Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-21T18:33:34.920Z Has data issue: false hasContentIssue false

A review on gait generation of the biped robot on various terrains

Published online by Cambridge University Press:  15 February 2023

Moh Shahid Khan*
Affiliation:
Department of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal 462003, India
Ravi Kumar Mandava
Affiliation:
Department of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal 462003, India
*
*Corresponding author. E-mail: ershahid20@gmail.com

Abstract

Day by day, biped robots’ usage is increasing enormously in all industrial and non-industrial applications due to their ability to move in any unstructured environment compared to wheeled robots. Keeping this in mind, worldwide, many researchers are working on various aspects of biped robots, such as gait generation, dynamic balance margin, and the design of controllers. The main aim of this review article is to discuss the main challenges encountered in the biped gait generation and design of various controllers while moving on different terrain conditions such as flat, ascending and descending slopes or stairs, avoiding obstacles/ditches, uneven terrain, and an unknown environment. As per the authors’ knowledge, no single study has been carried out in one place related to the gait generation and design of controllers for each joint of the biped robot on various terrains. This review will help researchers working in this field better understand the concepts of gait generation, dynamic balance margin, and the design of controllers while moving on various terrains. Moreover, the current article will also cover the different soft computing techniques used to tune the gains of the controllers. In this article, the authors have reviewed a vast compilation of research work on the gait generation of the biped robot on various terrains. Further, the authors have proposed taxonomies on various design issues identified while generating the gait in different aspects. The authors reviewed approximately 296 articles and discovered that all researchers attempted to generate the dynamically balanced biped gait on various terrains.

Type
Review Article
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Hobon, M., De-León-Gómez, V., Abba, G., Aoustin, Y. and Chevallereau, C., “Feasible speeds for two optimal periodic walking gaits of a planar biped robot,” Robotica 40(2), 126 (2021). doi: 10.1017/S0263574721000631.Google Scholar
Vukobratović, M. K., “Contribution to the study of anthropomorphic systems,” Kybernetika 8(5), 404418 (1972).Google Scholar
Vukobratović, M. and Stepanenko, J., “On the stability of anthropomorphic systems,” Math. Biosci. 15(1-2), 137 (1972). doi: 10.1016/0025-5564(72)90061-2.CrossRefGoogle Scholar
Seo, Y.-J. and Yoon, Y.-S., “Design of a robust dynamic gait of the biped using the concept of dynamic stability margin,” Robotica 13(5), 461468 (1995). doi: 10.1017/S0263574700018294.CrossRefGoogle Scholar
Vukobratović, M. and Borovac, B., “Zero-moment point—thirty five years of its life,” Int. J. Hum. Robot. 1(01), 157173 (2004).10.1142/S0219843604000083CrossRefGoogle Scholar
Hobbelen, D. G. E. and Wisse, M. Limit cycle walking In: Humanoid Robotics (M. Hackel ed.),  (I-Tech Education and Publishing, Vienna, Austria, 2007) pp. 277–294.Google Scholar
Huang, Q. and Ono, K., “Energy-Efficient Walking for Biped Robot Using Self-Excited Mechanism and Optimal Trajectory Planning,” In: Humanoid Robots: New Developments (2007).Google Scholar
Kajita, S., F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi and H. Hirukawa, “Biped Walking Pattern Generation by Using Preview Control of Zero-Moment Point,” IEEE International Conference on Robotics and Automation. IEEE ICRA 2003 (2003) pp. 16201626. doi: 10.1109/ROBOT.2003.1241826.CrossRefGoogle Scholar
Vundavilli, P. R. and Pratihar, D. K., “Gait Planning of Biped Robots Using Soft Computing: An Attempt to Incorporate Intelligence,” In: Intelligent Autonomous Systems: Foundations and Applications (Pratihar, D. K. and Jain, eds.), L. C. (Springer Berlin Heidelberg, Berlin, Heidelberg, 2010) pp. 5785. doi: 10.1007/978-3-642-11676-6_4.CrossRefGoogle Scholar
Zheng, Y. F., “A Neural Gait Synthesizer for Autonomous Biped Robots,” IEEE International Workshop on Intelligent Robots and Systems, Towards a New Frontier of Applications (1990) pp. 601608. doi: 10.1109/IROS.1990.262457.CrossRefGoogle Scholar
Yin, Y. and Hosoe, S.,“ Mixed Logic Dynamical Modeling and on Line Optimal Control of Biped Robot,” 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (2006) pp. 58955900.Google Scholar
Azevedo, C., Poignet, P. and Espiau, B., “On line optimal control for biped robots,” IFAC Proc. 35(1), 199204 (2002). doi: 10.3182/20020721-6-ES-1901.00845.CrossRefGoogle Scholar
Wieber, P.-B., “ Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations,” 2006 6th IEEE-RAS International Conference on Humanoid Robots (2006) pp. 137142.Google Scholar
Pratt, J. E. and Tedrake, R., “Velocity-based Stability Margins for Fast Bipedal Walking,” In: Fast Motions in Biomechanics and Robotics (Springer, 2006) pp. 299324.10.1007/978-3-540-36119-0_14CrossRefGoogle Scholar
Joe, H.-M. and Oh, J.-H., “Balance recovery through model predictive control based on capture point dynamics for biped walking robot,” Rob. Auton. Syst. 105, 110 (2018). doi: 10.1016/j.robot.2018.03.004.CrossRefGoogle Scholar
Pratt, J., Carff, J., Drakunov, S. and Goswami, A., “ Capture Point: A Step Toward Humanoid Push Recovery,” 2006 6th IEEE-RAS International Conference on Humanoid Robots (2006) pp. 200207.Google Scholar
Wight, D. L., Kubica, E. G. and Wang, D. W. L., “Introduction of the foot placement estimator: A dynamic measure of balance for bipedal robotics,” J. Comput. Nonlinear Dyn. 3(1) (2008).Google Scholar
Erbatur, K., Okazaki, A., Obiya, K., Takahashi, T. and Kawamura, A., “ A Study on the Zero Moment Point Measurement for Biped Walking Robots ,” 7th International Workshop on Advanced Motion Control. Proceedings (Cat. No. 02TH8623) (2002) pp. 431436.Google Scholar
Vundavilli, P. R., Sahu, S. K. and Pratihar, D. K., “Dynamically balanced ascending and descending gaits of a two-legged robot,” Int. J. Hum. Robot. 04(04), 717751 (2007). doi: 10.1142/S0219843607001266.CrossRefGoogle Scholar
Vundavilli, P. R., Sahu, S. K. and Pratihar, D. K., “Online dynamically balanced ascending and descending gait generations of a biped robot using soft computing,” Int. J. Hum. Robot. 04(04), 777814 (2007). doi: 10.1142/S0219843607001254.CrossRefGoogle Scholar
Vundavilli, P. R. and Pratihar, D. K., “Inverse dynamics learned gait planner for a two-legged robot moving on uneven terrains using neural networks,” Int. J. Adv. Intell. Paradig. 1(1), 80109 (2008).Google Scholar
Dekker, M. H. P., “Zero-moment point method for stable biped walking,” Eindhoven Univ. Technol. 2009, 1–15 (2009).Google Scholar
Goswami, A., “Postural stability of biped robots and the foot-rotation indicator (FRI) point,” Int. J. Rob. Res. 18(6), 523533 (1999). doi: 10.1177/02783649922066376.CrossRefGoogle Scholar
Cannon, R. H. Dynamics of Physical Systems (Courier Corporation, 2003).Google Scholar
Schaefer, J. F. On the Bounded Control of Some Unstable Mechanical Systems (Stanford University, 1965).Google Scholar
Xie, H., Zhao, X., Sun, Q., Yang, K. and Li, F., “A new virtual-real gravity compensated inverted pendulum model and ADAMS simulation for biped robot with heterogeneous legs,” J. Mech. Sci. Technol. 34(1), 401412 (2020). doi: 10.1007/s12206-019-1239-4.CrossRefGoogle Scholar
Hemami, H., Weimer, F. and Koozekanani, S., “Some aspects of the inverted pendulum problem for modeling of locomotion systems,” IEEE Trans. Autom. Control 18(6), 658661 (1973).CrossRefGoogle Scholar
Gubina, F., Hemami, H. and McGhee, R. B., “On the dynamic stability of biped locomotion,” IEEE Trans. Biomed. Eng. 21(2), 102108 (1974). doi: 10.1109/TBME.1974.324294.CrossRefGoogle ScholarPubMed
Miyazaki, F. and Arimoto, S., “A control theoretic study on dynamical biped locomotion,” J. Dyn. Syst. Meas. Control 102(4), 233239 (1980). doi: 10.1115/1.3149608.CrossRefGoogle Scholar
