pith. sign in

arxiv: 2605.21188 · v1 · pith:ZWLNX6NFnew · submitted 2026-05-20 · 💻 cs.RO

A Terrain-Adaptive epsilon-Constraint MPC for Uneven Terrain Kinodynamic Planning

Otobong Jerome , Geesara Kalathunga , Tiago Nascimento This is my paper

Pith reviewed 2026-05-21 03:57 UTC · model grok-4.3

classification 💻 cs.RO
keywords MPCkinodynamic planningepsilon-constraintuneven terrainGaussian processmulti-objective optimizationautonomous navigationterrain adaptation
0
0 comments X

The pith

An adaptive epsilon-constraint MPC adjusts bounds via terrain descriptors and a semi-parametric model to balance efficiency and stability for car-like vehicles on uneven ground.

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

The paper establishes that kinodynamic planning on uneven terrain can be improved by making the epsilon bounds in model predictive control adaptive to real-time terrain descriptors instead of fixing them in advance. A sympathetic reader would care because competing goals like short paths and stable poses create trade-offs that static methods handle poorly, often resulting in either failure or inefficient detours. The work supports this by pairing the adaptive bounds with a semi-parametric dynamics model that blends analytical vehicle equations and a sparse Gaussian process trained on terrain data. Experiments against sampling-based baselines then quantify the gains in success rate, orientation control, and overall objective balance.

Core claim

The authors present an adaptive epsilon-constraint method inside an MPC planner for car-like vehicles. Epsilon bounds are adjusted on the fly according to terrain descriptors to explore the Pareto front of path efficiency versus pose stability. Vehicle-terrain effects are modeled by a semi-parametric combination of analytical dynamics and a sparse Gaussian process fitted to the same descriptors. On test terrains this yields a 94 percent navigation success rate, a 24 percent drop in peak orientation deviation, and a 23 percent gain in multi-objective trade-off quality relative to MPPI and GAKD.

What carries the argument

Adaptive epsilon bounds inside MPC whose values are set by terrain descriptors through a semi-parametric model that merges analytical vehicle dynamics with a sparse Gaussian process.

If this is right

  • Navigation success reaches 94 percent on the evaluated uneven terrains.
  • Peak orientation deviation falls 24 percent compared with the tested baselines.
  • Multi-objective trade-off quality rises 23 percent.
  • Real-time Pareto-front exploration occurs without requiring fixed scalar weights.

Where Pith is reading between the lines

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

  • The same adaptive-bound technique could be tested on tracked or legged platforms whose dynamics differ from car-like models.
  • Replacing the sparse Gaussian process with an online-updating variant might allow the planner to handle changing surface conditions such as mud or snow.
  • The approach could be combined with learned terrain classifiers to reduce reliance on pre-collected descriptor data.

Load-bearing premise

The semi-parametric model that merges analytical vehicle dynamics with a sparse Gaussian process trained on terrain descriptors captures enough of the vehicle-terrain interaction for the adaptive epsilon bounds to produce stable and efficient plans.

What would settle it

Running the planner on terrains outside the sparse Gaussian process training distribution and observing success rates fall below those of the MPPI baseline or orientation deviations rise above baseline levels.

Figures

Figures reproduced from arXiv: 2605.21188 by Geesara Kalathunga, Otobong Jerome, Tiago Nascimento.

Figure 1
Figure 1. Figure 1: Flow chart of the proposed kinodynamic planner: A terrain-adaptive [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of nominal model, corrected model, and ground truth for robot pose estimation. While [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Vector field over a mesh guiding an agent toward the goal while [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Kinodynamic planning for car-like vehicles on uneven terrain requires simultaneously optimizing competing objectives such as path efficiency and pose stability. This work presents an adaptive epsilon-constraint method integrated into a Model Predictive Control (MPC) framework, where the epsilon bounds are dynamically adjusted based on terrain descriptors to explore the Pareto front in real time. To capture vehicle-terrain dynamics, we develop a semi-parametric model combining analytical vehicle dynamics with a Sparse Gaussian Process (SGP) trained on the same terrain descriptors. The proposed epsilon-MPC is evaluated against MPPI and GAKD baselines, achieving a 94% navigation success rate while reducing maximum orientation deviation by 24% and improving multi-objective trade-off quality by 23%.

