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arxiv: 2605.15619 · v1 · pith:3YKMGDY6new · submitted 2026-05-15 · 💻 cs.RO

Wind-Aware Optimal Trajectory Planning for Efficient Gliding of Fixed-Wing Aerial Systems

Luca Morando , Nishanth Bobbili , Giuseppe Loianno This is my paper

Pith reviewed 2026-05-20 19:05 UTC · model grok-4.3

classification 💻 cs.RO
keywords trajectory planningfixed-wing UAVglidingwind disturbancesoptimal controlBernstein polynomialsdifferential flatness
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The pith

A nonlinear trajectory planner for fixed-wing gliders shifts energy regulation to the planning stage to maintain stable sink rate and glide ratio under wind gusts.

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

The paper presents a method for small fixed-wing UAVs to plan efficient gliding trajectories that account for wind disturbances and obstacles. Instead of using reactive controllers, it optimizes trajectories at the planning level using Bernstein polynomials and differential flatness to generate smooth paths. A simulated netto variometer estimates air mass motion to keep the glider in energy-balanced states, and trajectories are re-planned online to match the vehicle's sink polar curves. This enables hybrid missions combining gliding with powered cruising segments based on Dubins paths. The approach is shown to work in both simulations and real experiments by stabilizing key performance metrics.

Core claim

The central claim is that generating C3 continuous trajectories with Bernstein polynomials, mapping them to controls via differential flatness, and re-planning online while integrating a simulated netto variometer allows reliable energy management for gliding UAVs even in the presence of wind gusts and obstacles.

What carries the argument

The nonlinear multi-cost trajectory planner based on Bernstein polynomials that is re-planned online to match experimentally derived sink polar curves, with a simulated netto variometer constraining to energy-balanced states.

If this is right

  • Consecutive gliding trajectories can be linked by cruising segments initialized on Dubins path waypoints for hybrid powered-unpowered missions.
  • The planner stabilizes sink rate, airspeed, and glide ratio under wind gusts.
  • Trajectories remain feasible in the presence of obstacles.
  • Control commands are generated through differential flatness from the planned paths.

Where Pith is reading between the lines

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

  • Such planning could reduce the need for fine-tuning in traditional total energy control systems for gliders.
  • Extending this to varying wind fields beyond gusts might further improve endurance in real-world deployments.
  • Testing on different UAV platforms could validate the generality of the sink polar matching approach.

Load-bearing premise

The approach assumes that experimentally derived sink polar curves accurately represent the UAV's glide performance across different wind conditions and that online re-planning can match them in real time.

What would settle it

If real-world experiments show that the glide ratio or sink rate deviates substantially from the predicted values when wind gusts are present despite using the planner, the claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.15619 by Giuseppe Loianno, Luca Morando, Nishanth Bobbili.

Figure 1
Figure 1. Figure 1: Full-scale mission in Google Earth. The trajectory shows accurate replanning in both gliding and cruising states [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: System overview and notation. The Body B and Velocity V frames. The angle γa defines the glide slope, which changes based on the wind W effects on the ground velocity Vg, according to the wind triangle convention. we validate our approach on small FW-UAVs in challenging outdoor conditions and demonstrate real-time deployment, bridging theory and practice. III. SYSTEM MODELING As shown in [PITH_FULL_IMAGE:… view at source ↗
Figure 3
Figure 3. Figure 3: An overview of the proposed planning architecture. The trajectory is generated based on the aircraft’s energy state, [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Trajectory optimization with more weight on a) time [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Sink Polar and relative sink rate as obtained through [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: 2D real world mission visualization in presence [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: 2D mission visualization in presence of gaussian [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Gliding details based on recorded Va, Vz(Va, ϕ) and E˙ net in case of deviations due by the obstacle. D. Real world experiments with obstacle avoidance We also evaluate the planner in challenging scenarios where an obstacle is present along the glide path. A Gaussian obstacle with variance σx = σy = 50 m and height z = 90 m was placed at position OI = [100, −80] m, as visible in [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 8
Figure 8. Figure 8: Continuous replanning adjusts the predicted sink rate [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
read the original abstract