Sangwan, V., Taneja, A. and Mukherjee, S., “Design of a robust self-excited biped walking mechanism,” Mech. Mach. Theory 39(12), 13851397 (2004). doi: 10.1016/j.mechmachtheory.2004.05.023.CrossRefGoogle Scholar
van Zutven, P., Kostić, D. and Nijmeijer, H., “ On the Stability of Bipedal Walking ,” International Conference on Simulation, Modeling, and Programming for Autonomous Robots (2010) pp. 521532.Google Scholar
Chevallereau, C. and Aoustin, Y., “Optimal reference trajectories for walking and running of a biped robot,” Robotica 19(5), 557569 (2001).CrossRefGoogle Scholar
Westervelt, E. R. and Grizzle, J. W., “ Design of Asymptotically Stable Walking for a 5-Link Planar Biped Walker via Optimization,” Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No. 02CH37292), vol. 3 (2002) pp. 31173122.Google Scholar
Chevallereau, C., Formal’sky, A. and Djoudi, D., “Tracking a joint path for the walk of an underactuated biped,” Robotica 22(1), 1528 (2004).CrossRefGoogle Scholar
Wang, K., Tobajas, P. T., Liu, J., Geng, T., Qian, Z. and Ren, L., “Towards a 3D passive dynamic walker to study ankle and toe functions during walking motion,” Rob. Auton. Syst. 115, 4960 (2019). doi: 10.1016/j.robot.2019.02.010.CrossRefGoogle Scholar
Goswami, A., Thuilot, B. and Espiau, B., Compass-Like Biped Robot Part I: Stability and Bifurcation of Passive Gaits (1996). INRIA, Jun. 1996. [Online]. Available at: https://hal.inria.fr/inria-00073701.Google Scholar
Goswami, A., Espiau, B. and Keramane, A., “Limit cycles in a passive compass gait biped and passivity-mimicking control laws,” Auton. Robots 4(3), 273286 (1997).CrossRefGoogle Scholar
Spong, M. W. and Bullo, F., “Controlled symmetries and passive walking,” IFAC Proc. 35(1), 557562 (2002).CrossRefGoogle Scholar
Goswami, A., Thuilot, B. and Espiau, B., “A study of the passive gait of a compass-Like biped robot: Symmetry and chaos,” Int. J. Rob. Res. 17(12), 12821301 (1998). doi: 10.1177/027836499801701202.CrossRefGoogle Scholar
Suzuki, S. and Furuta, K., “Enhancement of stabilization for passive walking by chaos control approach,” IFAC Proc. 35(1), 133138 (2002). doi: 10.3182/20020721-6-ES-1901.00103.CrossRefGoogle Scholar
Zheng, X.-D. and Wang, Q., “LCP method for a planar passive dynamic walker based on an event-driven scheme,” Acta Mech. Sin. 34(3), 578588 (2018). doi: 10.1007/s10409-018-0749-0.CrossRefGoogle Scholar
Vanderborght, B., Van Ham, R., Verrelst, B., Van Damme, M. and Lefeber, D., “Overview of the lucy project: Dynamic stabilization of a biped powered by pneumatic artificial muscles,” Adv. Robot. 22(10), 10271051 (2008).CrossRefGoogle Scholar
Matsuoka, K., “Mechanisms of frequency and pattern control in the neural rhythm generators,” Biol Cybern. 56(5), 345353 (1987).CrossRefGoogle ScholarPubMed
Pandy, M. G., Anderson, F. C. and Hull, D. G., “A parameter optimization approach for the optimal control of large-scale musculoskeletal systems,” J. Biomech. Eng. 114(4), 450460 (1992).CrossRefGoogle ScholarPubMed
Zielińska, T., “Coupled oscillators utilised as gait rhythm generators of a two-legged walking machine,” Biol. Cybern. 74(3), 263273 (1996).CrossRefGoogle ScholarPubMed
Or, J. and Takanishi, A., “ A Biologically Inspired CPG-ZMP Control System for the Real-Time Balance of a Single-Legged Belly Dancing Robot ,” 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)(IEEE Cat. No. 04CH37566), vol. 1 (2004) pp. 931936.Google Scholar
Al-Shuka, H. F. N., Allmendinger, F., Corves, B. and Zhu, W.-H., “Modeling, stability and walking pattern generators of biped robots: a review,” Robotica 32(6), 907934 (2014).CrossRefGoogle Scholar
Chevallereau, C., Bessonnet, G., Abba, G. and Aoustin, Y. Bipedal Robots: Modeling, Design and Walking Synthesis (John Wiley & Sons, 2013).Google Scholar
Shih, C.-L. and Gruver, W. A., “Control of a biped robot in the double-support phase,” IEEE Trans. Syst. Man. Cybern. 22(4), 729735 (1992).CrossRefGoogle Scholar
Sano, A. and Furusho, J., “ Control of Torque Distribution for the BLR-G2 Biped Robot,” Fifth International Conference on Advanced Robotics ’Robots in Unstructured Environments, vol. 1 (1991) pp. 729734. doi: 10.1109/ICAR.1991.240686.CrossRefGoogle Scholar
Choi, M. H. and Lee, B. H., “ A Real Time Optimal Load Distribution for Multiple Cooperating Robots,” Proceedings of 1995 IEEE International Conference on Robotics and Automation, vol.1 (1995) pp. 12111216.Google Scholar
Sonoda, N., Murakami, T. and Ohnishi, K., “ An Approach to Biped Robot Control Utilized Redundancy in Double Support Phase ,” Proceedings of the IECON’97 23rd International Conference on Industrial Electronics, Control, and Instrumentation (Cat. No. 97CH36066), vol. 3 (1997) pp. 13321336.Google Scholar
Zhu, W.-H.. Virtual Decomposition Control: Toward Hyper Degrees of Freedom Robots, vol. 60 (Springer Science & Business Media, 2010).10.1007/978-3-642-10724-5CrossRefGoogle Scholar
Duindam, V. and Stramigioli, S., “Port-based control of a compass-gait bipedal robot,” IFAC Proc. 38(1), 471476 (2005). doi: 10.3182/20050703-6-CZ-1902.00733.CrossRefGoogle Scholar
Duindam, V. and Stramigioli, S., Modeling and Control for Efficient Bipedal Walking Robots: A Port-Based Approach, vol. 53 (Springer, 2008).Google Scholar
Sangwan, V. and Agrawal, S. K., “Differentially flat design of bipeds ensuring limit cycles,” IEEE/ASME Trans. Mech. 14(6), 647657 (2009).10.1109/TMECH.2009.2033593CrossRefGoogle Scholar
Westervelt, E. R., Grizzle, J. W. and Koditschek, D. E., “Hybrid zero dynamics of planar biped walkers,” IEEE Trans. Autom. Control 48(1), 4256 (2003).CrossRefGoogle Scholar
Chevallereau, C., “Time-scaling control for an underactuated biped robot,” IEEE Trans. Robot. Autom. 19(2), 362368 (2003).CrossRefGoogle Scholar
Raibert, M., Tzafestas, S. and Tzafestas, C., “ Comparative Simulation Study of Three Control Techniques Applied to a Biped Robot,” Proceedings of IEEE Systems Man and Cybernetics Conference-SMC, vol.1 (1993) pp. 494502.Google Scholar
Park, I., Kim, J. and Oh, J., “Online Biped Walking Pattern Generation for Humanoid Robot KHR-3(KAIST Humanoid Robot - 3: HUBO),” 2006 6th IEEE-RAS International Conference on Humanoid Robots (2006) pp. 398403. doi: 10.1109/ICHR.2006.321303.CrossRefGoogle Scholar
Vukobratovic, M. and Juricic, D., “Contribution to the synthesis of biped gait,” IEEE Trans. Biomed. Eng. 16(1), 16 (1969). doi: 10.1109/TBME.1969.4502596.CrossRefGoogle Scholar
Tzafestas, S., Raibert, M. and Tzafestas, C., “Robust sliding-mode control applied to a 5-link biped robot,” J. Intell. Robot. Syst. 15(1), 67133 (1996). doi: 10.1007/BF00435728.CrossRefGoogle Scholar
Peca, M., Sojka, M. and Hanzálek, Z., “SPEJBL – The biped walking robot,” IFAC Proc. 40(22), 6370 (2007). doi: 10.3182/20071107-3-FR-3907.00010.CrossRefGoogle Scholar
Mehmeti, X., “Adaptive PID controller design for joints of humanoid robot,” IFAC-PapersOnLine 52(25), 110112 (2019). doi: 10.1016/j.ifacol.2019.12.456.CrossRefGoogle Scholar
Kolathaya, S., “Local stability of PD controlled bipedal walking robots,” Automatica 114, 108841 (2020). doi: 10.1016/j.automatica.2020.108841.CrossRefGoogle Scholar
Song, Z., Yi, J., Zhao, D. and Li, X., “A computed torque controller for uncertain robotic manipulator systems: Fuzzy approach,” Fuzzy Sets Syst. 154(2), 208226 (2005). doi: 10.1016/j.fss.2005.03.007.CrossRefGoogle Scholar
Markiewicz, B. R., Analysis of the Computed-Torque Drive Method and Comparision with the Conventional Position Servo for a Computer-Controlled Manipulator (1973). p. Technical Memorandum.Google Scholar
Middletone, R. H. and Goodwin, G. C., “Adaptive Computed Torque Control for Rigid Link Manipulators,” 1986 25th IEEE Conference on Decision and Control (1986) pp. 6873.Google Scholar
Spong, M. W. and Vidyasagar, M. Robot Dynamics and Control (John Wiley & Sons, 2008).Google Scholar
Piltan, F., Mirzaei, M., Shahriari, F., Nazari, I. and Emamzadeh, S., “Design baseline computed torque controller,” Int. J. Eng. 6(3), 129141 (2012).Google Scholar
Kurfess, T. R.. Robotics and Automation Handbook, vol. 414 (CRC press Boca, Raton, FL, 2005).Google Scholar
Siciliano, B., Khatib, O. and Kröger, T. Springer Handbook of Robotics, vol. 200 (Springer, 2008).CrossRefGoogle Scholar
Lewis, F. L., Jagannathan, S. and Yeşildirek, A., “Neural Network Control of Robot Arms and Nonlinear Systems,” In: Neural Systems for Control (Elsevier, 1997) pp. 161211.CrossRefGoogle Scholar
Albus, J. S., A new approach to manipulator control: The cerebellar model articulation controller (CMAC) (1975).CrossRefGoogle Scholar
Lin, C.-M. and Chen, T.-Y., “Self-organizing CMAC control for a class of MIMO uncertain nonlinear systems,” IEEE Trans. Neural Networks 20(9), 13771384 (2009).CrossRefGoogle ScholarPubMed
Guan, J., Hong, S., Kang, S., Zeng, Y., Sun, Y. and Lin, C.-M., “Robust adaptive recurrent cerebellar model neural network for non-linear system based on GPSO,” Front. Neurosci. 13, 390 (2019) https://doi.org/10.3389/fnins.2019.00390.CrossRefGoogle ScholarPubMed
Zadeh, L. A., “Fuzzy sets,” Inf. Control 8(3), 338353 (1965). doi: 10.1016/S0019-9958(65)90241-X.CrossRefGoogle Scholar
Ahmadian, M., “Active Control of Vehicle Vibration,” In: V. S. B. T.-E. of Braun (Elsevier, Oxford, 2001) pp. 3745, doi: 10.1006/rwvb.2001.0193.Google Scholar
Hogan, N., “Impedance Control: An Approach to Manipulation,” 1984 American Control Conference (1984) pp. 304313.Google Scholar
Hogan, N., Impedance control: An approach to manipulation: Part II—Implementation (1985).CrossRefGoogle Scholar
Hogan, N. and Buerger, S. P., “Impedance and Interaction Control,” In: Robotics and Automation Handbook (CRC Press, 2018) pp. 375398.Google Scholar
Gatti, P. L. Applied Structural and Mechanical Vibrations: Theory, Methods and Measuring Instrumentation (CRC Press, 1999).CrossRefGoogle Scholar
Sabanovic, A. and Ohnishi, K. Motion Control Systems (John Wiley & Sons, 2011).CrossRefGoogle Scholar
Lee, E. B. and Markus, L., Foundations of Optimal Control Theory (Minnesota Univ Minneapolis Center For Control Sciences, 1967).Google Scholar
García, C. E., Prett, D. M. and Morari, M., “Model predictive control: Theory and practice—A survey,” Automatica 25(3), 335348 (1989). doi: 10.1016/0005-1098(89)90002-2.CrossRefGoogle Scholar
Magni, L. and Scattolini, R., “An overview of nonlinear model predictive control,” Lect. Notes Control Inf. Sci. 402(4), 107117 (2010). doi: 10.1007/978-1-84996-071-7_7.Google Scholar
Richalet, J., “Industrial applications of model based predictive control,” Automatica 29(5), 12511274 (1993).CrossRefGoogle Scholar
Abu-Ayyad, M. and Dubay, R., “Real-time comparison of a number of predictive controllers,” ISA Trans. 46(3), 411418 (2007).CrossRefGoogle ScholarPubMed
Ren, Y. M., M. S. Alhajeri, J. Luo, S. Chen, F. Abdullah, Z. Wu and P. D. Christofides, “A tutorial review of neural network modeling approaches for model predictive control,” Comput. Chem. Eng. 165, 107956 (2022). doi: 10.1016/j.compchemeng.2022.107956.CrossRefGoogle Scholar
Mandava, R. K. and Vundavilli, P. R., “Design and development of an adaptive-torque-based proportional-integral-derivative controller for a two-legged robot,” Soft Comput. 25(16), 1095310968 (2021). doi: 10.1007/s00500-021-05811-4.CrossRefGoogle Scholar
Golliday, C. L. Toward Development of Biped Locomotion Controls: Planar Motion Control of the Kneeless Biped Standing and Walking Gaits (The Ohio State University, 1975).Google Scholar
Hemami, H. and Golliday, C. L., “The inverted pendulum and biped stability,” Math. Biosci. 34(1-2), 95110 (1977). doi: 10.1016/0025-5564(77)90038-4.CrossRefGoogle Scholar
Miura, H. and Shimoyama, I., “Dynamic walk of a biped,” Int. J. Rob. Res. 3(2), 6074 (1984). doi: 10.1177/027836498400300206.CrossRefGoogle Scholar
Hürmüzlü, Y. and Moskowitz, G. D., “The role of impact in the stability of bipedal locomotion,” Dyn. Stab. Syst. 1(3), 217234 (1986). doi: 10.1080/02681118608806015.Google Scholar
Furusho, J. and Masubuchi, M., “A theoretically motivated reduced order model for the control of dynamic biped locomotion,” J. Dyn. Syst. Meas. Control 109(2), 155163 (1987). doi: 10.1115/1.3143833.CrossRefGoogle Scholar
Kajita, S. and Tani, K., “Study of Dynamic Biped Locomotion on Rugged Terrain-Theory and Basic Experiment,” Fifth International Conference on Advanced Robotics ’Robots in Unstructured Environments, vol. 1 (1991) pp. 741746. doi: 10.1109/ICAR.1991.240688.CrossRefGoogle Scholar
Kajita, S. and Tani, K., “ Study of Dynamic Biped Locomotion on Rugged Terrain-Derivation and Application of the Linear Inverted Pendulum Mode,” 1991 IEEE International Conference on Robotics and Automation Proceedings, vol. 2 (1991) pp. 14051411. doi: 10.1109/ROBOT.1991.131811,CrossRefGoogle Scholar
Furusho, J. and Sano, A., “Development of Biped Robot,” In: Advances in Psychology, vol. 78 (Elsevier, 1991) pp. 277303. [Online]. Available at: https://linkinghub.elsevier.com/retrieve/pii/S0166411508607463 Google Scholar
Kurcmatsu, Y., Katayama, O., Iwata, M. and Kitamura, S., “Autonomous Trajectory Generation of a Biped Locomotive Robot,” 1991 IEEE International Joint Conference on Neural Networks, vol. 3 (1991) pp. 19831988. doi: 10.1109/IJCNN.1991.170671.CrossRefGoogle Scholar
Vanderborght, B., Verrelst, B., Van Ham, R., Van Damme, M. and Lefeber, D., “Objective locomotion parameters based inverted pendulum trajectory generator,” Rob. Auton. Syst. 56(9), 738750 (2008). doi: 10.1016/j.robot.2008.01.003.CrossRefGoogle Scholar
Latham, P., A Simulation Study of Bipedal Walking Robots: Modeling, Walking Algorithms, and Neural Network Control (1992). Doctoral Dissertations. Available at: https://scholars.unh.edu/dissertation/1698.Google Scholar
Kajita, S. and Tani, K., “Experimental Study of Biped Dynamic Walking in the Linear Inverted Pendulum Mode,” 1995 IEEE International Conference on Robotics and Automation, vol. 3 (1995) pp. 28852891. doi: 10.1109/ROBOT.1995.525693.CrossRefGoogle Scholar
Kajita, S. and Tani, K., “Experimental study of biped dynamic walking,” IEEE Control Syst. 16(1), 1319 (1996). doi: 10.1109/37.482132.Google Scholar
Kajita, S. and Tani, K., “Adaptive gait control of a biped robot based on realtime sensing of the ground profile,” Auton. Robots 4(3), 297305 (1997).CrossRefGoogle Scholar
Fujimoto, Y. and Kawamura, A., “Simulation of an autonomous biped walking robot including environmental force interaction,” IEEE Robot. Autom. Mag. 5(2), 3342 (1998). doi: 10.1109/100.692339.CrossRefGoogle Scholar
Kajita, S., Kanehiro, F., Kaneko, K., Yokoi, K. and Hirukawa, H., “ The 3D Linear Inverted Pendulum Mode: A Simple Modeling for a Biped Walking Pattern Generation,” RSJ/IEEE International Conference on Intelligent Robots and Systems, vol. 1 (2001) pp. 239246. doi: 10.1109/IROS.2001.973365.CrossRefGoogle Scholar
Miyashita, T. and Ishiguro, H., “Human-like natural behavior generation based on involuntary motions for humanoid robots,” Rob. Auton. Syst. 48(4), 203212 (2004). doi: 10.1016/j.robot.2004.07.008.CrossRefGoogle Scholar
Wisse, M., Atkeson, C. G. and Kloimwieder, D. K., “Swing Leg Retraction Helps Biped Walking Stability,” 5th IEEE-RAS International Conference on Humanoid Robots (2005) pp. 295300. doi: 10.1109/ICHR.2005.1573583.CrossRefGoogle Scholar
Kuo, A. D., “The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective,” Hum. Mov. Sci. 26(4), 617656 (2007). doi: 10.1016/j.humov.2007.04.003.CrossRefGoogle ScholarPubMed
Ghorbani, R., Wu, Q. and Wang, G. G., “Nearly optimal neural network stabilization of bipedal standing using genetic algorithm,” Eng. Appl. Artif. Intell. 20(4), 473480 (2007). doi: 10.1016/j.engappai.2006.09.007.CrossRefGoogle Scholar
Ha, T. and Choi, C.-H., “An effective trajectory generation method for bipedal walking,” Rob. Auton. Syst. 55(10), 795810 (2007). doi: 10.1016/j.robot.2007.06.001.CrossRefGoogle Scholar
Kajita, S., M. Morisawa, K. Miura, S. Nakaoka, K. Harada, K. Kaneko, F. Kanehiro and K. Yokoi, “Biped Walking Stabilization Based on Linear Inverted Pendulum Tracking,” 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (2010) pp. 44894496. doi: 10.1109/IROS.2010.5651082.CrossRefGoogle Scholar
A.M., B., A.S., K., Salehinia, Y. and Najafi, F., “An open loop walking on different slopes for NAO humanoid robot,” Procedia Eng. 41, 296304 (2012). doi: 10.1016/j.proeng.2012.07.176.Google Scholar
