GAIT GENERATION AND TRANSITION FOR BIPEDAL LOCOMOTION SYSTEM USING MORRIS-LECAR MODEL OF CENTRAL PATTERN GENERATOR

Authors

1 Rehabilitation Robotics Research Lab., Department of Mechatronics Engineering, University of Tabriz, P.O. Box 5166614761, Tabriz, Iran

2 Department of Mechatronics Engineering, University of Tabriz, P.O. Box 5166614761, Tabriz, Iran

Abstract

In this paper, we intend to improve the CPG network presented by Pinto et al. based on 4-cell model for bipedal locomotion systems. This model is composed of four coupled identical cells which internal dynamics of each one is described by the Morris-Lecar nonlinear differential equation and the couplings between the cells follow the synaptic type. We exploit an elitist non-dominated sorting genetic algorithm (NSGA II) to find the best set of coupling weights by which the phase differences become optimally close to the ones required for a primary bipedal gait. Thus, we achieve the rhythmic signals associated with four primary bipedal gaits of walk, run, two-legged jump, and two-legged hop. Also, we successfully obtain all secondary gaits corresponding to the bipedal locomotion identified by Pinto et al. from the 4-cell model, by symmetry breaking bifurcations of primary gaits. Particularly, we are able to produce the secondary gait called “hesitation walk” through transition from primary gaits of run and two-legged jump.

