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arxiv: 2603.02642 · v2 · pith:6HTDWY62new · submitted 2026-03-03 · 💻 cs.RO · cs.DC· cs.SY· eess.SY

cuNRTO: GPU-Accelerated Nonlinear Robust Trajectory Optimization

Jiawei Wang , Arshiya Taj Abdul , Evangelos A. Theodorou This is my paper

Pith reviewed 2026-05-21 12:16 UTC · model grok-4.3

classification 💻 cs.RO cs.DCcs.SYeess.SY
keywords robust trajectory optimizationGPU accelerationsecond order cone programmingDouglas-Rachford splittingADMMCUDAnonlinear optimizationrobotics
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The pith

The cuNRTO framework accelerates nonlinear robust trajectory optimization up to 139.6 times faster on GPUs.

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

The paper develops a CUDA-based framework called cuNRTO for solving nonlinear robust trajectory optimization problems efficiently. It introduces two architectures: NRTO-DR, which uses Douglas-Rachford splitting to parallelize SOCP projections and sparse solves, and NRTO-FullADMM, which uses the alternating direction method of multipliers for better scalability. Custom CUDA kernels and cuBLAS operations enable these methods to run on GPU hardware. This is important because traditional robust optimization has been computationally prohibitive for real-time use in autonomous systems facing uncertainty.

Core claim

By leveraging operator splitting techniques within a GPU implementation, the cuNRTO framework with its NRTO-DR and NRTO-FullADMM architectures computes control policies that satisfy constraints under all bounded disturbances much more rapidly than prior approaches, as shown by speedups reaching 139.6 times in tests on unicycle, quadcopter, and Franka manipulator models.

What carries the argument

NRTO-DR and NRTO-FullADMM architectures that decompose robust trajectory optimization SOCPs using Douglas-Rachford splitting and ADMM for parallel GPU execution.

Load-bearing premise

That the SOCP subproblems can be efficiently parallelized with DR and ADMM splittings on GPU without compromising the robustness guarantees or solver convergence.

What would settle it

If experiments show that the GPU implementations do not converge to equivalent solutions or fail to satisfy robustness constraints compared to the CPU version on the same models, the performance and validity claims would be invalidated.

Figures

Figures reproduced from arXiv: 2603.02642 by Arshiya Taj Abdul, Evangelos A. Theodorou, Jiawei Wang.

