N. Bernstein, The Coordination and Regulation of Movements, 1967.

P. Morasso, Spatial control of arm movements, Experimental Brain Research, vol.42, issue.2, pp.223-227, 1981.
DOI : 10.1007/BF00236911

J. Soechting and F. Lacquaniti, Invariant characteristics of a pointing movement in man, J Neurosci, vol.1, pp.710-720, 1981.

W. Abend, E. Bizzi, and P. Morasso, HUMAN ARM TRAJECTORY FORMATION, Brain, vol.105, issue.2, pp.331-348, 1982.
DOI : 10.1093/brain/105.2.331

M. Hollerbach and T. Flash, Dynamic interactions between limb segments during planar arm movement, Biological Cybernetics, vol.1, issue.1, pp.67-77, 1982.
DOI : 10.1007/BF00353957

C. Atkeson and J. Hollerbach, Kinematic features of unrestrained vertical arm movements, J Neurosci, vol.5, pp.2318-2330, 1985.

J. Boessenkool, E. Nijhof, and C. Erkelens, A comparison of curvatures of left and right hand movements in a simple pointing task, Experimental Brain Research, vol.120, issue.3, pp.369-376, 1998.
DOI : 10.1007/s002210050410

K. Nishikawa, S. Murray, and M. Flanders, Do arm postures vary with the speed of reaching?, J Neurophysiol, vol.81, pp.2582-2586, 1999.

F. Hermens and S. Gielen, Posture-based or trajectory-based movement planning: a comparison of direct and indirect pointing movements, Experimental Brain Research, vol.14, issue.3, pp.340-348, 2004.
DOI : 10.1007/s00221-004-1959-1

E. Todorov, Optimal Control Theory, Bayesian Brain: Probabilistic Approaches to Neural Coding Doya K, pp.269-298, 2006.
DOI : 10.7551/mitpress/9780262042383.003.0012

R. Kalman, When Is a Linear Control System Optimal?, Journal of Basic Engineering, vol.86, issue.1, pp.51-60, 1964.
DOI : 10.1115/1.3653115

A. Ng and S. Russell, Algorithms for inverse reinforcement learning, Proceedings of the 17th International Conference on Machine Learning, pp.663-670, 2000.

K. Körding and D. Wolpert, The loss function of sensorimotor learning, Proceedings of the National Academy of Sciences, vol.101, issue.26, pp.9839-9842, 2004.
DOI : 10.1073/pnas.0308394101

S. Ben-itzhak and A. Karniel, Minimum Acceleration Criterion with Constraints Implies Bang-Bang Control as an Underlying Principle for Optimal Trajectories of Arm Reaching Movements, Neural Computation, vol.3, issue.3, pp.779-812, 2007.
DOI : 10.1007/BF00204593

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

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.

E. Nakano, H. Imamizu, R. Osu, Y. Uno, and H. Gomi, Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model, J Neurophysiol, vol.81, pp.2140-2155, 1999.

A. Biess, D. Liebermann, and T. Flash, A Computational Model for Redundant Human Three-Dimensional Pointing Movements: Integration of Independent Spatial and Temporal Motor Plans Simplifies Movement Dynamics, Journal of Neuroscience, vol.27, issue.48, pp.13045-13064, 2007.
DOI : 10.1523/JNEUROSCI.4334-06.2007

W. Nelson, Physical principles for economies of skilled movements, Biological Cybernetics, vol.1, issue.2, pp.135-147, 1983.
DOI : 10.1007/BF00339982

J. Soechting, C. Buneo, U. Herrmann, and M. Flanders, Moving effortlessly in three dimensions: does Donders' law apply to arm movement?, J Neurosci, vol.15, pp.6271-6280, 1995.

R. Alexander, A minimum energy cost hypothesis for human arm trajectories, Biological Cybernetics, vol.76, issue.2, pp.97-105, 1997.
DOI : 10.1007/s004220050324

J. Nishii and T. Murakami, Energetic optimality of arm trajectory, Proceedings of the International Conference on Biomechanics of Man, pp.30-33, 2002.