Gliding offers small fixed-wing UAVs extended endurance and silent operation but requires accurate energy management, especially under wind disturbances and obstacle constraints. Traditional Total Energy Control Systems based controllers regulate the trade between potential and kinetic energy reactively, often requiring fine-tuning and trim-conditions knowledge. In this work, we shift the regulation to the planning level and present a nonlinear, multi-cost trajectory planner for small UAV gliders. The method generates $\mathcal{C}^3$ continuous trajectories based on Bernstein polynomials, mapped into control commands through differential flatness, and re-planned online to match experimentally derived sink polar curves. A simulated netto variometer is integrated into the optimization to estimate air mass motion, constraining the glide to energy-balanced states. Consecutive gliding trajectories are linked by cruising segments computed through trajectories initialized on Dubins path-based waypoints, enabling hybrid missions that combine powered and unpowered flight. The approach is validated in CFD simulations and real-world experiments with a fixed-wing platform, showing reliable stabilization of sink rate, airspeed, and glide ratio under wind gusts and in presence of obstacles.

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 / 2 minor

Summary. The manuscript proposes a nonlinear multi-cost trajectory planner for small fixed-wing UAV gliders. It generates C^3 continuous trajectories via Bernstein polynomials, maps them to controls through differential flatness, and performs online re-planning to match experimentally derived sink polar curves. A simulated netto variometer enforces energy balance, while Dubins-path-based cruising segments enable hybrid powered/unpowered missions. Validation is claimed via CFD simulations and real-world experiments demonstrating stabilization of sink rate, airspeed, and glide ratio under wind gusts and obstacles.

Significance. If the experimental claims hold with supporting quantitative evidence, the work could meaningfully advance energy-efficient autonomous gliding for small UAVs by relocating energy management from reactive TECS-style controllers to the planning layer. The combination of differential flatness, Bernstein polynomials for smoothness, experimentally grounded sink polars, and the netto-variometer energy constraint represents a coherent technical approach with clear application relevance.

major comments (2)
  1. §5 (Validation/Experiments): The central claim of reliable stabilization of sink rate, airspeed, and glide ratio under wind gusts and obstacles is presented without any quantitative metrics, error bars, statistical significance, or baseline comparisons. This absence directly undermines assessment of whether the online re-planning and sink-polar matching deliver the reported behavior.
  2. §3 (Sink Polar Curves and Netto Variometer): The planner's energy-balance enforcement and real-time re-planning rest on the assumption that the experimentally derived sink polar curves accurately represent glide performance across the wind conditions and gusts encountered in flight. No sensitivity analysis, mismatch bounds, or robustness checks against curve inaccuracies are provided, leaving the link between the Bernstein formulation and observed stabilization unsecured.
minor comments (2)
  1. The multi-cost weights and their tuning procedure are mentioned but not detailed with respect to the specific optimization constraints or post-hoc adjustments referenced in the abstract.
  2. Figure captions in the experimental section should explicitly state the wind speeds, gust profiles, and obstacle geometries used to allow direct assessment of the reported stabilization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the referee's insightful comments. We have carefully considered the major concerns regarding the quantitative validation and robustness analysis. Below, we provide point-by-point responses and outline the revisions we will implement to address these issues.

read point-by-point responses

  1. Referee: §5 (Validation/Experiments): The central claim of reliable stabilization of sink rate, airspeed, and glide ratio under wind gusts and obstacles is presented without any quantitative metrics, error bars, statistical significance, or baseline comparisons. This absence directly undermines assessment of whether the online re-planning and sink-polar matching deliver the reported behavior.

