Autonomous Robots

, Volume 38, Issue 4, pp 415–437 | Cite as

Pattern generation and compliant feedback control for quadrupedal dynamic trot-walking locomotion: experiments on RoboCat-1 and HyQ

  • Barkan UgurluEmail author
  • Ioannis Havoutis
  • Claudio Semini
  • Kana Kayamori
  • Darwin G. Caldwell
  • Tatsuo Narikiyo


In this paper, we introduce a method that synergistically combines an analytical pattern generator and a feedback controller frame, which are developed for the purpose of synthesizing dynamic quadrupedal trot-walking locomotion on flat and uneven surfaces. To begin with, the pattern generator analytically produces feasible and dynamically balanced joint motions in accordance with the desired trot-walking characteristics, with no empirical parameter tuning requirements. In concurrence with the pattern generation, a two-phased controller frame is constructed for closed-loop sensory feedback: (i) virtual admittance controller via force sensing, (ii) upper torso angular momentum regulation via gyro sensing. The former controller evaluates joint force errors and generates the corresponding joint displacement for a given set of virtual spring-damper couples. Together with the position constraints, these displacements are additionally fed-back to local servos for achieving compliant quadrupedal locomotion with which the position/force trade-off is addressed. The second controller, that is simultaneously used, evaluates the upper torso angular momentum rate change error using measured and reference orientation information. It then regulates the torso orientation in a dynamically consistent way as the rotational inertia is characterized. In order to validate the proposed methodology several experiments are conducted on both flat and uneven surfaces, using two robots with distinct properties; a \(\sim \)7 kg cat-sized electrically actuated quadruped (RoboCat-1), and a \(\sim \)80 kg Alpine Ibex-sized hydraulically actuated quadruped (HyQ). As a result we demonstrate continuous, repetitive, compliant and dynamically balanced trot-walking cycles in real-robot experiments, adequately confirming the effectiveness of the proposed approach.


Quadrupedal locomotion Dynamic trot-walking Active compliance Pattern generation 



In this study, the RoboCat-1 related portion is partially supported by Hitech Research Center, projects for private universities, supplied by the Ministry of Education, Culture, Sports, Science and Technology, Japan. The HyQ related portion is supported by Fondazione Istituto Italiano di Tecnologia, Genova, Italy. The authors would like to thank Takao Kawasaki, Kazuyuki Hyodo, Michihiro Kawanishi, Jesus Ortiz, Jake Goldsmith, Marco Frigero, Michele Focchi, Thiago Boaventura, Stephane Bazeille, Bilal Rehman, Hamza Khan, and the team of IIT Advanced Robotics technicians for their kind assistance and support.

Supplementary material

Supplementary material 1 (mp4 18685 KB)