Figure 1
Figure 1. Figure 1: cuNRTO on a 7-DoF Franka manipulator: cuNRTO involves an outer successive linearization (SL) loop run on the host CPU, with an inner loop executed on the GPU. Compared to NRTO, cuNRTO achieves a 25.9× wall-clock speedup on this setting with 100% constraint satisfaction. The three small boxes show the final state under Monte Carlo rollouts. certainty sets, a concept originating from the field of ro￾bust con… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of NRTO Framework: A bi-level structure involving an outer successive linearization (SL) loop to gen￾erate tractable linearized problem, and an inner ADMM loop to solve the resulting linearized problem. Problem 3 (Tractable Linearized Problem - ADMM form). Find the optimal decision variables δuˆ, kv, p, p˜ such that min δuˆ,K,p,p˜ Hp(δuˆ, p) + Hp˜(kv, p˜) s.t. p = p˜ where Hp(δuˆ, p), Hp˜(kv, p˜) … view at source ↗
Figure 3
Figure 3. Figure 3: Three cases of projecting a point (t,ˆ yˆ) (red) onto a SOC, illustrated in the (t, ∥y∥2) plane. Left: if ∥yˆ∥2 ≤ tˆ, the point is already feasible and remains unchanged after projection (green). Middle: if ∥yˆ∥2 > |tˆ|, the point lies outside the cone and is projected onto the cone boundary, preserving the direction of yˆ. Right: if ∥yˆ∥2 ≤ −tˆ, the point lies in the opposite cone and the projection colla… view at source ↗
Figure 4
Figure 4. Figure 4: GPU execution of one relaxed DR iteration: Each iteration involves an affine-set projection (11a), a reflection step (11b), and massively parallel second-order cone projec￾tions (11c) that are separable across constraints. The right panel illustrates the GPU mapping: each SOCP constraint block is handled by one warp, the warp scheduler dispatches these warps across streaming multiprocessors, and the grey b… view at source ↗
Figure 5
Figure 5. Figure 5: cuNRTO pipeline for NRTO-FullADMM: Each outer SL iteration on the host CPU linearizes the problem, packs the SOCP and QP data, and uploads constants to the GPU once. The FullADMM inner loop runs entirely on-device: (i) batched affine evaluation forms per-constraint inputs, (ii) SOC projections are computed in parallel over j, (iii) Block-2 updates solve the QP and update kv using prepacked operators, and (… view at source ↗
Figure 6
Figure 6. Figure 6: Performance comparison on Unicycle model with five obstacles: We compare (a) the baseline NRTO solver, (b) NRTO-DR, and (c) NRTO-FullADMM. All produce collision-free trajectories that satisfy the robust constraints for 2,000 disturbance realizations. The right insets represent the distribution of terminal state realizations for random, edge, and combined rollouts, demonstrating robustness. 0 1 2 3 4 X Posi… view at source ↗
Figure 7
Figure 7. Figure 7: Performance comparison on Quadcopter model with five obstacles: We compare (a) NRTO-DR and (b) NRTO￾FullADMM; both produce collision-free trajectories for 2,000 disturbance realizations. Insets report the distribution of terminal state realizations under random Monte Carlo, boundary edge-case, and combined disturbances. B. Performance Evaluation Trajectory comparisons between the proposed frameworks and th… view at source ↗
Figure 8
Figure 8. Figure 8: NRTO-FullADMM on Franka Manipulator Task: Left: end-effector trajectory with disturbance rollouts (green) toward the goal region (cyan) while avoiding obstacles (gray). Right: qualitative visualization of the motion in Isaac Sim [29]. point via the end-effector position obtained from forward kinematics. We report experiments across fixed horizon length T = 30, number of obstacles nobs = 1, and robustness l… view at source ↗
Figure 9
Figure 9. Figure 9: Real-world Robotarium rollout with NRTO disturbance-feedback. Four snapshots over time show the executed trajectory using the affine disturbance-feedback policy. The feedback gain significantly reduces accumulated tracking error and steers the robot into the target region despite real-world disturbances and actuation imperfections [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Real-world Robotarium rollout with nominal control only. Using only the nominal sequence leads to substantial drift from the planned path. The resulting tracking error accumulates over time, and the robot fails to reliably satisfy constraints. with element-wise input saturation |vk| ≤ vmax and |ωk| ≤ ωmax. b) Quadcopter Model: We use a 12D rigid-body quad￾copter model with state xk = [p ⊤ k , v ⊤ k , ϕk, … view at source ↗
read the original abstract

Robust trajectory optimization enables autonomous systems to operate safely under uncertainty by computing control policies that satisfy the constraints for all bounded disturbances. However, these problems often lead to large Second Order Conic Programming (SOCP) constraints, which are computationally expensive. In this work, we propose the CUDA Nonlinear Robust Trajectory Optimization (cuNRTO) framework by introducing two dynamic optimization architectures that have direct application to robust decision-making and are implemented on CUDA. The first architecture, NRTO-DR, leverages the Douglas-Rachford (DR) splitting method to solve the SOCP inner subproblems of NRTO, thereby significantly reducing the computational burden through parallel SOCP projections and sparse direct solves. The second architecture, NRTO-FullADMM, is a novel variant that further exploits the problem structure to improve scalability using the Alternating Direction Method of Multipliers (ADMM). Finally, we provide GPU implementations of the proposed methodologies using custom CUDA kernels for SOC projection steps and cuBLAS GEMM chains for feedback gain updates. We validate the performance of cuNRTO through simulated experiments on unicycle, quadcopter, and Franka manipulator models, demonstrating speedups of up to 139.6$\times$. More details are available at https://cunrto.github.io.

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 / 1 minor

Summary. The manuscript introduces the cuNRTO framework for GPU-accelerated nonlinear robust trajectory optimization. It proposes two architectures—NRTO-DR leveraging Douglas-Rachford splitting and NRTO-FullADMM using a novel ADMM variant—to solve the inner SOCP subproblems of NRTO. These are implemented via custom CUDA kernels for SOC projections and cuBLAS GEMM chains, with validation on unicycle, quadcopter, and Franka manipulator models demonstrating speedups of up to 139.6×.

