Abstract
In this paper, we discuss numerical foundations and computational results for inverse optimal control of human locomotion based on human motion capture data. The task of inverse optimal control is to identify the precise underlying objective function that is optimized in an observed motion. The presented methods can cope with partial and imprecise measurements of the state variables which is typically the case for motion capture recordings. We investigate human walking and running motions on different levels of detail and consequently different underlying models which all have their own motivation depending on the question asked. Whole-body models are used to explore the mechanisms of motions on joint level, while simple models describing the subject as a single entity can be used to describe overall locomotion behavior. At an intermediate level, template models describe some relative motions of bodies while maintaining simplicity and computational efficiency. Results will be presented for all model types and different walking tasks. We also show for some of them how the identified objective functions can be used to generate new waking motions for humanoid robots in novel scenarios.
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References
M. Ackermann, A.J. van den Bogert, Optimality principles for model-based prediction of human gait. J. Biomech. 43(6), 1055–1060 (2010)
N. Aghasadeghi, T. Bretl, Maximum entropy inverse reinforcement learning in continuous state spaces with path integrals, in Proceedings of IEEE/RSJ IROS (2011)
S. Albrecht, C. Passenberg, M. Sobotka, A. Peer, M. Buss, M. Ulbrich, Optimization criteria for human trajectory formation in dynamic virtual environments. in Haptics: Generating and Perceiving Tangible Sensations, LNCS (2010)
R.M. Alexander, The gaits of bipedal and quadrupedal animals. Intern. J. Robot. Res. 3(2), 49–59 (1984)
R.M. Alexander, Optima for Animals (Princeton University Press, New Jersey, 1996)
C.G. Atkeson, S. Schaal, Learning control in robotics. IEEE Robot. Autom. Mag. 17, 20–29 (2010)
C.G. Atkeson, C. Liu, Trajectory-based dynamic programming, in Modeling, Simulation and Optimization of Bipedal Walking Cognitive Systems Monographs, vol 18 (Springer, Berlin Heidelberg, 2013), pp. 1–15
B. Berret, E. Chiovetto, F. Nori, T. Pozzo, Evidence for composite cost functions in arm movement planning: an inverse optimal control approach. PLoS Comput. Biol. 7(10) (2011)
H.G. Bock, K.-J. Plitt, A multiple shooting algorithm for direct solution of optimal control problems, in Proceedings of the 9th IFAC World Congress, Budapest, (International Federation of Automatic Control, 1984), pp. 242–247
T. Buschmann, S. Lohmeier, M. Bachmayer, H. Ulbrich, F. Pfeiffer, A collocation method for real-time walking pattern generator, in Proceedings of the IEEE-RAS International Conference on Humanoid Robots (2007)
D. Clever, K. Mombaur, A new template model for optimization studies of human walking on different terrains, in 2014 14th IEEE-RAS International Conference on Humanoid Robots (Humanoids), (IEEE, 2014), pp. 500–505
D. Clever, K. Mombaur, An inverse optimal control approach for the transfer of human walking motions in constrained environment to humanoid robots, in Robotics: Science and Systems (RSS) (2016)
D. Clever, K. Mombaur, On the relevance of common humanoid gait generation strategies in human locomotion - an inverse optimal control approach, in Modeling, Simulation and Optimization of Complex Processes - HPSC 2015, ed. by X.P. Hoang, R. Rannacher, J. Schlöder, H.G. Bock (Springer, Heidelberg, 2016) (to appear)
D. Clever, R.M. Schemschat, M.L. Felis, K. Mombaur, Inverse optimal control based identification of optimality criteria in whole-body human walking on level ground, in Proceedings of International Conference on Biomedical Robotics and Biomechatronics (BioRob2016) (2016)
