Skip to main content
Log in

Fault-tolerant gait learning and morphology optimization of a polymorphic walking robot

  • Original Paper
  • Published:
Evolving Systems Aims and scope Submit manuscript

Abstract

This paper presents experiments with a morphology-independent, life-long strategy for online learning of locomotion gaits. The experimental platform is a quadruped robot assembled from the LocoKit modular robotic construction kit. The learning strategy applies a stochastic optimization algorithm to optimize eight open parameters of a central pattern generator based gait implementation. We observe that the strategy converges in roughly ten minutes to gaits of similar or higher velocity than a manually designed gait and that the strategy readapts in the event of failed actuators. We also optimize offline the reachable space of a foot based on a reference design but finds that the reality gap hardens the successfully transference to the physical robot. To address this limitation, in future work we plan to study co-learning of morphological and control parameters directly on physical robots.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Bongard J (2002) Evolving modular genetic regulatory networks. In: Proceedings of the congress on evolutionary computation (CEC), IEEE Computer Society, Washington, DC, CEC ’02, pp 1872–1877

  • Bongard J, Zykov V, Lipson H (2006) Resilient machines through continuous self-modeling. Science 314(5802):1118–1121

    Article  Google Scholar 

  • Braitenberg V (1986) Vehicles: Experiments in synthetic psychology. MIT press, Cambridge

  • Brooks RA (1992) Artificial life and real robots. In: Toward a practice of autonomous systems: proceedings of the first european conference on artificial life. Cambridge, pp 3–10

  • Christensen DJ, Bordignon M, Schultz UP, Shaikh D, Stoy K (2008a) Morphology independent learning in modular robots. In: Proceedings of international symposium on distributed autonomous robotic systems 8 (DARS 2008), pp 379–391

  • Christensen DJ, Schultz UP, Brandt D, Stoy K (2008b) A unified simulator for self-reconfigurable robots. In: Proceedings of IEEE/RSJ international conference on intelligent robots and systems

  • Christensen DJ, Schultz UP, Stoy K (2010a) A distributed strategy for gait adaptation in modular robots. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), pp 2765–2770

  • Christensen DJ, Sproewitz A, Ijspeert AJ (2010b) Distributed online learning of central pattern generators in modular robots. In: Proceedings of the 11th international conference on simulation of adaptive behavior (SAB2010). Paris, pp 402–412

  • Christensen DJ, Schultz UP, Moghadam M (2011) The assemble and animate control framework for modular reconfigurable robots. In: Proceedings of the IROS workshop on reconfigurable modular robotics: challenges of mechatronic and Bio-Chemo-Hybrid Systems

  • Christensen DJ, Larsen JC, Stoy K (2012) Adaptive strategy for online gait learning evaluated on the polymorphic robotic locokit. In: Proceedings of the IEEE conference on evolving and adaptive intelligent systems (EAIS)

  • Crespi A, Ijspeert AJ (2006) AmphiBot II: An Amphibious Snake Robot that Crawls and Swims using a Central Pattern Generator. In: Proceedings of the 9th international conference on climbing and walking robots (CLAWAR 2006), pp 19–27

  • Duff D, Yim M, Roufas K (2001) Evolution of polybot: A modular reconfigurable robot. In: Proceedings of harmonic drive international symposium, Nagano

  • Fitch R, Rus D, Vona M (2000) A basis for self-repair using crystalline modules. In: Proceedings, intelligent autonomous systems (IAS-6), Venice

  • Fukuda T, Nakagawa S (1988) Dynamically reconfigurable robotic system. In: Proceedings of the IEEE international conference on robotics & automation (ICRA’88), pp 1581–1586

  • Groß R, Bonani M, Mondada F, Dorigo M (2006) Autonomous self-assembly in a swarm-bot. In: Proceedings of the 3rd international symposium on autonomous minirobots for research and edutainment (AMiRE 2005), Springer, Berlin, pp 314–322

  • Ijspeert AJ (2008) Central pattern generators for locomotion control in animals and robots: a review. Neural Netw 21(4):642–653

    Article  Google Scholar 

  • Jakobi N (1998) Running across the reality gap: Octopod locomotion evolved in a minimal simulation. In: Evolutionary Robotics, Springer, Berlin, pp 39–58

  • Jansen T (2007) Theo Jansen: The Great Pretender. OIO Publishers, New Zealand

  • Kamimura A, Kurokawa H, Yoshida E, Murata S, Tomita K, Kokaji S (2005) Automatic locomotion design and experiments for a modular robotic system. IEEE/ASME Trans Mech 10(3):314–325

    Article  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings. IEEE international conference on neural networks, 1995. IEEE 4:1942–1948

  • van den Kieboom J (2009) Biped locomotion and stability a practical approach. Master’s thesis, University of Groningen, The Netherlands

  • Kimura H, Akiyama S, Sakurama K (1999) Realization of dynamic walking and running of the quadruped using neural oscillator. Auton Robot 7(3):247–258

    Article  Google Scholar 

  • Kohl N, Stone P (2004) Machine learning for fast quadrupedal locomotion. In: The Nineteenth National Conference on Artificial Intelligence, pp 611–616

  • Lappe M, Frenz H (2009) Visual estimation of travel distance during walking. Exp Brain Res 199(3):369–375

    Article  Google Scholar 

  • Larsen J, Garcia R, Stoy K (2010) Increased versatility of modular robots through layered heterogeneity. In: Proceedings of the ICRA Workshop on Modular Robots, State of the Art, Anchorage, Alaska, pp 24–29