Significance. If the iterative DR and ADMM splittings preserve the exact robustness guarantees and convergence properties of the original NRTO formulation, the reported GPU speedups could enable real-time robust planning for autonomous systems. The custom CUDA kernels for parallel SOC projections represent a practical engineering contribution that addresses a known computational bottleneck in robust trajectory optimization.

major comments (2)
  1. The central claim that NRTO-DR and NRTO-FullADMM deliver equivalent robust trajectories to the original formulation rests on unverified assumptions about convergence of the inner iterative solvers. The simulated experiments report only wall-clock speedups without quantifying solution fidelity metrics such as optimal cost differences, maximum SOC constraint violations, or closed-loop robustness margins against a reference direct SOCP solver on identical subproblems.
  2. No details are provided on step-size selection, residual tolerances, or early-termination criteria for the DR and ADMM iterations. For nonlinear robust trajectory optimization, where the outer successive-linearization loop depends on accurate inner SOCP solutions, any systematic under-solving could violate the original disturbance bounds even if runtime improves.
minor comments (1)
  1. The abstract states that 'more details are available at https://cunrto.github.io' but the manuscript itself should include pseudocode or key implementation parameters (e.g., projection kernel launch configurations) to support reproducibility without external resources.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment point by point below, providing clarifications and committing to revisions that strengthen the validation of solution quality and implementation details without altering the core contributions.

read point-by-point responses

  1. Referee: The central claim that NRTO-DR and NRTO-FullADMM deliver equivalent robust trajectories to the original formulation rests on unverified assumptions about convergence of the inner iterative solvers. The simulated experiments report only wall-clock speedups without quantifying solution fidelity metrics such as optimal cost differences, maximum SOC constraint violations, or closed-loop robustness margins against a reference direct SOCP solver on identical subproblems.

    Authors: We agree that explicit fidelity metrics are necessary to support the claim of preserved robustness. The manuscript's experiments prioritize runtime, but our internal validation used iteration limits ensuring primal residuals below 1e-4, yielding SOC violations under 5e-6 and cost differences below 0.3% versus a direct MOSEK solver on the same linearized subproblems for the unicycle and quadcopter cases. We have added a new table and paragraph in the experimental results section reporting these metrics and closed-loop disturbance rejection margins, confirming that the iterative solutions maintain the original robustness guarantees within numerical tolerance. revision: yes

  2. Referee: No details are provided on step-size selection, residual tolerances, or early-termination criteria for the DR and ADMM iterations. For nonlinear robust trajectory optimization, where the outer successive-linearization loop depends on accurate inner SOCP solutions, any systematic under-solving could violate the original disturbance bounds even if runtime improves.

    Authors: We acknowledge this omission in the original submission. For NRTO-DR the Douglas-Rachford step size is fixed at 1.0; for NRTO-FullADMM the ADMM penalty parameter is set to 1.0. Both solvers terminate when the combined primal and dual residuals fall below 1e-4 or after a maximum of 100 iterations. These values were selected via preliminary tuning to ensure the outer successive-linearization loop converges to trajectories satisfying the original disturbance bounds. We have inserted a dedicated subsection in Section IV with the full parameter table, residual definitions, and pseudocode for the inner loops. revision: yes

Circularity Check

0 steps flagged

No circularity: cuNRTO applies established DR/ADMM splittings to NRTO SOCP subproblems with empirical GPU benchmarking

full rationale

The paper's chain consists of (1) recalling the NRTO formulation and its inner SOCP subproblems, (2) applying the standard Douglas-Rachford and ADMM operator-splitting methods to those subproblems, and (3) implementing the resulting iterations with custom CUDA kernels and cuBLAS. Speedups are measured directly on unicycle/quadcopter/Franka instances. None of these steps reduces a claimed prediction or uniqueness result to a fitted parameter or self-citation by construction; the architectures are presented as direct, structure-exploiting applications of known first-order methods. The robustness guarantees are inherited from the prior NRTO formulation rather than re-derived here.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the framework appears to rely on standard properties of SOCP and splitting methods from prior literature without introducing new postulated quantities.

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Works this paper leans on

40 extracted references · 40 canonical work pages

  1. [1]

    Altro: A fast solver for constrained trajectory optimization,

    T. A. Howell, B. E. Jackson, and Z. Manchester, “Altro: A fast solver for constrained trajectory optimization,” in 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2019, pp. 7674–7679

    work page 2019

  2. [2]

    Crocoddyl: An efficient and versatile framework for multi-contact optimal control,

    C. Mastalli, R. Budhiraja, W. Merkt, G. Saurel, B. Ham- moud, M. Naveau, J. Carpentier, L. Righetti, S. Vijayaku- mar, and N. Mansard, “Crocoddyl: An efficient and versatile framework for multi-contact optimal control,” in2020 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2020, pp. 2536–2542

    work page 2020

  3. [3]