M. Admiraal, M. Kusters, and S. Gielen, Modeling Kinematics and Dynamics of Human Arm Movements, Motor Control, vol.8, issue.3, pp.312-338, 2004.
DOI : 10.1123/mcj.8.3.312

T. Kang, J. He, and S. Tillery, Determining natural arm configuration along reaching trajectory, Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No.03CH37439), pp.352-361, 2005.
DOI : 10.1109/IEMBS.2003.1279599

E. Guigon, P. Baraduc, and M. Desmurget, Computational Motor Control: Redundancy and Invariance, Journal of Neurophysiology, vol.97, issue.1, pp.331-347, 2007.
DOI : 10.1152/jn.00290.2006

URL : https://hal.archives-ouvertes.fr/inserm-00214133

C. Harris and D. Wolpert, Signal-dependent noise determines motor planning, Nature, vol.394, issue.6695, pp.780-784, 1998.
DOI : 10.1038/29528

E. Todorov and M. Jordan, Optimal feedback control as a theory of motor coordination, Nature Neuroscience, vol.5, issue.11, pp.1226-1235, 2002.
DOI : 10.1038/nn963

E. Todorov, Optimality principles in sensorimotor control, Nature Neuroscience, vol.4, issue.9, pp.907-915, 2004.
DOI : 10.1038/73964

S. Scott, Optimal feedback control and the neural basis of volitional motor control, Nature Reviews Neuroscience, vol.195, issue.7, pp.532-546, 2004.
DOI : 10.1038/nn1102-1110

M. Flanders and U. Herrmann, Two components of muscle activation: scaling with the speed of arm movement, J Neurophysiol, vol.67, pp.931-943, 1992.

C. Buneo, J. Soechting, and M. Flanders, Muscle activation patterns for reaching: the representation of distance and time, J Neurophysiol, vol.71, pp.1546-1558, 1994.

J. Soechting and M. Flanders, Movement planning: kinematics, dynamics, both or neither? In: Vision and Action Harris LR, pp.332-349, 1998.

K. Thoroughman and K. Feller, Gravitational effects on torque change and variance optimization in reaching movements In: Abstract Viewer/Itinerary Planner, 2003.

C. Papaxanthis, T. Pozzo, and P. Stapley, Effects of movement direction upon kinematic characteristics of vertical arm pointing movements in man, Neuroscience Letters, vol.253, issue.2, pp.103-106, 1998.
DOI : 10.1016/S0304-3940(98)00604-1

C. Papaxanthis, T. Pozzo, and M. Schieppati, Trajectories of arm pointing movements on the sagittal plane vary with both direction and speed, Experimental Brain Research, vol.99, issue.4, pp.498-503, 2003.
DOI : 10.1007/s002210050397

R. Gentili, V. Cahouet, and C. Papaxanthis, Motor planning of arm movements is direction-dependent in the gravity field, Neuroscience, vol.145, issue.1, pp.20-32, 2007.
DOI : 10.1016/j.neuroscience.2006.11.035

URL : https://hal.archives-ouvertes.fr/hal-00280944

A. Seac-'h and J. Mcintyre, Multimodal reference frame for the planning of vertical arms movements, Neurosci Lett, vol.423, pp.211-215, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00306375

C. Papaxanthis, T. Pozzo, and J. Mcintyre, Kinematic and dynamic processes for the control of pointing movements in humans revealed by short-term exposure to microgravity, Neuroscience, vol.135, issue.2, pp.371-383, 2005.
DOI : 10.1016/j.neuroscience.2005.06.063

M. Hirsch, Differential Topology. Graduate Texts in Mathematics, 1976.

L. Pontryagin, V. Boltyanskii, R. Gamkrelidze, and E. Mishchenko, The Mathematical Theory of Optimal Processes, 1964.

F. Clarke, Optimisation and Nonsmooth Analysis, 1983.

B. Berret, J. Gauthier, and C. Papaxanthis, How humans control arm movements, Proceedings of the Steklov Institute of Mathematics, vol.261, issue.1, pp.44-58, 2008.
DOI : 10.1134/S0081543808020053

