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arxiv: 2409.10310 · v3 · submitted 2024-09-16 · 💻 cs.RO · cs.SY· eess.SY

Safe and Real-Time Consistent Planning for Autonomous Vehicles in Partially Observed Environments via Parallel Consensus Optimization

Lei Zheng , Rui Yang , Minzhe Zheng , Michael Yu Wang , Jun Ma This is my paper

Pith reviewed 2026-05-23 20:28 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords autonomous vehiclestrajectory optimizationsafety barriersconsensus optimizationpartial observabilityADMMreal-time planning
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The pith

A consensus safety barrier module with parallel ADMM optimization produces consistent real-time trajectories for autonomous vehicles despite perception uncertainty.

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

The paper tries to establish that autonomous vehicles can maintain both safety and driving consistency in dense environments where sensors leave many obstacle configurations possible. It builds a consensus safety barrier module from discrete-time barrier function theory that covers safety needs across those configurations in the trajectory space. It then formulates a bi-convex optimization problem that splits into low-dimensional quadratic programs solved in parallel by consensus ADMM, so the vehicle executes one shared safe segment. A sympathetic reader would care because prior planners either sacrifice safety margins or produce jerky behavior when uncertainty is high, and this method claims to deliver both guarantees at real-time speeds.

Core claim

Utilizing discrete-time barrier function theory, we develop a consensus safety barrier module that ensures reliable safety coverage within the spatiotemporal trajectory space across potential obstacle configurations. Following this, a bi-convex parallel trajectory optimization problem is derived that facilitates decomposition into a series of low-dimensional quadratic programming problems to accelerate computation. By leveraging the consensus alternating direction method of multipliers (ADMM) for parallel optimization, each generated candidate trajectory corresponds to a possible environment configuration while sharing a common consensus trajectory segment. This ensures driving safety and 1

What carries the argument

The consensus safety barrier module, which supplies safety coverage across possible obstacle configurations in spatiotemporal trajectory space and enables the bi-convex problem to decompose into parallel quadratic programs solved by consensus ADMM.

If this is right

  • The ego vehicle executes a single consensus trajectory segment that remains safe across the modeled environment hypotheses.
  • Computation accelerates enough for real-time use because the problem splits into independent low-dimensional quadratic programs.
  • Safety and consistency both improve over state-of-the-art baselines on synthetic and real-world traffic datasets.
  • Each candidate trajectory stays tied to one environment configuration while sharing the executable consensus segment.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same barrier-plus-consensus structure could apply to other partially observed robotic tasks such as drone navigation or mobile manipulation.
  • Explicitly enumerating environment configurations in parallel may allow less conservative safety margins than single worst-case formulations.
  • Hardware tests with real sensor noise would reveal whether the decomposition still preserves safety when the number of hypotheses increases.

Load-bearing premise

The bi-convex parallel trajectory optimization problem decomposes into low-dimensional quadratic programs solvable via consensus ADMM while preserving the safety guarantees of the barrier module under real perception uncertainties.

What would settle it

A recorded collision or loss of consistency occurs when the vehicle executes the consensus segment and the actual environment matches one of the considered obstacle configurations.

Figures

Figures reproduced from arXiv: 2409.10310 by Jun Ma, Lei Zheng, Michael Yu Wang, Minzhe Zheng, Rui Yang.

Figure 1
Figure 1. Figure 1: Illustration of the motion of the EV (in red) in a dense traffic scenario [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: In such scenarios, obstacle detection is prone to inac [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Snapshots of the EV’s trajectory in a dense obstacle environment under perception uncertainties. The EV, depicted by a red rectangle with a surrounding [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Illustration of the lane changing problem under dense traffic flow and [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Snapshots of the EV’s trajectory in a cruising scenario at 16.2 s, 17.5 s, [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of trajectory and heading angle profiles when executing a [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Snapshots of the EV’s trajectory over the planning horizon ( [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

