPC and chance-constraint machinery plus a learned residual oracle. Free parameters are the usual MPC weights/horizons plus several hand-set risk and envelope constants and the diffusion sampling budget. Domain assumptions include the Beal–Gerdes envelope intent, soft-constraint feasibility instead of recursive feasibility certificates, and Gaussian moment tightening despite non-Gaussian residuals. The main invented object is the shared conditional diffusion residual generator used as a tabulated moment oracle rather than an in-loop planner.

free parameters (7)
  • one-sided chance level κ=Φ^{-1}(0.95)=1.645 (η=0.05)
    Fixed risk level for all active envelope facets; not identified from closed-loop risk targets beyond post-hoc audit.
  • yaw risk split k1=0.25 k2
    Hand-tuned allocation between state-spread and reference-spread terms in the joint yaw bound (Section IV-C), not derived from independence or optimality.
  • diffusion sample count S=64
    Chosen via 7-DOF convergence study of fleet-median β_peak; offline moment estimation budget.
  • MPC horizons Np=18, Nc=8, Ts=10 ms and cost weights Q,R,Sδ,wξ
    Shared design constants across all rungs; standard free tuning of the baseline LTV-MPC.
  • envelope limits β_max=6°, α_r,max=4° (floor 1°)
    Conservative side-slip box and rear-slip limits defining the polytope facets.
  • friction-circle stiffness floor kmin=0.45 and usage cap ρ̄=0.98
    Deterministic in-loop adaptation (Eq. 3) shared by all controllers; still a hand-set lumped adaptation rule.
  • diffusion architecture/training (2×64 tanh MLP, T=50, Adam 2e-3, 300 epochs, batch 256)
    Model-capacity and optimization choices that define the residual oracle.
axioms (6)
  • domain assumption Nominal plant is the speed-scheduled 2-DOF bicycle with additive residual H capturing (ΔA,ΔB) effects.
    Section II-A / Eq. (1)–(2); all prediction and residual definitions rest on this structure.
  • domain assumption Beal–Gerdes stable-handling envelope (side-slip, rear-slip, friction-limited yaw) is the correct safety set for directional stabilization (not drift).
    Section II-B, constraints (4d)–(4f) and (12)–(13).
  • ad hoc to paper Gaussian moment approximation yields a valid one-sided chance back-off for facet projections even when residuals are non-Gaussian.
    Section IV-B explicitly calls this a surrogate whose risk is audited in closed loop; later notes VaR vs 1.645σ mismatch.
  • ad hoc to paper Residual is fully correlated across the committed horizon (conservative covariance propagation).
    Eq. (16b)–(17); structural modeling choice for Σx,k.
  • domain assumption Soft shared slack ξ provides persistent QP feasibility; recursive feasibility and closed-loop stability need not be certified a priori.
    Section II-B / IV-B; stability left empirical.
  • standard math Linear covariance propagation of additive residual through LTV prediction is adequate for back-off sizing.
    Standard cautious-MPC form cited from Mesbah/Hewing-style SMPC.
invented entities (2)
  • Shared conditional diffusion residual generator as offline moment oracle for both state residual H and reference residual Δr_ref no independent evidence
    purpose: Supply command-conditioned mean and spread used by D-ref and D-env without in-loop sampling.
    Core methodological object of the paper; independent evidence is only the closed-loop simulation ablations and oracle spread checks in Fig. 4, not external physical measurement of the residual law.
  • D-res controller (= D-env + D-ref) no independent evidence
    purpose: Name the combined reference re-sizing and chance-envelope back-off policy.
    Composition of known MPC pieces with the learned moments; not a new physical entity, but a paper-specific controller construct.

pith-pipeline@v1.1.0-grok45 · 32902 in / 4333 out tokens · 38612 ms · 2026-07-14T13:15:08.837384+00:00 · methodology

0 comments
read the original abstract

At the limit of handling, a stabilizing MPC depends on the yaw-rate reference it tracks and the stable-handling envelope it enforces, both operating-point-dependent and unknown a priori, so fixed or worst-case settings are either too conservative or unsafe. We learn this uncertainty with a conditional diffusion residual model and apply it to the controller's reference and constraints rather than its control law. Conditioned on the steering command, the model returns the residual's mean and a predictive spread: the mean re-sizes the tracked yaw reference, while the spread, propagated over the prediction horizon, tightens the stable-handling envelope through a one-sided chance back-off. Together these form the proposed diffusion-residual MPC (D-res), so caution is anticipated ahead of the tracking error rather than corrected after it by a high-gain loop. Because only two moments per command are needed, the generator is tabulated offline and the online controller adds a single table lookup to the baseline MPC, with no in-loop diffusion; it runs within the 100 Hz budget on an NVIDIA Jetson AGX Xavier (worst-case 4.08 ms per step). Across a 7-DOF model and high-fidelity CarMaker co-simulation spanning vehicle, tire, road, and maneuver diversity, D-res reduces peak side-slip where the fixed bicycle model is least accurate and restores directional stability on low-friction maneuvers, where the fixed reference over-commands the available grip.

