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.
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
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
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
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
Dorigo M (2007) Ant colony optimization. Scholarpedia 2:1461. https://doi.org/10.4249/scholarpedia.1461
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Author information
Authors and Affiliations
Corresponding author
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
About this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-020-05515-1