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Backward walking simulation of humans using optimization

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Abstract

The objective of this study is to formulate, simulate and study the backward walking motion of a full-body skeletal digital human model using an optimization approach. Predictive dynamics is used to simulate the task in which joint angle profiles are treated as primary unknowns in the formulation. The joint torques are treated as dependent variables that are evaluated directly from the equations of motion. For the performance measure, the normalized dynamic effort represented by the integral of the squares of all the normalized joint torques is minimized subject to the associated physical constraints. Backward walking at different speeds is simulated and analyzed. The backward walking is validated with motion capture data and the available data in the literature. The results of the backward walking motion are compared to those of the forward walking motion in order to study the differences between the two walking patterns. It is seen that the joint torque profiles for hip and knee of backward walk are quite similar to those of forward walk with reverse sequence, but with different time duration of flexion and extension activations. These findings can impact many fields, such as improvement of human performance, rehabilitation from injuries, and others.

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References

  • Arora JS (2012) Introduction to optimum design, 3rd edn. Academic Press

  • Cheng H, Obergefell L, Rizer A (1994) Generator of body (GEBOD) manual, AL/CF-TR-1994-0051. Armstrong Laboratory, Wright-Patterson Air Force Base, Ohio

    Google Scholar 

  • De Boor C (2001) A practical guide to splines. Springer-Verlag

  • Eriksson A (2008) Optimization in target movement simulations. Comput Methods Appl Mech Eng 197:4207–4215

    Article  MATH  Google Scholar 

  • Eriksson A, Nordmark A (2010) Temporal finite element formulation of optimal control in mechanisms. Comput Methods Appl Mech Eng 199:1783–1792

    Article  MATH  MathSciNet  Google Scholar 

  • Fregly BJ, Reinbolt JA, Rooney KL, Mitchell KH, Chmielewski TL (2007) Design of patient-specific gait modifications for knee osteoarthritis rehabilitation. IEEE Trans Biomed Eng 54(9):1687–1695

    Article  Google Scholar 

  • Fu C, Tan F, Chen K (2010) A simple walking strategy for biped walking based on an intermittent sinusoidal oscillator. Robotica 28:869–884

    Article  Google Scholar 

  • Fu KS, Gonzalez RC, Lee CSG (1987) Robotics: control, sensing, vision, and intelligence. McGraw-Hill, New York

    Google Scholar 

  • Gill PE, Murray W, Saunders MA (2002) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM J Optim 12:979–1006

    Article  MATH  MathSciNet  Google Scholar 

  • Grasso R, Bianchi L, Lacquaniti F (1998) Motor patterns for human gait: backward versus forward locomotion. J Neurophysiol 80:1868–1885

    Google Scholar 

  • Hardt M, von Stryk O, Wollherr D, Buss M (2003) Development and control of autonomous, biped locomotion using efficient modeling, simulation, and optimization techniques. Proceeding of IEEE International Conference on Robotics and Automation. 14-19 September. Taipe, page 1356–1361

  • Hollerbach JM (1980) A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity. IEEE Trans Syst Man Cybern 11(10):730–736

    Article  MathSciNet  Google Scholar 

  • Kim JH, Xiang Y, Yang J, Arora JS, Abdel-Malek K (2010) Dynamic motion planning of overarm throw for a biped human multibody system. Multibody Syst Dyn 24(1):1–24

    Article  MATH  MathSciNet  Google Scholar 

  • Kim JH, Xiang Y, Bhatt R, Yang J, Chung HJ, Arora JS, Abdel-Malek K (2009) Generating effective whole-body motions of a human-like mechanism with efficient ZMP formulation. Int J Robot Autom 24(2):125–136

    Google Scholar 

  • Laufer Y (2005) Effect of age on characteristics of forward and backward gait at preferred and accelerated walking speed. J Gerontol Med Sci 60(5):627–632

    Article  Google Scholar 

  • Lin YC, Walter JP, Banks SA, Pandy MG, Fregly BJ (2010) Simultaneous prediction of muscle and contact forces in the knee during gait. J Biomech 43(5):945–952

    Article  Google Scholar 

  • Ma B, Wu Q (2002) Parametric study of repeatable gait of a 5-link biped. Robotica 20:493–498

    Article  Google Scholar 

  • McGeer T (1990) Passive dynamic walking. Int J Robot Res 9:68–82

    Article  Google Scholar 

  • Mu X, Wu Q (2003) Synthesis of a complete sagittal gait cycle for a five-link biped robot. Robotica 21:581–587

    Article  Google Scholar 

  • Pandy MG (2001) Computer modeling and simulation of human movement. Annu Rev Biomed Eng 3:245–273