Figures

Figures reproduced from arXiv: 2607.10243 by Bongsob Song.

Figure 1
Figure 1. Figure 1: Overview of the diffusion-residual MPC and its simu [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Side-slip (β), yaw rate (r), and residual, in steady cornering. (a) load and tire: the bicycle model (dashed) against CarMaker (Tire A, Tire B, five-occupant load). (b) open￾loop state residual eβ, er across the four-vehicle fleet (Sedan, Compact, Sports, SUV). θe + arctan k elat/vx  with cross-track error elat, heading error θe, and gain k=1.5 [42]. The second one is a black￾box model for the high-fideli… view at source ↗
Figure 3
Figure 3. Figure 3: The three featured limit maneuvers (M1, M7, M3-low) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: D-env on the M7-high brake-in-turn (sports car, 7- [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Diffusion reference correction E[∆r ref | vx, δ] over the command plane (7-DOF sedan); the marked point is the M3- step operating point, where the linear reference over-predicts the achievable yaw and the diffusion mean re-sizes it. lope back-off (15) formed from Σx,k (16), both negligible against the fixed-iteration QP that dominates the step. The interpolated moment surfaces are smooth ( [PITH_FULL_IMAG… view at source ↗
Figure 6
Figure 6. Figure 6: Low-µ step (M3-low, µ ≈ 0.3, SUV), live CarMaker. (a) Vehicle path: NOM vs. D-res. (b) Side-slip β(t) (zoomed to ±8 ◦ ). 2.48◦ of NOM on that set, as it over-tightens the benign maneuvers without re-sizing the reference; the conditioned D￾res instead reaches 0.83◦ , so the gain is the conditioning, not the conservatism. The entire comparison, however, rests on a 7-DOF model—a reduced description of the rea… view at source ↗

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Reference graph

Works this paper leans on

48 extracted references · 11 linked inside Pith

  1. [1]

    Predictive active steering control for autonomous vehicle systems,

    P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, and D. Hrovat, “Predictive active steering control for autonomous vehicle systems,”IEEE Trans. Control Syst. Technol., vol. 15, no. 3, pp. 566–580, 2007

    2007

  2. [2]

    Bosch ESP systems: 5 years of experience,

    A. T. van Zanten, “Bosch ESP systems: 5 years of experience,” inProc. SAE Automot. Dyn. Stability Conf., 2000, SAE Technical Paper 2000- 01-1633

    2000

  3. [3]

    A controller framework for au- tonomous drifting: Design, stability, and experimental validation,

    R. Y . Hindiyeh and J. C. Gerdes, “A controller framework for au- tonomous drifting: Design, stability, and experimental validation,”J. Dyn. Syst. Meas. Control, vol. 136, no. 5, p. 051015, 2014

    2014

  4. [4]

    Toward automated vehicle control beyond the stability limits: Drifting along a general path,

    J. Y . Goh, T. Goel, and J. C. Gerdes, “Toward automated vehicle control beyond the stability limits: Drifting along a general path,”J. Dyn. Syst. Meas. Control, vol. 142, no. 2, p. 021004, 2020

    2020

  5. [5]

    One model to drift them all: Physics-informed condi- tional diffusion model for driving at the limits,

    F. Djeumou, T. J. Lew, N. Ding, M. Thompson, M. Suminaka, M. Greiff, and J. Subosits, “One model to drift them all: Physics-informed condi- tional diffusion model for driving at the limits,” inProc. Conf. Robot Learn. (CoRL), vol. 270, 2025, pp. 604–630

    2025

  6. [6]

    Model predictive control tuning methods: A review,

    J. L. Garriga and M. Soroush, “Model predictive control tuning methods: A review,”Ind. Eng. Chem. Res., vol. 49, no. 8, pp. 3505–3515, 2010. DIFFUSION-RESIDUAL MODEL PREDICTIVE STEERING CONTROL 16

    2010

  7. [7]

