Mechanic of Advanced and Smart Materials
Quarterly

Modeling, Simulation, and Stability Analysis of Biped Robots Constructed of Flexible Links

Document Type : Original Article

Authors

Mohammad Ehsan Yousefzadeh Kouhbanani 1
Ali Mohamad Shafei 2

1 Graduate of Mechanical Engineering of Shahid Bahonar University of Kerman

2 Faculty Of Engineering, Shahid Bahonar University Of Kerman, Kerman, 7616913439, Iran

https://doi.org/10.61186/masm.4.2.207
Abstract
The self-driven movement of biped robots along an inclined surface is a topic that, despite its inherent complexities, has attracted the attention of many researchers. However, what distinguishes this research from similar works is the consideration of flexibility in the links that constitute such robotic systems. This assumption is not far-fetched, as in the transition phase (impact), the impulse force applied to the system significantly increases the likelihood of exciting vibrational modes. On the other hand, the bones involved in walking are enveloped by muscles, which have viscoelastic properties. Therefore, to achieve more accurate results, modeling the links with viscoelastic properties becomes inevitable. In the discussion of the autonomous movement of bipedal robots, the most important issue is determining the initial configuration of the robot so that the system can perform a periodic and stable motion solely under the influence of gravitational attraction. The highly unstable nature of the system under study, along with the vibrations created by the impact force resulting from the foot striking the inclined surface, constitutes one of the very serious challenges in the progress of this research. Nevertheless, this paper overcomes these challenges by presenting a completely systematic method with very strong mathematical frameworks. Finally, the effect of the intrinsic parameters of elastic links, including the modulus of elasticity and the Kelvin-Voigt coefficient, on the stability of the movement of such robotic systems is examined.

