Skip to main content
Log in

Optimization of stability of humanoid robot NAO using ant colony optimization tuned MPC controller for uneven path

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The primary conventional method for simplifying legged robots’ complex walking dynamics involves using low-dimensional models such as the linear inverted pendulum model (LIPM). This paper emphasizes utilizing the LIPM plus flywheel model (LIPPFM) for analysis of the complete dynamic motion of the humanoid robot. Inclining toward a more realistic case, the model is improvised to remove the COM’s height constraint (center of mass) and consider the effect of the upper body part using the mass of the pendulum. Furthermore, the double support phase is being discussed in the locomotion phase of the humanoid robot. MPC (model predictive control) approach has been used in this paper, which is tuned with the ACO (ant colony optimization) technique. The desired trajectory, joint angles, has been imparted to the MPC, which provides the robot’s joint motion. This joint motion has been further transferred to ACO, optimizing the step adjustment and providing an expected trajectory to walk over an uneven surface. The simulation has been carried out in an uneven environment based on ACO tuned MPC controller, and further, it has been validated using real-time experiments on humanoid robot NAO. The controller shows a reasonable degree of efficiency in both the real NAO and simulated NAO with a deviation under 5%. The comparative study among various controller shows that the proposed controller lowers the peak overshoot and the settling time. In comparison with the previously developed controller, the deviation in roll angle and pitch angle justifies the selection of the proposed controller.

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
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  • Abedinnia H, Glock CH, Brill A (2016) Computers & Operations Research New simple constructive heuristic algorithms for minimizing total flow-time in the permutation flowshop scheduling problem. Comput Oper Res 74:165–174. https://doi.org/10.1016/j.cor.2016.04.007

    Article  MathSciNet  MATH  Google Scholar 

  • Aoustin Y, Formal’sky A, Martynenko Y (2006) Stabilization of unstable equilibrium postures of a two-link pendulum using a flywheel. J Comput Syst Sci Int 45:204–211. https://doi.org/10.1134/S1064230706020043

    Article  MathSciNet  MATH  Google Scholar 

  • Blondin M-J, Sicard P (2013) ACO based controller and anti-windup tuning for motion systems with flexible transmission. In: 2013 26th IEEE Canadian conference on electrical and computer engineering (CCECE). IEEE, pp 1–4

  • Blondin M-J, Sicard P (2014) A Hybrid ACO and Nelder-Mead constrained algorithm for controller and anti-windup tuning. In: 2014 16th European conference on power electronics and applications. IEEE, pp 1–10

  • Chen G, Liu J (2019) Mobile robot path planning using ant colony algorithm and improved potential field method. Comput Intell Neurosci 2019:1–10. https://doi.org/10.1155/2019/1932812

    Article  Google Scholar 

  • de Moura Oliveira PB, Freire H, Solteiro Pires EJ (2016) Grey wolf optimization for PID controller design with prescribed robustness margins. Soft Comput 20:4243–4255. https://doi.org/10.1007/s00500-016-2291-y

    Article  Google Scholar 

  • Dorigo M (2007) Ant colony optimization. Scholarpedia 2:1461. https://doi.org/10.4249/scholarpedia.1461

    Article  Google Scholar 

  • Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B Cybern 26:29–41. https://doi.org/10.1109/3477.484436

    Article  Google Scholar 

  • Du L, Cao F (2015) Nonlinear controller design of the inverted pendulum system based on extended state observer. In: Proceedings of the 2015 international conference on automation, mechanical control and computational engineering. Atlantis Press, Paris, France, pp 1–6

  • El-Gendy EM, Saafan MM, Elksas MS et al (2020) Applying hybrid genetic–PSO technique for tuning an adaptive PID controller used in a chemical process. Soft Comput 24:3455–3474. https://doi.org/10.1007/s00500-019-04106-z

    Article  Google Scholar 

  • Faraji S, Pouya S, Atkeson CG, Ijspeert AJ (2014) Versatile and robust 3D walking with a simulated humanoid robot (Atlas): a model predictive control approach. In: 2014 IEEE international conference on robotics and automation (ICRA). IEEE, pp 1943–1950

  • Gonzalez R, Fiacchini M, Guzman JL, Alamo T (2009) Robust tube-based MPC for constrained mobile robots under slip conditions. In: Proceedings of the IEEE conference on decision and control. IEEE, pp 5985–5990

  • Kamioka T, Kaneko H, Kuroda M, et al (2017) Dynamic gait transition between walking, running and hopping for push recovery. In: 2017 IEEE-RAS 17th international conference on humanoid robotics (humanoids). IEEE, pp 1–8