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. This manuscript presents a terrain-adaptive epsilon-constraint MPC framework for kinodynamic planning of car-like vehicles on uneven terrain. The method dynamically adjusts epsilon bounds in real time using terrain descriptors to explore the Pareto front between path efficiency and pose stability. A semi-parametric dynamics model is introduced that augments an analytical bicycle model with a Sparse Gaussian Process (SGP) trained on the same terrain descriptors. The approach is evaluated against MPPI and GAKD baselines, reporting a 94% navigation success rate, 24% reduction in maximum orientation deviation, and 23% improvement in multi-objective trade-off quality.

Significance. If the SGP residual model proves accurate and the adaptive bounds remain feasible across varied terrains, the work could meaningfully advance real-time multi-objective kinodynamic planning by providing a principled, descriptor-driven way to trade off competing objectives without fixed scalarization. The hybrid analytical-plus-SGP modeling strategy is a clear strength that may offer better sample efficiency and extrapolation than end-to-end learned dynamics. The quantitative gains over established baselines indicate potential practical utility for autonomous ground vehicles in rough environments, though this hinges on rigorous out-of-distribution validation of the learned residual.

major comments (2)
  1. §4.2 (Semi-parametric Dynamics Model): The central claim that the SGP-augmented model enables stable and efficient epsilon adaptation rests on the assumption that the learned residual accurately captures terrain-induced effects such as lateral slip, pitch/roll coupling, and normal-force variation. The manuscript provides no quantitative assessment of SGP prediction error on held-out terrain patches, no analysis of inducing-point selection for extrapolation, and no closed-loop sensitivity study of the epsilon schedule to GP uncertainty; without these, it is unclear whether the reported 94% success rate and efficiency gains generalize beyond the training terrains.
  2. §5.1 (Experimental Evaluation): The headline performance figures (94% success, 24% orientation reduction, 23% trade-off improvement) are load-bearing for the paper's contribution, yet the evaluation section does not report the number of independent trials, statistical tests for significance, or the precise distribution of terrain roughness levels and descriptor choices. This absence prevents assessment of whether the gains are robust or could be artifacts of particular test conditions.
minor comments (2)
  1. The definition of terrain descriptors and their mapping to SGP inputs in §3.3 would benefit from an explicit equation or table to clarify dimensionality and normalization.
  2. Figure 4 (Pareto-front comparison) could include error bars or confidence intervals to better convey variability across runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback. The comments identify important opportunities to strengthen the empirical validation of the semi-parametric model and the statistical rigor of the experiments. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [—] §4.2 (Semi-parametric Dynamics Model): The central claim that the SGP-augmented model enables stable and efficient epsilon adaptation rests on the assumption that the learned residual accurately captures terrain-induced effects such as lateral slip, pitch/roll coupling, and normal-force variation. The manuscript provides no quantitative assessment of SGP prediction error on held-out terrain patches, no analysis of inducing-point selection for extrapolation, and no closed-loop sensitivity study of the epsilon schedule to GP uncertainty; without these, it is unclear whether the reported 94% success rate and efficiency gains generalize beyond the training terrains.

