R. M. Alexander, A minimum energy cost hypothesis for human arm trajectories, Biol. Cybern, vol.76, pp.97-105, 1997.

F. S. Alnajjar, T. Wojtara, H. Kimura, and S. Shimoda, Muscle synergy space: learning model to create an optimal muscle synergy, Front. Comput. Neurosci, vol.7, p.136, 2013.

K. J. Astrom, Adaptive feedback control, Proc. IEEE, vol.75, pp.185-217, 1987.

A. J. Bastian, T. A. Martin, J. G. Keating, and W. T. Thach, Cerebellar ataxia: abnormal control of interaction torques across multiple joints, J. Neurophysiol, vol.76, pp.492-509, 1996.

N. Bernstein, The Co-ordination and Regulation of Movements, 1967.

, Frontiers in Computational Neuroscience www.frontiersin.org February, vol.8, 2014.

E. Bizzi, F. A. Mussa-ivaldi, and S. Giszter, Computations underlying the execution of movement: a biological perspective, Science, vol.253, pp.287-291, 1991.

D. A. Braun, A. Aertsen, D. M. Wolpert, and C. Mehring, Learning optimal adaptation strategies in unpredictable motor tasks, J. Neurosci, vol.29, pp.6472-6478, 2009.

W. Caarls, MatODE. Available online at, 2010.

M. Coesmans, J. T. Weber, C. I. De-zeeuw, H. , and C. , Bidirectional parallel fiber plasticity in the cerebellum under climbing fiber control, Neuron, vol.44, pp.691-700, 2004.

A. D'avella, P. Saltiel, and E. Bizzi, Combinations of muscle synergies in the construction of a natural motor behavior, Nat. Neurosci, vol.6, p.300, 2003.

P. De-leva, Adjustments to Zatsiorsky-Seluyanov's segment inertia parameters, J. Biomech, vol.29, 1996.

M. Desmurget and S. Grafton, Forward modeling allows feedback control for fast reaching movements, Trends Cogn. Sci, vol.4, pp.1537-1537, 2000.

T. Flash and N. Hogan, The coordination of arm movements: an experimentally confirmed mathematical model, J. Neurosci, vol.5, pp.1688-1703, 1985.

P. L. Gribble and D. J. Ostry, Compensation for interaction torques during single-and multijoint limb movement, J. Neurophysiol, vol.82, pp.2310-2326, 1999.

E. Guigon, P. Baraduc, and M. Desmurget, Computational motor control: redundancy and invariance, J. Neurophysiol, vol.97, pp.331-347, 2007.
URL : https://hal.archives-ouvertes.fr/inserm-00214133

C. Harris and D. Wolpert, Signal-dependent noise determines motor planning, Nature, vol.394, pp.780-784, 1998.

M. Ito, Neural design of the cerebellar motor control system, Brain Res, vol.40, pp.81-84, 1972.

M. Kawato, Internal models for motor control and trajectory planning, Curr. Opin. Neurobiol, vol.9, pp.718-727, 1999.

M. Kawato, K. Furukawa, and R. Suzuki, A hierarchical neural-network model for control and learning of voluntary movement, Biol. Cybern, vol.57, pp.169-185, 1987.

M. Kawato and H. Gomi, A computational model of four regions of the cerebellum based on feedback-error learning, Biol. Cybern, vol.68, pp.95-103, 1992.

M. Kawato and H. Gomi, The cerebellum and VOR/OKR learning models, Trends Neurosci, vol.15, pp.445-453, 1992.

S. Kitazawa, T. Kimura, and P. B. Yin, Cerebellar complex spikes encode both destinations and errors in arm movements, Nature, vol.392, pp.494-497, 1998.

R. Marino and P. Tomei, Global adaptive output-feedback control of nonlinear systems. II. Nonlinear parameterization, IEEE Trans. Autom. Control, vol.38, pp.33-48, 1993.

Y. Nakamura, Advanced Robotics: Redundancy and Optimization. Series in electrical and computer engineering, 1991.

J. Nakanishi, R. Cory, M. Mistry, J. Peters, and S. Schaal, Operational space control: a theoretical and empirical comparison, Int. J. Robot. Res, vol.27, pp.737-757, 2008.

J. Nakanishi and S. Schaal, Feedback error learning and nonlinear adaptive control, Neural Netw, vol.17, pp.1453-1465, 2004.

D. Nguyen-tuong and J. Peters, Model learning for robot control: a survey, Cogn. Process, vol.12, pp.319-340, 2011.

J. Peters and S. Schaal, Learning to control in operational space, Int. J. Robot. Res, vol.27, pp.197-212, 2008.

R. Smith, Open dynamics engine, 2000.

N. Schweighofer, J. Spoelstra, M. A. Arbib, and M. Kawato, Role of the cerebellum in reaching movements in humans. II. A neural model of the intermediate cerebellum, Eur. J. Neurosci, vol.10, pp.95-105, 1998.

R. Shadmehr and F. A. Mussa-ivaldi, Adaptive representation of dynamics during learning of a motor task, J. Neurosci, vol.14, pp.3208-3224, 1994.

R. Shadmehr and S. P. Wise, The Computational Neurobiology of Reaching and Pointing: A Foundation for Motor Learning, 2005.

S. Shimoda and H. Kimura, Biomimetic approach to tacit learning based on compound control, IEEE Trans. Syst. Man Cybern. B Cybern, vol.40, pp.77-90, 2010.

S. Shimoda, Y. Yoshihara, and H. Kimura, Adaptability of tacit learning in bipedal locomotion, IEEE Trans. Auton. Ment. Dev, vol.5, pp.152-161, 2013.

E. Todorov, Optimality principles in sensorimotor control, Nat. Neurosci, vol.7, pp.907-915, 2004.

E. Todorov, J. , and M. I. , Optimal feedback control as a theory of motor coordination, Nat. Neurosci, vol.5, pp.1226-1235, 2002.

Y. Uno, M. Kawato, and R. Suzuki, Formation and control of optimal trajectory in human multijoint arm movement. Minimum torque-change model, Biol. Cybern, vol.61, pp.89-101, 1989.

R. Van-den-brand, J. Heutschi, Q. Barraud, J. Digiovanna, K. Bartholdi et al., Restoring voluntary control of locomotion after paralyzing spinal cord injury, Science, vol.336, pp.1182-1185, 2012.

D. M. Wolpert, R. C. Miall, and M. Kawato, Internal models in the cerebellum, Trends Cogn. Sci, vol.2, pp.338-347, 1998.

, Conflict of Interest Statement: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest