Education, Science, Technology, Innovation and Life
Open Access
Sign In
  1. Home
  2. Journals
  3. Automation and Machine Learning
  4. Vol 7, Issue 2, 2026

Lyapunov-Certified Parameter Search and Terrain-Adaptive Feedback Control for Legged Locomotion Systems

Download as PDF

DOI: 10.23977/autml.2026.070209 | Downloads: 5 | Views: 124

Author(s)

Jialin Li 1

Affiliation(s)

1 School of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, China

Corresponding Author

Jialin Li

ABSTRACT

Stable high-speed locomotion of legged robotic platforms depends on gait parameters that are usually tuned by hand, with no guarantee that the resulting cycle is stable or efficient. This paper builds a hybrid dynamical model of the center-of-mass trajectory using a spring-loaded inverted pendulum abstraction, with separate governing equations for the contact and flight phases and explicit event conditions for phase switching. An adaptive-step Runge-Kutta integrator recovers the full single-cycle trajectory. Stability is certified by the largest Lyapunov exponent rather than by visual inspection of the trajectory. A global grid search over contact durations from 0.05 to 0.35 seconds and flight durations from 0.10 to 0.35 seconds, at a fixed forward speed of 3 meters per second, isolates the feasible region in which periodic motion remains stable. Within that region, minimizing mechanical energy per unit distance selects 0.2470 seconds of contact and 0.1293 seconds of flight, at a cost of 45.12 joules per meter. The model is then extended with a terrain height function, and a leg-length feedback law combined with a feedforward and proportional-integral foothold controller keeps the largest exponent negative across three consecutive cycles on uneven ground. The pipeline turns gait tuning into a certified search problem.

KEYWORDS

Hybrid Dynamical Modeling; Lyapunov Exponent Stability Analysis; Global Grid Search Optimization; Adaptive-Step Numerical Integration; Terrain-Adaptive Feedback Control; Energy-Optimal Parameter Selection

CITE THIS PAPER

Jialin Li. Lyapunov-Certified Parameter Search and Terrain-Adaptive Feedback Control for Legged Locomotion Systems. Automation and Machine Learning (2026). Vol. 7, No. 2, 76-85. DOI: http://dx.doi.org/10.23977/autml.2026.070209.