  • Larsen JC, Brandt D, Stoy K (2012) Locokit: A robot construction kit for studying and developing functional morphologies. In: Proceedings of 12th international conference on simulation of adaptive behavior (SAB 2012), Odense, Denmark, Lecture Notes in Computer Science, vol 7426, pp 12–22

  • Lipson H, Pollack JB (2000) Automatic design and manufacture of robotic lifeforms. Nature 406:974–978

    Article  Google Scholar 

  • Maes P, Brooks RA (1990) Learning to coordinate behaviors. In: National conference on artificial intelligence, pp 796–802

  • Mahdavi SH, Bentley PJ (2003) An evolutionary approach to damage recovery of robot motion with muscles. In: Seventh european conference on artificial life (ECAL03). Springer, Berlin, pp 248–255

  • Marbach D, Ijspeert AJ (2004) Co-evolution of configuration and control for homogenous modular robots. In: Proc., 8th international conference on intelligent autonomous systems, Amsterdam, pp 712–719

  • Marbach D, Ijspeert AJ (2005) Online Optimization of Modular Robot Locomotion. In: Proceedings of the IEEE international conference on mechatronics and automation (ICMA 2005), pp 248–253

  • Mataric M, Cliff D (1996) Challenges in evolving controllers for physical robots. Robot Auton Sys 19(1):67 – 83

    Article  Google Scholar 

  • Morimoto J, Doya K (2001) Acquisition of stand-up behavior by a real robot using hierarchical reinforcement learning. Robot Auton Sys 36(1):37–51

    Article  MATH  Google Scholar 

  • Murata S, Kurokawa H (2012) Self-organizing robots. Springer, Berlin

  • Pfeifer R, Lungarella M, Iida F (2007) Self-organization, embodiment, and biologically inspired robotics. Science 318(5853):1088–1093

    Article  Google Scholar 

  • Pouya S, van den Kieboom J, Spröwitz A, Ijspeert AJ (2010) Automatic gait generation in modular robots: "to oscillate or to rotate; that is the question". In: Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Taipei, pp 514–520

  • Righetti L, Ijspeert A (2006) Programmable central pattern generators: an application to biped locomotion control. In: Proceedings 2006 IEEE international conference on robotics and automation (ICRA), pp 1585–1590. doi:10.1109/ROBOT.2006.1641933

  • Silva MF, Machado JT (2012) A literature review on the optimization of legged robots. J Vib Contr 18(12):1753–1767

    Article  Google Scholar 

  • Sims K (1994) Evolving 3d morphology and behavior by competition. In: Brooks R, Maes P (eds) Proceedings of the artificial life IV. MIT Press, Cambridge, pp 28–39

  • Spall JC (1992) Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans Automat Contr 37(3):332–341

    Article  MATH  MathSciNet  Google Scholar 

  • Sproewitz A, Moeckel R, Maye J, Ijspeert AJ (2008) Learning to move in modular robots using central pattern generators and online optimization. Int J Rob Res 27(3-4):423–443

    Article  Google Scholar 

  • Stoy K, Nagpal R (2004) Self-repair through scale independent self-reconfiguration. In: Proceedings of IEEE/RSJ international conference on robots and systems (IROS). Sendai, pp 2062–2067

  • Stoy K, Lyder A, Garcia R, Christensen DJ (2007) Hierarchical robots. In: Proceedings of the of the IROS workshop on self-reconfigurable modular robot, San Diego

  • Stoy K, Brandt D, Christensen DJ (2010) Self-Reconfigurable Robots: An Introduction. Intelligent Robotics and Autonomous Agents series. MIT Press, Cambridge

  • Taga G, Yamaguchi Y, Shimizu H (1991) Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment. Biol Cybern 65:147–159. doi:10.1007/BF00198086

    Google Scholar 

  • Warren W, Kay B, Zosh W, Duchon A, Sahuc S (2001) Optic flow is used to control human walking. Nat Neurosci 4(2):213

    Google Scholar 

  • Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1(1):67–82

    Article  Google Scholar 

  • Yim M, Shen WM, Salemi B, Rus D, Moll M, Lipson H, Klavins E (2007a) Modular self-reconfigurable robot systems: Challenges and opportunities for the future. IEEE Robot Automat Mag 14(1):43–52

    Article  Google Scholar 

  • Yim M, Shirmohammadi B, Sastra J, Park M, Dugan M, Taylor CJ (2007b) Towards robotic self-reassembly after explosion. In: Video Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS), San Diego

  • Yoshida E, Murata S, Tomita K, Kurokawa H, Kokaji S (1999) An experimental study on a self-repairing modular machine. Robot Auton Sys 29:79–89

    Article  Google Scholar 

  • Zahadat P, Christensen DJ, Schultz UP, Katebi SD, Stoy K (2010) Fractal gene regulatory networks for robust locomotion control of modular robots. In: Proceedings of the 11th international conference on simulation of adaptive behavior (SAB2010). Paris

  • Zahadat P, Schmickl T, Crailsheim K (2012) Evolving reactive controller for a modular robot: Benefits of the property of state-switching in fractal gene regulatory networks. From Animals to Animats, vol 12, pp 209–218

Download references

Acknowledgments

This work was performed as part of the “Locomorph” project funded by the EU’s Seventh Framework Programme (Future Emerging Technologies, Embodied Intelligence) and as part of the “Assemble and Animate” project funded by the Danish Council for Independent Research.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David Johan Christensen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Christensen, D.J., Larsen, J.C. & Stoy, K. Fault-tolerant gait learning and morphology optimization of a polymorphic walking robot. Evolving Systems 5, 21–32 (2014). https://doi.org/10.1007/s12530-013-9088-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12530-013-9088-3

Keywords

Navigation