  1. Barasuol, V., Buchli, J., Semini, C., Frigero, M., De Pieri, E. R., & Caldwell, D. G. (2013). A reactive controller framework for quadrupedal locomotion on challenging terrain. In IEEE International conference on robotics and automation (ICRA), Karlsruhe, Germany (pp. 2539–2546).Google Scholar
  2. Bazeille, S., Barasuol, V., Focchi, M., Havoutis, I., Frigerio, M., Buchli, J., et al. (2014). Quadruped robot trotting over irregular terrain assisted by stereo-vision. Journal of Intelligent Service Robotics, 7(2), 67–77.CrossRefGoogle Scholar
  3. Boaventura, T., Medrano-Cerda, G. A., Semini, C., Buchli, J., & Caldwell, D. G. (2013). Stability and performance of the compliance controller of the quadruped robot HyQ. In IEEE international conference on intelligent robots and systems (IROS), Tokyo, Japan (pp. 1458–1464).Google Scholar
  4. Boaventura, T., Semini, C., Buchli, J., Frigero, M., Focchi, M., & Caldwell, D. G. (2012). Dynamic torque control of a hydraulic quadruped robot. In IEEE international conference on robotics and automation (ICRA), St. Paul, US (pp. 1889–1894).Google Scholar
  5. Buschmann, T., Lohmeier, S., & Ulbrich, H. (2009). Biped walking control based on hybrid position/force control. In IEEE international conference on intelligent robots and systems (IROS), St. Louis, US (pp. 3019–3024).Google Scholar
  6. Byl, K., Shkolnik, A., Prentice, S., Roy, N., & Tedrake, R. (2009). Reliable dynamic motions for a stiff quadruped. Springer Tracks in Advanced Robotics, 54, 319–328.CrossRefGoogle Scholar
  7. Colgate, E., & Hogan, N. (1989). An analysis of contact instability in terms of passive physical equivalents. In IEEE international conference on robotics and automation (ICRA), Scottsdale, US (pp. 404–409).Google Scholar
  8. Colgate, J. E. (1994). Coupled stability of multiport systems—theory and experiments. Transactions on ASME, Journal of Dynamic Systems, Measurement, and Control, 116(3), 419–428.CrossRefzbMATHGoogle Scholar
  9. Fasse, E. (1987). Stability robustness of impedance controlled manipulators coupled to passive environments. Massachusetts Institute of Technology: Master’s Dissertation.Google Scholar
  10. Ferris, D. P., Louie, M., & Farley, C. T. (1998). Running in the real world: Adjusting leg stiffness for different surfaces. Royal Society London, 265, 989–993.CrossRefGoogle Scholar
  11. Focchi, M., Barasuol, V., Havoutis, I., Buchli, J., Semini, C., & Caldwell, D. G. (2013). Local reflex generation for obstacle negotiation in quadrupedal locomotion. In International conference on climbing and walking robots (CLAWAR), Sydney, Australia (pp. 1–8).Google Scholar
  12. Fujimoto, Y., Obata, S., & Kawamura, A. (1998). Robust bipedal walking with active interaction control between foot and ground. In IEEE international conference on robotics and automation (ICRA), Leuven, Belgium (pp. 2030–2035).Google Scholar
  13. Galloway, K. C., Clark, J. E., & Koditschek, D. E. (2013). Variable stiffness legs for robust, efficient, and stable dynamic running. ASME Journal of Mechanisms and Robotics, 5(1), 677–688.Google Scholar
  14. Havoutis, I., Ortiz, J., Bazeille, S., Barasuol, V., Semini C., & Caldwell, D.G. (2013). Onboard perception-based trotting and crawling with the hydraulic quadruped robot (HyQ). In IEEE international conference on intelligent robots and systems (IROS), Tokyo, Japan (pp. 6052–6057).Google Scholar
  15. Hutter, M., Remy, C. D., Hoepflinger, M. A., & Siegwart, R. (2013). Efficient and versatile locomotion with highly compliant legs. IEEE Transactions on Mechatronics, 18(2), 449–458.CrossRefGoogle Scholar
  16. Hyon, S.-H. (2009). Compliant terrain adaptation for biped humanoids without measuring ground surface and contact forces. IEEE Transactions on Robotics, 25(1), 677–688.Google Scholar
  17. Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K., & Hirukawa, H. (2003). Biped walking pattern generation by using preview control of zero-moment point. In IEEE international conference on robotics and automation (ICRA), Taipei, Taiwan (pp. 1620–1626).Google Scholar
  18. Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., & Schaal, S. (2011). Learning, planning and control for quadruped locomotion over challenging terrain. International Journal of Robotics Research, 30(2), 236–258.CrossRefGoogle Scholar
  19. Kim, Y.-D., Lee, B.-J., Ryu, J.-H., & Kim, J.-H. (2007). Landing force control for humanoid robot by time-domain passivity approach. IEEE Transactions on Robotics, 23(6), 1294–1301.CrossRefGoogle Scholar
  20. Kimura, H., Fukuoka, Y., & Cohen, A. H. (2007). Adaptive dynamic walking of a quadruped robot on natural ground based on biological concepts. International Journal of Robotics Research, 26(5), 475–490.CrossRefGoogle Scholar
  21. Koolen, T., de Boer, T., Rebula, J. R., Goswami, A., & Pratt, J. E. (2012). Capturability-based analysis and control of legged locomotion, part 1: Theory and application to three simple gait models. International Journal of Robotics Research, 31(9), 1094–1113.CrossRefGoogle Scholar
  22. Kurazume, R., Yoneda, K., & Hirose, S. (2002). Feedforward and feedback dynamic trot gait control for quadruped walking vehicle. Autonomous Robots, 12(2), 157–172.CrossRefzbMATHGoogle Scholar
  23. Maufroy, C., Kimura, H., & Takase, K. (2010). Integration of posture and rhythmic motion controls in quadrupedal dynamic walking using phase modulations based on leg loading/unloading. Autonomous Robots, 28(3), 331–353.CrossRefGoogle Scholar
  24. Morimoto, J., Endo, G., Nakanishi, J., & Cheng, G. (2008). A biologically inspired biped locomotion strategy for humanoid robots: Modulation of sinusoidal patterns by a coupled oscillator model. IEEE Transactions on Robotics, 24(1), 185–191.CrossRefGoogle Scholar
  25. Moro, F. L., Sproewitz, A., Tuleu, A., Vespignani, M., Tsagarakis, N. G., Ijspeert, A. J., et al. (2013). Horse-like walking, trotting, and galloping derived from kinematic motion primitives (kMPs) and their application to walk/trot transitions in a compliant quadruped robot. Biological Cybernetics, 107(3), 309–320.CrossRefMathSciNetGoogle Scholar
  26. Murakami, T., Yu, F., & Ohnishi, K. (1993). Torque sensorless control in multidegree-of-freedom manipulator. IEEE Transactions on Industrial Electronics, 40(2), 259–265.CrossRefGoogle Scholar
  27. Ott, C., Roa, M. A., & Hirzinger, G. (2011). Posture and balance control for biped robots based on contact force optimization. In IEEE international conference on humanoid robots (humanoids), Bled, Slovenia (pp. 26–32).Google Scholar
  28. Raibert, M., Blankespoor, K., Nelson, G., Playtor, R., & the Big-Dog Team (2008). BigDog, the rough-terrain quadruped robot. In The 17th world cong. The international federation automatic control, Seoul, Korea (pp. 10822–10825).Google Scholar
  29. Righetti, L., & Ijspeert, A. J. (2008). Pattern generators with sensory feedback for the control of quadruped locomotion. In IEEE international conference on robotics and automation (ICRA), Pasadena, US (pp. 819–824).Google Scholar
  30. Rutishauser, S., Sproewitz, A., Righetti, L., & Ijspeert, A. J. (2008). Passive compliant quadruped robot using central pattern generators for locomotion control. In IEEE international conference on biomedical robotics and biomechatronics (BioRob), Scottsdale, US (pp. 710–715).Google Scholar
  31. Sangok, S., Wang, A., Chuah, M. Y., Otten, D., Lang, J., & Kim S. (2013). Design principles for highly efficient quadrupeds and implementation on the MIT Cheetah robot. In Proceedings of the IEEE conference on robotics and automation Karlsruhe, Germany (pp. 3292–3297).Google Scholar
  32. Semini, C., Barasuol, V., Boaventura, T., Frigerio, M., & Buchli, J. (2013). Is active impedance the key to a breakthrough for legged robots? In IEEE international symposium on robotics research (ISRR), Singapore (pp. 1–16).Google Scholar
  33. Semini, C., Tsagarakis, N. G., Guglielmino, E., Focchi, M., Cannella, F., & Caldwell, D. G. (2011). Design of HyQ—A hydraulically and electrically actuated quadruped robot. Institute of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 225(6), 831–849.CrossRefGoogle Scholar
  34. Sproewitz, A., Tuleu, A., Vespignani, M., Ajallooeian, M., Badri, E., & Ijspeert, A. J. (2011). Towards dynamic trot gait locomotion: Design, control, and experiments with Cheetah-cub, a compliant quadruped robot. International Journal of Robotics Research, 32(8), 932–950.CrossRefGoogle Scholar
  35. Sugihara, T., & Nakamura, Y. (2009). Boundary condition relaxation method for stepwise pedipulation planning of biped robots. IEEE Transactions on Robotics, 25(3), 658–669.CrossRefGoogle Scholar
  36. Ugurlu, B., Havoutis, I., Semini, C., & Caldwell, D. G. (2013). Dynamic trot-walking with the hydraulic quadruped robot—HyQ: Analytical trajectory generation and active compliance control. In IEEE international conference on intelligent robots and systems (IROS), Tokyo, Japan (pp. 6044–6051).Google Scholar
  37. Ugurlu, B., Kotaka, K., & Narikiyo, T. (2013). Actively compliant locomotion control on rough terrain: Cyclic jumping and trotting experiments on a stiff-by-nature quadruped. In IEEE international conference on robotics and automation (ICRA), Karlsruhe, Germany (pp. 3298–3305).Google Scholar
  38. Ugurlu, B., Saglia, J. A., Tsagarakis, N. G., Morfey, S., & Caldwell, D. G. (2014). Bipedal hopping pattern generation for passively compliant humanoids: Exploiting the resonance. IEEE Transactions on Industrial Electronics, 61(10), 5431–5443.CrossRefGoogle Scholar
  39. Winkler, A., Havoutis, I., Bazeille, S., Ortiz, J., Focchi, M., Dillmann, R., Caldwell, D. G., & Semini, C. (2014). Path planning with force-based foothold adaptation and virtual model control for torque controlled quadruped robots. In IEEE international conference on robotics and automation (ICRA), Hong Kong (pp. 6476–6482).Google Scholar
  40. Yamada, Y., Nishikawa, S., Shida, K., Niiyama, R., & Kuniyoshi Y. (2011). Neural-body coupling for emergent locomotion: A musculoskeletal quadruped robot with spinobulbar model. In IEEE international conference on intelligent robots and systems (IROS), San Francisco, US (pp. 1499–1506).Google Scholar
  41. Yoneda, K., Iiyama, H., & Hirose, S. (1996). Intermittent trot gait of a quadruped walking machine dynamic stability control of an omnidirectional walk. In IEEE international conference on robotics and automation (ICRA), Minnesota, US (pp. 3002–3007).Google Scholar
  42. Zheng, Y.-F., & Hemami, H. (1985). Mathematical modeling of a robot collision with its environment. Journal of Robotic Systems, 2(3), 289–307.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Barkan Ugurlu
    • 1
    Email author
  • Ioannis Havoutis
    • 2
  • Claudio Semini
    • 2
  • Kana Kayamori
    • 3
  • Darwin G. Caldwell
    • 2
  • Tatsuo Narikiyo
    • 3
  1. 1.Department of Mechanical EngineeringOzyegin UniversityIstanbulTurkey
  2. 2.Department of Advanced RoboticsIstituto Italiano di Tecnologia (IIT)GenoaItaly
  3. 3.Department of Advanced Science and TechnologyToyota Technological InstituteNagoyaJapan

Personalised recommendations