Al-Shuka, H. F. N., Corves, B. J., Vanderborght, B. and Zhu, W.-H., “Zero-moment point-based biped robot with different walking patterns,” Int. J. Intell. Syst. Appl. 7(1), 31 (2014).Google Scholar
Kobayashi, T., Sekiyama, K., Hasegawa, Y., Aoyama, T. and Fukuda, T., “Unified bipedal gait for autonomous transition between walking and running in pursuit of energy minimization,” Rob. Auton. Syst. 103, 2741 (2018). doi: 10.1016/j.robot.2018.02.005.CrossRefGoogle Scholar
Chevallereau, C., Razavi, H., Six, D., Aoustin, Y. and Grizzle, J., “Self-synchronization and self-stabilization of 3D bipedal walking gaits,” Rob. Auton. Syst. 100, 4360 (2018). doi: 10.1016/j.robot.2017.10.018.CrossRefGoogle Scholar
Bae, H. and Oh, J.-H., “Biped robot state estimation using compliant inverted pendulum model,” Rob. Auton. Syst. 108, 3850 (2018). doi: 10.1016/j.robot.2018.06.004.CrossRefGoogle Scholar
De-León-Gómez, V., Luo, Q., Kalouguine, A., Pámanes, J. A., Aoustin, Y. and Chevallereau, C., “An essential model for generating walking motions for humanoid robots,” Rob. Auton. Syst. 112, 229243 (2019). doi: 10.1016/j.robot.2018.11.015.CrossRefGoogle Scholar
Jeong, H., Lee, I., Sim, O., Lee, K. and Oh, J.-H., “A robust walking controller optimizing step position and step time that exploit advantages of footed robot,” Rob. Auton. Syst. 113, 1022 (2019). doi: 10.1016/j.robot.2018.12.003.CrossRefGoogle Scholar
Chang, L., Piao, S., Leng, X., He, Z. and Zhu, Z., “Inverted pendulum model for turn-planning for biped robot,” Phys. Commun. 42, 101168 (2020). doi: 10.1016/j.phycom.2020.101168.CrossRefGoogle Scholar
Kashyap, A. K. and Parhi, D. R., “Particle swarm optimization aided PID gait controller design for a humanoid robot,” ISA Trans. 114, 306330 (2021). doi: 10.1016/j.isatra.2020.12.033.CrossRefGoogle ScholarPubMed
Ding, J., Xin, S., Lam, T. L. and Vijayakumar, S., Versatile Locomotion by Integrating Ankle, Hip, Stepping, and Height Variation Strategies (2021). Jun. 2021. [Online]. Available at: https://www.research.ed.ac.uk/en/publications/versatile-locomotion-by-integrating-ankle-hip-stepping-and-height.Google Scholar
Khan, A. T., Li, S. and Zhou, X., “Trajectory optimization of 5-link biped robot using beetle antennae search,” IEEE Trans. Circ. Syst. II Exp. Briefs, 1(10), 32763280 (2021). doi: 10.1109/TCSII.2021.3062639.Google Scholar
Hemami, H. and Wyman, B., “Modeling and control of constrained dynamic systems with application to biped locomotion in the frontal plane,” IEEE Trans. Autom. Control 24(4), 526535 (1979). doi: 10.1109/TAC.1979.1102105.CrossRefGoogle Scholar
D.A.Bravo, M. and Rodas, C. F. R., “Design of a dynamic simulator for a biped robot,” Model Simul. Eng. 2021, 112 (2021). doi: 10.1155/2021/5539123.CrossRefGoogle Scholar
Caux, S. and Zapata, R., “Modeling and control of biped robot dynamics,” Robotica 17(4), 413426 (1999). doi: 10.1017/S0263574799001411.CrossRefGoogle Scholar
Vundavilli, P. R. and Pratihar, D. K., “Balanced gait generations of a two-legged robot on sloping surface,” Sadhana 36(4), 525550 (2011). doi: 10.1007/s12046-011-0031-7.CrossRefGoogle Scholar
Hernández-Santos, C., Rodriguez-Leal, E., Soto, R. and Gordillo, J. L., “Kinematics and dynamics of a new 16 DOF humanoid biped robot with active toe joint,” Int. J. Adv. Robot. Syst. 9(5), 190 (2012).CrossRefGoogle Scholar
Gautam, R. and Patil, A. T., “Modeling and Control of Joint Angles of a Biped Robot Leg Using PID Controllers,” 2015 IEEE International Conference on Engineering and Technology (ICETECH) (2015) pp. 15. doi: 10.1109/ICETECH.2015.7275042.CrossRefGoogle Scholar
Mandava, R. K. and Vundavilli, P. R., “Implementation of modified chaotic invasive weed optimization algorithm for optimizing the PID controller of the biped robot,” Sādhanā 43(5), 118 (2018).CrossRefGoogle Scholar
Mandava, R. K. and Vundavilli, P. R., “ Tuning of PID Controller Parameters of a Biped Robot Using IWO Algorithm ,” Proceedings of the 2018 4th International Conference on Mechatronics and Robotics Engineering (2018) pp. 9094.Google Scholar
Mandava, R. K. and Vundavilli, P. R., “Whole body motion generation of 18-DOF biped robot on flat surface during SSP & DSP,” Int. J. Model. Identif. Control 29(3), 266277 (2018).CrossRefGoogle Scholar
Navaneeth, M. G., Sudheer, A. P. and Joy, M. L., “Contact wrench cone-based stable gait generation and contact slip estimation of a 12-DoF biped robot,” Arab J. Sci. Eng 47(12), 1594715971 (2022). doi: 10.1007/s13369-022-06763-z.CrossRefGoogle Scholar
Shih, C. L., Li, Y. Z., Churng, S., Lee, T. T. and Gruver, W. A.Trajectory Synthesis and Physical Admissibility for a Biped Robot During the Single-Support Phase,” IEEE International Conference on Robotics and Automation (1990) pp. 16461652. doi: 10.1109/ROBOT.1990.126246.CrossRefGoogle Scholar
Shih, C.-L., Gruver, W. A. and Lee, T.-T., “Inverse kinematics and inverse dynamics for control of a biped walking machine,” J. Robot. Syst. 10(4), 531555 (1993). doi: 10.1002/rob.4620100408.CrossRefGoogle Scholar
Kljuno, E. and Williams, R. L., “Humanoid walking robot: Modeling, inverse dynamics, and gain scheduling control,” J. Robot. 2010, 119 (2010). doi: 10.1155/2010/278597 2010-06.CrossRefGoogle Scholar
Shih, C.-L., Zhu, Y. and Gruver, W. A., “Optimization of the Biped Robot Trajectory,” IEEE International Conference on Systems, Man, and Cybernetics (1991) pp. 899903. doi: 10.1109/ICSMC.1991.169801.CrossRefGoogle Scholar
O’Flaherty, R., P. Vieira, M. Grey, P. Oh, A. Bobick, M. Egerstedt and M. Stilman, Kinematics and Inverse Kinematics for the Humanoid Robot HUBO2+ (Georgia Institute of Technology, 2013).Google Scholar
Kumar, M. R., Lathan, L. S. and Vundavilli, P. R., “Dynamically balanced obstacle crossing gait generation of a biped robot using neural networks,” Int. J. Mech. Robot. Syst. 2(3-4), 232253 (2015).CrossRefGoogle Scholar
Mandava, R. K. and Vundavilli, P. R., “Forward and Inverse Kinematic Based Full Body Gait Generation of Biped Robot,” 2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT) (2016) pp. 33013305.Google Scholar
Mandava, R. K. and Vundavilli, P. R., “Study on Influence of Hip Trajectory on the Balance of a Biped Robot,” In: Emerging Trends in Electrical, Communications and Information Technologies (Springer, 2017) pp. 265272.CrossRefGoogle Scholar
Kazemi, J. and Ozgoli, S., “Real-time walking pattern generation for a lower limb exoskeleton, implemented on the exoped robot,” Rob. Auton. Syst. 116, 123 (2019). doi: 10.1016/j.robot.2019.02.012.CrossRefGoogle Scholar
Oh, J., Sim, O., Jeong, H. and Oh, J.-H., “Humanoid whole-body remote-control framework with delayed reference generator for imitating human motion,” Mechatronics 62, 102253 (2019). doi: 10.1016/j.mechatronics.2019.102253.CrossRefGoogle Scholar
H.T., K., Balachandran, A. and Shah, S. V., “Optimal whole-body motion planning of humanoids in cluttered environments,” Rob. Auton. Syst. 118, 263277 (2019). doi: 10.1016/j.robot.2019.04.004.Google Scholar
Mandava, R. K. and Vundavilli, P. R., “An analytical approach for generating balanced gaits of a biped robot on stairs and sloping surfaces,” Int. J. Model. Identif. Control 33(1), 2850 (2019).CrossRefGoogle Scholar
Ceranowicz, A. Z., Planar Biped Dynamics and Control (1980). p. 1, Jun. 1980, [Online]. Available at: https://www.elibrary.ru/item.asp?id=7277031.Google Scholar
Ceranowicz, A. Z. Planar Biped Dynamics and Control (The Ohio State University, 1979).Google Scholar
Cambrini, L., Chevallereau, C., Moog, C. H. and Stojic, R., “Stable Trajectory Tracking for Biped Robots,” 39th IEEE Conference on Decision and Control, vol. 5 (2000) pp. 48154820. doi: 10.1109/CDC.2001.914690.CrossRefGoogle Scholar
Chevallereau, C., Aoustin, Y. and Formal’sky, A., “Optimal Walking Trajectories for a Biped,” Proceedings of the First Workshop on Robot Motion and Control. RoMoCo’99 (Cat. No.99EX353) (1999) pp. 171176. doi: 10.1109/ROMOCO.1999.791071.CrossRefGoogle Scholar
Townsend, M. A. and Seireg, A., “The synthesis of bipedal locomotion,” J. Biomech. 5(1), 7183 (1972). doi: 10.1016/0021-9290(72)90020-6.CrossRefGoogle ScholarPubMed