    Article  Google Scholar 

  • Rahmatalla S, Xiang Y, Smith R, Meusch J, Bhatt R (2011) A validation framework for predictive human models. Int J Hum Factors Model Simul 2(1/2):67–84

    Article  Google Scholar 

  • Ren L, Jones RK, Howard D (2007) Predictive modelling of human walking over a complete gait cycle. J Biomech 40(7):1567–1574

    Article  Google Scholar 

  • Stansfield BW, Hillman SJ, Hazlewood ME, Robb JE (2006) Regression analysis of gait parameters with speed in normal children walking at self-selected speeds. Gait and Posture 23(3):288–294

    Article  Google Scholar 

  • Thelen DG, Anderson FC (2006) Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. J Biomech 39(6):1107–1115

    Article  Google Scholar 

  • Thorstensson A (1986) How is the normal locomotor program modified to produce backward walking?Exp Brain Res 61:664–668

    Article  Google Scholar 

  • von Stryk O, Bulirsch R (1992) Direct and indirect methods for trajectory optimization. Ann Oper Res 37:357–373

    Article  MATH  MathSciNet  Google Scholar 

  • Vilensky JA, Ganlkiewicz E, Gehlsen G (1987) A kinematic comparison of backward and forward walking in humans. J Hum Mov Stud 13:29–50

    Google Scholar 

  • Wang Q, Huang Y, Wang L (2010) Passive dynamic walking with flat feet and ankle compliance. Robotica 28:413–425

    Article  Google Scholar 

  • Winter DA (1984) Kinematic and kinetic patterns in human gait: variability and compensating effects. Hum Mov Sci 3(1–2):51–76

    Article  Google Scholar 

  • Winter DA (1991) The biomechanics and motor control of human gait: normal, elderly and pathological. University of Waterloo Press, Waterloo

    Google Scholar 

  • Winter DA, Pluck N, Yang JF (1989) Backward walking: a simple reversal of forward walking?J Mot Behav 21(3):291–305

    Article  Google Scholar 

  • Xiang Y, Arora JS, Abdel-Malek K (2009a) Optimization-based motion prediction of mechanical systems: sensitivity analysis. Struct Multidiscip Optim 37(6):595–608

    Article  MATH  MathSciNet  Google Scholar 

  • Xiang Y, Arora JS, Rahmatalla S, Abdel-Malek K (2009b) Optimization-based dynamic human walking prediction: one step formulation. Int J Numer Methods Eng 79(6):667–695

    Article  MATH  Google Scholar 

  • Xiang Y, Chung HJ, Kim JH, Bhatt R, Rahmatalla S, Yang J, Marler T, Arora JS, Abdel-Malek K (2010a) Predictive dynamics: an optimization-based novel approach for human motion simulation. Struct Multidiscip Optim 41(3):465–479

    Article  MATH  MathSciNet  Google Scholar 

  • Xiang Y, Arora JS, Rahmatalla S, Marler T, Bhatt R, Abdel-Malek K (2010b) Human lifting simulation using a multi-objective optimization approach. Multibody Syst Dyn 23(4):431–451

    Article  MATH  MathSciNet  Google Scholar 

  • Xiang Y, Arora JS, Abdel-Malek K (2010c) Physics-based modeling and simulation of human walking: a review of optimization-based and other approaches. Struct Multidiscip Optim 42(1):1–23

    Article  MATH  MathSciNet  Google Scholar 

  • Xiang Y, Arora JS, Abdel-Malek K (2011) Optimization-based prediction of asymmetric human gait. J Biomech 44(4):683–693

    Article  Google Scholar 

  • Xiang Y, Arora JS, Chung HJ, Kwon HJ, Rahmatalla S, Bhatt R, Abdel-Malek K (2012a) Predictive simulation of human walking transitions using an optimization formulation. Struct Multidiscip Optim 45(5):759–772

    Article  MATH  MathSciNet  Google Scholar 

  • Xiang Y, Arora JS, Abdel-Malek K (2012b) Hybrid predictive dynamics: a new approach to simulate human motion. Multibody Syst Dyn 28(3):199–224

    Article  MathSciNet  Google Scholar 

  • Zajac FE (1989) Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng 17(4):359–411

    Google Scholar 

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Acknowledgment

This research was supported by projects from US Army TACOM and USCAR.

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Correspondence to Yujiang Xiang.

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Kwon, HJ., Xiang, Y., Bhatt, R. et al. Backward walking simulation of humans using optimization. Struct Multidisc Optim 50, 169–179 (2014). https://doi.org/10.1007/s00158-013-1039-x

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  • DOI: https://doi.org/10.1007/s00158-013-1039-x

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