P. De Leva, Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters. J. biomech. 29(9), 1223–1230 (1996)
S. Dempe, N. Gadhi, Necessary optimality conditions for bilevel set optimization problems. Glob. Optim. 39(4), 529–542 (2007)
A. Dörr, N. Ratliff, J. Bohg, M. Toussaint, S. Schaal, Direct loss minimization inverse optimal control, in Proceedings of Robotics Sciece and Systems (RSS) (2015)
M.L. Felis, K. Mombaur, Synthesis of full-body 3-D human gait using optimal control methods, in IEEE International Conference on Robotics and Automation (ICRA 2016) (2016)
M.L. Felis, K. Mombaur, A. Berthoz, An optimal control approach to reconstruct human gait dynamics from kinematic data, in IEEE/RAS International Conference on Humanoid Robots (Humanoids 2015) (2015), pp. 1044–1051
T. Flash, N. Hogan, The coordination of arm movements: an experimentally confirmed mathematical model. J. Neurosci. 5, 1688–1703 (1984)
T. Geijtenbeek, M. van de Panne, A.F. van der Stappen, Flexible muscle-based locomotion for bipedal creatures. ACM Trans. Graph. 32(6) (2013)
H. Geyer, H. Herr, A muscle-reflex model that encodes principles of legged mechanics produces human walking dynamics and muscle activities. IEEE Trans. Neural Syst. Rehabil. Eng. 18(3), 263–273 (2010)
K. Hatz, Efficient Numerical Methods for Hierarchical Dynamic Optimization with Application to Cerebral Palsy Gait Modeling. Ph.D. thesis, University of Heidelberg (2014)
K. Hatz, J.P. Schlöder, H.G. Bock, Estimating parameters in optimal control problems. SIAM J. Sci. Comput. 34(3), 1707–1728 (2012)
H. Hicheur, Q.-C. Pham, G. Arechavaleta, J.-P. Laumond, A. Berthoz, The formation of trajectories during goal-oriented locomotion in humans I: a stereotyped behaviour. Eur. J. Neurosci. 27(8), 2376–2390 (2007)
M. Horn, M. Sreenivasa, K. Mombaur, Optimization model of the predictive head orientation for humanoid robots, in IEEE/RAS International Conference on Humanoid Robots (Humanoids 2014) (2014)
Y. Hu, K. Mombaur, Analysis of human leg joints compliance in different walking scenarios with an optimal control approach, in IFAC International Workshop on Periodic Control Systems (PSYCO 2016) (2016)
Y. Hu, K. Mombaur, F. Nori, Using optimal control to generate squat motions for the humanoid robot iCub with SEA, in Proceedings of Dynamic Walking (2015)
S. Kajita, T. Nagasaki, K. Kaneko, K. Yokoi, K. Tanie, A running controller of humanoid biped HRP-2LR, in ICRA (2005)
K. Kaneko, F. Kanehiro, S. Kajita, K. Yokoyama, K. Akachi, T. Kawasaki, S. Ota, T. Isozumi, Design of prototype humanoid robotics platform for HRP, in 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3 (IEEE, 2002), pp. 2431–2436
K.H. Koch, K. Mombaur, P. Souères, Studying the effect of different optimization criteria on humanoid walking motions, in Simulation, Modeling, and Programming for Autonomous Robots, Lecture Notes in Computer Science, ed. by I. Noda, N. Ando, D. Brugali, J.J. Kuffner, vol. 7628 (Springer, Berlin Heidelberg, 2012), pp. 221–236
KoroiBot Motion Capture Database. https://koroibot-motion-database.humanoids.kit.edu/ (2016) Last visited, May 2016
J.P. Laumond, G. Arechavaleta, T.-V.-A. Truong, H. Hicheur, Q.-C. Pham, A. Berthoz, The words of the human locomotion, in Proceedings of 13th International Symposium on Robotics Research (ISRR-2007) (Springer Star Series, 2007)
D.B. Leineweber, I. Bauer, H.G. Bock, J.P. Schlöder, An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization - Part I: theoretical aspects (2003), pp. 157 – 166
S. Levine, V. Koltun, Guided policy search, in ICML (2013)
C.K. Liu, A. Hertzmann, Z. Popovic, Learning physics-based motion style with inverse optimization. ACM Trans. Graph. (SIGGRAPH 2005) 24(3), 1071 (2005)