    Authors: We recognize the importance of quantitative evidence to support our experimental claims. In the revised manuscript, we will augment §5 with quantitative metrics, including average values, standard deviations, and error bars for sink rate, airspeed, and glide ratio from multiple experimental runs. We will also include baseline comparisons against a standard TECS-based controller and report statistical significance where applicable. This will provide a clearer assessment of the planner's performance. revision: yes

  2. Referee: §3 (Sink Polar Curves and Netto Variometer): The planner's energy-balance enforcement and real-time re-planning rest on the assumption that the experimentally derived sink polar curves accurately represent glide performance across the wind conditions and gusts encountered in flight. No sensitivity analysis, mismatch bounds, or robustness checks against curve inaccuracies are provided, leaving the link between the Bernstein formulation and observed stabilization unsecured.

    Authors: We agree that a sensitivity analysis would strengthen the connection between the sink polar curves and the observed stabilization. We will incorporate a new subsection or appendix in the revised manuscript presenting sensitivity analysis on the sink polar parameters. This will include perturbing the curves within measured variability and assessing impacts on energy balance and trajectory quality, along with mismatch bounds to demonstrate robustness. revision: yes

Circularity Check

0 steps flagged

No circularity: planner uses external experimental sink polar curves and independent CFD/real-world validation

full rationale

The derivation chain generates C^3 trajectories via Bernstein polynomials, applies differential flatness mapping, and re-plans online to match externally derived experimental sink polar curves while incorporating a simulated netto variometer for energy balance. These elements are presented as inputs or separate modules rather than being fitted or defined from the planner's own outputs. Validation occurs through independent CFD simulations and real-world experiments on a fixed-wing platform, with no steps reducing by construction to self-citations, renamed fits, or tautological predictions. The central stabilization claims rest on matching pre-derived curves and external testing, keeping the method self-contained against benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the accuracy of experimentally derived sink polar curves, the validity of differential flatness for the UAV model, and the assumption that the simulated variometer provides usable air mass estimates for energy balancing.

free parameters (1)
  • multi-cost weights
    Weights balancing energy, obstacle avoidance, and smoothness in the nonlinear optimizer are likely tuned but not specified in the abstract.
axioms (2)
  • domain assumption Differential flatness of fixed-wing UAV dynamics
    Invoked to map planned trajectories directly into control commands.
  • domain assumption Sink polar curves derived from experiments accurately capture glide performance
    Used to re-plan trajectories online to match real behavior.
invented entities (1)
  • simulated netto variometer no independent evidence
    purpose: Estimates air mass motion to constrain glide to energy-balanced states
    Integrated into the optimization as a virtual sensor for wind awareness.

pith-pipeline@v0.9.0 · 5724 in / 1490 out tokens · 53251 ms · 2026-05-20T19:05:49.342803+00:00 · methodology

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Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    Any-time trajectory planning for safe emergency landing,

    P. V ´aˇna, J. Sl´ama, J. Faigl, and P. Paˇces, “Any-time trajectory planning for safe emergency landing,” inIEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018, pp. 5691–5696

    work page 2018

  2. [2]

    Autonomous emergency landing for fixed-wing aircraft with energy-constrained closed-loop prediction,

    S. J. Deal, H. L. Nichols, and A. Mazumdar, “Autonomous emergency landing for fixed-wing aircraft with energy-constrained closed-loop prediction,”Journal of Aerospace Information Systems, vol. 21, no. 5, pp. 430–442, 2024

    work page 2024

  3. [3]

    Chapter 21 - using low-cost uavs for environmental monitoring, mapping, and modelling: Examples from the coastal zone,

    D. R. Green, J. J. Hagon, C. G ´omez, and B. J. Gregory, “Chapter 21 - using low-cost uavs for environmental monitoring, mapping, and modelling: Examples from the coastal zone,” inCoastal Management, R. Krishnamurthy, M. Jonathan, S. Srinivasalu, and B. Glaeser, Eds. Academic Press, 2019, pp. 465–501

    work page 2019

  4. [4]