    Model predictive control in industry: Challenges and opportunities,

    M. G. Forbes, R. S. Patwardhan, H. Hamadah, and R. B. Gopaluni, “Model predictive control in industry: Challenges and opportunities,” IFAC-PapersOnLine, vol. 48, no. 8, pp. 531–538, 2015

    2015

  8. [8]

    Robust model predic- tive control of constrained linear systems with bounded disturbances,

    D. Q. Mayne, M. M. Seron, and S. V . Rakovi ´c, “Robust model predic- tive control of constrained linear systems with bounded disturbances,” Automatica, vol. 41, no. 2, pp. 219–224, 2005

    2005

  9. [9]

    Stochastic model predictive control: An overview and perspectives for future research,

    A. Mesbah, “Stochastic model predictive control: An overview and perspectives for future research,”IEEE Control Syst. Mag., vol. 36, no. 6, pp. 30–44, 2016

    2016

  10. [10]

    Learning- based model predictive control: Toward safe learning in control,

    L. Hewing, K. P. Wabersich, M. Menner, and M. N. Zeilinger, “Learning- based model predictive control: Toward safe learning in control,”Annu. Rev. Control Robot. Auton. Syst., vol. 3, pp. 269–296, 2020

    2020

  11. [11]

    Model predictive control for vehicle stabilization at the limits of handling,

    C. E. Beal and J. C. Gerdes, “Model predictive control for vehicle stabilization at the limits of handling,”IEEE Trans. Control Syst. Technol., vol. 21, no. 4, pp. 1258–1269, 2013

    2013

  12. [12]

    Cautious model predictive control using Gaussian process regression,

    L. Hewing, J. Kabzan, and M. N. Zeilinger, “Cautious model predictive control using Gaussian process regression,”IEEE Trans. Control Syst. Technol., vol. 28, no. 6, pp. 2736–2743, 2020, arXiv:1705.10702

    Pith/arXiv arXiv 2020

  13. [13]

    Friction-adaptive stochastic nonlinear model predictive control for autonomous vehicles,

    S. Vaskov, R. Quirynen, M. Menner, and K. Berntorp, “Friction-adaptive stochastic nonlinear model predictive control for autonomous vehicles,” Veh. Syst. Dyn., vol. 62, no. 2, pp. 347–371, 2024

    2024

  14. [14]

    Rajamani,Vehicle Dynamics and Control, 2nd ed

    R. Rajamani,Vehicle Dynamics and Control, 2nd ed. Springer, 2012

    2012

  15. [15]

    CarMaker: Virtual test-driving software for ve- hicle dynamics,

    IPG Automotive GmbH, “CarMaker: Virtual test-driving software for ve- hicle dynamics,” Software, version 13, Karlsruhe, Germany, 2023, https: //www.ipg-automotive.com/en/products-solutions/software/carmaker/

    2023

  16. [16]

    H. B. Pacejka,Tire and Vehicle Dynamics, 3rd ed. Butterworth- Heinemann, 2012

    2012

  17. [17]

    Polytopic LPV approaches for intelligent automotive systems: State of the art and future challenges,

    P. Li, A.-T. Nguyen, H. Du, Y . Wang, and H. Zhang, “Polytopic LPV approaches for intelligent automotive systems: State of the art and future challenges,”Mech. Syst. Signal Process., vol. 161, p. 107931, 2021

    2021

  18. [18]

    Robust MPC with recursive model update,

    M. Lorenzen, M. Cannon, and F. Allg ¨ower, “Robust MPC with recursive model update,”Automatica, vol. 103, pp. 461–471, 2019

    2019

  19. [19]

    Robust model predictive control: A survey,

    A. Bemporad and M. Morari, “Robust model predictive control: A survey,” inRobustness in Identification and Control, ser. Lecture Notes in Control and Information Sciences, A. Garulli, A. Tesi, and A. Vicino, Eds. London: Springer-Verlag, 1999, vol. 245, pp. 207–226

    1999

  20. [20]

    The scenario approach to robust control design,

    G. C. Calafiore and M. C. Campi, “The scenario approach to robust control design,”IEEE Trans. Autom. Control, vol. 51, no. 5, pp. 742– 753, 2006

    2006

  21. [21]

    Stochastic predictive control of autonomous vehicles in uncertain environments,

    A. Carvalho, Y . Gao, S. Lef `evre, and F. Borrelli, “Stochastic predictive control of autonomous vehicles in uncertain environments,” inProc. 12th Int. Symp. Adv. Veh. Control (AVEC), Tokyo, Japan, 2014

    2014

  22. [22]

