The DOI matches its Crossref record; 18 of the 19 references it cites were found in a registry or an index.
Per-Contact Iteration Method for Solving Contact Dynamics
Open accessAbstract
This letter introduces a new iterative method for contact dynamics problems. The proposed method is based on an efficient bisection method which iterates over each contact. We compared our approach to two existing ones for the same model and found that it is about twice as fast as the existing ones. We also introduce four different robotic simulation experiments and compare the proposed method to the most common contact solver, the projected Gauss-Seidel (PGS) method. We show that, while both methods are very efficient in solving simple problems, the proposed method significantly outperforms the PGS method in more complicated contact scenarios. Simulating one time step of an 18-DOF quadruped robot with multiple contacts took less than 20 μs with a single core of a CPU. This is at least an order of magnitude faster than many other simulators which employ multiple relaxation methods to the major dynamic principles in order to boost their computational speed. The proposed simulation method is also stable at 50 Hz due to its strict adherence to the dynamical principles. Although the accuracy might be compromised at such a low update rate, this means that we can simulate an 18-DOF robot more than thousand times faster than the real time.
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“Present-day technology is severely limited in its ability to simulate compliant contact, slippage, and deformable and crumbling terrain. As a result, phenomena such as mud, snow, thick vegetation, gushing water, and many others are beyond the capabilities of robotics simulation frameworks [30-32].”
From Learning quadrupedal locomotion over challenging terrain (2020) · cites this paper as [30]
Citations
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Hammoud, B., Olivieri, L., Righetti, L., Carpentier, J., & Prete, A. D. (2021) · arXiv (Cornell University) · Cited by 1
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Inverse dynamics‐based formulation of finite horizon optimal control problems for rigid‐body systems
Katayama, S., & Ohtsuka, T. (2021) · Optimal Control Applications and Methods · doi:10.1002/oca.2750
“The C/GMRES method computes U̇ by solving linear problem (35) using the GMRES method,30 a fast inexact numerical solver of the linear problem, and updates the solution by U(t + Δt) = U(t) + U̇Δt, (36) where Δt > 0 is the sampling period.”
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Liu, R., Sontakke, N., & Ha, S. (2021) · arXiv (Cornell University)
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Contact Force Distribution Using Centroidal Momentum Feedback for Quadruped Locomotion
Ozcinar, E. C., Bebek, Ö., & Uğurlu, B. (2023) · IEEE International Conference on Mechatronics (ICM) · doi:10.1109/icm54990.2023.10101987
“The quadruped robot model in our simulation environment [7].”
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Ozkaynak, B., & Uğurlu, B. (2023) · IEEE International Conference on Industrial Informatics (INDIN) · doi:10.1109/indin51400.2023.10217866
“The presented CoM trajectory generation approach was verified in a series of simulations with a realistic model of the quadruped robot Kara in Raisim environment [6], and it was compared against other methods.”
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Xiao, M., Luo, X., & Ding, Y. (2023) · Lecture notes in computer science · doi:10.1007/978-981-99-6486-4_44
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Dance, C. R. (2024) · ESAIM Mathematical Modelling and Numerical Analysis · doi:10.1051/m2an/2024018
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Perceptive Motion Planning with Friction Constraints for Quadruped Robot Locomotion
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“The environment is implemented with RaiSim (Hwangbo et al. 2018) with a simulation timestep of 1 ms.”