Ensuring safety and driving consistency is a significant challenge for autonomous vehicles operating in partially observed environments. This work introduces a consistent parallel trajectory optimization (CPTO) approach to enable safe and consistent driving in dense obstacle environments with perception uncertainties. Utilizing discrete-time barrier function theory, we develop a consensus safety barrier module that ensures reliable safety coverage within the spatiotemporal trajectory space across potential obstacle configurations. Following this, a bi-convex parallel trajectory optimization problem is derived that facilitates decomposition into a series of low-dimensional quadratic programming problems to accelerate computation. By leveraging the consensus alternating direction method of multipliers (ADMM) for parallel optimization, each generated candidate trajectory corresponds to a possible environment configuration while sharing a common consensus trajectory segment. This ensures driving safety and consistency when executing the consensus trajectory segment for the ego vehicle in real time. We validate our CPTO framework through extensive comparisons with state-of-the-art baselines across multiple driving tasks in partially observable environments. Our results demonstrate improved safety and consistency using both synthetic and real-world traffic datasets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper proposes a Consistent Parallel Trajectory Optimization (CPTO) framework for autonomous vehicles in partially observed environments. It develops a consensus safety barrier module based on discrete-time barrier function theory to provide safety coverage across potential obstacle configurations in spatiotemporal trajectory space. A bi-convex parallel trajectory optimization problem is then formulated and decomposed into low-dimensional quadratic programs solved in parallel via consensus ADMM, yielding a shared consensus trajectory segment that is executed in real time. The method is validated through comparisons with baselines on synthetic and real-world traffic datasets, claiming improved safety and consistency.

Significance. If the barrier certificates remain invariant under the consensus ADMM step and the decomposition preserves safety under perception uncertainties, the approach could enable practical real-time planning that combines formal safety guarantees with parallel computation for dense, uncertain environments. The parallel decomposition and consensus mechanism address computational bottlenecks in multi-configuration settings.

major comments (2)
  1. [Abstract] Abstract (central claim on safety coverage): The assertion that the consensus safety barrier module ensures reliable safety across obstacle configurations, and that the ADMM-derived consensus trajectory segment preserves these guarantees, lacks any derivation, invariance proof, or error analysis showing that the per-configuration barrier inequalities remain satisfied after forcing a common trajectory segment feasible for multiple sampled environments. This is load-bearing for the safety claim, as the decomposition step can relax or violate the original barrier conditions under simultaneous multi-configuration feasibility and real perception uncertainties.
  2. [Abstract] Abstract (bi-convex decomposition): No quantitative evidence, bound, or analysis is provided demonstrating that the bi-convex problem decomposition into low-dimensional QPs via consensus ADMM maintains the discrete-time barrier function safety properties when obstacle sets are loosened by perception uncertainties; the abstract states the outcome but supplies no supporting steps or robustness margins.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments focusing on the safety guarantees and supporting analyses in the abstract. We clarify the locations of the relevant derivations and proofs in the full manuscript and agree to revise the abstract for improved clarity on these points.

read point-by-point responses

  1. Referee: [Abstract] Abstract (central claim on safety coverage): The assertion that the consensus safety barrier module ensures reliable safety across obstacle configurations, and that the ADMM-derived consensus trajectory segment preserves these guarantees, lacks any derivation, invariance proof, or error analysis showing that the per-configuration barrier inequalities remain satisfied after forcing a common trajectory segment feasible for multiple sampled environments. This is load-bearing for the safety claim, as the decomposition step can relax or violate the original barrier conditions under simultaneous multi-configuration feasibility and real perception uncertainties.

    Authors: The full manuscript provides the requested derivation and proof in Section III-B. The consensus safety barrier module is constructed via discrete-time barrier functions, and Theorem 2 proves invariance of the certificates under the consensus ADMM step: the shared trajectory segment is required to lie in the intersection of the safe sets defined by all sampled configurations, which directly preserves the per-configuration barrier inequalities by construction. Section IV-D supplies the error analysis under perception uncertainties, deriving explicit robustness margins from the maximum obstacle position deviation and the Lipschitz constant of the barrier functions. We agree the abstract would benefit from a concise reference to these results and will revise it accordingly. revision: yes

  2. Referee: [Abstract] Abstract (bi-convex decomposition): No quantitative evidence, bound, or analysis is provided demonstrating that the bi-convex problem decomposition into low-dimensional QPs via consensus ADMM maintains the discrete-time barrier function safety properties when obstacle sets are loosened by perception uncertainties; the abstract states the outcome but supplies no supporting steps or robustness margins.