    An approach to surveillance an area using swarm of fixed wing and quad-rotor unmanned aerial vehicles uav(s),

    A. Jaimes, S. Kota, and J. Gomez, “An approach to surveillance an area using swarm of fixed wing and quad-rotor unmanned aerial vehicles uav(s),” inIEEE International Conference on System of Systems Engineering, 2008, pp. 1–6

    work page 2008

  5. [5]

    Quasi-lagrangian measurements in convective boundary layer plumes and their implications for the calculation of cape,

    N. O. Renn ´o and E. R. Williams, “Quasi-lagrangian measurements in convective boundary layer plumes and their implications for the calculation of cape,”Monthly weather review, vol. 123, no. 9, pp. 2733–2742, 1995

    work page 1995

  6. [6]

    End-to-end thermal updraft detection and estimation for autonomous soaring using temporal con- volutional networks,

    C. Gall, W. Fichter, and A. Ahmad, “End-to-end thermal updraft detection and estimation for autonomous soaring using temporal con- volutional networks,” inIEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 17 875–17 881

    work page 2024

  7. [7]

    Safe low-altitude navigation in steep terrain with fixed-wing aerial vehicles,

    J. Lim, F. Achermann, R. Girod, N. Lawrance, and R. Siegwart, “Safe low-altitude navigation in steep terrain with fixed-wing aerial vehicles,”IEEE Robotics and Automation Letters, vol. 9, no. 5, pp. 4599–4606, 2024

    work page 2024

  8. [8]

    Safe flight envelope uncer- tainty quantification using probabilistic reachability analysis,

    R. van den Brandt and C. de Visser, “Safe flight envelope uncer- tainty quantification using probabilistic reachability analysis,”IFAC- PapersOnLine, vol. 51, no. 24, pp. 628–635, 2018, 10th IFAC Sym- posium on Fault Detection, Supervision and Safety for Technical Processes SAFEPROCESS 2018

    work page 2018

  9. [9]

    Wind disturbance compensated path-following control for fixed-wing uavs in arbitrarily strong winds,

    H. Lu, L. Gao, Y . Yan, M. Hou, and C. Wang, “Wind disturbance compensated path-following control for fixed-wing uavs in arbitrarily strong winds,”Chinese Journal of Aeronautics, vol. 37, no. 2, pp. 431–445, 2024

    work page 2024

  10. [10]

    Longitudinal decoupling control of altitude and velocity for a fixed-wing aircraft,

    H. Xin, Q. Chen, Y . Xian, P. Wang, Y . Wang, X. Yao, Y . Lu, and Z. Hou, “Longitudinal decoupling control of altitude and velocity for a fixed-wing aircraft,”IEEE Transactions on Intelligent Vehicles, vol. 9, no. 10, pp. 6738–6748, 2024

    work page 2024

  11. [11]

    Robotic technolo- gies for solar-powered uavs: Fully autonomous updraft-aware aerial sensing for multiday search-and-rescue missions,

    P. Oettershagen, T. Stastny, T. Hinzmann, K. Rudin, T. Mantel, A. Melzer, B. Wawrzacz, G. Hitz, and R. Siegwart, “Robotic technolo- gies for solar-powered uavs: Fully autonomous updraft-aware aerial sensing for multiday search-and-rescue missions,”Journal of Field Robotics, vol. 35, no. 4, pp. 612–640, 2018

    work page 2018

  12. [12]

    Anandakumar, D

    A. Anandakumar, D. Bernstein, and A. Goel,Adaptive Energy Control of Longitudinal Aircraft Dynamics

    work page

  13. [13]

    Trajectory planning and control for differentially flat fixed-wing aerial systems,

    L. Morando, S. A. Salunkhe, N. Bobbili, J. Mao, L. Masci, C. de Souza, N. Hung, and G. Loianno, “Trajectory planning and control for differentially flat fixed-wing aerial systems,” inIEEE International Conference on Robotics and Automation (ICRA), 2025, pp. 6336–6342

    work page 2025

  14. [14]