Formalsky, A. M., “Impulsive Control for Anthropomorphic Biped,” In: Theory and Practice of Robots and Manipulators (Morecki, A., Bianchi, G. and Jaworek, K., eds.) (Springer Vienna, Vienna, 1995) pp. 387393. [Online]. Available at: http://link.springer.com/10.1007/978-3-7091-2698-1_50.CrossRefGoogle Scholar
Yi, K. Y. and Zheng, Y. F., “Biped locomotion by reduced ankle power,” Auton. Robots 4(3), 307314 (1997).CrossRefGoogle Scholar
Sabourin, C. and Bruneau, O., “Robustness of the dynamic walk of a biped robot subjected to disturbing external forces by using CMAC neural networks,” Rob. Auton. Syst. 51(2-3), 8199 (2005). doi: 10.1016/j.robot.2005.02.001.CrossRefGoogle Scholar
Mandava, R. K. and Vundavilli, P. R., “Design of Near-Optimal Trajectories for the Biped Robot Using MCIWO Algorithm,” In: Soft Computing for Problem Solving (Springer, 2019) pp. 355364.CrossRefGoogle Scholar
Hemami, H. and Zheng, Y.-F., “Dynamics and control of motion on the ground and in the air with application to biped robots: dynamics and control of motion,” J. Robot. Syst. 1(1), 101116 (1984). doi: 10.1002/rob.4620010107.CrossRefGoogle Scholar
Vukobratović, M., Hristić, D., Stokić, D. and Gluhajić, N., “New method of artificial motion synthesis and application to locomotion robots and manipulators,” IFAC Proc. 9(1), 680700 (1976). doi: 10.1016/S1474-6670(17)67156-8.CrossRefGoogle Scholar
Hobbelen, D., de Boer, T. and Wisse, M., “System Overview of Bipedal Robots Flame and TUlip: Tailor-Made for Limit Cycle Walking,” 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems (2008) pp. 24862491. doi: 10.1109/IROS.2008.4650728.CrossRefGoogle Scholar
Nicolau, V., Albero, M., Blanes, J. F. and Simó, J. E., “Biped robot monitoring using a C.A.N. – Wifi bridge,” IFAC Proc. 40(22), 299302 (2007). doi: 10.3182/20071107-3-FR-3907.00043.CrossRefGoogle Scholar
Hurmuzlu, Y., Génot, F. and Brogliato, B., “Modeling, stability and control of biped robots—a general framework,” Automatica 40(10), 16471664 (2004). doi: 10.1016/j.automatica.2004.01.031.CrossRefGoogle Scholar
Hardt, M., Kreutz-Delgado, K. and Helton, J. W., “Optimal biped walking with a complete dynamical model,” 1999 Conference on Decision and Control 3, 29993004 (1999). doi: 10.1109/CDC.1999.831393.CrossRefGoogle Scholar
Hodgins, J. K., “Biped Gait Transitions,” 1991 IEEE International Conference on Robotics and Automation (1991) pp. 20922097. doi: 10.1109/ROBOT.1991.131936.CrossRefGoogle Scholar
Ji, Q., Qian, Z., Ren, L. and Ren, L., “Simulation analysis of impulsive ankle push-Off on the walking speed of a planar biped robot,” Front Bioeng. Biotechnol. 8, 621560 (2021). doi: 10.3389/fbioe.2020.621560.CrossRefGoogle ScholarPubMed
Sardain, P., Rostami, M. and Bessonnet, G., “An anthropomorphic biped robot: Dynamic concepts and technological design, - Part a syst,” IEEE Trans. Syst. Man, Cybern. - Part A Syst. Hum. 28(6), 823838 (1998). doi: 10.1109/3468.725353 .CrossRefGoogle Scholar
Muscato, G., Spampinato, G. and Costa, M., “Virtual forces based locomotion strategy and energy balance analysis,” IFAC Proc. 39(15), 677682 (2006). doi: 10.3182/20060906-3-IT-2910.00113.CrossRefGoogle Scholar
Canudas-de-Wit, C., “Virtual constraints: A tool for walking robot control and balancing,” Ann. Rev. Control 28(2), 4148 (2004). doi: 10.1016/S1474-6670(17)33367-0.CrossRefGoogle Scholar
Kagami, S., M. Mochimaru, Y. Ehara, N. Miyata, K. Nishiwaki, T. Kanade and H. Inoue, “Measurement and comparison of humanoid H7 walking with human being,” Rob. Auton. Syst. 48(4), 177187 (2004). doi: 10.1016/j.robot.2004.07.006.CrossRefGoogle Scholar
Li, Q., Takanishi, A. and Kato, I., “A Biped Walking Robot Having a ZMP Measurement System Using Universal Force-Moment Sensors,” IROS’91:IEEE/RSJ International Workshop on Intelligent Robots and Systems’91 (1991) pp. 15681573. doi: 10.1109/IROS.1991.174736.CrossRefGoogle Scholar
Yazdani, M., Salarieh, H. and Foumani, M. S., “Decentralized control of rhythmic activities in fully-actuated/under-actuated robots,” Rob. Auton. Syst. 101, 2033 (2018). doi: 10.1016/j.robot.2017.12.003.CrossRefGoogle Scholar
Héliot, R. and Espiau, B., “Online generation of cyclic leg trajectories synchronized with sensor measurement,” Rob. Auton. Syst. 56(5), 410421 (2008). doi: 10.1016/j.robot.2007.09.019.CrossRefGoogle Scholar
Furusho, J. and Sano, A., “Sensor-based control of a nine-link biped,” Int. J. Rob. Res. 9(2), 8398 (1990). doi: 10.1177/027836499000900207.CrossRefGoogle Scholar
Ogura, Y., H. Aikawa, K. Shimomura, H. Kondo, A. Morishima, H.-o. Lim and A. Takanishi, “Development of a New Humanoid Robot WABIAN-2,” 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006 (2006) pp. 7681. doi: 10.1109/ROBOT.2006.1641164.CrossRefGoogle Scholar
Yamaguchi, J., Inoue, S., Nishino, D. and Takanishi, A., “Development of a Bipedal Humanoid Robot Having Antagonistic Driven Joints and Three DOF Trunk,” Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications, vol. 1 (1998) pp. 96101. doi: 10.1109/IROS.1998.724603.CrossRefGoogle Scholar
Yamaguchi, J., Soga, E., Inoue, S. and Takanishi, A., “Development of a Bipedal Humanoid Robot-Control Method of Whole Body Cooperative Dynamic Biped Walking,” International Conference on Robotics and Automation, vol. 1 (1999) pp. 368374. doi: 10.1109/ROBOT.1999.770006.CrossRefGoogle Scholar
Omer, A. M. M., Y. Ogura, H. Kondo, A. Morishima, G. Carbone, M. Ceccarelli, H.-o. Lim and A. Takanishi, “Development of a Humanoid Robot Having 2-DOF Waist and 2-DOF Trunk,” 5th IEEE-RAS International Conference on Humanoid Robots, 2005 (2005) pp. 333338. doi: 10.1109/ICHR.2005.1573589.CrossRefGoogle Scholar
Carbone, G., Lim, H., Takanishi, A. and Ceccarelli, M., “Stiffness analysis of biped humanoid robot WABIAN-RIV,” Mech. Mach. Theory 41(1), 1740 (2006). doi: 10.1016/j.mechmachtheory.2005.05.001.CrossRefGoogle Scholar
Azimi, E., Ghobadi, M., Esfahani, E. T., Keshmiri, M. and Tehrani, A. F., “Three-Dimensional Smooth Trajectory Planning Using Realistic Simulation,” In: RoboCup 2004: Robot Soccer World Cup VIII (Nardi, D., Riedmiller, M., Sammut, C. and Santos-Victor, J., eds.)vol. 3276 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2005) pp. 381393. [Online]. Available at: http://link.springer.com/10.1007/978-3-540-32256-6_31.CrossRefGoogle Scholar
Ogura, Y., Ando, S., Lim, H. and Takanishi, A., “Sensory-based walking motion instruction for biped humanoid robot,” Rob. Auton. Syst. 48(4), 223230 (2004). doi: 10.1016/j.robot.2004.07.002.CrossRefGoogle Scholar
Lippi, V., “Prediction in the context of a human-inspired posture control model,” Rob. Auton. Syst. 107, 6370 (2018). doi: 10.1016/j.robot.2018.05.012.CrossRefGoogle Scholar
Manchester, I. R., Mettin, U., Iida, F. and Tedrake, R., “Stable dynamic walking over uneven terrain,” Int. J. Rob. Res. 30(3), 265279 (2011). doi: 10.1177/0278364910395339.CrossRefGoogle Scholar
Arcos-Legarda, J., Cortes-Romero, J. and Tovar, A., “Robust compound control of dynamic bipedal robots,” Mechatronics 59, 154167 (2019). doi: 10.1016/j.mechatronics.2019.04.002.CrossRefGoogle Scholar
De Magistris, G., Pajon, A., Miossec, S. and Kheddar, A., “Optimized humanoid walking with soft soles,” Rob. Auton. Syst. 95, 5263 (2017). doi: 10.1016/j.robot.2017.05.006.CrossRefGoogle Scholar
Chang, Y.-H., Oh, Y., Kim, D. and Hong, S., “Vibration suppression and balance control for biped humanoid walking,” IFAC Proc. 41(2), 17111716 (2008). doi: 10.3182/20080706-5-KR-1001.00293.CrossRefGoogle Scholar
D’Apolito, F., “Obstacle detection and avoidance of a cost-oriented humanoid robot,” IFAC-PapersOnLine 51(30), 198203 (2018). doi: 10.1016/j.ifacol.2018.11.286.CrossRefGoogle Scholar
D’Apolito, F., “Legs’ trajectory generation for a cost-oriented humanoid robot: A symmetrical approach,” IFAC-PapersOnLine 52(25), 9599 (2019). doi: 10.1016/j.ifacol.2019.12.453.CrossRefGoogle Scholar
Konno, A., Kato, N., Shirata, S., Furuta, T. and Uchiyama, M., “Development of a Light-Weight Biped Humanoid Robot,” Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000), vol. 3 (2000) pp. 15651570. doi: 10.1109/IROS.2000.895196.CrossRefGoogle Scholar
Lee, B.-J, Kim, Y.-D. and Kim, J.-H., “Balance control of humanoid robot for hurosot,” IFAC Proc. 38(1), 215220 (2005). doi: 10.3182/20050703-6-CZ-1902.02088.CrossRefGoogle Scholar