    On distributionally robust chance- constrained linear programs,

    G. C. Calafiore and L. El Ghaoui, “On distributionally robust chance- constrained linear programs,”J. Optim. Theory Appl., vol. 130, no. 1, pp. 1–22, 2006

    2006

  23. [23]

    Gaus- sian processes for dynamics learning in model predictive control,

    A. Scampicchio, E. Arcari, A. Lahr, and M. N. Zeilinger, “Gaus- sian processes for dynamics learning in model predictive control,” arXiv:2502.02310, 2025

    Pith/arXiv arXiv 2025

  24. [24]

    Learning model predictive control for iterative tasks: A data-driven control framework,

    U. Rosolia and F. Borrelli, “Learning model predictive control for iterative tasks: A data-driven control framework,”IEEE Trans. Autom. Control, vol. 63, no. 7, pp. 1883–1896, 2018, arXiv:1609.07220

    Pith/arXiv arXiv 2018

  25. [25]

    Neural lander: Stable drone landing control using learned dynamics,

    G. Shi, X. Shi, M. O’Connell, R. Yu, K. Azizzadenesheli, A. Anand- kumar, Y . Yue, and S.-J. Chung, “Neural lander: Stable drone landing control using learned dynamics,” inProc. IEEE Int. Conf. Robot. Autom. (ICRA), 2019, pp. 9784–9790

    2019

  26. [26]

    DroneD- iffusion: Robust quadrotor dynamics learning with diffusion models,

    A. Das, R. D. Yadav, S. Sun, M. Sun, S. Kaski, and W. Pan, “DroneD- iffusion: Robust quadrotor dynamics learning with diffusion models,” in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), 2025, arXiv:2409.11292

    Pith/arXiv arXiv 2025

  27. [27]

    Vehicle yaw stability control by coordinated active front steering and differential braking in the tire sideslip angles domain,

    S. Di Cairano, H. E. Tseng, D. Bernardini, and A. Bemporad, “Vehicle yaw stability control by coordinated active front steering and differential braking in the tire sideslip angles domain,”IEEE Trans. Control Syst. Technol., vol. 21, no. 4, pp. 1236–1248, 2013

    2013

  28. [28]

    Autonomous vehicle control at the limits of handling,

    K. Kritayakirana and J. C. Gerdes, “Autonomous vehicle control at the limits of handling,”Int. J. Veh. Auton. Syst., vol. 10, no. 4, pp. 271–296, 2012

    2012

  29. [29]

    Staying within the nullcline boundary for vehicle envelope control using a sliding surface,

    C. G. Bobier and J. C. Gerdes, “Staying within the nullcline boundary for vehicle envelope control using a sliding surface,”Veh. Syst. Dyn., vol. 51, no. 2, pp. 199–217, 2013

    2013

  30. [30]

    Soft constraints and exact penalty functions in model predictive control,

    E. C. Kerrigan and J. M. Maciejowski, “Soft constraints and exact penalty functions in model predictive control,” inProc. UKACC Int. Conf. Control, Cambridge, UK, 2000

    2000

  31. [31]

    Collision avoidance and stabilization for autonomous vehicles in emergency scenarios,

    J. Funke, M. Brown, S. M. Erlien, and J. C. Gerdes, “Collision avoidance and stabilization for autonomous vehicles in emergency scenarios,”IEEE Trans. Control Syst. Technol., vol. 25, no. 4, pp. 1204–1216, 2017

    2017

  32. [32]

    Shared steering control using safe envelopes for obstacle avoidance and vehicle stability,

    S. M. Erlien, S. Fujita, and J. C. Gerdes, “Shared steering control using safe envelopes for obstacle avoidance and vehicle stability,”IEEE Trans. Intell. Transp. Syst., vol. 17, no. 2, pp. 441–451, 2016

    2016

  33. [33]

    Optimization-based au- tonomous racing of 1:43 scale RC cars,

    A. Liniger, A. Domahidi, and M. Morari, “Optimization-based au- tonomous racing of 1:43 scale RC cars,”Optim. Control Appl. Methods, vol. 36, no. 5, pp. 628–647, 2015, arXiv:1711.07300

    Pith/arXiv arXiv 2015

  34. [34]

    Information-theoretic model predictive control: Theory and applications to autonomous driving,

    G. Williams, P. Drews, B. Goldfain, J. M. Rehg, and E. A. Theodorou, “Information-theoretic model predictive control: Theory and applications to autonomous driving,”IEEE Trans. Robot., vol. 34, no. 6, pp. 1603– 1622, 2018