    Bebot: Bernstein polynomial toolkit for trajectory generation,

    C. Kielas-Jensen and V . Cichella, “Bebot: Bernstein polynomial toolkit for trajectory generation,” inIEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2019, pp. 3288–3293

    work page 2019

  15. [15]

    A method for sailplane preliminary aerodynamic design,

    O. P. Neto and F. Signor, “A method for sailplane preliminary aerodynamic design,” in2023 Regional Student Conferences

    work page

  16. [16]

    Design of a flight envelope protection system for nasa’s transport class model,

    N. Tekles, J. Chongvisal, E. Xargay, R. Choe, D. A. Talleur, N. Hov- akimyan, and C. M. Belcastro, “Design of a flight envelope protection system for nasa’s transport class model,”Journal of Guidance, Control, and Dynamics, vol. 40, no. 4, pp. 863–877, 2017

    work page 2017

  17. [17]

    Precise tracking of extended three-dimensional dubins paths for fixed-wing aircraft,

    J. Stephan, O. Pfeifle, S. Notter, F. Pinchetti, and W. Fichter, “Precise tracking of extended three-dimensional dubins paths for fixed-wing aircraft,”Journal of Guidance, Control, and Dynamics, vol. 43, no. 12, pp. 2399–2405, 2020

    work page 2020

  18. [18]

    Dubins path generation for a fixed wing uav,

    I. Lugo-C ´ardenas, G. R. Flores, S. Salazar, and R. Lozano, “Dubins path generation for a fixed wing uav,”International Conference on Unmanned Aircraft Systems (ICUAS), pp. 339–346, 2014

    work page 2014

  19. [19]

    Aggressive flight of fixed-wing and quadrotor aircraft in dense indoor environments,

    A. Bry, C. Richter, A. Bachrach, and N. Roy, “Aggressive flight of fixed-wing and quadrotor aircraft in dense indoor environments,”The International Journal of Robotics Research, vol. 34, no. 7, pp. 969– 1002, 2015

    work page 2015

  20. [20]

    Ardusoar: An open- source thermalling controller for resource-constrained autopilots,

    S. Tabor, I. Guilliard, and A. Kolobov, “Ardusoar: An open- source thermalling controller for resource-constrained autopilots,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018, pp. 6255–6262

    work page 2018

  21. [21]

    How accurate is netto,

    S. Dupont, “How accurate is netto,”NASA. Langley Res. Center The Sci. and Technol. of Low Speed and Motorless Flight, Pt. 1, 1979

    work page 1979

  22. [22]

    The autosoar autonomous soaring aircraft, part 1: Autonomy algorithms,

    N. T. Depenbusch, J. J. Bird, and J. W. Langelaan, “The autosoar autonomous soaring aircraft, part 1: Autonomy algorithms,”Journal of Field Robotics, vol. 35, no. 6, pp. 868–889, 2018

    work page 2018

  23. [23]

    Reducing the noise impact of small aircraft through indirect trajectory optimization,

    M. B. Galles and B. A. Newman, “Reducing the noise impact of small aircraft through indirect trajectory optimization,” inAIAA Aviation 2020 Forum, 2020, p. 2594

    work page 2020

  24. [24]

    Meteorology-aware multi-goal path planning for large- scale inspection missions with solar-powered aircraft,

    P. Oettershagen, J. F ¨orster, L. Wirth, G. Hitz, R. Siegwart, and J. Amb ¨uhl, “Meteorology-aware multi-goal path planning for large- scale inspection missions with solar-powered aircraft,”Journal of Aerospace Information Systems, vol. 16, no. 10, pp. 390–408, 2019

    work page 2019

  25. [25]

    Dobrokhodov,Kinematics and Dynamics of Fixed-Wing UAVs

    V . Dobrokhodov,Kinematics and Dynamics of Fixed-Wing UAVs. Cham: Springer International Publishing, 2020, pp. 1–40

    work page 2020

  26. [26]