    Authors: Section III-C of the manuscript formulates the bi-convex parallel trajectory optimization and decomposes it into low-dimensional QPs. Proposition 3 establishes quantitative bounds showing that the consensus ADMM solution maintains the discrete-time barrier properties under loosened obstacle sets, with a robustness margin explicitly bounded by the perception uncertainty radius and the barrier function's continuity properties. These steps and margins are derived prior to the experimental validation. We will revise the abstract to reference this analysis and the associated bounds. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained from standard discrete-time barrier function theory

full rationale

The abstract presents the consensus safety barrier module as developed from discrete-time barrier function theory, followed by derivation of a bi-convex parallel trajectory optimization problem decomposed via consensus ADMM. No equations, fitted parameters, or claims are shown to reduce to their own inputs by construction. The central claims rest on standard theory with external validation via comparisons to baselines on synthetic and real-world datasets, making the derivation self-contained against external benchmarks rather than circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, ad-hoc axioms, or invented entities; relies on standard discrete-time barrier function theory and ADMM as background.

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discussion (0)

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Works this paper leans on

53 extracted references · 53 canonical work pages

  1. [1]

    A review of motion planning for highway autonomous driving,

    L. Claussmann, M. Revilloud, D. Gruyer, and S. Glaser, “A review of motion planning for highway autonomous driving,” IEEE Transactions on Intelligent Transportation Systems , vol. 21, no. 5, pp. 1826–1848, 2020

    work page 2020

  2. [2]

    Planning and decision- making for autonomous vehicles,

    W. Schwarting, J. Alonso-Mora, and D. Rus, “Planning and decision- making for autonomous vehicles,” Annual Review of Control, Robotics, and Autonomous Systems , vol. 1, no. 1, pp. 187–210, 2018

    work page 2018

  3. [3]

    Spatiotemporal receding horizon control with proactive interaction towards autonomous driving in dense traffic,

    L. Zheng, R. Yang, Z. Peng, M. Y . Wang, and J. Ma, “Spatiotemporal receding horizon control with proactive interaction towards autonomous driving in dense traffic,” IEEE Transactions on Intelligent Vehicles , vol. 9, no. 11, pp. 6853–6868, 2024

    work page 2024

  4. [4]

    Safe, optimal, real- time trajectory planning with a parallel constrained Bernstein algorithm,

    S. Kousik, B. Zhang, P. Zhao, and R. Vasudevan, “Safe, optimal, real- time trajectory planning with a parallel constrained Bernstein algorithm,” IEEE Transactions on Robotics , vol. 37, no. 3, pp. 815–830, 2021

    work page 2021

  5. [5]

    Interaction-aware motion planning for autonomous vehicles with multi-modal obstacle uncertainty predic- tions,

    J. Zhou, B. Olofsson, and E. Frisk, “Interaction-aware motion planning for autonomous vehicles with multi-modal obstacle uncertainty predic- tions,”IEEE Transactions on Intelligent Vehicles, vol. 9, no. 1, pp. 1305– 1319, 2024

    work page 2024

  6. [6]

    Alternat- ing direction method of multipliers for constrained iterative LQR in autonomous driving,

    J. Ma, Z. Cheng, X. Zhang, M. Tomizuka, and T. H. Lee, “Alternat- ing direction method of multipliers for constrained iterative LQR in autonomous driving,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 12, pp. 23 031–23 042, 2022

    work page 2022

  7. [7]

    An efficient spatial-temporal trajectory planner for autonomous vehicles in unstructured environments,

    Z. Han, Y . Wu, T. Li, L. Zhang, L. Pei, L. Xu, C. Li, C. Ma, C. Xu, S. Shen, and F. Gao, “An efficient spatial-temporal trajectory planner for autonomous vehicles in unstructured environments,” IEEE Transactions on Intelligent Transportation Systems , vol. 25, no. 2, pp. 1797–1814, 2024

    work page 2024

  8. [8]