Shih, C.-L., Gruver, W. A. and Zhu, Y., “Fuzzy Logic Force Control for a Biped Robot,” 1991 IEEE International Symposium on Intelligent Control (1991) pp. 269274. doi: 10.1109/ISIC.1991.187369.CrossRefGoogle Scholar
Park, J. H., “Fuzzy-logic zero-moment-point trajectory generation for reduced trunk motions of biped robots,” Fuzzy Sets Syst. 134(1), 189203 (2003). doi: 10.1016/S0165-0114(02)00237-3.CrossRefGoogle Scholar
Vanderborght, B., Verrelst, B., van Ham, R., Vermeulen, J. and Lefeber, D., “Dynamic Control of a Bipedal Walking Robot actuated with Pneumatic Artificial Muscles,” 2005 IEEE International Conference on Robotics and Automation (2005) pp. 16. doi: 10.1109/ROBOT.2005.1570087.CrossRefGoogle Scholar
Aghbali, B., Yousefi-Koma, A., Toudeshki, A. G. and Shahrokhshahi, A., “ZMP Trajectory Control of a Humanoid Robot Using Different Controllers Based on an Offline Trajectory Generation,” 2013 First RSI/ISM International Conference on Robotics and Mechatronics (ICRoM 2013) (2013) pp. 530534. doi: 10.1109/ICRoM.2013.6510161.CrossRefGoogle Scholar
Wang, B., Xu, X. and Tan, J., “Intelligent control of biped robot with heterogeneous legs,” IFAC Proc. 38(1), 181186 (2005). doi: 10.3182/20050703-6-CZ-1902.01300.CrossRefGoogle Scholar
Figliolini, G. and Ceccarelli, M., “Walking programming for an electropneumatic biped robot,” Mechatronics 9(8), 941964 (1999). doi: 10.1016/S0957-4158(99)00040-9.CrossRefGoogle Scholar
Verrelst, B., Vanderborght, B., Vermeulen, J., Van Ham, R., Naudet, J. and Lefeber, D., “Control architecture for the pneumatically actuated dynamic walking biped lucy,” Mechatronics 15(6), 703729 (2005). doi: 10.1016/j.mechatronics.2005.01.002.CrossRefGoogle Scholar
Westervelt, E. R., Buche, G. and Grizzle, J. W., “Experimental validation of a framework for the design of controllers that induce stable walking in planar bipeds,” Int. J. Rob. Res. 23(6), 559582 (2004). doi: 10.1177/0278364904044410.CrossRefGoogle Scholar
Bouhajar, S., Maherzi, E., Khraief, N., Besbes, M. and Belghith, S., “Trajectory generation using predictive PID control for stable walking humanoid robot,” Procedia Comput. Sci. 73, 8693 (2015). doi: 10.1016/j.procs.2015.12.052.CrossRefGoogle Scholar
Abba, G. and Chaillet, N., “Robot dynamic modeling using a power flow approach with application to biped locomotion,” Auton. Robots 6(1), 3952 (1999). doi: 10.1023/A:1008820525412.CrossRefGoogle Scholar
Katić, D. M. and Rodić, A. D., “Dynamic control algorithm for biped walking based on policy gradient fuzzy reinforcement learning,” IFAC Proc. 41(2), 17171722 (2008). doi: 10.3182/20080706-5-KR-1001.00294.CrossRefGoogle Scholar
Fradkov, A. L. and Pogromsky, A. Y., Introduction to Control of Oscillations and Chaos, vol. 35 (World Scientific, 1998).CrossRefGoogle Scholar
Deng, K., Zhao, M. and Xu, W., “Bifurcation gait suppression of a bipedal walking robot with a torso based on model predictive control,” Rob. Auton. Syst. 89, 2739 (2017). doi: 10.1016/j.robot.2016.11.023.CrossRefGoogle Scholar
Berger, G. P., One way of stabilizing a bipedal walking machine (1972).Google Scholar
Mandava, R. K. and Vundavilli, P. R., “An optimal PID controller for a biped robot walking on flat terrain using MCIWO algorithms,” Evol. Intell. 12(1), 3348 (2019).CrossRefGoogle Scholar
Mandava, R. K. and Vundavilli, P. R., “Design and Comparison of Two Evolutionary and Hybrid Neural Network Algorithms in Obtaining Dynamic Balance for Two-Legged Robots,” In: Frontier Applications of Nature Inspired Computation (Springer, 2020) pp. 344363.CrossRefGoogle Scholar
Gan, C.-B., Ding, C.-T. and Yang, S.-X., “Dynamical analysis and performance evaluation of a biped robot under multi-source random disturbances,” Acta Mech. Sin. 30(6), 983994 (2014). doi: 10.1007/s10409-014-0074-1.CrossRefGoogle Scholar
Puga, J. R. T., Silva, F. M. T. and Santos, V. M. F., “Motion planning and control strategies for a distributed architecture humanoid robot,” IFAC Proc. 39(15), 773778 (2006). doi: 10.3182/20060906-3-IT-2910.00129.CrossRefGoogle Scholar
Katić, D. and Vukobratović, M., “Survey of intelligent control algorithms for humanoid robots,” IFAC Proc. 38(1), 3142 (2005). doi: 10.3182/20050703-6-CZ-1902.01276.CrossRefGoogle Scholar
Zhou, C., “Robot learning with GA-based fuzzy reinforcement learning agents,” Inf. Sci. 145(1-2), 4568 (2002). doi: 10.1016/S0020-0255(02)00223-2.CrossRefGoogle Scholar
Magdalena, L. and Monasterio-Huelin, F., “A fuzzy logic controller with learning through the evolution of its knowledge base,” Int. J. Approx. Reason 16(3-4), 335358 (1997). doi: 10.1016/S0888-613X(97)80098-9.CrossRefGoogle Scholar
Zhou, C. and Meng, Q., “Dynamic balance of a biped robot using fuzzy reinforcement learning agents,” Fuzzy Sets Syst. 134(1), 169187 (2003). doi: 10.1016/S0165-0114(02)00236-1.CrossRefGoogle Scholar
Zhou, C., Jagannathan, K. and Myint, T., “Prescribed Synergy Method-based Hybrid Intelligent Gait Synthesis for Biped Robot,” International Conference on Robotics and Automation, vol. 2 (1999) pp. 13841389. doi: 10.1109/ROBOT.1999.772554.CrossRefGoogle Scholar
Zhou, C. and Ruan, D., “Integration of linguistic and numerical information for biped control,” Rob. Auton. Syst. 28(1), 5370 (1999). doi: 10.1016/S0921-8890(99)00029-9.CrossRefGoogle Scholar
Folgheraiter, M., Keldibek, A., Aubakir, B., Gini, G., Franchi, A. M. and Bana, M., “A neuromorphic control architecture for a biped robot,” Rob. Auton. Syst. 120, 103244 (2019). doi: 10.1016/j.robot.2019.07.014.CrossRefGoogle Scholar
Pratt, J. E., Exploiting Inherent Robustness and Natural Dynamics in the Control of Bipedal Walking Robots. Massachusetts Inst of Tech Cambridge Dept of Electrical Engineering and Computer Science (2000). Available at: https://apps.dtic.mil/sti/citations/ADA475455 [Online].Google Scholar
Hwang, S. W., Yeon, J. S. and Park, J. H., “Trajectory Generation Method for Biped Robots to Climb up an Inclined Surface,” IEEE ISR 2013 (2013) pp. 15. doi: 10.1109/ISR.2013.6695712.CrossRefGoogle Scholar
Ito, S., Nishio, S., Ino, M., Morita, R., Matsushita, K. and Sasaki, M., “Design and adaptive balance control of a biped robot with fewer actuators for slope walking,” Mechatronics 49, 5666 (2018). doi: 10.1016/j.mechatronics.2017.11.007.CrossRefGoogle Scholar
Gong, L. and Schiehlen, W., “Impactless biped walking on a slope,” Theor. Appl. Mech. Lett. 3(1), 13002 (2013). doi: 10.1063/2.1301302.CrossRefGoogle Scholar
Behera, P. K., Mandava, R. K. and Vundavilli, P. R., “Push recovery system and balancing of a biped robot on steadily increasing slope of an inclined plane,” Int. J. Comput. Vis. Robot. 9(1), 7089 (2019).CrossRefGoogle Scholar
Zheng, Y. F. and Shen, J., “Gait synthesis for the SD-2 biped robot to climb sloping surface,” IEEE Trans. Robot. Autom. 6(1), 8696 (1990). doi: 10.1109/70.88120.CrossRefGoogle Scholar
Nakanishi, J., Morimoto, J., Endo, G., Cheng, G., Schaal, S. and Kawato, M., “Learning from demonstration and adaptation of biped locomotion,” Rob. Auton. Syst. 47(2-3), 7991 (2004). doi: 10.1016/j.robot.2004.03.003.CrossRefGoogle Scholar
Song, K.-T. and Hsieh, C.-H., “CPG-based Control Design for Bipedal Walking on Unknown Slope Surfaces,” 2014 IEEE International Conference on Robotics and Automation (ICRA) (2014) pp. 51095114. doi: 10.1109/ICRA.2014.6907608.CrossRefGoogle Scholar
Macedo, J., André, J. and Santos, C. P., “Toward a flexible framework for learning: F3L,” Rob. Auton. Syst. 98, 276291 (2017). doi: 10.1016/j.robot.2017.06.007.CrossRefGoogle Scholar
Hasegawa, Y., Arakawa, T. and Fukuda, T., “Trajectory generation for biped locomotion robot,” Mechatronics 10(1-2), 6789 (2000). doi: 10.1016/S0957-4158(99)00052-5.CrossRefGoogle Scholar
Maniscalco, U., Messina, A. and Storniolo, P., “ASS4HR — An artificial somatosensory system for a humanoid robot. The ROS package,” SoftwareX 11, 100501 (2020). doi: 10.1016/j.softx.2020.100501.CrossRefGoogle Scholar
Vundavilli, P. R. and Pratihar, D. K., “Soft computing-based gait planners for a dynamically balanced biped robot negotiating sloping surfaces,” Appl. Soft Comput. 9(1), 191208 (2009). doi: 10.1016/j.asoc.2008.04.004.CrossRefGoogle Scholar