Reinforcement Learning in Robotic Systems: A Review on Sim-to-Real TransferPreprint
Khapre, S. P., Tiwari, R., & Singh, A. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5387665
Efficient Algorithms for Whole-Body and Second-Order Robot Trajectory Optimization
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High-Order Adaptive Integration of Contact Dynamics in MuJoCo
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Dynamically-Consistent Trajectory Optimization for Legged Robots via Contact Point Decomposition
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Sensor Data-Driven Modular Network Model for Jump Motion in One-Legged Robot
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Real-Time Inertial Parameter Identification of Robot Links for Software Defined Robots
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Quadrupedal Locomotion Control in Complex Terrains Based on Deep Reinforcement Learning
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KRITTER - A Novel Wheel-on-Limb Robot for Training Planetary Rover Suspension Control
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Wang, D., Chen, Z., Yu, J., Zhang, L., Wang, Y., Lu, H., Qu, S., & Xiong, R. (2026) · Robotic Intelligence and Automation · doi:10.1108/ria-03-2025-0083
Beyond Backpropagation: Smarter Neural Networks for Smart Manufacturing
Terziyan, V. Y., Vitko, O., & Terziyan, O. (2026) · Procedia Computer Science · doi:10.1016/j.procs.2026.02.203
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Li, N., Shi, F., Zhang, X., & Wang, A. Y. (2025) · Graphics Interface · doi:10.1145/3769872.3769898
“Despite available simulation tools [15, 28, 37, 51] and data visualization methods [17, 26], policy training using RL remains an iterative and complex process.”
A Convergent Continuous Contact Solver With Explicit Separation Time for High-Stiffness Contact
Lei, T., Chen, J., Li, Q., Dai, J. S., & Pan, Y. (2026) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2026.3692328
“Therefore, the ability to simulate multi-body systems (MBS) with contact accurately and efficiently has become a cornerstone of modern robotics research and development [3], [4].”
Predictive modeling of wheeled mobile robot dynamics based on transformative learning
Amertet, S., Alarazhi, H. M., & Zhang, J. (2026) · Journal of Dynamics and Vibroacoustics · doi:10.18287/2409-4579-2026-12-1-112-126
Height-Aware Local Planning for Quadruped Robots Using Learned Forward Dynamics
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Hierarchical policy learning for high-precision cylindrical assembly under tight tolerances
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“Since applying RL alone has slow convergence and low exploration e ffi ciency [22, 23, 24], combining RL and other learning algorithms has become a promising solution.”
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Cross-Modal Distillation With Latent Consistency for Proprioceptive Quadruped Locomotion
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“Whole-Body Control (WBC), and Model Predictive Control (MPC) forming the main technical paradigms [11], [12], [13], [14].”
Evolution of humanoid locomotion control
Gu, Y., Shi, G., Shi, F., Chang, I.-C., Wang, Y., Cheng, Q., Olkin, Z., López-Sánchez, I., Feng, Y., Zhang, J., et al. (2026) · Science Robotics · doi:10.1126/scirobotics.aed3973
Contact-implicit modeling of snake robot sidewinding on compliant and granular terrain
Salagame, A., Hublikar, H. I., Sihite, E. N., & Ramezani, A. (2026) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2026.105705
Soliman, A. F., Wensing, P. M., & Uğurlu, B. (2026) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2026.3729200
“To verify the feasibility of the proposed identification algorithm, a series of dynamic walking simulations were conducted using the 3D dynamic simulator RaiSim [41].”
Metadata
- Authors
- Hwangbo, J., Lee, J., & Hutter, M.
- Affiliations
- ETH Zurich (CH)
- Venue
- IEEE Robotics and Automation Letters
- Published
- 2018-04
- Volume
- 3
- Issue
- 2
- Pages
- 895-902
- ISSN
- 2377-3766 (ISSN-L)
- 2377-3774
- OpenAlex
- W2779458783
- Cited by
- 243
- References
- 19
- Citations by year
- 2026: 20 · 2025: 43 · 2024: 41 · 2023: 42 · 2022: 49 · 2021: 33 · 2020: 12 · 2019: 2 · 2018: 1
- FWCI
- 7.43
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Locations
- IEEE Robotics and Automation Letters (publishedVersion)
- Repository for Publications and Research Data (ETH Zurich) (submittedVersion, other-oa)
- ETH Zürich Research Collection
- Funders
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- National Centre of Competence in Research Robotics and Project (200021-166232)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Dynamics and Control of Mechanical Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Robotic Locomotion and Control
- Physical Sciences › Engineering › Computational Mechanics › Contact Mechanics and Variational Inequalities
- Keywords
- contact dynamics, bisection method, computational efficiency
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