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Gait Optimization Method for Quadruped Locomotion

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Advances in Nonlinear Dynamics

Part of the book series: NODYCON Conference Proceedings Series ((NCPS))

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Abstract

The scope of the paper is to develop a methodology for finding optimal gaits of a quadruped robot using genetic algorithm, comparing the results to the ones resulting from natural evolution. The optimization is performed over pre-imposed contact forces to find the best shapes that guarantees the minimum energy consumption during a single stride cycle. The dynamic formulation of the four-dimensional model is developed without involving any specific kinematic mechanism for the legs, considering the entire gait spectrum a quadruped can exhibit. The optimization model consists of a set of constraints that ensure the feasibility and stability of the gaits. Results are presented for an optimization requiring a constant speed of 1.35 m/s. The optimal gait was found to be consistent to nature, suggesting that energy consumption is one of the key factors contributing to the evolution of gaiting patterns in quadrupeds. Eventually, a comparison between different existing gait patterns is carried out in terms of foot contact time and energy consumption.

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References

  1. M. Srinivasan, A. Ruina, Computer optimization of a minimal biped model discovers walking and running. Nature 439, 72–75 (2006). https://doi.org/10.1038/nature04113

    Article  Google Scholar 

  2. X. Meng, S. Wang, Z. Cao, L. Zhang, A review of quadruped robots and environment perception, in 2016 35th Chinese Control Conference (CCC), 27–29 July 2016, (2016), pp. 6350–6356. https://doi.org/10.1109/ChiCC.2016.7554355

    Chapter  Google Scholar 

  3. L. Hu, C. Zhou, EDA-based optimization and learning methods for biped gait generation. Lect. Notes Control Informat. Sci. 362, 541–549 (2007)

    Article  Google Scholar 

  4. A. Masuri, O. Medina, S. Hacohen, N. Shvalb, Gait and trajectory optimization by self-learning for quadrupedal robots with an active back joint. J. Robot. 2020, 8051510 (2020). https://doi.org/10.1155/2020/8051510

    Article  Google Scholar 

  5. T. Kato, K. Shiromi, M. Nagata, H. Nakashima, K. Matsuo, Gait pattern acquisition for four-legged mobile robot by genetic algorithm, in IECON 2015 - 41st Annual Conference of the IEEE Industrial Electronics Society, 9–12 Nov. 2015, (2015), pp. 004854–004857. https://doi.org/10.1109/IECON.2015.7392860

    Chapter  Google Scholar 

  6. E. Koco, S. Glumac, Z. Kovacic, Multiobjective optimization of a quadruped robot gait, in 22nd Mediterranean Conference on Control and Automation, 16–19 June 2014, (2014), pp. 1520–1526. https://doi.org/10.1109/MED.2014.6961591

    Chapter  Google Scholar 

  7. M. Focchi, A. Del Prete, I. Havoutis, R. Featherstone, D. Caldwell, C. Semini, High-slope terrain locomotion for torque-controlled quadruped robots. Autonomous Robots 41, 259–272 (2016)

    Article  Google Scholar 

  8. S.N. Miandoab, F. Kiani, E. Uslu, Generation of automatic six-legged walking behavior using genetic algorithms, in 2020 International Conference on INnovations in Intelligent SysTems and Applications (INISTA), 24–26 Aug. 2020, (2020), pp. 1–5. https://doi.org/10.1109/INISTA49547.2020.9194620

    Chapter  Google Scholar 

  9. S. Zhai, B. Jin, Y. Cheng, Mechanical design and gait optimization of hydraulic hexapod robot based on energy conservation. Appl. Sci. 10(11), 3884 (2020). https://doi.org/10.3390/app10113884

  10. C. Cai, H. Jiang, Performance comparisons of evolutionary algorithms for walking gait optimization, in 2013 International Conference on Information Science and Cloud Computing Companion, 7–8 Dec. 2013, (2013), pp. 129–134. https://doi.org/10.1109/ISCC-C.2013.100

    Chapter  Google Scholar 

  11. M. Neunert, F. Farshidian, A. W. Winkler, and J. Buchli, Trajectory Optimization through Contacts and Automatic Gait Discovery for Quadrupeds, 2016

    Google Scholar 

  12. W.-L. Ma, K.A. Hamed, A.D. Ames, First Steps Towards Full Model Based Motion Planning and Control of Quadrupeds: A Hybrid Zero Dynamics Approach (IEEE, 2019), pp. 5498–5503

    Google Scholar 

  13. A. Srisuchinnawong et al., Neural Control for Gait Generation and Adaptation of a Gecko Robot (IEEE, 2019), pp. 468–473

    Google Scholar 

  14. D. Antonelli, L. Nesi, G. Pepe, A. Carcaterra, Mechatronic control of the car response based on VFC, in Proceedings of the ISMA2018, Leuven, Belgium, (2018), pp. 17–19

