This content is not included in
your SAE MOBILUS subscription, or you are not logged in.
Alternative Formulations for Optimization-based-Digital Human Motion Prediction
Technical Paper
2005-01-2691
ISSN: 0148-7191, e-ISSN: 2688-3627
Annotation ability available
Sector:
Language:
English
Abstract
Simulating human motion is a complex problem due to redundancy of the human musculoskeletal system. The concept of task-based motion prediction using single- or multi-objective optimization techniques provides a viable approach for predicting intermediate motions of digital humans. It is shown that task-based motion prediction is in fact a numerical optimal control problem. Alternative formulations for simulation of human motion are possible and can be solved by modern nonlinear optimization methods. Three techniques based on state variable elimination, direct collocation and differential inclusion are presented and compared. The basic idea of the formulations is to treat different combinations of the state variables, such as the joint profiles and torques or their parametric representations as independent variables in the optimization process. Different ways to discretize the equations of motion are also presented, namely finite difference, piecewise polynomial interpolation and series expansion. The advantages and disadvantages of different formulations are discussed. A numerical example is used to illustrate the basic ideas, and is solved by a large-scale sparse nonlinear programming solver. It is concluded that with the aid of motion tracking for validation, optimal control techniques based on nonlinear optimization have great potential to provide a useful tool for realistic human motion prediction.
Authors
Citation
Wang, Q., Xiang, Y., Kim, H., Arora, J. et al., "Alternative Formulations for Optimization-based-Digital Human Motion Prediction," SAE Technical Paper 2005-01-2691, 2005, https://doi.org/10.4271/2005-01-2691.Also In
References
- Abdel-Malek, K. Yu, W. Jaber, M. Duncan, J. 2002 Realistic posture prediction for maximum dexterity SAE Transactions J. Passenger Cars-Mechanical Sytems 110 6 2241 2249
- Albuquerque, J.S. Biegler, L.T. 1997 Decomposition algorithms for on-line estimation with nonlinear DAE models Comp. & Chem. Eng. 21 3 283 299
- Alexander, R.M. 1997 A minimum energy cost hypothesis for human arm trajectories Biological Cybernetics 76 97 105
- Anderson, F.C. Ziegler, J.M. Pandy, M.G. Whalen, R.T. 1995 Application of high-performance computing to simulation of human movement J. Biomechanical Eng., Transactions of the ASME, 117 155 157
- Atkinson, K.E. 1988 An Introduction to Numerical Analysis New York John Wiley and Sons
- Arora, J.S. 1999 Optimization of structures subjected to dynamic loads Leondes, C.T. Structural Dynamic Systems Computational Techniques and Optimization: Optimization Techniques 1 72 The Netherlands Gordon and Breach Science Publishers
- Arora, J.S. 2004 Introduction to Optimum Design Second Elsevier Academic Press
- Audu, M.L. Davy, D.T. 1988 Comparison of optimal control algorithms for complex bioengineering studies Optim. Cont. Appl. & Meth. 9 1 101 106
- Bathe, K.-J. 1982 Finite Element Procedures in Engineering Analysis Englewood Cliffs, New Jersey Prentice-Hall Inc.
- Betts, J.T. 1990 Sparse Jacobian updates in the collocation method for optimal control problems J. Guidance, Cont. Dyn. 13 3 409 415
- Betts, J.T. Huffman, W.P. 1992 Application of sparse nonlinear programming to trajectory optimization J. Guidance, Cont. Dyn. 15 1 198 206
- Betts, J.T. 1998 Survey of numerical methods for trajectory optimization J. Guidance, Cont. Dyn. 21 2 193 207
- Betts, J.T. 2000 Very low-thrust trajectory optimization using a direct SQP method J. Comp. Appl. Math. 120 1 27 40
- Betts, J.T. Biehn, N. Campbell, S.L. Huffman, W.P. 2000 Compensating for order variation in mesh refinement for direct transcription methods J. Comp. Appl. Math. 125 1-2 147 158
- Betts, J.T. Biehn, N. Campbell, S.L. Huffman, W.P. 2002 Compensating for order variation in mesh refinement for direct transcription methods II: computational experience J. Comp. Appl. Math . 143 2 237 261
- Biegler, L.T. 1988 On the simultaneous solution and optimization of large scale engineering systems Comp. Chem. Eng. 12 357 369