Mandava, R. K. and Vundavilli, P. R., “An adaptive PID control algorithm for the two-legged robot walking on a slope,” Neural Comput. Appl. 32(8), 34073421 (2020).CrossRefGoogle Scholar
McGrath, S., Baltes, J. and Anderson, J., “Active balancing reflexes for small humanoid robots,” IFAC Proc. 41(2), 30483053 (2008). doi: 10.3182/20080706-5-KR-1001.00517.CrossRefGoogle Scholar
Wu, W. and Gao, L., “Posture self-stabilizer of a biped robot based on training platform and reinforcement learning,” Rob. Auton. Syst. 98, 4255 (2017). doi: 10.1016/j.robot.2017.09.001.CrossRefGoogle Scholar
Channon, P. H., Hopkins, S. H. and Pham, D. T., “Derivation of optimal walking motions for a bipedal walking robot,” Robotica 10(2), 165172 (1992). doi: 10.1017/S026357470000758X.CrossRefGoogle Scholar
Znegui, W., Gritli, H. and Belghith, S., “A new poincaré map for investigating the complex walking behavior of the compass-gait biped robot,” Appl. Math. Model. 94, 534557 (2021). doi: 10.1016/j.apm.2021.01.036.CrossRefGoogle Scholar
Safartoobi, M., Dardel, M. and Daniali, H. M., “Gait cycles of passive walking biped robot model with flexible legs,” Mech. Mach. Theory 159, 104292 (2021). doi: 10.1016/j.mechmachtheory.2021.104292.CrossRefGoogle Scholar
Townsend, M. A. and Tsai, T. C., “Biomechanics and modelling of bipedal climbing and descending,” J. Biomech. 9(4), 227239 (1976). doi: 10.1016/0021-9290(76)90008-7.CrossRefGoogle ScholarPubMed
Espiau, B., “BIP: A Joint Project for the Development of an Anthropomorphic Biped Robot,” 1997 8th International Conference on Advanced Robotics. Proceedings. ICAR’97 (1997) pp. 267272,. doi: 10.1109/ICAR.1997.620193.CrossRefGoogle Scholar
Albert, A., “Climbing of stairs of an autonomous, bipedal robot,” IFAC Proc. 33(26), 591596 (2000). doi: 10.1016/S1474-6670(17)39209-1.CrossRefGoogle Scholar
Shih, C.-L., “Ascending and descending stairs for a biped robot, - part a syst,” IEEE Trans. Syst. Hum. 29(3), 255268 (1999). doi: 10.1109/3468.759271.Google Scholar
Zachariah, S. K. and Kurian, T., “Hybrid-state driven autonomous control for planar bipedal locomotion over randomly sloped non-uniform stairs,” Rob. Auton. Syst. 97, 1839 (2017). doi: 10.1016/j.robot.2017.08.003.CrossRefGoogle Scholar
Mandava, R. K. and Vundavilli, P. R., “Near optimal PID controllers for the biped robot while walking on uneven terrains,” Int. J. Autom. Comput. 15(6), 689706 (2018).CrossRefGoogle Scholar
Rakovic, M., Borovac, B., Santos-Victor, J., Batinica, A., Nikolic, M. and Savic, S., “Biped Walking and Stairs Climbing Using Reconfigurable Adaptive Motion Primitives,” 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids) (2016) pp. 5762. doi: 10.1109/HUMANOIDS.2016.7803254.CrossRefGoogle Scholar
Sun, Z. and Roos, N., “Dynamically stable walk control of biped humanoid on uneven and inclined terrain,” Neurocomputing 280, 111122 (2018). doi: 10.1016/j.neucom.2017.08.077.CrossRefGoogle Scholar
Jha, R. K., Singh, B. and Pratihar, D. K., “On-line stable gait generation of a two-legged robot using a genetic-fuzzy system,” Rob. Auton. Syst. 53(1), 1535 (2005). doi: 10.1016/j.robot.2005.06.006.CrossRefGoogle Scholar
Zhong, Q. and Chen, F., “Trajectory planning for biped robot walking on uneven terrain – Taking stepping as an example, CAAI trans,” Intell. Technol. 1(3), 197209 (2016). doi: 10.1016/j.trit.2016.10.009.Google Scholar
Lum, H. K., Zribi, M. and Soh, Y. C., “Planning and control of a biped robot,” Int. J. Eng. Sci. 37(10), 13191349 (1999). doi: 10.1016/S0020-7225(98)00118-9.CrossRefGoogle Scholar
Mousavi, P. N. and Bagheri, A., “Mathematical simulation of a seven link biped robot on various surfaces and ZMP considerations,” Appl. Math. Model. 31(1), 1837 (2007). doi: 10.1016/j.apm.2006.06.018.CrossRefGoogle Scholar
Vatankhah, M., Kobravi, H. R. and Ritter, A., “Intermittent control model for ascending stair biped robot using a stable limit cycle model,” Rob. Auton. Syst. 121, 103255 (2019). doi: 10.1016/j.robot.2019.103255.CrossRefGoogle Scholar
Vukobratović, M., Ćirić, V., Hristić, D. and Stepanenko, J., “Contribution to the study of anthropomorphic robots,” IFAC Proc. 5(1), 8896 (1972). doi: 10.1016/S1474-6670(17)68455-6.CrossRefGoogle Scholar
Takanishi, A., Lim, H., Tsuda, M. and Kato, I., “Realization of Dynamic Biped Walking Stabilized by Trunk Motion on a Sagittally Uneven Surface,” IEEE International Workshop on Intelligent Robots and Systems, Towards a New Frontier of Applications (1990) pp. 323330. doi: 10.1109/IROS.1990.262408.CrossRefGoogle Scholar
Denk, J. and Schmidt, G., “Walking primitive databases for perception-based guidance control of biped robots,” Eur. J. Control 13(2-3), 171188 (2007). doi: 10.3166/ejc.13.171-188.CrossRefGoogle Scholar
Vukobratović, M. and Stepanenko, J., “Mathematical models of general anthropomorphic systems,” Math. Biosci. 17(3-4), 191242 (1973). doi: 10.1016/0025-5564(73)90071-0.CrossRefGoogle Scholar
Raibert, M. H., Brown, J., Chepponis, M., Koechling, J. and Hodgins, J. K., Dynamically Stable Legged Locomotion. Massachusetts Inst of Tech Cambridge Artificial Intelligence Lab (1989). [Online]. Available at: https://apps.dtic.mil/sti/citations/ADA225713.Google Scholar
Igarashi, E. and Nogai, T., “Study of lower level adaptive walking in the sagittal plane by a biped locomotion robot,” Adv. Robot. 6(4), 441459 (1991). doi: 10.1163/156855392X00286.CrossRefGoogle Scholar
Kashyap, A. K. and Parhi, D. R., “Dynamic walking of humanoid robot on flat surface using amplified LIPM plus flywheel model,” Int. J. Intell. Unmanned Syst. ahead-of-p(ahead-of-print), 316329 (2021). doi: 10.1108/IJIUS-09-2020-0039 .CrossRefGoogle Scholar
Lee, Y., Lee, H., Hwang, S. and Park, J., “Terrain edge detection for biped walking robots using active sensing with vCoP-position hybrid control,” Rob. Auton. Syst. 96, 4157 (2017). doi: 10.1016/j.robot.2017.05.011.CrossRefGoogle Scholar
Kumar, P. B., Sahu, C. and Parhi, D. R., “A hybridized regression-adaptive ant colony optimization approach for navigation of humanoids in a cluttered environment,” Appl. Soft Comput. 68, 565585 (2018). doi: 10.1016/j.asoc.2018.04.023.CrossRefGoogle Scholar
Yagi, M. and Lumelsky, V., “Biped Robot Locomotion in Scenes with Unknown Obstacles,” International Conference on Robotics and Automation, vol. 1 (1999) pp. 375380. doi: 10.1109/ROBOT.1999.770007.CrossRefGoogle Scholar
Kumar, P. B., Muni, M. K. and Parhi, D. R., “Navigational analysis of multiple humanoids using a hybrid regression-fuzzy logic control approach in complex terrains,” Appl. Soft Comput. 89, 106088 (2020). doi: 10.1016/j.asoc.2020.106088.CrossRefGoogle Scholar
Rath, A. K., Parhi, D. R., Das, H. C., Muni, M. K. and Kumar, P. B., “Analysis and use of fuzzy intelligent technique for navigation of humanoid robot in obstacle prone zone,” Def. Technol. 14(6), 677682 (2018). doi: 10.1016/j.dt.2018.03.008.CrossRefGoogle Scholar
Kumar, A., Kumar, P. B. and Parhi, D. R., “Intelligent navigation of humanoids in cluttered environments using regression analysis and genetic algorithm,” Arab J. Sci. Eng. 43(12), 76557678 (2018). doi: 10.1007/s13369-018-3157-7.CrossRefGoogle Scholar
Delfin, J., Becerra, H. M. and Arechavaleta, G., “Humanoid navigation using a visual memory with obstacle avoidance,” Rob. Auton. Syst. 109, 109124 (2018). doi: 10.1016/j.robot.2018.08.010.CrossRefGoogle Scholar
Tsuru, M., Escande, A., Tanguy, A., Chappellet, K. and Harad, K., “Online object searching by a humanoid robot in an unknown environment,” IEEE Robot. Autom. Lett. 6(2), 28622869 (2021). doi: 10.1109/LRA.2021.3061383.CrossRefGoogle Scholar
Kashyap, A. K. and Parhi, D. R., “Optimization of stability of humanoid robot NAO using ant colony optimization tuned MPC controller for uneven path,” Soft Comput. 25(7), 51315150 (2021). doi: 10.1007/s00500-020-05515-1.CrossRefGoogle Scholar
Kashyap, A. K., Parhi, D. R., Muni, M. K. and Pandey, K. K., “A hybrid technique for path planning of humanoid robot NAO in static and dynamic terrains,” Appl. Soft Comput. 96, 106581 (2020). doi: 10.1016/j.asoc.2020.106581.CrossRefGoogle Scholar