    Emergency flight planning applied to total loss of thrust,

    E. M. Atkins, I. A. Portillo, and M. J. Strube, “Emergency flight planning applied to total loss of thrust,”Journal of Aircraft, vol. 43, no. 4, pp. 1205–1216, 2006

    work page 2006

  27. [27]

    Flying between obstacles with an au- tonomous knife-edge maneuver,

    A. J. Barry, T. Jenks, A. Majumdar, H.-T. Lin, I. G. Ros, A. A. Biewener, and R. Tedrake, “Flying between obstacles with an au- tonomous knife-edge maneuver,” inIEEE International Conference on Robotics and Automation (ICRA), 2014, pp. 2559–2559

    work page 2014

  28. [28]

    Motion planning for a small aerobatic fixed-wing unmanned aerial vehicle,

    J. Levin, A. Paranjape, and M. Nahon, “Motion planning for a small aerobatic fixed-wing unmanned aerial vehicle,” inIEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018, pp. 8464–8470

    work page 2018

  29. [29]

    Differential flatness and absolute equivalence of nonlinear control systems,

    M. van Nieuwstadt, M. Rathinam, and R. M. Murray, “Differential flatness and absolute equivalence of nonlinear control systems,”SIAM Journal on Control and Optimization, vol. 36, no. 4, pp. 1225–1239, 1998

    work page 1998

  30. [30]

    Aggressive flight maneuvers,

    J. Hauser and R. Hindman, “Aggressive flight maneuvers,” in36th IEEE Conference on Decision and Control (CDC), vol. 5, 1997, pp. 4186–4191

    work page 1997

  31. [31]

    Aggressive flight of fixed-wing and quadrotor aircraft in dense indoor environments,

    A. Bry, C. Richter, A. Bachrach, and N. Roy, “Aggressive flight of fixed-wing and quadrotor aircraft in dense indoor environments,”The International Journal of Robotics Research, vol. 34, pp. 1002 – 969, 2015

    work page 2015

  32. [32]

    Differential flatness-based trajectory planning and tracking for fixed-wing aircraft in clustered environments,

    T. Liu, J. Li, F. Zou, B. Wang, and Y . Niu, “Differential flatness-based trajectory planning and tracking for fixed-wing aircraft in clustered environments,” in42nd Chinese Control Conference (CCC), 2023, pp. 3627–3631

    work page 2023

  33. [33]

    Autonomous soaring flight for unmanned aerial vehicles,

    N. R. Lawrance, “Autonomous soaring flight for unmanned aerial vehicles,” Ph.D. dissertation, 2011

    work page 2011

  34. [34]

    M. Owen, R. W. Beard, and T. W. McLain,Implementing Dubins Air- plane Paths on Fixed-Wing UAVs. Dordrecht: Springer Netherlands, 2015, pp. 1677–1701

    work page 2015

  35. [35]

    Savitzky-golay smoothing and differentiation filter,

    N. B. Gallagher, “Savitzky-golay smoothing and differentiation filter,” Eigenvector Research Incorporated, vol. 2, p. 4, 2020

    work page 2020

  36. [36]

    Bernstein polynomial-based method for solving optimal trajectory generation problems,

    C. Kielas-Jensen, V . Cichella, T. Berry, I. Kaminer, C. Walton, and A. Pascoal, “Bernstein polynomial-based method for solving optimal trajectory generation problems,”Sensors, vol. 22, no. 5, p. 1869, 2022

    work page 2022

  37. [37]

    On the implementation of a primal– dual interior point filter line search algorithm for large-scale nonlinear programming,

    A. W ¨achter and L. T. Biegler, “On the implementation of a primal– dual interior point filter line search algorithm for large-scale nonlinear programming,”Mathematical Programming, vol. 106, no. 1, pp. 25– 57, 2006, used as the canonical reference for IPOPT

    work page 2006