- Biegler, L.T. Ghattas, O. Heinkenschloss, M. Bloemen Waanders, B.v. 2003 Large-Scale PDE-Constrained Optimization, Lecture Notes in Computational Science and Engineering 30 Berlin Springer-Verlag
- Bottasso, C. Croce, A. 2004 Optimal control of multibody systems using an energy preserving direct transcript method Multibody Sys. Dyn. 12 17 45
- Bryson, A.E. Ho, Y.C. 1975 Applied Optimal Control . New York Hemishper Publishing
- Cervantes, A. Biegler, L.T. 1998 Large-scale DAE optimization using a simultaneous NLP formulation AIChE J. 44 5 1038 1050
- Cervantes, A.M. Wächter, A. Tütüncü, R.H. Biegler, L.T. 2000 A reduced space interior point strategy for optimization of differential algebraic systems Comp. & Chem. Eng. 24 1 39 51
- Chaffin, D.B. 1997 Development of computerized human static strength simulation model for job design Human Factors & Ergonomics in Manufacturing , 7 305 322
- Chen, Y.-C. 1991 Solving robot trajectory planning problems with uniform cubic B-splines Optim. Cont. Appl. & Meth. 12 247 262
- Chow, C.K. Jacobson, D.H. 1971 Studies of human locomotion via optimal programming Math. Biosci. 10 293 306
- Conway, B.A. Larson, K.M. 1998 Collocation versus differential inclusion in direct optimization J. Guidance, Cont. Dyn. 21 5 780 785
- Coverstone-Carroll, V. Williams, S.N. 1994 Optimal low thrust trajectories using differential inclusion concepts J. Astron. Sci. 42 4 379 393
- Denavit, J. Hartenberg, R.S. 1955 A Kinematic notation for lower-pair mechanisms based on matrices J. Applied Mechanics , 77 215 221
- Dissanayake, M.W.M.G. Goh, C.J. Phan-Thien, N. 1991 Time-optimal trajectories for robot manipulators Robotica , 9 131 138
- Enright, P.J. Conway, B.A. 1992 Discrete approximation to optimal trajectories using direct transcription and nonlinear programming J. Guidance, Cont. Dyn . 15 4 994 1002
- Fahroo, F. Ross, I.M. 2002 Direct trajectory optimization by a Chebyshev pseudospectral method J. Guidance, Cont. Dyn . 25 1 160 166
- Faraway, J.J. Zhang, X.D. Chaffin, D.B. 1999 Rectifying postures reconstructed from joint angles to meet constraints J. Biomechanics , 32 733 736
- Furukawa, T. 2002 Time-subminimal trajectory planning for discrete non-linear systems Eng. Optim. 34 219 243
- Gill, P.E. Murray, W. Saunders, M.A. 2002 SNOPT: An SQP algorithm for large-scale constrained optimization SIAM J. Optim. 12 979 1006
- Goh, C.J. Edwards, N.J. Zomaya, A.Y. 1993 Feedback control of minimum-time optimal control problems using neural networks Optim. Cont. Appl. & Meth. 14 1 16
- Haftka, R.T. 1985 Simultaneous analysis and design AIAA J. 23 7 1099 1103
- Hargraves, C.R. Paris, S.W. 1987 Direct trajectory optimization using nonlinear programming and collocation J. Guidance, Cont. Dyn. 10 4 338 342
- Hase, K. Yamazaki, N. 1997 Development of three-dimensional whole-body musculoskeletal model for various motion analyses JSME Int. J. , Series C 40 1 25 32
- Herman, A.L. Conway, B.A. 1995 Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules J. Guidance, Cont. Dyn. 19 3 592 599
- Hsieh, C.C. Arora, J.S. 1984 Design sensitivity analysis and optimization of dynamic response Appl. Math. & Optim . 43 2 195 219
- Hu, G.S. Ong, C.J. Teo, C.L. 2002 An enhanced transcribing scheme for the numerical solution of a class of optimal control problems Eng. Optim. 34 2 155 173
- Hull, D.G. 1997 Conversion of optimal control problems into parameter optimization problems J. Guidance, Cont. Dyn. 20 1 57 60
- Hull, D.G. 2003 Optimal Control Theory for Applications New York Springer-Verlag
- Jung, E.S. Choe, J. 1996 Human reach posture prediction based on psychophysical discomfort” Int. J. of Industrial Ergonomics 18 2-3 173 179
- Kaplan, M.L. Heegaard J.H. 2001 Predictive algorithms for neuromuscular control of human locomotion J. Biomechanics 34 8 1077 1083
- Kaplan, M.L. Heegaard, J.H. 2002 Second-order optimal control algorithm for complex systems Int. J. Num. Meth. Eng. 53 9 2043 2060
- Khang, G. Zajac, F.E. 1989a Paraplegic standing controlled by functional neuromuscular stimulation -I: Computer model and control-system design IEEE Transactions on Biomedical Eng. 36 9 873 884
- Khang, G. Zajac, F.E. 1989b Paraplegic standing controlled by functional neuromuscular stimulation -II: Computer simulation studies IEEE Transactions on Biomedical Eng. 36 9 885 894
- Kim, J.H. 2004 Human performance measures Technical Report No. VSR-04.02. Virtual Soldier Research program/CCAD The University of Iowa Iowa City, IA 52242