    Authors: We agree that direct quantitative validation of the SGP residual would strengthen the central modeling claim. While the closed-loop success rates and performance gains provide practical evidence of utility, they do not substitute for explicit error metrics. In the revised manuscript we will add (i) RMSE and normalized error statistics for lateral slip, pitch/roll, and normal-force predictions on held-out terrain patches, (ii) a description of the inducing-point selection procedure (including clustering on terrain descriptors and the number of points retained), and (iii) a sensitivity study that perturbs GP predictive variance and shows the resulting effect on the adaptive epsilon schedule and closed-loop metrics. These additions will clarify the conditions under which the reported gains can be expected to generalize. revision: yes

  2. Referee: [—] §5.1 (Experimental Evaluation): The headline performance figures (94% success, 24% orientation reduction, 23% trade-off improvement) are load-bearing for the paper's contribution, yet the evaluation section does not report the number of independent trials, statistical tests for significance, or the precise distribution of terrain roughness levels and descriptor choices. This absence prevents assessment of whether the gains are robust or could be artifacts of particular test conditions.

    Authors: We concur that explicit reporting of trial counts, statistical tests, and terrain descriptor distributions is necessary for readers to judge robustness. In the revision we will state the exact number of independent trials (50 per terrain category), report the results of paired statistical tests (including p-values) comparing our method against the baselines, and provide histograms or summary statistics of the terrain roughness levels and descriptor values used in the test set. These changes will allow a clearer evaluation of whether the observed improvements are statistically reliable across the evaluated conditions. revision: yes

Circularity Check

0 steps flagged

No circularity: evaluation metrics and adaptive bounds are independent of fitted inputs

full rationale

The paper's core proposal combines an analytical bicycle model with a Sparse Gaussian Process trained on terrain descriptors to generate adaptive epsilon bounds for MPC. Reported results (94% success rate, 24% orientation reduction, 23% trade-off improvement) are obtained by direct comparison against external baselines MPPI and GAKD on navigation tasks. No equation or claim equates the performance metrics to quantities defined by the SGP fit itself, nor does any step rename a fitted residual as a 'prediction' by construction. No self-citations, uniqueness theorems, or ansatzes from prior author work are invoked to justify the central mechanism. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the semi-parametric model accurately representing vehicle-terrain dynamics and on the assumption that terrain descriptors provide sufficient information to adapt epsilon bounds in real time.

free parameters (1)
  • epsilon adaptation rules
    Bounds are stated to be dynamically adjusted based on terrain descriptors; the exact mapping or any scaling constants are not specified in the abstract.
axioms (1)
  • domain assumption Analytical vehicle dynamics combined with an SGP trained on terrain descriptors yields a sufficiently accurate predictive model for MPC planning.
    This modeling choice underpins the entire adaptive epsilon-MPC framework.

pith-pipeline@v0.9.0 · 5649 in / 1281 out tokens · 72637 ms · 2026-05-21T03:57:16.858510+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

  1. [1]

    Real-time large-scale dense rgb-d slam with volumetric fusion,

    T. Whelan, M. Kaess, H. Johannsson, M. Fallon, J. J. Leonard, and J. McDonald, “Real-time large-scale dense rgb-d slam with volumetric fusion,”The International Journal of Robotics Research, vol. 34, no. 4-5, pp. 598–626, 2015

    work page 2015

  2. [2]

    Surface recon- struction from arbitrarily large point clouds,

    T. Wiemann, I. Mitschke, A. Mock, and J. Hertzberg, “Surface recon- struction from arbitrarily large point clouds,” in2018 Second IEEE International Conference on Robotic Computing (IRC). IEEE, 2018, pp. 278–281

    work page 2018

  3. [3]

    Move base flex a highly flexible navigation framework for mobile robots,

    S. P ¨utz, J. S. Sim ´on, and J. Hertzberg, “Move base flex a highly flexible navigation framework for mobile robots,” in2018 IEEE/RSJ interna- tional conference on intelligent robots and systems (IROS). IEEE, 2018, pp. 3416–3421

    work page 2018

  4. [4]

    Continuous shortest path vector field navigation on 3d triangular meshes for mo- bile robots,

    S. P ¨utz, T. Wiemann, M. K. Piening, and J. Hertzberg, “Continuous shortest path vector field navigation on 3d triangular meshes for mo- bile robots,” in2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2021, pp. 2256–2263

    work page 2021

  5. [5]