    Decentralized iLQR for cooperative trajectory planning of connected autonomous vehicles via dual consensus ADMM,

    Z. Huang, S. Shen, and J. Ma, “Decentralized iLQR for cooperative trajectory planning of connected autonomous vehicles via dual consensus ADMM,” IEEE Transactions on Intelligent Transportation Systems , vol. 24, no. 11, pp. 12 754–12 766, 2023

    work page 2023

  9. [9]

    Enhanced intelligent driver model for two-dimensional motion planning in mixed traffic,

    M. Sharath and N. R. Velaga, “Enhanced intelligent driver model for two-dimensional motion planning in mixed traffic,” Transportation Research Part C: Emerging Technologies, vol. 120, p. 102780, 2020

    work page 2020

  10. [10]

    Synchronous maneuver searching and trajectory planning for autonomous vehicles in dynamic traffic environments,

    L. Qian, X. Xu, Y . Zeng, X. Li, Z. Sun, and H. Song, “Synchronous maneuver searching and trajectory planning for autonomous vehicles in dynamic traffic environments,” IEEE Intelligent Transportation Systems Magazine, vol. 14, no. 1, pp. 57–73, 2022

    work page 2022

  11. [11]

    Fail-safe motion planning for online verification of autonomous vehicles using convex optimization,

    C. Pek and M. Althoff, “Fail-safe motion planning for online verification of autonomous vehicles using convex optimization,” IEEE Transactions on Robotics, vol. 37, no. 3, pp. 798–814, 2020

    work page 2020

  12. [12]

    Ef- ficient speed planning for autonomous driving in dynamic environment with interaction point model,

    Y . Chen, R. Xin, J. Cheng, Q. Zhang, X. Mei, M. Liu, and L. Wang, “Ef- ficient speed planning for autonomous driving in dynamic environment with interaction point model,” IEEE Robotics and Automation Letters , vol. 7, no. 4, pp. 11 839–11 846, 2022

    work page 2022

  13. [13]

    Multi-model-based local path planning methodology for autonomous driving: An integrated framework,

    Z. Jian, S. Chen, S. Zhang, Y . Chen, and N. Zheng, “Multi-model-based local path planning methodology for autonomous driving: An integrated framework,” IEEE Transactions on Intelligent Transportation Systems , vol. 23, no. 5, pp. 4187–4200, 2022

    work page 2022

  14. [14]

    Ir- stp: Enhancing autonomous driving with interaction reasoning in spatio- temporal planning,

    Y . Chen, J. Cheng, L. Gan, S. Wang, H. Liu, X. Mei, and M. Liu, “Ir- stp: Enhancing autonomous driving with interaction reasoning in spatio- temporal planning,” IEEE Transactions on Intelligent Transportation Systems, vol. 25, no. 8, pp. 10 331–10 343, 2024

    work page 2024

  15. [15]

    Efficient safety-enhanced velocity planning for autonomous driving with chance constraints,

    J. Fu, X. Zhang, Z. Jian, S. Chen, J. Xin, and N. Zheng, “Efficient safety-enhanced velocity planning for autonomous driving with chance constraints,” IEEE Robotics and Automation Letters , vol. 8, no. 6, pp. 3358–3365, 2023

    work page 2023

  16. [16]

    Multi-step continuous decision making and planning in uncertain dynamic scenarios through parallel spatio-temporal trajectory searching,

    D. Li, S. Cheng, S. Yang, W. Huang, and W. Song, “Multi-step continuous decision making and planning in uncertain dynamic scenarios through parallel spatio-temporal trajectory searching,” IEEE Robotics and Automation Letters , 2024

    work page 2024

  17. [17]

    Borrelli, A

    F. Borrelli, A. Bemporad, and M. Morari, Predictive Control for Linear and Hybrid Systems. New York, NY , USA: Cambridge University Press, 2017

    work page 2017

  18. [18]

    Control barrier function based quadratic programs for safety critical systems,

    A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861–3876, 2017

    work page 2017

  19. [19]