Seara, J. F. and Schmidt, G., “Intelligent gaze control for vision-guided humanoid walking: Methodological aspects,” Rob. Auton. Syst. 48(4), 231248 (2004). doi: 10.1016/j.robot.2004.07.003.CrossRefGoogle Scholar
Park, S., Han, Y. and Hahn, H., “Balance control of a biped robot using camera image of reference object,” Int. J. Control. Autom. Syst. 7(1), 7584 (2009). doi: 10.1007/s12555-009-0110-2.CrossRefGoogle Scholar
Subburaman, R., Kanoulas, D., Muratore, L., Tsagarakis, N. G. and Lee, J., “Human inspired fall prediction method for humanoid robots,” Rob. Auton. Syst. 121, 103257 (2019). doi: 10.1016/j.robot.2019.103257.CrossRefGoogle Scholar
Chestnut, J., “Planning Biped Navigation strategies in Complex Environments,” IEEE International Conference on Humanoid Robots (Humanoids) (2003) https://ci.nii.ac.jp/naid/10013044752/.Google Scholar
Mandava, R. K., Katla, M. and Vundavilli, P. R., “Application of hybrid fast marching method to determine the real-time path for the biped robot,” Intell. Serv. Robot. 12(1), 125136 (2019).CrossRefGoogle Scholar
Mandava, R. K., Mrudul, K. and Vundavilli, P. R., “Dynamic motion planning algorithm for a biped robot using fast marching method hybridized with regression search,” Acta Polytech. Hung 16, 189208 (2019).Google Scholar
Kashyap, A. K., Parhi, D. and Pandey, A., “Improved modified chaotic invasive weed optimization approach to solve multi-target assignment for humanoid robot,” J. Robot. Control 2(3) (2021). doi: 10.18196/jrc.2377.Google Scholar
Mrudul, K., Mandava, R. K. and Vundavilli, P. R., “An efficient path planning algorithm for biped robot using fast marching method,” Procedia Comput. Sci. 133, 116123 (2018).CrossRefGoogle Scholar
Vundavilli, P. R. and Pratihar, D. K., “Dynamically balanced optimal gaits of a ditch-crossing biped robot,” Rob. Auton. Syst. 58(4), 349361 (2010). doi: 10.1016/j.robot.2009.10.004.CrossRefGoogle Scholar
Janardhan, V. and Kumar, R. P., “Online trajectory generation for wide ditch crossing of biped robots using control constraints,” Rob. Auton. Syst. 97, 6182 (2017). doi: 10.1016/j.robot.2017.07.014.CrossRefGoogle Scholar
J., V. and P.K., R., “Generating feasible solutions for dynamically crossing a wide ditch by a biped robot,” J. Intell. Robot. Syst. 88(1), 3756 (2017). doi: 10.1007/s10846-017-0550-5.Google Scholar
Vundavilli, P. R. and Pratihar, D. K., “Gait Planning of Biped Robots Using Soft Computing: An Attempt to Incorporate Intelligence,” In: Intelligent Autonomous Systems (2010) pp. 5785.CrossRefGoogle Scholar
Dunn, E. R. and Howe, R. D., “Foot Placement and Velocity Control in Smooth Bipedal Walking,” IEEE International Conference on Robotics and Automation, vol. 1 (1996) pp. 578583. doi: 10.1109/ROBOT.1996.503837.CrossRefGoogle Scholar
Grizzle, J. W., Abba, G. and Plestan, F., “Asymptotically stable walking for biped robots: Analysis via systems with impulse effects,” IEEE Trans. Autom. Control 46(1), 5164 (2001). doi: 10.1109/9.898695.CrossRefGoogle Scholar
Yamaguchi, J., Takanishi, A. and Kato, I., “Development of a Biped Walking Robot Adapting to a Horizontally Uneven Surface,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS’94), vol. 2 (1994) pp. 11561163. doi: 10.1109/IROS.1994.407468.CrossRefGoogle Scholar
Park, J. H. and Chung, H., “Hybrid Control for Biped Robots Using Impedance Control and Computed-Torque Control,” International Conference on Robotics and Automation, vol. 2 (1999) pp. 13651370. doi: 10.1109/ROBOT.1999.772551.CrossRefGoogle Scholar
Chew, C.-M. and Pratt, G. A., “Adaptation to load variations of a planar biped: Height control using robust adaptive control,” Rob. Auton. Syst. 35(1), 122 (2001). doi: 10.1016/S0921-8890(00)00130-5.CrossRefGoogle Scholar
Kanoulas, D. and Vona, M., “Sparse Surface Modeling with Curved Patches,” 2013 IEEE International Conference on Robotics and Automation (2013) pp. 42094215.Google Scholar
Kanoulas, D., Tsagarakis, N. G. and Vona, M., “Curved patch mapping and tracking for irregular terrain modeling: Application to bipedal robot foot placement,” Rob. Auton. Syst. 119, 1330 (2019). doi: 10.1016/j.robot.2019.05.012.CrossRefGoogle Scholar
Pratt, J., Chew, C.-M., Torres, A., Dilworth, P. and Pratt, G., “Virtual model control: An intuitive approach for bipedal locomotion,” Int. J. Rob. Res. 20(2), 129143 (2001). doi: 10.1177/02783640122067309.CrossRefGoogle Scholar
Iida, F. and Tedrake, R., “Minimalistic control of biped walking in rough terrain,” Auton. Robots 28(3), 355368 (2010). doi: 10.1007/s10514-009-9174-3.CrossRefGoogle Scholar
Ma, X., Li, X. and Qiao, H., “Fuzzy neural network-based real-time self-reaction of mobile robot in unknown environments,” Mechatronics 11(8), 10391052 (2001). doi: 10.1016/S0957-4158(00)00061-1.CrossRefGoogle Scholar
Chen, T. and Goodwine, B., “Robust gait design for a compass gait biped on slippery surfaces,” Rob. Auton. Syst. 140, 103762 (2021). doi: 10.1016/j.robot.2021.103762.CrossRefGoogle Scholar
Zamparelli, A., Scianca, N., Lanari, L. and Oriolo, G., “Humanoid gait generation on uneven ground using intrinsically stable MPC,” IFAC-PapersOnLine 51(22), 393398 (2018). doi: 10.1016/j.ifacol.2018.11.574.CrossRefGoogle Scholar
Zamparelli, A., Scianca, N., Lanari, L. and Oriolo, G., “Humanoid gait generation on uneven ground using intrinsically stable MPC **This work is supported by the EU H2020 project COMANOID,” IFAC-PapersOnLine 51(22), 393398 (2018). doi: 10.1016/j.ifacol.2018.11.574.CrossRefGoogle Scholar
Fukuda, T. and Arakawa, T., “Intelligent systems: Robotics versus mechatronics,” Ann. Rev. Control 22, 1322 (1998). doi: 10.1016/S1367-5788(98)00002-9.CrossRefGoogle Scholar
Ding, C.-T., Yang, S.-X. and Gan, C.-B., “Input torque sensitivity to uncertain parameters in biped robot,” Acta Mech. Sin. 29(3), 452461 (2013). doi: 10.1007/s10409-013-0025-2.CrossRefGoogle Scholar
Bian, Y., Shao, J., Yang, J. and Liang, A., “Jumping motion planning for biped robot based on hip and knee joints coordination control,” J. Mech. Sci. Technol. 35(3), 12231234 (2021). doi: 10.1007/s12206-021-0236-6.CrossRefGoogle Scholar
Yamaguchi, J., Kinoshita, N., Takanishi, A. and Kato, I., “Development of a Dynamic Biped Walking System for Humanoid - Development of a Biped Walking Robot Adapting to the Humans’ Living Floor,” IEEE International Conference on Robotics and Automation, vol. 1 (1996) pp. 232239. doi: 10.1109/ROBOT.1996.503783.CrossRefGoogle Scholar
Capi, G., Nasu, Y., Barolli, L. and Mitobe, K., “Real time gait generation for autonomous humanoid robots: A case study for walking,” Rob. Auton. Syst. 42(2), 107116 (2003). doi: 10.1016/S0921-8890(02)00351-2.CrossRefGoogle Scholar
Nakamura, Y., Mori, T., Sato, M. and Ishii, S., “Reinforcement learning for a biped robot based on a CPG-actor-critic method,” Neural Networks 20(6), 723735 (2007). doi: 10.1016/j.neunet.2007.01.002.CrossRefGoogle ScholarPubMed
Pasandi, V., Dinale, A., Keshmiri, M. and Pucci, D., “A programmable central pattern generator with bounded output,” Rob. Auton. Syst. 125, 103423 (2020). doi: 10.1016/j.robot.2020.103423.CrossRefGoogle Scholar
Mousavi, P. N., Nataraj, C., Bagheri, A. and Entezari, M. A., “Mathematical simulation of combined trajectory paths of a seven link biped robot,” Appl. Math. Model. 32(7), 14451462 (2008). doi: 10.1016/j.apm.2007.11.026.CrossRefGoogle Scholar
Bagheri, B. M.-F. and Mousavi, P. N. Mathematical Modelling and Simulation of Combined Trajectory Paths of a Seven Link Biped Robot (Climbing and Walking Robots) (BoD – Books on Demand, 2010).Google Scholar
Rioux, A. and Suleiman, W., “Autonomous SLAM based humanoid navigation in a cluttered environment while transporting a heavy load,” Rob. Auton. Syst. 99, 5062 (2018). doi: 10.1016/j.robot.2017.10.001.CrossRefGoogle Scholar
Luo, A., S. Bhattacharya, S. Dutta, Y. Ochi, M. Miura-Mattausch, J. Weng, Y. Zhou and H. J. Mattausch, “Surface recognition via force-sensory walking-pattern classification for biped robot,” IEEE Sens. J. 21(8), 1006110072 (2021). doi: 10.1109/JSEN.2021.3059099.CrossRefGoogle Scholar
Yang, W., Young, N. and You, B.-J.. Biologically Inspired Robotic Systems Control: Multi-DOF Robotic Arm Control (VDM Publishing, 2010).Google Scholar