M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities. Graduate Texts in Mathematics, 1973.
DOI : 10.1007/978-1-4615-7904-5

M. Dornay, M. Kawato, and R. Suzuki, Minimum Muscle-Tension Change Trajectories Predicted by Using a 17-Muscle Model of the Monkey's Arm, Journal of Motor Behavior, vol.60, issue.2, pp.83-100, 1996.
DOI : 10.1007/BF00204593

J. Nishii, An analytical estimation of the energy cost for legged locomotion, Journal of Theoretical Biology, vol.238, issue.3, pp.636-645, 2006.
DOI : 10.1016/j.jtbi.2005.06.027

A. Feldman, V. Goussev, A. Sangole, and M. Levin, Threshold position control and the principle of minimal interaction in motor actions, Prog Brain Res, vol.165, pp.267-281, 2007.
DOI : 10.1016/S0079-6123(06)65017-6

D. Flament, J. Hore, and T. Vilis, Braking of fast and accurate elbow flexions in the monkey., The Journal of Physiology, vol.349, issue.1, pp.195-202, 1984.
DOI : 10.1113/jphysiol.1984.sp015152

S. Engelbrecht, Minimum Principles in Motor Control, Journal of Mathematical Psychology, vol.45, issue.3, pp.497-542, 2001.
DOI : 10.1006/jmps.2000.1295

J. Pellegrini and M. Flanders, Force path curvature and conserved features of muscle activation, Experimental Brain Research, vol.110, issue.1, pp.80-90, 1996.
DOI : 10.1007/BF00241377

A. Avella, A. Portone, L. Fernandez, and F. Lacquaniti, Control of Fast-Reaching Movements by Muscle Synergy Combinations, Journal of Neuroscience, vol.26, issue.30, pp.7791-7810, 2006.
DOI : 10.1523/JNEUROSCI.0830-06.2006

M. Flanders, J. Pellegrini, and S. Geisler, Basic features of phasic activation for reaching in vertical planes, Experimental Brain Research, vol.110, issue.1, pp.67-79, 1996.
DOI : 10.1007/BF00241376

I. Kurtzer, T. Herter, and S. Scott, Random change in cortical load representation suggests distinct control of posture and movement, Nature Neuroscience, vol.13, pp.498-504, 2005.
DOI : 10.1016/j.tics.2004.09.009

I. Loram, S. Kelly, and M. Lakie, Human balancing of an inverted pendulum: is sway size controlled by ankle impedance?, The Journal of Physiology, vol.80, issue.3, pp.879-891, 2001.
DOI : 10.1111/j.1469-7793.2001.0879e.x

J. Soechting, Effect of target size on spatial and temporal characteristics of a pointing movement in man, Experimental Brain Research, vol.54, issue.1, pp.121-132, 1984.
DOI : 10.1007/BF00235824

E. Lee and M. L. , Foundations of Optimal Control Theory, 1967.

D. Winter, Biomechanics and Motor Control of Human Movement, 1990.
DOI : 10.1002/9780470549148

R. Abraham and R. J. , Transversal Mappings and Flows, 1967.

J. Gauthier and I. Kupka, Deterministic observation theory and applications, 2001.
DOI : 10.1017/CBO9780511546648

B. Bonnard, Invariants in the feedback classification of nonlinear systems, pp.13-22, 1989.
DOI : 10.1007/BFb0043013

J. Gauthier and V. Zakalyukin, On the One-Step-Bracket-Generating Motion Planning Problem, Journal of Dynamical and Control Systems, vol.74, issue.8, pp.215-235, 2005.
DOI : 10.1007/s10883-005-4171-0

M. Hallett and C. Marsden, Ballistic flexion movements of the human thumb., The Journal of Physiology, vol.294, issue.1, pp.33-50, 1979.
DOI : 10.1113/jphysiol.1979.sp012913