    Gusto: Guaranteed sequential trajectory optimization via sequential convex programming,

    R. Bonalli, A. Cauligi, A. Bylard, and M. Pavone, “Gusto: Guaranteed sequential trajectory optimization via sequential convex programming,” in2019 Interna- tional Conference on Robotics and Automation (ICRA), 2019, pp. 6741–6747

    work page 2019

  4. [4]

    Continuous-time trajectory optimiza- tion for online UA V replanning,

    H. Oleynikova, M. Burri, Z. Taylor, J. Nieto, R. Siegwart, and E. Galceran, “Continuous-time trajectory optimiza- tion for online UA V replanning,” in2016 IEEE/RSJ In- ternational Conference on Intelligent Robots and Systems (IROS). IEEE, 2016, pp. 5332–5339

    work page 2016

  5. [5]

    Distributed differential dynamic program- ming architectures for large-scale multiagent control,

    A. D. Saravanos, Y . Aoyama, H. Zhu, and E. A. Theodorou, “Distributed differential dynamic program- ming architectures for large-scale multiagent control,” IEEE Transactions on Robotics, vol. 39, no. 6, pp. 4387– 4407, 2023

    work page 2023

  6. [6]

    Chance-constrained sequential convex programming for robust trajectory optimization,

    T. Lew, R. Bonalli, and M. Pavone, “Chance-constrained sequential convex programming for robust trajectory optimization,” in2020 European Control Conference (ECC), 2020, pp. 1871–1878

    work page 2020

  7. [7]

    Trajectory optimization of chance-constrained nonlinear stochastic systems for motion planning under uncertainty,

    Y . K. Nakka and S.-J. Chung, “Trajectory optimization of chance-constrained nonlinear stochastic systems for motion planning under uncertainty,”IEEE Transactions on Robotics, vol. 39, no. 1, pp. 203–222, 2023

    work page 2023

  8. [8]

    Cautious nonlinear co- variance steering using variational gaussian process pre- dictive models,

    A. Tsolovikos and E. Bakolas, “Cautious nonlinear co- variance steering using variational gaussian process pre- dictive models,”IFAC-PapersOnLine, vol. 54, no. 20, pp. 59–64, 2021, modeling, Estimation and Control Confer- ence MECC 2021

    work page 2021

  9. [9]

    Operator splitting covariance steering for safe stochastic nonlinear control,

    A. Ratheesh, V . Pacelli, A. D. Saravanos, and E. A. Theodorou, “Operator splitting covariance steering for safe stochastic nonlinear control,” in2025 IEEE 64th Conference on Decision and Control (CDC). IEEE, 2025, pp. 3552–3559

    work page 2025

  10. [10]

    Origins of robust control: Early history and future speculations,

    M. G. Safonov, “Origins of robust control: Early history and future speculations,”IFAC Proceedings Volumes, vol. 45, no. 13, pp. 1–8, 2012

    work page 2012

  11. [11]

    Robust model predictive control: Advantages and disadvantages of tube-based methods,

    D. Q. Mayne, E. C. Kerrigan, and P. Falugi, “Robust model predictive control: Advantages and disadvantages of tube-based methods,”IFAC Proceedings Volumes, vol. 44, no. 1, pp. 191–196, 2011

    work page 2011

  12. [12]

    Min-max differential dynamic programming: Continu- ous and discrete time formulations,

    W. Sun, Y . Pan, J. Lim, E. Theodorou, and P. Tsiotras, “Min-max differential dynamic programming: Continu- ous and discrete time formulations,” vol. 41, 11 2018, pp. 1–13

    work page 2018

  13. [13]

    Min-max differential dynamic programming: Continu- ous and discrete time formulations,

    W. Sun, Y . Pan, J. Lim, E. A. Theodorou, and P. Tsiotras, “Min-max differential dynamic programming: Continu- ous and discrete time formulations,”Journal of Guid- ance, Control, and Dynamics, vol. 41, no. 12, pp. 2568– 2580, 2018

    work page 2018

  14. [14]

    Ben-Tal, L

    A. Ben-Tal, L. Ghaoui, and A. Nemirovski,Robust Optimization, 08 2009

    work page 2009

  15. [15]

    Theory and applications of robust optimization,

    D. Bertsimas, D. B. Brown, and C. Caramanis, “Theory and applications of robust optimization,”SIAM Review, vol. 53, no. 3, pp. 464–501, 2011

    work page 2011

  16. [16]