Keywords

Bipedal Robots
Inclined Surfaces : Viscoelastic Links
Stability of Motion
Impact Force
[1] Kerimoğlu D, Morgül Ö, Saranli U. Stability and control of planar compass gait walking with series-elastic ankle actuation. Transactions of the Institute of Measurement and Control. 2017; 39(3); 312-323.
[2] Iida F, Minekawa Y, Rummel J, Seyfarth A. Toward a human-like biped robot with compliant legs. Robotics and Autonomous Systems. 2009; 57:139–144.
[3] Zelik KE, Huang TWP, Adamczyk PG, Kou AD. The role of series ankle elasticity in bipedal walking. Journal of Theoretical Biology. 2014; 346:75–85.
[4] Deng K, Zhao M, Xu W. Level-ground walking for a bipedal robot with a torso via hip series elastic actuators and its gait bifurcation control. Robot Auton Syst. 2016; 79:58–71.
[5] Wu Y, Yao D, Xiao X. The effects of ground compliance on flexible planar passive biped dynamic walking. Journal of Mechanical Science and Technology. 2018; 32:1793–1804.
[6] Fathizadeh M, Mohammadi H, Taghvaei S. A modified passive walking biped model with two feasible switching patterns of motion to resemble multi-pattern human walking. Chaos, Solitons & Fractals. 2019; 127:83-95.
[7] Kino H, Sakata K, Uemura M, Mori N. Simulation verification for the robustness of passive compass gait with a joint stiffness adjustment. Advanced Robotics. 2019; 33:1129-1143.
[8] Tokhi M. M. O, Azad A. Flexible Robot Manipulators: Modelling, Simulation and Control. Second edition; IET, 2017.
[9] Hastings G, Book W. Verification of a linear dynamic model for flexible robotic manipulators. Proceedings of the IEEE International Conference on Robotics and Automation, IEEE, 1986.
[10] Chen B, Huang J, Ji JC. Control of flexible single-link manipulators having Duffing oscillator dynamics. Mechanical Systems and Signal Processing. 2019; 121:44–57.
[11] Khairudin M, Mohamed Z, Husain AR, Mamat R. Dynamic characterization of a two-link flexible manipulator: theory and experiments. Advances in robotics research. 2014; 1:61–79.
[12] Garcia-Perez OA, Silva-Navarro G, Peza-Solis JF. Flexible-link robots with combined trajectory tracking and vibration control. Applied Mathematical Modelling. 2019; 70:285–298.
[13] Qiu Z, Li C, Zhang X. Experimental study on active vibration control for a kind of two-link flexible manipulator. Mechanical Systems and Signal Processing. 2019; 11:623-644.
[14] Morlock M, Meyer N, Pick M. Robert Seifried, Real-time trajectory tracking control of a parallel robot with flexible links. Mechanism and Machine Theory. 2021; 158:104220.
[15] Shang D, Li X, Yin M, Li F. Dynamic modeling and fuzzy compensation sliding mode control for flexible manipulator servo system. Applied Mathematical Modelling. 2022; 107:30-556.
[16] Li F, Zhang Z, Wu Y, Chen Y, Liu K, Yao J. Improved fuzzy sliding mode control in flexible manipulator actuated by PMAs. Robotica. 2022; 40:2683-2696.
[17] Korayem MH, Shafei AM. A new approach for dynamic modeling of n-viscoelastic-link robotic manipulators mounted on a mobile base. Nonlinear Dynamics. 2015; 79;2767–2786.
[18] Patil O, Gandhi P. On the dynamics and multiple equilibria of an inverted flexible pendulum with tip mass on a cart. Journal of Dynamic Systems, Measurement and Control. 2014; 136:041017.
[19] Peng Y, Liu J, He W. Boundary control for a flexible inverted pendulum system based on a PDE model. Asian Journal of Control. 2018; 20:12–21.
[20] Shen Y, Kuang Y. Transient contact-impact behavior for passive walking of compliant bipedal robots. Extreme Mechanics Letters. 2021; 42:101076.
[21] Safartoobi M, Dardel M, Mohammadi Daniali H. Gait cycles of passive walking biped robot model with flexible legs. Mechanism and Machine Theory. 2021; 159:104292.
[22] Safartoobi M, Dardel M, Mohammadi Daniali H. Passive walking biped robot model with flexible viscoelastic legs. Nonlinear Dynamics. 2022; 109:2615–2636.
[23] Shin HC, Choi SB. Position control of a two-link flexible manipulator featuring piezoelectric actuators and sensors. Mechatronics. 2001; 11:707–729.
[24] Tang LW, Gouttefarde M, Sun HN, Yin LR, Zhou CJ. Dynamic modelling and vibration suppression of a single-link flexible manipulator with two cables. Mechanism and Machine Theory. 2021; 162:104347.
[25] Li D, Zu J, Goldenberg A. Dynamic modeling and mode analysis of flexible-link flexible-joint robots. Mechanism and Machine Theory. 1998; 33:1031–1044.
[26] Wei J, Cao D, Liu L, Huang W. Global mode method for dynamic modeling of a flexible-link flexible-joint manipulator with tip mass. Applied Mathematical Modelling. 2017; 48:787–805.
[27] Mattioni A, Wu Y, Le Gorrec Y. Infinite dimensional model of a double flexible-link manipulator: The PortHamiltonian approach. Applied Mathematical Modelling. 2020; 83:59-75.
[28] Khalil W, Boyer F, Morsli F. General Dynamic Algorithm for Floating Base Tree Structure Robots with Flexible Joints and Links. Journal of Mechanisms and Robotics. 2017; 9:031003.
[29] Mata V, Provenzano S, Cuadrado JI, Valero F. Serial-robot dynamics algorithms for moderately large number large number of joints. Mechanism and Machine Theory. 2002; 37:739–755.
[30] Korayem MH, Shafei AM. Application of recursive Gibbs–Appell formulation in deriving the equations of motion of N-viscoelastic robotic manipulators in 3D space using Timoshenko beam theory. Acta Astronautica. 2013; 83:273-294.
[31] Korayem MH, Shafei AM, Doosthoseini M, Absalan F, Kadkhodaei B. Theoretical and experimental investigation of viscoelastic serial robotic manipulators with motors at the joints using Timoshenko beam theory and Gibbs–Appell formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics. 2016; 230:37-51.
[32] Shafei AM, Korayem MH. Theoretical and experimental study of dynamic load‐ carrying capacity for flexible robotic arms in point‐ to‐ point motion. Optimal Control Applications and Methods. 2017 38:963-972.
[33] Rezaei V, Shafei AM. Dynamic Analysis of Flexible Robotic Manipulators Constructed of Functionally Graded Materials. Iranian Journal of Science and Technology. Transactions of Mechanical Engineering. 2019; 43:327-342.
[34] Korayem MH, Dehkordi SF. Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs–Appell formulation. Applied Mathematical Modelling. 2019; 65:443-463.
[35] Kim J, Choi CH, Spong MW. Passive dynamic walking with symmetric fixed flat feet, International conference on control and automation, Guangzhou, China, 2007.
[36] Obayashi I, Aoi S, Tsuchiya K, Kokubu H. Common formation mechanism of basin of attraction for bipedal walking models by saddle hyperbolicity and hybrid dynamics. Japan Journal of Industrial and Applied Mathematics. 2015; 32:315–332.
[37] Obayashi I, Aoi S, Tsuchiya K, Kokubu H. Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2016; 472:1–19.
[38] Gritli H, Khraeif N, Belghith S. Period-three route to chaos induced by a cyclic-fold bifurcation in passive dynamic walking of a compass-gait biped robot. Communications in Nonlinear Science and Numerical Simulation. 2012; 17:4356–72.
[39] Dardel M, Safartoobi M, Pashaei MH, Ghasemi MH, Navaei MK. Finite difference method to find periodone gait cycles of simple passive walkers. Communications in Nonlinear Science and Numerical Simulation. 2015; 20:79–97
Mechanic of Advanced and Smart Materials
Volume 4, Issue 2
Summer 2024
Pages 207-237

  • Receive Date 05 June 2024
  • Revise Date 19 June 2024
  • Accept Date 07 July 2024

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