  • Kasaei SM, Lau N, Pereira A, Shahri E (2017a) A reliable model-based walking engine with push recovery capability. In: 2017 IEEE international conference on autonomous robot systems and competitions (ICARSC). IEEE, pp 122–127

  • Kasaei SM, Lau N, Perira A (2017b) A reliable hierarchical omnidirectional walking engine for a bipedal robot by using the enhanced LIP plus flywheel. In: Human-Centric Robotics. WORLD SCIENTIFIC, pp 399–406

  • Kashyap AK, Pandey A (2018) Different nature-inspired techniques applied for motion planning of wheeled robot: a critical review. Int J Adv Robot Autom 3:1–10. https://doi.org/10.15226/2473-3032/3/2/00136

  • Kashyap AK, Pandey A, Chhotray A, Parhi DR (2020a) Controlled gait planning of humanoid robot NAO Based on 3D-LIPM Model. Available SSRN 3552498

  • Kashyap AK, Parhi DR, Kumar S (2020b) Dynamic stabilization of NAO humanoid robot based on whole-body control with simulated annealing. Int J Humanoid Robot 17:2050014. https://doi.org/10.1142/S0219843620500140

    Article  Google Scholar 

  • Kashyap AK, Parhi DR, Muni MK, Pandey KK (2020c) A hybrid technique for path planning of humanoid robot NAO in static and dynamic terrains. Appl Soft Comput 96:106581. https://doi.org/10.1016/j.asoc.2020.106581

    Article  Google Scholar 

  • Khatib O, Groen F (2014) Robotics research 13th international symposium

  • Kim JY, Park IW, Oh JH (2007) Walking control algorithm of biped humanoid robot on uneven and inclined floor. J Intell Robot Syst Theory Appl 48:457–484. https://doi.org/10.1007/s10846-006-9107-8

    Article  Google Scholar 

  • Krishnamoorthy D, Foss B, Skogestad S (2019) A Primal decomposition algorithm for distributed multistage scenario model predictive control. J Process Control 81:162–171. https://doi.org/10.1016/j.jprocont.2019.02.003

    Article  Google Scholar 

  • Kundu S, Parhi DR (2016) Navigation of underwater robot based on dynamically adaptive harmony search algorithm. Memetic Comput 8:125–146. https://doi.org/10.1007/s12293-016-0179-0

    Article  Google Scholar 

  • Lee D-W, Lee M-J, Kim M-S (2015) Whole body imitation of human motion with humanoid robot via ZMP stability criterion. In: 2015 IEEE-RAS 15th international conference on humanoid robots (humanoids). IEEE, pp 1003–1006

  • Li D, Cao H, Zhang X et al (2019) Model predictive control based active chatter control in milling process. Mech Syst Signal Process 128:266–281. https://doi.org/10.1016/j.ymssp.2019.03.047

    Article  Google Scholar 

  • Mandava RK, Vundavilli PR (2018) Near optimal PID controllers for the biped robot while walking on uneven terrains. Int J Autom Comput 15:689–706. https://doi.org/10.1007/s11633-018-1121-3

    Article  Google Scholar 

  • Mandava RK, Vundavilli PR (2019) An optimal PID controller for a biped robot walking on flat terrain using MCIWO algorithms. Evol Intell 12:33–48. https://doi.org/10.1007/s12065-018-0184-y

    Article  Google Scholar 

  • Mohammadi Asl R, Pourabdollah E, Salmani M (2018) Optimal fractional order PID for a robotic manipulator using colliding bodies design. Soft Comput 22:4647–4659. https://doi.org/10.1007/s00500-017-2649-9

    Article  Google Scholar 

  • Mohanty PK, Parhi DR (2014) Navigation of autonomous mobile robot using adaptive network based fuzzy inference system. J Mech Sci Technol 28:2861–2868. https://doi.org/10.1007/s12206-014-0640-2

    Article  Google Scholar 

  • Olivares M, Albertos P (2013) On the linear control of underactuated systems: The flywheel inverted pendulum. In: IEEE international conference on control and automation, ICCA. IEEE, pp 27–32

  • Omatu S, Deris S (1996) Stabilization of inverted pendulum by the genetic algorithm. IEEE Symp Emerg Technol Fact Autom ETFA 1:282–287. https://doi.org/10.1109/icsmc.1995.538481

    Article  Google Scholar 

  • Pandey A, Parhi DR (2014) MATLAB simulation for mobile robot navigation with hurdles in cluttered environment using minimum rule based fuzzy logic controller. Procedia Technol 14:28–34. https://doi.org/10.1016/j.protcy.2014.08.005