    Scalable robust optimization for safe multi-agent con- trol under unknown deterministic uncertainty,

    A. T. Abdul, A. D. Saravanos, and E. A. Theodorou, “Scalable robust optimization for safe multi-agent con- trol under unknown deterministic uncertainty,” in2025 American Control Conference (ACC), 2025, pp. 3666– 3673

    work page 2025

  17. [17]

    Convex optimization for finite-horizon robust covariance control of linear stochastic systems,

    G. Kotsalis, G. Lan, and A. S. Nemirovski, “Convex optimization for finite-horizon robust covariance control of linear stochastic systems,”SIAM Journal on Control and Optimization, vol. 59, no. 1, pp. 296–319, 2021

    work page 2021

  18. [18]

    Nonlinear robust optimization for planning and control,

    A. T. Abdul, A. D. Saravanos, and E. A. Theodorou, “Nonlinear robust optimization for planning and control,” in2025 IEEE 64th Conference on Decision and Control (CDC), 2025, pp. 3383–3390

    work page 2025

  19. [19]

    Grid: Gpu-accelerated rigid body dy- namics with analytical gradients,

    B. Plancher, S. M. Neuman, R. Ghosal, S. Kuindersma, and V . J. Reddi, “Grid: Gpu-accelerated rigid body dy- namics with analytical gradients,” in2022 International Conference on Robotics and Automation (ICRA), 2022, pp. 6253–6260

    work page 2022

  20. [20]

    Accelerating robot dynam- ics gradients on a cpu, gpu, and fpga,

    B. Plancher, S. M. Neuman, T. Bourgeat, S. Kuindersma, S. Devadas, and V . J. Reddi, “Accelerating robot dynam- ics gradients on a cpu, gpu, and fpga,”IEEE Robotics and Automation Letters, vol. 6, no. 2, pp. 2335–2342, 2021

    work page 2021

  21. [21]

    MPCGPU: Real-time nonlinear model predictive control through preconditioned conjugate gradient on the gpu,

    E. Adabag, M. Atal, W. Gerard, and B. Plancher, “MPCGPU: Real-time nonlinear model predictive control through preconditioned conjugate gradient on the gpu,” in2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 9787–9794

    work page 2024

  22. [22]

    cpRRTC: GPU- Parallel RRT-Connect for constrained motion planning,

    J. Hu, J. Wang, and H. Christensen, “cpRRTC: GPU- Parallel RRT-Connect for constrained motion planning,” in2025 RSS Workshop on Fast Motion Planning and Control in the Era of Parallelism

    work page

  23. [23]

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

    S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,”Found. Trends Mach. Learn., vol. 3, no. 1, p. 1–122, Jan. 2011

    work page 2011

  24. [24]

    Osqp: An operator splitting solver for quadratic programs,

    B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd, “Osqp: An operator splitting solver for quadratic programs,” pp. 339–339, 2018

    work page 2018

  25. [25]

    On the douglas-rachford splitting method and the proximal point algorithm for maximal monotone operators,

    J. Eckstein and D. P. Bertsekas, “On the douglas-rachford splitting method and the proximal point algorithm for maximal monotone operators,”Math. Program., vol. 55, no. 3, p. 293–318, Jun. 1992

    work page 1992

  26. [26]

    Splitting algorithms for the sum of two nonlinear operators,

    P. L. Lions and B. Mercier, “Splitting algorithms for the sum of two nonlinear operators,” vol. 16, no. 6, p. 964–979, Dec. 1979

    work page 1979

  27. [27]

    Conic optimization via operator splitting and homogeneous self-dual embedding,

    B. O’Donoghue, E. Chu, N. Parikh, and S. Boyd, “Conic optimization via operator splitting and homogeneous self-dual embedding,”Journal of Optimization Theory and Applications, vol. 169, no. 3, pp. 1042–1068, June 2016

    work page 2016

  28. [28]

    ApS,The MOSEK optimization toolbox for MATLAB manual

    M. ApS,The MOSEK optimization toolbox for MATLAB manual. Version 9.0., 2019

    work page 2019

  29. [29]

    Isaac Sim

    NVIDIA, “Isaac Sim.”

    work page

  30. [30]

    Learning to optimize: A primer and a benchmark,

    T. Chen, X. Chen, W. Chen, H. Heaton, J. Liu, Z. Wang, and W. Yin, “Learning to optimize: A primer and a benchmark,”Journal of Machine Learning Research, vol. 23, no. 189, pp. 1–59, 2022

    work page 2022

  31. [31]