- Kota, N.N. 1996 Computational Methods for Nonlinear Optimal Control Ph.D. Dissertation Department of Mechanical Engineering, University of Iowa Iowa City 52242
- Kraft, D. 1985 On converting optimal control problems into nonlinear programming codes Schittkowski, K. Computational Mathematical Programming 261 280 Berlin Springer
- Kumar, R.R. Seywald, H. 1996 Should controls be eliminated while solving optimal control problems via direct methods? J. Guidance, Cont. Dyn . 19 2 418 423
- Leineweber, D.B. Bauer, I. Bock, H.G. Schloder, J.P. 2003 An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: Theoretical aspects Comp. & Chem. Eng. 27 2 157 166
- Lo, J. Huang, G. Metaxas, D. 2002 Human motion planning based on recursive dynamics and optimal control techniques Multibody Sys. Dyn. 8 4 433 458
- Luo, Z.-Q. Pang, J.-S. Ralph, D. 1996 Mathematical Programs with Equilibrium Constraints Cambridge Cambridge University Press
- Marler, R.T. 2004 Development of real-time multi-objective optimization-based posture prediction Technical Report No. VSR-04.02. Virtual Soldier Research program/CCAD The University of Iowa Iowa City, IA 52242
- Marler, R.T. Arora, J.S. 2004 Survey of multi-objective optimization methods for engineering Struct. Multidisc. Optim. 26 6 369 395
- Mi, Z. 2004 Task-based Prediction of Upper Body Motion PhD Dissertation Department of Mechanical Engineering, University of Iowa Iowa City, IA 52242
- Mortenson, M.E. 1985 Geometric Modeling New York, NY John Wiley & Sons, Inc.
- Neptune, R.R Hull, M.L. 1998 Evaluation of performance criteria for simulation of submaximal steady-state cycling using a forward dynamic model J. Biomechanical Eng. 120 334 340
- Pandy, M.G. Zajac, F.E. Sim, E. Levine, W.S. 1990 Optimal control model for maximum-height human jumping J. Biomechanics 23 12 1185 1198
- Pandy, M.G. Anderson, F.C. Hull, D.G. 1992 A Parameter optimization approach for the optimal control of large-scale musculoskeletal systems J. Biomechanical Eng., Transactions of the ASME, 114 4 450 460
- Pandy, M.G. Garner, B.A. Anderson, F.C. 1995 Optimal control of non-ballistic muscular movements: A constraint-based performance criterion for rising from a chair J. Biomechanical Eng., Transactions of the ASME 117 1 15 26
- Paul, R.P. 1981 Robot Manipulators: Mathematics, Programming, and Control. Cambridge, Massachusetts MIT Press
- Piegl, L. Tiller, W. 1997 The NURBS Book 2nd New York, NY Springer-Verlag
- Pontryagin, L.S. Boltyanskii, V. Gamkrelidze, R. Mishchenko, E. 1962 The mathematical Theory of Optimal Process New York Interscience Publishers Inc.
- Ross, I.M. Fahroo, F. 2004 Pseudospectral knotting methods for solving optimal control problems J. Guidance, Cont. Dyn. 27 3 397 405
- Seywald, H. 1994 Trajectory optimization based on differential inclusion J. Guidance, Cont. Dyn. 17 3 480 487
- Schulz, V. 2004 Simultaneous solution approaches for large optimization problems J. Comp. Appl. Math. 164 1 629 641
- Tanartkit, P. Biegler, L.T. 1996 Reformulating ill-conditioned differential - algebraic equation optimization problems Indus. & Eng. Chem. Res. 35 6 1853 1865
- Tashman, S. Zajac, F.E. Perkash, I. 1995 Modeling and simulation of paraplegic ambulation in a reciprocating gait orthosis J. Biomechanical Eng., Transactions of the ASME 117 3 300 308
- Tseng, C.H. Arora, J.S. 1989 Optimum design of systems for dynamics and controls using sequential quadratic programming AIAA J. 27 1793 1800
- Vlassenbroeck, J. 1988 A Chebyshev polynomial method for optimal control with state constraints Automatica 24 4 499 506
- von Stryk, O. Bulirsch, R. 1992 Direct and indirect methods for trajectory optimization Annals of Operations Research , 37 357 373
- Wang, C.-Y.E. Timoszyk, W.K. Bobrow, J.E. 2001 Payload maximization for open chained manipulators: Finding weightlifting motions for a Puma 762 robot IEEE Trans. Robot. & Autom. 17 2 218 224
- Wang, Q. Arora, J.S. 2004 Alternate formulations for transient dynamic response optimization AIAA J.
- Williams, P. 2004 Jacobi pseudospectral method for solving optimal control problems J. Guidance, Cont. Dyn. 27 2 293 297
- Yang, J. Marler, R.T. Kim, H. Arora, J. Abdel-Malek, K. 2004 Multi-objective optimization for upper body posture prediction 10th AIAA/ISSMO Multi-disciplinary Analysis and Optimization Conf. August Albany, NY