    Google Scholar 

  15. G. Pepe, D. Antonelli, L. Nesi, A. Carcaterra, Flop: Feedback Local Optimality Control of the Inverse Pendulum Oscillations (Presented at the ISMA, Leuven, 2018)

    Google Scholar 

  16. D. Antonelli, L. Nesi, G. Pepe, A. Carcaterra, A novel approach in Optimal trajectory identification for Autonomous driving in racetrack, in 2019 18th European Control Conference (ECC), 25–28 June 2019, (2019), pp. 3267–3272. https://doi.org/10.23919/ECC.2019.8795637

    Chapter  Google Scholar 

  17. D. Antonelli, L. Nesi, G. Pepe, A. Carcaterra, A novel control strategy for autonomous cars, in 2019 American Control Conference (ACC), , 10–-12 July 2019, (2019), pp. 711–716. https://doi.org/10.23919/ACC.2019.8814944

    Chapter  Google Scholar 

  18. G. Pepe, M. Laurenza, D. Antonelli, A. Carcaterra, A new optimal control of obstacle avoidance for safer autonomous driving, in 2019 AEIT International Conference of Electrical and Electronic Technologies for Automotive (AEIT AUTOMOTIVE), 2–4 July 2019, (2019), pp. 1–6. https://doi.org/10.23919/EETA.2019.8804549

    Chapter  Google Scholar 

  19. M. Laurenza, G. Pepe, D. Antonelli, A. Carcaterra, Car collision avoidance with velocity obstacle approach: Evaluation of the reliability and performace of the collision avoidance maneuver, in 5th International Forum on Research and Technologies for Society and Industry: Innovation to Shape the Future, RTSI 2019 - Proceedings, (2019), pp. 465–470. https://doi.org/10.1109/RTSI.2019.8895525.

    Chapter  Google Scholar 

  20. J. Dentinger, G. Street, Animal locomotion (second edition). Andrew a. Biewener and Sheila N. Patek. 2018. Oxford university press, Oxford, U.K. 240 pp. $95.00 hardcover. ISBN: 978-019874316. J. Wildl. Manag. 83, 07/01 (2019). https://doi.org/10.1002/jwmg.21713

    Article  Google Scholar 

  21. Z. Yu et al., Disturbance rejection for biped walking using zero-moment point variation based on body acceleration. IEEE Transactions on Industrial Informatics, Industrial Informatics, IEEE Transactions on, IEEE Trans. Ind. Inf., Periodical 15(4), 2265–2276 (2019). https://doi.org/10.1109/TII.2018.2890195

    Article  Google Scholar 

  22. A.S. Baskoro, M.G. Priyono, Design of humanoid robot stable walking using inverse kinematics and zero moment point (IEEE, 2016), pp. 335–339

    Google Scholar 

  23. H. Gritli, S. Belghith, Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: Analysis of local bifurcations via the hybrid Poincaré map, in Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, vol. 98, (2017), pp. 72–87. https://doi.org/10.1016/j.chaos.2017.03.004

    Chapter  MATH  Google Scholar 

  24. W. Znegui, H. Gritli, and S. Belghith, Stabilization of the Passive Walking Dynamics of the Compass-Gait Biped Robot by Developing the Analytical Expression of the Controlled Poincare Map, 2020

    Book  Google Scholar 

  25. P.R. Roan, A. Burmeister, A. Rahimi, K. Holz, D. Hooper, Real-world validation of three tipover algorithms for mobile robots (2010), pp. 4431–4436

    Google Scholar 

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Authors and Affiliations

  1. Sapienza University of Rome, Rome, Italy

    Maicol Laurenza, Gianluca Pepe & Antonio Carcaterra

Authors
  1. Maicol Laurenza
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  2. Gianluca Pepe
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  3. Antonio Carcaterra
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Corresponding author

Correspondence to Maicol Laurenza .

Editor information

Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

    Walter Lacarbonara

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, USA

    Balakumar Balachandran

  3. Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Michael J. Leamy

  4. Department of Physics, Lanzhou University of Technology, Lanzhou, Gansu, China

    Jun Ma

  5. ISEP-Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    J. A. Tenreiro Machado

  6. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Gabor Stepan

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Laurenza, M., Pepe, G., Carcaterra, A. (2022). Gait Optimization Method for Quadruped Locomotion. In: Lacarbonara, W., Balachandran, B., Leamy, M.J., Ma, J., Tenreiro Machado, J.A., Stepan, G. (eds) Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series. Springer, Cham. https://doi.org/10.1007/978-3-030-81166-2_39

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  • DOI: https://doi.org/10.1007/978-3-030-81166-2_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81165-5

  • Online ISBN: 978-3-030-81166-2

  • eBook Packages: EngineeringEngineering (R0)

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