    Article  Google Scholar 

  • Pandey A, Kashyap AK, Parhi DR, Patle BK (2019) Autonomous mobile robot navigation between static and dynamic obstacles using multiple ANFIS architecture. World J Eng 16:275–286. https://doi.org/10.1108/WJE-03-2018-0092

    Article  Google Scholar 

  • Pollard NS, Hodgins JK, Riley MJ, Atkenson CG (2002) Adapting human motion for the control of a humanoid robot. Proc - IEEE Int Conf Robot Autom 2:1390–1397. https://doi.org/10.1109/ROBOT.2002.1014737

    Article  Google Scholar 

  • Pratt J, Carff J, Drakunov S, Goswami A (2006) Capture point: a step toward humanoid push recovery. In: 2006 6th IEEE-RAS international conference on humanoid robots. IEEE, pp 200–207

  • Rashid R, Perumal N, Elamvazuthi I, et al (2016) Mobile robot path planning using ant colony optimization. In: 2016 2nd IEEE international symposium on robotics and manufacturing automation (ROMA). IEEE, pp 1–6

  • Saleem O, Rizwan M, Zeb AA et al (2020) Online adaptive PID tracking control of an aero-pendulum using PSO-scaled fuzzy gain adjustment mechanism. Soft Comput 24:10629–10643. https://doi.org/10.1007/s00500-019-04568-1

    Article  Google Scholar 

  • Segovia P, Rajaoarisoa L, Nejjari F et al (2019) Model predictive control and moving horizon estimation for water level regulation in inland waterways. J Process Control 76:1–14. https://doi.org/10.1016/j.jprocont.2018.12.017

    Article  Google Scholar 

  • Shafiee-Ashtiani M, Yousefi-Koma A, Shariat-Panahi M, Khadiv M (2016) Push recovery of a humanoid robot based on model predictive control and capture point. In: 2016 4th International Conference on Robotics and Mechatronics (ICROM). IEEE, pp 433–438

  • Stephens BJ (2011) State estimation for force-controlled humanoid balance using simple models in the presence of modeling error. In: Proceedings—IEEE international conference on robotics and automation. IEEE, pp 3994–3999

  • Uriol R, Moran A (2017) Mobile robot path planning in complex environments using ant colony optimization algorithm. In: 2017 3rd international conference on control, automation and robotics (ICCAR). IEEE, pp 15–21

  • Wang F, Wang Y, Wen S, et al (2012) Nao humanoid robot gait planning based on the linear inverted pendulum. In: Proceedings of the 2012 24th Chinese control and decision conference, CCDC 2012. IEEE, pp 986–990

  • Xu Q-L, Cai M-M, Zhao L-H (2017) The robot path planning based on ant colony and particle swarm fusion algorithm. In: 2017 Chinese Automation Congress (CAC). IEEE, pp 411–415

  • Yi J, Zhu Q, Xiong R, Wu J (2016) Walking algorithm of humanoid robot on uneven terrain with terrain estimation. Int J Adv Robot Syst 13:35. https://doi.org/10.5772/62245

    Article  Google Scholar 

  • Yu S, Guo Y, Meng L et al (2018) MPC for path following problems of wheeled mobile robots. IFAC-PapersOnLine 51:247–252. https://doi.org/10.1016/j.ifacol.2018.11.021

    Article  Google Scholar 

  • Yuan K, Li Z (2018) An improved formulation for model predictive control of legged robots for gait planning and feedback control. In: 2018 IEEE/RSJ international conference on intelligent robots and systems (IROS). IEEE, pp 1–9

  • Zamparelli A, Scianca N, Lanari L, Oriolo G (2018) Humanoid gait generation on uneven ground using intrinsically stable MPC. IFAC-PapersOnLine 51:393–398. https://doi.org/10.1016/j.ifacol.2018.11.574

    Article  Google Scholar 

  • Zhao Z, Liu H, Chen H et al (2019) Kinematics-aware model predictive control for autonomous high-speed tracked vehicles under the off-road conditions. Mech Syst Signal Process 123:333–350. https://doi.org/10.1016/j.ymssp.2019.01.005

    Article  Google Scholar 

  • Zhong Q, Chen F (2016) Trajectory planning for biped robot walking on uneven terrain: taking stepping as an example. CAAI Trans Intell Technol 1:197–209. https://doi.org/10.1016/j.trit.2016.10.009

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Abhishek Kumar Kashyap.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kashyap, A.K., Parhi, D.R. Optimization of stability of humanoid robot NAO using ant colony optimization tuned MPC controller for uneven path. Soft Comput 25, 5131–5150 (2021). https://doi.org/10.1007/s00500-020-05515-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05515-1

Keywords

Navigation