Z.-Q. Luo, J.-S. Pang, D. Ralph, Mathematical Programs with Equilibrium Constraints (Cambridge University Press, Cambridge, 1996)
J. Mainprice, R. Hayne, D. Berenson, Predicting human reaching motion in collaborative tasks using inverse optimal control and iterative re-planning, in 2015 IEEE International Conference on Robotics and Automation (ICRA), (IEEE, 2015), pp. 885–892
C. Mandery, Ö. Terlemez, M. Do, N. Vahrenkamp, T. Asfour, The KIT whole-body human motion database, in IEEE International Conference on Advanced Robotics (ICAR 2015) (2015), pp. 329–336
G. Metta, L. Natale, F. Nori, G. Sandini, D. Vernon, L. Fadiga, C. Von Hofsten, K. Rosander, M. Lopes, J. Santos-Victor et al., The iCub humanoid robot: an open-systems platform for research in cognitive development. Neural Netw. 23(8), 1125–1134 (2010)
K. Mombaur, A.H. Olivier, A. Crétual, Forward and inverse optimal control of bipedal running, in Modeling, Simulation and Optimization of Bipedal Walking, Cognitive Systems Monographs, vol. 18 (Springer, Berlin Heidelberg, 2013), pp. 165–179
K. Mombaur, A. Truong, J.-P. Laumond, From human to humanoid locomotion an inverse optimal control approach. Auton. Robots 28(3), 369–383 (2010)
Motion Similarity Study. https://orb.iwr.uni-heidelberg.de/ratingapp/similarity/ (2016) Last visited, May 2016
J.A. Nelder, R. Mead, A simplex method for function minimization. Comput. J. 7, 308–313 (1965)
J. Ondřej, J. Pettré, A.-H. Olivier, S. Donikian, A synthetic-vision based steering approach for crowd simulation. ACM Trans. Graph. 29(4), 123:1–123:9 (2010)
T. Park, S. Levine, Inverse optimal control for humanoid locomotion, in Robotics Science and Systems-Workshop on Inverse Optimal Control and Robotic Learning from Demonstration (2013)
M.J.D. Powell, A direct search optimization method that models the objective and constraint functions by linear interpolation, in Advances in Optimization and Numerical Analysis (Springer, Heidelberg, 1994), pp. 51–67
M.J.D. Powell, The BOBYQA algorithm for bound constrained optimization without derivatives. Report No. DAMTP 2009/NA06, Centre for Mathematical Sciences, University of Cambridge, UK, 2009
T. Pozzo, A. Berthoz, L. Lefort, Head stabilization during various locomotor tasks in humans. Exp. Brain Res. 82(1), 97–106 (1990)
G. Schultz, K. Mombaur, Modeling and optimal control of human-like running. Trans. Mechatron. 15(5) (2010)
M. Sreenivasa, K. Mombaur, J.P. Laumond, Walking paths to and from a goal differ: on the role of bearing angle in the formation of human locomotion paths. PLOS ONE 10(4) (2015)
Ö. Terlemez, S. Ulbrich, C. Mandery, M. Do, N. Vahrenkamp, T. Asfour, Master motor map (MMM) framework and toolkit for capturing, representing, and reproducing human motion on humanoid robots, in IEEE/RAS International Conference on Humanoid Robots (Humanoids 2014) (2014), pp. 894–901
E. Todorov, Optimality principles in sensorimotor control. Nat. Neurosci. 7(9), 907–915 (2004)
J.J. Ye, Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints. J. Math. Anal. Appl. 307, 350–369 (2005)
Acknowledgements
The research leading to these results has received funding from the EU seventh Framework Program (FP7/2007-2013) under grant agreement no 611909 (KoroiBot), the German Excellence Initiative and the French ANR project Locanthrope. We thank the Simulation and Optimization group of H.G. Bock at Heidelberg University for providing the optimal control code Muscod-II.
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Mombaur, K., Clever, D. (2017). Inverse Optimal Control as a Tool to Understand Human Movement. In: Laumond, JP., Mansard, N., Lasserre, JB. (eds) Geometric and Numerical Foundations of Movements . Springer Tracts in Advanced Robotics, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-51547-2_8
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