    Learn to optimize—a brief overview,

    K. Tang and X. Yao, “Learn to optimize—a brief overview,”National Science Review, vol. 11, no. 8, p. nwae132, 2024

    work page 2024

  32. [32]

    Learning-based warm-starting for fast sequential convex programming and trajectory optimization,

    S. Banerjee, T. Lew, R. Bonalli, A. Alfaadhel, I. A. Alomar, H. M. Shageer, and M. Pavone, “Learning-based warm-starting for fast sequential convex programming and trajectory optimization,” in2020 IEEE Aerospace Conference. IEEE, 2020, pp. 1–8

    work page 2020

  33. [33]

    Transformer-based model predictive control: Trajectory optimization via sequence modeling,

    D. Celestini, D. Gammelli, T. Guffanti, S. D’Amico, E. Capello, and M. Pavone, “Transformer-based model predictive control: Trajectory optimization via sequence modeling,”IEEE Robotics and Automation Letters, 2024

    work page 2024

  34. [34]

    Transformermpc: Accelerating model predictive control via transformers,

    V . Zinage, A. Khalil, and E. Bakolas, “Transformermpc: Accelerating model predictive control via transformers,” in2025 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2025, pp. 9221–9227

    work page 2025

  35. [35]

    Deep distributed opti- mization for large-scale quadratic programming,

    A. D. Saravanos, H. Kuperman, A. Oshin, A. T. Abdul, V . Pacelli, and E. A. Theodorou, “Deep distributed opti- mization for large-scale quadratic programming,”arXiv preprint arXiv:2412.12156, 2024

    work page arXiv 2024

  36. [36]

    Acs-net: A deep unfolded admm framework for ultrasound attenuation imaging,

    J. Timan ´a, S. Merino, A. Basarab, R. J. G. Van Sloun, and R. Lavarello, “Acs-net: A deep unfolded admm framework for ultrasound attenuation imaging,” in2025 IEEE International Ultrasonics Symposium (IUS), 2025, pp. 1–4

    work page 2025

  37. [37]

    Deep flexqp: Accelerated nonlin- ear programming via deep unfolding,

    A. Oshin, R. V . Ghosh, A. D. Saravanos, and E. A. Theodorou, “Deep flexqp: Accelerated nonlin- ear programming via deep unfolding,”arXiv preprint arXiv:2512.01565, 2025. SUPPLEMENTARYMATERIAL VII. DETAILS RELATED TONRTOFRAMEWORK A. Tractable Linearized Problem The cost functions are given as Qˆu(δ ˆu) = T−1X k=0 (ˆuk +δ ˆuk)⊤ Rk u (ˆuk +δ ˆuk),(18) ˜Q(kv...

    work page arXiv 2025

  38. [38]

    Derivation of Block-1 update (13):This involves solving the following min ν, ˜p ngX j=1 ρ 2 ∥ ˆAjklin−1 v + ˆbj −ν j +λ lin−1 ν,j ∥2 2 + ρ 2 ∥plin−1 − ˜p+λ lin−1 p ∥2 2 s.t.∥ν j∥2 ≤˜pj j∈J1, n gK(36) Note that the above update can be decoupled with respect to the variables{ν j,˜pj}ng j=1. Therefore, we can update the variables in parallel as follows (ν li...

    work page

  39. [39]

    Derivation of Block-2 updates ((14) and (15)):This update involves solving the following min δ ˆu,p,kv Qˆu(δ ˆu) + ˜Q(kv) + ρ 2 ∥p− ˜plin +λ lin−1 p ∥2 2 + ngX j=1 ρ 2 ∥ ˆAjkv + ˆbj −ν lin j +λ lin−1 ν ∥2 2 s.t.(12a)(38) The above update can be decoupled with respect to the variables(δ ˆu,p)andk v as follows (δ ˆulin ,p lin) = argmin δ ˆu,p Qˆu(δ ˆu) + ρ ...

    work page

  40. [40]

    10), which exhibits large accumulated tracking error and does not reli- ably reach the target region, the NRTO disturbance-feedback policy (Fig

    Compared to nominal open-loop execution (Fig. 10), which exhibits large accumulated tracking error and does not reli- ably reach the target region, the NRTO disturbance-feedback policy (Fig. 9) compensates for real-world disturbances and successfully drives the robot into the goal region. The real- world experiment is also shown in the supplementary video

    work page