    2018

  35. [35]

    Denoising diffusion probabilistic models,

    J. Ho, A. Jain, and P. Abbeel, “Denoising diffusion probabilistic models,” inProc. Adv. Neural Inf. Process. Syst. (NeurIPS), vol. 33, 2020, pp. 6840–6851, arXiv:2006.11239

    Pith/arXiv arXiv 2020

  36. [36]

    Score-based generative modeling through stochastic differ- ential equations,

    Y . Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, “Score-based generative modeling through stochastic differ- ential equations,” inProc. Int. Conf. Learn. Represent. (ICLR), 2021, arXiv:2011.13456

    Pith/arXiv arXiv 2021

  37. [37]

    Diffusion model predictive control,

    G. Zhou, S. Swaminathan, R. Vasudeva Raju, J. S. Guntupalli, W. Lehrach, J. Ortiz, A. Dedieu, M. L ´azaro-Gredilla, and K. Murphy, “Diffusion model predictive control,”Trans. Mach. Learn. Res., 2024, arXiv:2410.05364

    Pith/arXiv arXiv 2024

  38. [38]

    Diffusion predictive control with constraints,

    R. R ¨omer, A. von Rohr, and A. P. Schoellig, “Diffusion predictive control with constraints,” inProc. Learn. Dyn. Control Conf. (L4DC), 2025, arXiv:2412.09342

    Pith/arXiv arXiv 2025

  39. [39]

    Planning with diffusion for flexible behavior synthesis,

    M. Janner, Y . Du, J. B. Tenenbaum, and S. Levine, “Planning with diffusion for flexible behavior synthesis,” inProc. Int. Conf. Mach. Learn. (ICML), 2022, arXiv:2205.09991

    Pith/arXiv arXiv 2022

  40. [40]

    Is conditional generative modeling all you need for decision-making?

    A. Ajay, Y . Du, A. Gupta, J. B. Tenenbaum, T. S. Jaakkola, and P. Agrawal, “Is conditional generative modeling all you need for decision-making?” inProc. Int. Conf. Learn. Represent. (ICLR), 2023, arXiv:2211.15657

    Pith/arXiv arXiv 2023

  41. [41]

    Reference and com- mand governors for systems with constraints: A survey on theory and applications,

    E. Garone, S. Di Cairano, and I. Kolmanovsky, “Reference and com- mand governors for systems with constraints: A survey on theory and applications,”Automatica, vol. 75, pp. 306–328, 2017

    2017

  42. [42]

    Stanley: The robot that won the DARPA Grand Challenge,

    S. Thrun, M. Montemerlo, H. Dahlkampet al., “Stanley: The robot that won the DARPA Grand Challenge,”J. Field Robot., vol. 23, no. 9, pp. 661–692, 2006

    2006

  43. [43]

    On the vehicle sideslip angle estimation: A literature review of methods, models, and innovations,

    D. Chindamo, B. Lenzo, and M. Gadola, “On the vehicle sideslip angle estimation: A literature review of methods, models, and innovations,” Appl. Sci., vol. 8, no. 3, p. 355, 2018

    2018

  44. [44]

    U-Net: Convolutional net- works for biomedical image segmentation,

    O. Ronneberger, P. Fischer, and T. Brox, “U-Net: Convolutional net- works for biomedical image segmentation,” inProc. Med. Image Com- put. Comput.-Assist. Interv. (MICCAI), 2015, pp. 234–241

    2015

  45. [45]

    A connection between score matching and denoising au- toencoders,

    P. Vincent, “A connection between score matching and denoising au- toencoders,”Neural Comput., vol. 23, no. 7, pp. 1661–1674, 2011

    2011

  46. [46]

    Probabilistic constrained MPC for multiplicative and additive stochastic uncertainty,

    M. Cannon, B. Kouvaritakis, and X. Wu, “Probabilistic constrained MPC for multiplicative and additive stochastic uncertainty,”IEEE Trans. Autom. Control, vol. 54, no. 7, pp. 1626–1632, 2009

    2009

  47. [47]

    Analysis on vehicle stability in critical cornering using phase-plane method,

    S. Inagaki, I. Kushiro, and M. Yamamoto, “Analysis on vehicle stability in critical cornering using phase-plane method,” inProc. Int. Symp. Adv. Veh. Control (AVEC), 1994, pp. 287–292

    1994

  48. [48]

    C. E. Rasmussen and C. K. I. Williams,Gaussian Processes for Machine Learning. Cambridge, MA: MIT Press, 2006

    2006