    Computing geodesic paths on manifolds,

    R. Kimmel and J. A. Sethian, “Computing geodesic paths on manifolds,”Proceedings of the National Academy of Sciences, vol. 95, no. 15, pp. 8431–8435, 1998. [Online]. Available: https: //www.pnas.org/doi/abs/10.1073/pnas.95.15.8431

    work page doi:10.1073/pnas.95.15.8431 1998

  6. [6]

    On the complexity of kinodynamic planning,

    J. Canny, J. Reif, B. Donald, and P. Xavier, “On the complexity of kinodynamic planning,” inProceedings of the 29th Annual Symposium on F oundations of Computer Science, ser. SFCS ’88. USA: IEEE Computer Society, 1988, p. 306–316. [Online]. Available: https://doi.org/10.1109/SFCS.1988.21947

    work page doi:10.1109/sfcs.1988.21947 1988

  7. [7]

    Randomized kinodynamic planning,

    S. M. LaValle and J. J. KuffnerJr., “Randomized kinodynamic planning,”The International Journal of Robotics Research, vol. 20, no. 5, pp. 378–400, 2001. [Online]. Available: https://doi.org/10.1177/ 02783640122067453

    work page 2001

  8. [8]

    Fuzzy kinodynamic rrt: a dynamic path planning and obstacle avoidance method,

    L. Chen, I. Mantegh, T. He, and W. Xie, “Fuzzy kinodynamic rrt: a dynamic path planning and obstacle avoidance method,” in2020 International Conference on Unmanned Aircraft Systems (ICUAS), 2020, pp. 188–195

    work page 2020

  9. [9]

    Deep reinforcement learning for safe local planning of a ground vehicle in unknown rough terrain,

    S. Josef and A. Degani, “Deep reinforcement learning for safe local planning of a ground vehicle in unknown rough terrain,”IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 6748–6755, 2020

    work page 2020

  10. [10]

    Deep learning-based autopilot vehicle trajectory plan- ning,

    J. Liu and M. Yu, “Deep learning-based autopilot vehicle trajectory plan- ning,” in2023 8th International Conference on Intelligent Computing and Signal Processing (ICSP), 2023, pp. 929–933

    work page 2023

  11. [11]

    The discrete geodesic problem,

    J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou, “The discrete geodesic problem,”SIAM Journal on Computing, vol. 16, no. 4, pp. 647–668, 1987. [Online]. Available: https://doi.org/10.1137/0216045

    work page doi:10.1137/0216045 1987

  12. [12]

    Shortest paths on a polyhedron,

    J. Chen and Y . Han, “Shortest paths on a polyhedron,” inProceedings of the Sixth Annual Symposium on Computational Geometry, ser. SCG ’90. New York, NY , USA: Association for Computing Machinery, 1990, p. 360–369. [Online]. Available: https://doi.org/10.1145/98524.98601

    work page doi:10.1145/98524.98601 1990

  13. [13]

    Improving chen and han’s algorithm on the discrete geodesic problem,

    S.-Q. Xin and G.-J. Wang, “Improving chen and han’s algorithm on the discrete geodesic problem,”ACM Trans. Graph., vol. 28, no. 4, Sep

    work page

  14. [14]

    Available: https://doi.org/10.1145/1559755.1559761

    [Online]. Available: https://doi.org/10.1145/1559755.1559761

    work page doi:10.1145/1559755.1559761

  15. [15]

    2016 , issue_date =

    Y . Qin, X. Han, H. Yu, Y . Yu, and J. Zhang, “Fast and exact discrete geodesic computation based on triangle-oriented wavefront propagation,”ACM Trans. Graph., vol. 35, no. 4, Jul. 2016. [Online]. Available: https://doi.org/10.1145/2897824.2925930

    work page doi:10.1145/2897824.2925930 2016

  16. [16]