REFERENCES

[1] Asai, H., Noda, T. and Morimoto, J. (2025) Dynamical modeling of torso stability in running via hip-knee three pairs of six springs. Bioinspiration & Biomimetics, 20(6), 066016.
[2] Wu, B., Ding, Z. and Huang, J. (2026) A review of continual learning in edge AI. IEEE Transactions on Network Science and Engineering.
[3] Austin, M., Ma, L., Vasquez, D., Van Stratum, B. and Clark, J. E. (2025) Added mass and accuracy of the FF-SLIP model for legged swimming. Proceedings of the IEEE International Conference on Robotics and Automation, 7661-7667.
[4] Wu, B., Ding, Z., Ostigaard, L. and Huang, J. (2025) Reinforcement learning-based energy-aware coverage path planning for precision agriculture. Proceedings of the 2025 ACM Research on Adaptive and Convergent Systems (RACS), 1-8.
[5] Bakare, M. S., Abdulkarim, A., Shuaibu, A. N. and Muhamad, M. M. (2025) Enhancing solar power efficiency with hybrid GEP ANFIS MPPT under dynamic weather conditions. Scientific Reports, 15(1), 5890.
[6] Wu, B., Cai, Z., Wu, W. and Yin, X. (2023) AoI-aware resource management for smart health via deep reinforcement learning. IEEE Access, 11, 81180-81195.
[7] Asano, F. and Sedoguchi, T. (2025) Instantaneous walkability determination method for almost linear passive dynamic walker with nontrivial limit cycle stability. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 20776-20781.
[8] Wu, B. and Wu, W. (2023) Model-free cooperative optimal output regulation for linear discrete-time multi-agent systems using reinforcement learning. Mathematical Problems in Engineering, 6350647.
[9] Hassan, M. S. U. and Hubicki, C. (2025) Single-stage optimization of open-loop stable limit cycles with smooth, symbolic derivatives. Proceedings of the IEEE International Conference on Robotics and Automation, 418-424.
[10] Nurfebriyanti, E., Gultom, P. and Tulus, T. (2025) Min–max fuzzy TOPSIS with entropy weighting for strategic location multicriteria decision making. ZERO: Jurnal Sains, Matematika dan Terapan, 9(3), 932-942.
[11] Mahdi Hosseini, S., Broumandnia, A. and Karimi, R. (2026) Blockchain-enabled hybrid evolutionary scheduling for cloud resource optimization. Computing, 108, 4.
[12] Asghari, A., Zeinalabedinmalekmian, M., Azgomi, H., Alimoradi, M. and Ghaziantafrishi, S. (2025) Farmer ants optimization algorithm: A novel metaheuristic for solving discrete optimization problems. Information, 16, 207.
[13] Beck, F. and Sakamoto, N. (2026) Optimal stabilization of periodic orbits: a symplectic geometry approach. IEEE Transactions on Automatic Control.
[14] Huang, J., Wu, B., Duan, Q., Dong, L. and Yu, S. (2025) A fast UAV trajectory planning framework in RIS-assisted communication systems with accelerated learning via multithreading and federating. IEEE Transactions on Mobile Computing.
[15] Mayora-Cebollero, C., Mayora-Cebollero, A., Lozano, Á. and Barrio, R. (2025) Full Lyapunov exponents spectrum with deep learning from single-variable time series. Physica D: Nonlinear Phenomena, 472, 134510.
[16] Velichko, A., Belyaev, M. and Boriskov, P. (2025) A novel approach for estimating largest Lyapunov exponents in one-dimensional chaotic time series using machine learning. Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(10).
[17] Wu, B., Huang, J. and Yu, S. (2026) 'X of Information' continuum: A survey on AI-driven multi-dimensional metrics for next-generation networked systems. IEEE Communications Surveys & Tutorials.
[18] Wu, B., Huang, J., Duan, Q., Dong, L. and Cai, Z. (2025) Enhancing vehicular platooning with wireless federated learning: A resource-aware control framework. IEEE/ACM Transactions on Networking, 33, 1-16.
[19] Schperberg, A., Menner, M. and Di Cairano, S. (2025) Energy-efficient motion planner for legged robots. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 18888-18895.
[20] Wu, B., Huang, J. and Duan, Q. (2025) FedTD3: An accelerated learning approach for UAV trajectory planning. Proceedings of the International Conference on Wireless Artificial Intelligent Computing Systems and Applications (WASA), 13-24.
[21] Gilbert, J. B., Miratrix, L. W., Joshi, M. and Domingue, B. W. (2025) Disentangling person-dependent and item-dependent causal effects: applications of item response theory to the estimation of treatment effect heterogeneity. Journal of Educational and Behavioral Statistics, 50(1), 72-101.
[22] Mazzolai, B., Del Dottore, E., Speck, T., Rowe, N. and Laschi, C. (2025) Energy-saving movement strategies in animals and plants for robot design. Nature Reviews Bioengineering, 3(11), 921-938.
[23] Wu, B., Huang, J. and Duan, Q. (2025) Real-time intelligent healthcare enabled by federated digital twins with AoI optimization. IEEE Network, 1.
[24] Pant, Y.R., Leigh, L. and Fajardo Rueda, J. (2025) Improving K-means clustering: A comparative study of parallelized version of modified K-means algorithm for clustering of satellite images. Algorithms, 18, 532.
[25] Pan, D., Wu, B.-N., Sun, Y.-L. and Xu, Y.-P. (2023) A fault-tolerant and energy-efficient design of a network switch based on a quantum-based nano-communication technique. Sustainable Computing: Informatics and Systems, 37, 100827.
[26] Huan, T. T. and Anh, H. P. H. (2025) Optimum gait for quadruped robot using multi-objective Jaya optimization algorithm. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 47(3), 111.

Subscription
E-Mail Alert
Most popular papers
Call for Special Issue
Publication Ethics & OA Statement
Plagiarism Policy
Contact Us
Downloads: 5660
Visits: 323217

Sponsors, Associates, and Links

All published work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © 2016 - 2031 Clausius Scientific Press Inc. All Rights Reserved.