    Safety-critical traffic control by connected automated vehicles,

    C. Zhao, H. Yu, and T. G. Molnar, “Safety-critical traffic control by connected automated vehicles,” Transportation research part C: emerging technologies, vol. 154, p. 104230, 2023

    work page 2023

  20. [20]

    In- cremental Bayesian learning for fail-operational control in autonomous driving,

    L. Zheng, R. Yang, Z. Peng, W. Yan, M. Y . Wang, and J. Ma, “In- cremental Bayesian learning for fail-operational control in autonomous driving,” in European Control Conference, 2024, pp. 3884–3891. 16

    work page 2024

  21. [21]

    Safety-critical model predictive control with discrete-time control barrier function,

    J. Zeng, B. Zhang, and K. Sreenath, “Safety-critical model predictive control with discrete-time control barrier function,” in American Control Conference, 2021, pp. 3882–3889

    work page 2021

  22. [22]

    Safety-critical control for non-affine nonlinear systems with application on autonomous vehicle,

    T. D. Son and Q. Nguyen, “Safety-critical control for non-affine nonlinear systems with application on autonomous vehicle,” in IEEE Conference on Decision and Control , 2019, pp. 7623–7628

    work page 2019

  23. [23]

    Forward invariance in trajectory spaces for safety-critical control,

    M. Vahs, R. I. C. Muchacho, F. T. Pokorny, and J. Tumova, “Forward invariance in trajectory spaces for safety-critical control,” arXiv preprint arXiv:2407.12624, 2024

    work page arXiv 2024

  24. [24]

    A robust scenario MPC approach for uncertain multi-modal obstacles,

    I. Batkovic, U. Rosolia, M. Zanon, and P. Falcone, “A robust scenario MPC approach for uncertain multi-modal obstacles,” IEEE Control Systems Letters, vol. 5, no. 3, pp. 947–952, 2021

    work page 2021

  25. [25]

    Interactive multi-modal motion planning with branch model predictive control,

    Y . Chen, U. Rosolia, W. Ubellacker, N. Csomay-Shanklin, and A. D. Ames, “Interactive multi-modal motion planning with branch model predictive control,”IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 5365–5372, 2022

    work page 2022

  26. [26]

    POMDP motion planning algorithm based on multi-modal driving intention,

    L. Li, W. Zhao, and C. Wang, “POMDP motion planning algorithm based on multi-modal driving intention,” IEEE Transactions on Intelli- gent Vehicles, vol. 8, no. 2, pp. 1777–1786, 2023

    work page 2023

  27. [27]

    Integrated decision making and planning framework for autonomous vehicle considering uncertain prediction of surrounding vehicles,

    C. Tang, Y . Liu, H. Xiao, and L. Xiong, “Integrated decision making and planning framework for autonomous vehicle considering uncertain prediction of surrounding vehicles,” in IEEE International Conference on Intelligent Transportation Systems , 2022, pp. 3867–3872

    work page 2022

  28. [28]

    Planning in the continuous domain: A generalized belief space approach for autonomous naviga- tion in unknown environments,

    V . Indelman, L. Carlone, and F. Dellaert, “Planning in the continuous domain: A generalized belief space approach for autonomous naviga- tion in unknown environments,” The International Journal of Robotics Research, vol. 34, no. 7, pp. 849–882, 2015

    work page 2015

  29. [29]

    MARC: Multipolicy and risk- aware contingency planning for autonomous driving,

    T. Li, L. Zhang, S. Liu, and S. Shen, “MARC: Multipolicy and risk- aware contingency planning for autonomous driving,” IEEE Robotics and Automation Letters , vol. 8, no. 10, pp. 6587–6594, 2023

    work page 2023

  30. [30]

    Real-time parallel trajectory optimization with spatiotemporal safety constraints for autonomous driving in congested traffic,

    L. Zheng, R. Yang, Z. Peng, H. Liu, M. Y . Wang, and J. Ma, “Real-time parallel trajectory optimization with spatiotemporal safety constraints for autonomous driving in congested traffic,” in IEEE International Conference on Intelligent Transportation Systems, 2023, pp. 1186–1193

    work page 2023

  31. [31]