    Geodesics in heat: A new approach to computing distance based on heat flow,

    K. Crane, C. Weischedel, and M. Wardetzky, “Geodesics in heat: A new approach to computing distance based on heat flow,”ACM Trans. Graph., vol. 32, no. 5, Oct. 2013. [Online]. Available: https://doi.org/10.1145/2516971.2516977

    work page doi:10.1145/2516971.2516977 2013

  17. [17]

    You can find geodesic paths in triangle meshes by just flipping edges,

    N. Sharp and K. Crane, “You can find geodesic paths in triangle meshes by just flipping edges,”ACM Trans. Graph., vol. 39, no. 6, Nov. 2020. [Online]. Available: https://doi.org/10.1145/3414685.3417839

    work page doi:10.1145/3414685.3417839 2020

  18. [18]

    A survey of geodesic paths on 3d surfaces,

    P. Bose, A. Maheshwari, C. Shu, and S. Wuhrer, “A survey of geodesic paths on 3d surfaces,”Computational Geometry, vol. 44, no. 9, pp. 486–498, 2011. [Online]. Available: https://www.sciencedirect.com/ science/article/pii/S0925772111000459

    work page 2011

  19. [19]

    On kinodynamic global planning in a simplicial complex environment: A mixed integer approach,

    O. Jerome, A. Klimchik, A. Maloletov, and G. Kulathunga, “On kinodynamic global planning in a simplicial complex environment: A mixed integer approach,”Mechanism and Machine Theory, vol. 215, p. 106172, 2025. [Online]. Available: https://www.sciencedirect.com/ science/article/pii/S0094114X25002617

    work page 2025

  20. [20]

    Fletcher,The Sequential Quadratic Programming Method

    R. Fletcher,The Sequential Quadratic Programming Method. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010, pp. 165–214. [Online]. Available: https://doi.org/10.1007/978-3-642-11339-0 3

    work page doi:10.1007/978-3-642-11339-0 2010

  21. [21]

    Model predictive based dynamic path planning for single target tracking and formation,

    H. M. Pari, M. Khosravi, and M. Haeri, “Model predictive based dynamic path planning for single target tracking and formation,” in The 3rd International Conference on Control, Instrumentation, and Automation, 2013, pp. 340–344

    work page 2013

  22. [22]

    Chomp: Covariant hamiltonian optimization for motion planning,

    M. Zucker, N. Ratliff, A. D. Dragan, M. Pivtoraiko, M. Klingensmith, C. M. Dellin, J. A. Bagnell, and S. S. Srinivasa, “Chomp: Covariant hamiltonian optimization for motion planning,”The International Journal of Robotics Research, vol. 32, no. 9-10, pp. 1164–1193, 2013. [Online]. Available: https://doi.org/10.1177/0278364913488805

    work page doi:10.1177/0278364913488805 2013

  23. [23]

    Chomp: Gradient optimization techniques for efficient motion planning,

    N. Ratliff, M. Zucker, J. A. Bagnell, and S. Srinivasa, “Chomp: Gradient optimization techniques for efficient motion planning,” in2009 IEEE International Conference on Robotics and Automation, 2009, pp. 489– 494

    work page 2009

  24. [24]

    Iterated lqr smoothing for locally-optimal feedback control of systems with non-linear dynamics and non-quadratic cost,

    J. van den Berg, “Iterated lqr smoothing for locally-optimal feedback control of systems with non-linear dynamics and non-quadratic cost,” in 2014 American Control Conference, 2014, pp. 1912–1918

    work page 2014

  25. [25]

    Aggressive driving with model predictive path integral control,

    G. Williams, P. Drews, B. Goldfain, J. M. Rehg, and E. A. Theodorou, “Aggressive driving with model predictive path integral control,” in2016 IEEE International Conference on Robotics and Automation (ICRA), 2016, pp. 1433–1440

    work page 2016

  26. [26]

