Simultaneous Optimization of a Convex Sole as a Foot and Hip Trajectory for a Biped Robot with an Ankle without an Additional Degree of Freedom

Document Type : Research Article

Authors

1 BMMS Lab., Mechanical Engineering Dpt., Yazd University

2 Faculty member / Mechanical Engineering Dpt., Yazd university

3 Faculty member / Mechanical engineering dpt., Yazd University

Abstract

Foot geometry greatly affects gait characteristics and it determinants. This research deals with analyzing gait when foot-ground contact occurs on a convex curve namely sole curve. Designing sole curve is also included in this work, targeting least energy consumption during walking on a flat ground. The famous point mass model has been improved to a model with a moving contact point on a convex sole without adding an extra degree of freedom. As the convex sole is added to the model, motion reconstruction is needed because of the effects of the model’s geometry on optimized gait cycle. Therefore, in this research, simultaneous optimization has been done to find the optimized sole shape and hip trajectory. To avoid high computational cost, optimization variables have been coded into vectors with limited dimensions and obtained by using particle swarm optimization and steepest descent algorithm together. Kinematic constraints and requirements of a continues, repetitive and symmetrical locomotion have been driven and satisfied during optimization. The results have been shown that optimization of the sole shape and hip trajectory has great effects on the cost function

Keywords

Main Subjects


[1] J.R. C. Pongmala, C. Price, R. Baker, Is Foot Contact a Collision?, Proceedings of Gait & Clinical Movement Analysis Society 2015 Annual Conference, (2015).
[2] M. Srinivasan, A. Ruina, Computer optimization of a minimal biped model discovers walking and running, Nature, 439(7072) (2006) 72.
 [3] M. Wisse, D.G. Hobbelen, R.J. Rotteveel, S.O. Anderson, G.J. Zeglin, Ankle springs instead of arc-shaped feet for passive dynamic walkers, in: Humanoid Robots, 2006 6th IEEE-RAS International Conference on, IEEE, 2006, pp. 110-116.
[4] L. Humphrey, H. Hemami, A computational human model for H[SORULQJ the role of the feet in balance, Journal of biomechanics, 43(16) (2010) 3199-3206.
 [5] S. Aoi, Y. Sato, K. Tsuchiya, Arc feet effects on stability based on a simple oscillator-driven walking model, Journal of Robotics and Mechatronics, 20(5) (2008) 709.
 [6] K. Hyodo, T. Oshimura, S. Mikami, S.j. Suzuki, Stabilizing passive dynamic walk under wide range of environments by constraint mechanism fitted to sole of foot, Journal of Robotics and Mechatronics, 21(3) (2009) 403.
 [7] S. Sadati, M. Borgheinejad, H. Fooladi, M. Naraghi, A. Ohadi, Optimum Design, Manufacturing and ([SHULPHQW of a Passive Walking Biped: Effects of Structural Parameters on Efficiency, Stability and Robustness on Uneven Trains, in: Applied Mechanics and Materials, Trans Tech Publ, 2013, pp. 107-111.
[8] P. Mahmoodi, R.S. Ransing, M.I. Friswell, Modelling the effect of ‘heel to toe’ roll-over contact on the walking dynamics of passive biped robots, Applied Mathematical Modelling, 37(12-13) (2013) 7352-7373.
[9] F. Asano, Z.-W. Luo, The effect of semicircular feet on energy dissipation by heel-strike in dynamic biped locomotion, in: Robotics and Automation, 2007 IEEE International Conference on, IEEE, 2007, pp. 3976-3981.