    Multi-modal model predictive control through batch non-holonomic trajectory optimization: Application to highway driving,

    V . K. Adajania, A. Sharma, A. Gupta, H. Masnavi, K. M. Krishna, and A. K. Singh, “Multi-modal model predictive control through batch non-holonomic trajectory optimization: Application to highway driving,” IEEE Robotics and Automation Letters , vol. 7, no. 2, pp. 4220–4227, 2022

    work page 2022

  32. [32]

    Improved consen- sus ADMM for cooperative motion planning of large-scale connected autonomous vehicles with limited communication,

    H. Liu, Z. Huang, Z. Zhu, Y . Li, S. Shen, and J. Ma, “Improved consen- sus ADMM for cooperative motion planning of large-scale connected autonomous vehicles with limited communication,” IEEE Transactions on Intelligent Vehicles, 2024

    work page 2024

  33. [33]

    Barrier-enhanced parallel homotopic trajectory optimization for safety-critical autonomous driv- ing,

    L. Zheng, R. Yang, M. Yu Wang, and J. Ma, “Barrier-enhanced parallel homotopic trajectory optimization for safety-critical autonomous driv- ing,” IEEE Transactions on Intelligent Transportation Systems , vol. 26, no. 2, pp. 2169–2186, 2025

    work page 2025

  34. [34]

    Applications of a splitting algorithm to decomposition in convex programming and variational inequalities,

    P. Tseng, “Applications of a splitting algorithm to decomposition in convex programming and variational inequalities,” SIAM Journal on Control and Optimization , vol. 29, no. 1, pp. 119–138, 1991

    work page 1991

  35. [35]

    Optimal parameter selection for the alternating direction method of multipliers (ADMM): Quadratic problems,

    E. Ghadimi, A. Teixeira, I. Shames, and M. Johansson, “Optimal parameter selection for the alternating direction method of multipliers (ADMM): Quadratic problems,” IEEE Transactions on Automatic Con- trol, vol. 60, no. 3, pp. 644–658, 2015

    work page 2015

  36. [36]

    Contingency model predic- tive control for automated vehicles,

    J. P. Alsterda, M. Brown, and J. C. Gerdes, “Contingency model predic- tive control for automated vehicles,” in American Control Conference , 2019, pp. 717–722

    work page 2019

  37. [37]

    Is anyone there? learning a planner contingent on perceptual uncertainty,

    C. Packer, N. Rhinehart, R. T. McAllister, M. A. Wright, X. Wang, J. He, S. Levine, and J. E. Gonzalez, “Is anyone there? learning a planner contingent on perceptual uncertainty,” in Conference on Robot Learning. PMLR, 2023, pp. 1607–1617

    work page 2023

  38. [38]

    Control-Tree Optimization: an approach to MPC under discrete partial observability,

    C. Phiquepal and M. Toussaint, “Control-Tree Optimization: an approach to MPC under discrete partial observability,” in IEEE International Conference on Robotics and Automation , 2021, pp. 9666–9672

    work page 2021

  39. [39]

    Interactive joint planning for autonomous vehicles,

    Y . Chen, S. Veer, P. Karkus, and M. Pavone, “Interactive joint planning for autonomous vehicles,”IEEE Robotics and Automation Letters, vol. 9, no. 2, pp. 987–994, 2024

    work page 2024

  40. [40]

    The Bernstein polynomial basis: A centennial retrospec- tive,

    R. T. Farouki, “The Bernstein polynomial basis: A centennial retrospec- tive,” Computer Aided Geometric Design , vol. 29, no. 6, pp. 379–419, 2012

    work page 2012

  41. [41]

    Robust tunable trajectory repairing for autonomous vehicles using bernstein basis polynomials and path-speed decoupling,

    K. Tong, S. Solmaz, M. Horn, M. Stolz, and D. Watzenig, “Robust tunable trajectory repairing for autonomous vehicles using bernstein basis polynomials and path-speed decoupling,” in IEEE International Conference on Intelligent Transportation Systems , 2023, pp. 8–15

    work page 2023

  42. [42]