Keywords

Main Subjects


References
1. Semwal, V.B., Kumar, C., Mishra, P.K., and Nandi,
G.C., IEEE Transactions on Automation Science and
Engineering, 15(1), pp. 104-110 (Jan. 2018).
Semwal, V.B., Kumar, C., Mishra, P.K., and Nandi,
G.C. \Design of vector eld for di erent subphases of
gait and regeneration of gait pattern", IEEE Transactions
on Automation Science and Engineering, 15(1),
pp. 104-110 (Jan. 2018).
2. Semwal, V.B., Mondal, K., and Nandi, G.C. \Robust
and accurate feature selection for humanoid push
recovery and classi cation: deep learning approach",
Neural Computing and Applications, pp. 1-10 (2015).
3. Semwal, V.B., Katiyar, S.A., Chakraborty, R., and
Nandi, G.C. \Biologically-inspired push recovery capable
bipedal locomotion modeling through hybrid
automata", Robotics and Autonomous Systems, 70,
pp. 181-190 (2015).
4. Semwal, V.B. and Nandi, G.C. \Generation of joint
trajectories using hybrid automate-based model: A
rocking block-based approach", IEEE Sensors Journal,
16(14), pp. 5805-5816 (2016).
5. Ijspeert, A.J. \Central pattern generators for locomotion
control in animals and robots: A review", Neural
Networks, 21, pp. 642-653 (2008).
6. Wu, Q., Liu, Ch., Zhang, J., and Chen, Q. \Survey of
locomotion control of legged robots inspired by biological
concept", Sci. China. Ser. F-Inf. Sci., 52(10), pp.
1715-1729 (2009).
7. Wilson, D.M. \The central nervous control of
ight in
a locust", J. Exp. Biol., 38(47), pp. 47l-490 (1961).
8. Marder, E. and Bucher, D. \Central pattern generators
and the control of rhythmic movements", Current.
Biology., 11, pp. 986-996 (2001).
9. Guertin, P.A. \The mammalian central pattern generator
for locomotion", Brain research reviews, 62, pp.
45-56 (2009).
10. Aoi, S., Egi, Y., Sugimoto, R., Yamashita, T., Fujiki,
S., and Tsuchiya, K. \Functional roles of phase
resetting in the gait transition of a biped robot from
quadrupedal to bipedal locomotion", IEEE Transactions
on Robotics, 28(6), pp. 1244-1259 (2012).
11. Aguirre-Ollinger, G. \Exoskeleton control for lowerextremity
assistance based on adaptive frequency oscillators:
Adaptation of muscle activation and movement
frequency", Proc. IMechE. Part H: J. Engineering in
Medicine, 229(1), pp. 52-68 (2015).
3602 M.R. Sayyed Noorani et al./Scientia Iranica, Transactions D: Computer Science & ... 25 (2018) 3591{3603
12. Zhang, X. and Hashimoto, M. \Evaluation on interaction
ability of a walking robotic suit with synchronization
based control", IEEE Int. Conf. Robotics and
Biomimetics, Tianjin, China, pp. 265-27 (2010).
13. Taga, G. \A model of the neuro-musculo-skeletal
system for human locomotion; I. Emergence of basic
gait", Biological Cybernetics, 73, pp. 97-111 (1995).
14. Endo, G., Morimoto, J., Matsubara, T., Nakanishi,
J., and Cheng, G. \Learning CPG-based biped locomotion
with a policy gradient method: application
to a humanoid robot", The International Journal of
Robotics Research, 27(2), pp. 213-228 (2008).
15. Collins, J.J. and Richmond, S.A. \Hard-wired central
pattern generators for quadrupedal locomotion", Biological
Cybernetics, 71, pp. 375-385 (1994).
16. Fukuoka, Y., Kimura, H., and Cohen, A.H. \Adaptive
dynamic walking of a quadruped robot on irregular
terrain based on biological concepts", The International
Journal of Robotics Research, 22(3-4), pp. 187-
202 (2003).
17. Buchli, J. and Ijspeert, A.J. \Self-organized adaptive
legged locomotion in a compliant quadruped robot",
Autonomous Robots, 25, pp. 331-347 (2008).
18. Crespi, A., Lachat, D., Pasquier, A., and Ijspeert,
A.J. \Controlling swimming and crawling in a sh
robot using a central pattern generator", Autonomous
Robots, 25, pp. 3-13 (2008).
19. Wua, X. and Ma, S. \CPG-based control of serpentine
locomotion of a snake-like robot", Mechatronics, 20,
pp. 326-334 (2010).
20. Ryu, J-K., Chong, N.Y., You, B.J., and Christensen,
H.I. \Locomotion of snake-like robots using adaptive
neural oscillators", Intelligent Service Robotics, 3, pp.
1-10 (2010).
21. Wu, X., Teng, L., Chen, W., Ren, G., Jin, Y.
and Li, H. \CPGs with continuous adjustment of
phase di erence for locomotion control", International
Journal of Advanced Robotic Systems, 10, pp. 269-28
(2013).
22. Zhang, J., Gao, F., Han, X., Chen, X., and Han, X.
\Trot Gait Design and CPG Method for a Quadruped
Robot", Journal of Bionic Engineering, 11, pp. 18-25
(2014).
23. Liu, C., Chen, Q., and Wang, D. \CPG-inspired
workspace trajectory generation and adaptive locomotion
control for quadruped robots", IEEE Transactions
on Systems, Man, and Cybernetics-Cybernetics, 41(3),
pp. 867-880 (2011).
24. Liu, C., Chen, Q., and Wang, D. \Central Pattern
Generator inspired control for adaptive walking of
biped robots", IEEE Transactions on Systems, Man,
and Cybernetics-Systems, 43(5), pp. 1206-1215 (2013).
25. Cristiano, J., Puig, D., and Garca, M.A. \Locomotion
control of a biped robot through a feedback
cpg network", in First Iberian Robotics Conference
on Advances in Intelligent Systems and Computing,
Springer International Publishing, Switzerland, pp.
527-540 (2014).
26. Cristiano, J., Puig, D., and Garcia, M.A. \Ecient
locomotion control of biped robots on unknown sloped
surfaces with central pattern generators", Electronics
Letters, 51(3), pp. 220-229 (2015).
27. Chen, W., Ren, G., Zhang, J., and Wang, J. \Smooth
transition between di erent gaits of a hexapod robot
via a central pattern generators algorithm", J. Intell.
Robot. Syst., 67, pp. 255-270 (2012).
28. Liu, C. and Chen, Q. \Methods synthesis of central
pattern generator inspired biped walking control",
in the 2015 Chinese Intelligent Automation Conference,
Springer-Verlag, Berlin Heidelberg, pp. 371-379
(2015).
29. Kim, J.-J., Lee, J-W., and Lee, J.-J. \Central pattern
generator parameter search for a biped walking robot
using nonparametric estimation based particle swarm
optimization", International Journal of Control, Automation,
and Systems, 7(3), pp. 447-457 (2009).
30. Oliveira, M., Matos, V., Santos, C.P., and Costa,
L. \Multi-objective parameter CPG optimization for
gait generation of a biped robot", in IEEE Int. Conf.
Robotics and Automation, Karlsruhe, Germany, pp.
3130-3135 (2013).
31. Golubitsky, M., Stewart, I., Buono, P.L. and Collins,
J.J. \A modular network for legged locomotion", Physica
D, 115, pp. 56-72 (1998).
32. Buono, P.L., and Golubitsky, M. \Models of central
pattern generators for quadruped locomotion. I: Primary
gaits", Journal of Mathematical Biology, 42, pp.
291-326 (2001).
33. Pinto, M. and Golubitsky, M. \Central pattern generators
for bipedal locomotion", Journal of Mathematical
Biology, 53(3), pp. 474-489 (2006).
34. Pinto, M. and Santos, A.P. \Modelling gait transition
in two-legged animals", Communications in Nonlinear
Science and Numerical Simulation, 16(12), pp. 4625-
4631 (2011).
35. Deb, K., Agrawal, S., Pratap, A., and Meyarivan, T.
\A fast elitist non-dominated sorting genetic algorithm
for multi-objective optimization: NSGA-II", Lecture
Notes in Computer Science, 1917, pp. 849-858 (2000).
36. Konaka, A.D., Coitb, W., and Smith, A.E. \Multiobjective
optimization using genetic algorithms: A
tutorial", Reliability Engineering and System Safety,
91, pp. 992-1007 (2006).
37. Farshbaf Rashidi, S., Sayyed Noorani, M.-R., and
Shoaran, M. \Optimization of coupling weights in a
4-cell central pattern generator network for bipedal
locomotion gait generation", Modares Mechanical Engineering,
16(12), pp. 144-152 (2016) (in Persian).

Volume 25, Issue 6
Transactions on Computer Science & Engineering and Electrical Engineering (D)
November and December 2018
Pages 3591-3603
  • Receive Date: 13 May 2016
  • Revise Date: 16 January 2017
  • Accept Date: 08 April 2017