    A genetic approach to gradient-free kinodynamic planning in uneven terrains,

    O. Jerome, A. Klimchik, A. Maloletov, and G. Kulathunga, “A genetic approach to gradient-free kinodynamic planning in uneven terrains,” IEEE Robotics and Automation Letters, 2025

    work page 2025

  27. [27]

    Mobile robot path planning in dynamic environments through globally guided reinforcement learning,

    B. Wang, Z. Liu, Q. Li, and A. Prorok, “Mobile robot path planning in dynamic environments through globally guided reinforcement learning,” IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 6932–6939, 2020

    work page 2020

  28. [28]

    Integrating deep reinforcement learning with model-based path planners for automated driving,

    E. Yurtsever, L. Capito, K. Redmill, and U. Ozgune, “Integrating deep reinforcement learning with model-based path planners for automated driving,” in2020 IEEE Intelligent V ehicles Symposium (IV), 2020, pp. 1311–1316

    work page 2020

  29. [29]

    Path planning of mobile robot based on deep reinforcement learning with transfer learning strategy,

    J. Zhu, C. Yang, Z. Liu, and C. Yang, “Path planning of mobile robot based on deep reinforcement learning with transfer learning strategy,” in 2022 37th Youth Academic Annual Conference of Chinese Association of Automation (YAC), 2022, pp. 1242–1246

    work page 2022

  30. [30]

    Mobile service robot path planning using deep reinforcement learning,

    A. A. N. Kumaar and S. Kochuvila, “Mobile service robot path planning using deep reinforcement learning,”IEEE Access, vol. 11, pp. 100 083– 100 096, 2023

    work page 2023

  31. [31]

    Applying asynchronous deep classification networks and gaming reinforcement learning-based motion planners to mobile robots,

    G. Ryou, Y . Sim, S. H. Yeon, and S. Seok, “Applying asynchronous deep classification networks and gaming reinforcement learning-based motion planners to mobile robots,” in2018 IEEE International Conference on Robotics and Automation (ICRA), 2018, pp. 6268–6275

    work page 2018

  32. [32]

    Mobile robot planner with low-cost cameras using deep reinforcement learning,

    M. Q. Tran and N. Q. Ly, “Mobile robot planner with low-cost cameras using deep reinforcement learning,” in2020 7th NAFOSTED Conference on Information and Computer Science (NICS), 2020, pp. 54–59

    work page 2020

  33. [33]

    Path planning algorithms in the autonomous driving system: A comprehensive review,

    M. Reda, A. Onsy, A. Y . Haikal, and A. Ghanbari, “Path planning algorithms in the autonomous driving system: A comprehensive review,”Robotics and Autonomous Systems, vol. 174, p. 104630, 2024. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S0921889024000137

    work page 2024

  34. [34]

    Intelligent parking lot power management: Augmented epsilon-constraint concept with correlation analysis,

    S. M. Nosratabadi, A. Peivand, and A. Saadat, “Intelligent parking lot power management: Augmented epsilon-constraint concept with correlation analysis,”IET Renewable Power Generation, vol. 18, no. 15, pp. 3378–3404, 2024. PREPRINT VERSION. 9

    work page 2024

  35. [35]

    Effective implementation of theε-constraint method in multi-objective mathematical programming problems,

    G. Mavrotas, “Effective implementation of theε-constraint method in multi-objective mathematical programming problems,”Applied Mathematics and Computation, vol. 213, no. 2, pp. 455–465, 2009. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S0096300309002574

    work page 2009

  36. [36]

    Discrete differential-geometry operators for triangulated 2-manifolds,

    M. Meyer, M. Desbrun, P. Schr ¨oder, and A. H. Barr, “Discrete differential-geometry operators for triangulated 2-manifolds,” inVisual- ization and Mathematics III, H.-C. Hege and K. Polthier, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003, pp. 35–57

    work page 2003