 [10] P.G. Adamczyk, S.H. Collins, A.D. Kuo, The advantages of a rolling foot in human walking, J ([S Biol, 209(Pt 20) (2006) 3953-3963. [11] M. Kwan, M. Hubbard, Optimal foot shape for a passive dynamic biped, J Theor Biol, 248(2) (2007) 331-339.
[12] J. Li, Y. Tian, X. Huang, H. Chen, Foot shape for passive dynamic kneed biped robot, in: Robotics and Biomimetics (ROBIO), 2010 IEEE International Conference on, IEEE, 2010, pp. 1281-1286.
[13] M.H. F. Ghafouri, M. Jalili, Mechanical and energetic consequences of FRQYH[-curved sole in human walking with different patterns, ICROM International Conference (2017).
[14] S. Fallah, N. Keshavarzi, M.H. Honarvar, Joint torques in biped gait following changes in leg length, in: 2016 4th International Conference on Robotics and Mechatronics (ICROM), IEEE, 2016, pp. 554-559.
[15] M.H. N. Shojaei, Kinemtacs, Kinetics, and Numerical Simulation of Walking with a 1-DoF Dynamic Boot with Passive Controller and Arbitrary Contact Surface, Biomedical Engineering Conference (2016).
[16] J.M. Donelan, R. Kram, A.D. Kuo, Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking, Journal of ([SHULPHQWDO Biology, 205(23) (2002) 3717-3727.
[17] J.M. Donelan, R. Kram, A.D. Kuo, Simultaneous positive and negative H[WHUQDO mechanical work in human walking, Journal of biomechanics, 35(1) (2002) 117-124.
[18] P. Channon, S. Hopkins, D. Pham  simulation and optimization of gait for a bipedal robot, Mathematical and Computer Modelling, 14 (1990) 463-467.
[19] P. Channon, S. Hopkins, D. Pham, A variational approach to the optimization of gait for a bipedal robot, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 210(2) (1996) 177-186.
[20] L. Roussel, C. Canudas-de-Wit, A. Goswami, Generation of energy optimal complete gait cycles for biped robots, in: Robotics and Automation, 1998. Proceedings. 1998 IEEE International Conference on, IEEE, 1998, pp. 2036-2041.
[21] C. Chevallereau, Y. Aoustin, Optimal reference trajectories for walking and running of a biped robot, Robotica, 19(05) (2001).
 [22] G. Capi, S.-i. Kaneko, K. Mitobe, L. Barolli, Y. Nasu, Optimal trajectory generation for a prismatic joint biped robot using genetic algorithms, Robotics and autonomous systems, 38(2) (2002) 119-128.
 [23] S.H. Collins, Dynamic Walking Principles Applied to Human Gait, (2008).
[24] N.T. Phuong, T.D. Huy, N.C. Cuong, H.D. Loc, A simple walking control method for biped robot with stable gait, Journal of Computer Science and Cybernetics, 29(2) (2013) 105-115.
 [25] A.D. Kuo, J.M. Donelan, A. Ruina, Energetic consequences of walking like an inverted pendulum: step-to-step transitions, ([HUFLVH and sport sciences reviews, 33(2) (2005) 88-97.
[26] T. McGeer, Passive walking with knees, in: Proceedings., IEEE International Conference on Robotics and Automation, IEEE, 1990, pp. 1640-1645.
[27] P.G. Adamczyk, A.D. Kuo, Mechanical and energetic consequences of rolling foot shape in human walking, J ([S Biol, 216(Pt 14) (2013) 2722-2731.
 [28] O. Darici, H. Temeltas, A.D. Kuo, Optimal regulation of bipedal walking speed despite an XQH[SHFWHG bump in the road, PLoS One, 13(9) (2018) e0204205.
[29] P.G. Adamczyk, A.D. Kuo, Redirection of center-of[1]mass velocity during the step-to-step transition of human walking, J ([S Biol, 212(Pt 16) (2009) 2668-2678.
 [30] B.R. Whittington, D.G. Thelen, A simple mass-spring model with roller feet can induce the ground reactions observed in human walking, J Biomech Eng, 131(1) (2009) 011013.
 [31] W. Zijlstra, A.L. Hof, Displacement of the pelvis during human walking: H[SHULPHQWDO data and model predictions, Gait & posture, 6(3) (1997)249-262.