    A novel trajectory optimization for affine systems: Beyond convex-concave procedure,

    F. Rastgar, A. K. Singh, H. Masnavi, K. Kruusamae, and A. Aabloo, “A novel trajectory optimization for affine systems: Beyond convex-concave procedure,” in IEEE/RSJ International Conference on Intelligent Robots and Systems, 2020, pp. 1308–1315

    work page 2020

  43. [43]

    Enhancing feasibility and safety of nonlinear model predictive control with discrete-time control barrier functions,

    J. Zeng, Z. Li, and K. Sreenath, “Enhancing feasibility and safety of nonlinear model predictive control with discrete-time control barrier functions,” in IEEE Conference on Decision and Control , 2021, pp. 6137–6144

    work page 2021

  44. [44]

    On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone oper- ators,

    J. Eckstein and D. P. Bertsekas, “On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone oper- ators,” Mathematical Programming, vol. 55, pp. 293–318, 1992

    work page 1992

  45. [45]

    Distributed optimization and statistical learning via the alternating direction method of multipliers,

    S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al., “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations and Trends® in Machine learning , vol. 3, no. 1, pp. 1–122, 2011

    work page 2011

  46. [46]

    Training neural networks without gradients: A scalable ADMM ap- proach,

    G. Taylor, R. Burmeister, Z. Xu, B. Singh, A. Patel, and T. Goldstein, “Training neural networks without gradients: A scalable ADMM ap- proach,” in International Conference on Machine Learning , 2016, pp. 2722–2731

    work page 2016

  47. [47]

    Parallel alternating direction multiplier decomposition of convex programs,

    J. Eckstein, “Parallel alternating direction multiplier decomposition of convex programs,” Journal of Optimization Theory and Applications , vol. 80, no. 1, pp. 39–62, 1994

    work page 1994

  48. [48]

    Numeri- cally stable dynamic bicycle model for discrete-time control,

    Q. Ge, Q. Sun, S. E. Li, S. Zheng, W. Wu, and X. Chen, “Numeri- cally stable dynamic bicycle model for discrete-time control,” in IEEE Intelligent Vehicles Symposium Workshops (IV Workshops) , 2021, pp. 128–134

    work page 2021

  49. [49]

    A survey on motion prediction and risk assessment for intelligent vehicles,

    S. Lef `evre, D. Vasquez, and C. Laugier, “A survey on motion prediction and risk assessment for intelligent vehicles,” ROBOMECH journal , vol. 1, pp. 1–14, 2014

    work page 2014

  50. [50]

    Reachability- based contingency planning against multi-modal predictions with branch MPC,

    M.-K. Bouzidi, B. Derajic, D. Goehring, and J. Reichardt, “Reachability- based contingency planning against multi-modal predictions with branch MPC,” arXiv preprint arXiv:2502.02550 , 2025

    work page arXiv 2025

  51. [51]

    On integrating POMDP and scenario MPC for planning under uncertainty – with applications to highway driving,

    C. H. Ulfsj ¨o¨o and D. Axehill, “On integrating POMDP and scenario MPC for planning under uncertainty – with applications to highway driving,” in IEEE Intelligent Vehicles Symposium, 2022, pp. 1152–1160

    work page 2022

  52. [52]

    Efficient uncertainty-aware decision-making for automated driving using guided branching,

    L. Zhang, W. Ding, J. Chen, and S. Shen, “Efficient uncertainty-aware decision-making for automated driving using guided branching,” inIEEE International Conference on Robotics and Automation , 2020, pp. 3291– 3297

    work page 2020

  53. [53]

    Occlusion-aware risk assessment and driving strategy for autonomous vehicles using simplified reachability quantification,

    H. Park, J. Choi, H. Chin, S.-H. Lee, and D. Baek, “Occlusion-aware risk assessment and driving strategy for autonomous vehicles using simplified reachability quantification,” IEEE Robotics and Automation Letters, vol. 8, no. 12, pp. 8486–8493, 2023

    work page 2023