R. Alexander, Energy-saving mechanisms in walking and running, J Exp Biol, vol.160, pp.55-69, 1991.

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

S. Amano, D. Kegelmeyer, and S. Hong, Rethinking energy in parkinsonian motor symptoms: a potential role for neural metabolic deficits, Frontiers in Systems Neuroscience, vol.51, p.242, 2014.
DOI : 10.1212/wnl.51.6.1583

M. Anderson and F. Horak, Influence of the globus pallidus on arm movements in monkeys. iii. timing of movement-related information, J Neurophysiol, vol.54, pp.433-448, 1985.

P. Baraduc, S. Thobois, J. Gan, E. Broussolle, and M. Desmurget, A Common Optimization Principle for Motor Execution in Healthy Subjects and Parkinsonian Patients, Journal of Neuroscience, vol.33, issue.2, pp.665-677, 2013.
DOI : 10.1523/JNEUROSCI.1482-12.2013

P. Battaglia and P. Schrater, Humans Trade Off Viewing Time and Movement Duration to Improve Visuomotor Accuracy in a Fast Reaching Task, Journal of Neuroscience, vol.27, issue.26, pp.6984-6994, 2007.
DOI : 10.1523/JNEUROSCI.1309-07.2007

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, 2008.
DOI : 10.1007/BF00204593

D. Benson, G. Huntington, T. Thorvaldsen, and A. Rao, Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method, Journal of Guidance, Control, and Dynamics, vol.29, issue.6, pp.1435-1440, 2006.
DOI : 10.2514/1.20478

A. Berardelli, J. Rothwell, P. Thompson, and M. Hallett, Pathophysiology of bradykinesia in Parkinson's disease, Brain, vol.124, issue.11, pp.2131-2146, 2001.
DOI : 10.1093/brain/124.11.2131

B. Berret, E. Chiovetto, F. Nori, and T. Pozzo, Evidence for Composite Cost Functions in Arm Movement Planning: An Inverse Optimal Control Approach, PLoS Computational Biology, vol.22, issue.10, p.1002183, 2011.
DOI : 10.1371/journal.pcbi.1002183.s002
URL : https://hal.archives-ouvertes.fr/inserm-00704789

B. Berret, C. Darlot, F. Jean, T. Pozzo, C. Papaxanthis et al., The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements, PLoS Computational Biology, vol.294, issue.21, p.1000194, 2008.
DOI : 10.1371/journal.pcbi.1000194.s001
URL : https://hal.archives-ouvertes.fr/inserm-00705805

L. Botzer and A. Karniel, A simple and accurate onset detection method for a measured bellshaped speed profile, Front Neurosci, vol.3, p.61, 2009.

C. Brücke, J. Huebl, T. Schönecker, W. Neumann, K. Yarrow et al., Scaling of Movement Is Related to Pallidal ?? Oscillations in Patients with Dystonia, Journal of Neuroscience, vol.32, issue.3, pp.1008-1019, 2012.
DOI : 10.1523/JNEUROSCI.3860-11.2012

S. Brown, H. Hefter, M. Mertens, and H. Freund, Disturbances in human arm movement trajectory due to mild cerebellar dysfunction., Journal of Neurology, Neurosurgery & Psychiatry, vol.53, issue.4, pp.306-313, 1990.
DOI : 10.1136/jnnp.53.4.306

H. Collewijn, C. Erkelens, and R. Steinman, Binocular co-ordination of human horizontal saccadic eye movements., The Journal of Physiology, vol.404, issue.1, pp.157-182, 1988.
DOI : 10.1113/jphysiol.1988.sp017284

P. Croxson, M. Walton, O. Reilly, J. Behrens, T. Rushworth et al., Effort-Based Cost-Benefit Valuation and the Human Brain, Journal of Neuroscience, vol.29, issue.14, pp.4531-4541, 2009.
DOI : 10.1523/JNEUROSCI.4515-08.2009

M. Dean, S. Wu, and L. Maloney, Trading off speed and accuracy in rapid, goal-directed movements, Journal of Vision, vol.7, issue.5, pp.10-11, 2007.
DOI : 10.1167/7.5.10

M. Desmurget and R. Turner, Testing Basal Ganglia Motor Functions Through Reversible Inactivations in the Posterior Internal Globus Pallidus, Journal of Neurophysiology, vol.99, issue.3, pp.1057-1076, 2008.
DOI : 10.1152/jn.01010.2007

M. Desmurget and R. Turner, Motor Sequences and the Basal Ganglia: Kinematics, Not Habits, Journal of Neuroscience, vol.30, issue.22, pp.7685-7690, 2010.
DOI : 10.1523/JNEUROSCI.0163-10.2010

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

A. Ferrante, G. Marro, and L. Ntogramatzidis, A parametrization of the solutions of the finite-horizon LQ problem with general cost and boundary conditions, Automatica, vol.41, issue.8, pp.1359-1366, 2005.
DOI : 10.1016/j.automatica.2005.01.018

P. Fitts, The information capacity of the human motor system in controlling the amplitude of movement., Journal of Experimental Psychology, vol.47, issue.6, pp.381-391, 1954.
DOI : 10.1037/h0055392

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

D. Garg, M. Patterson, W. Hager, A. Rao, D. Benson et al., A unified framework for the numerical solution of optimal control problems using pseudospectral methods (to appear) Automatica, 2009.

J. Gaveau, B. Berret, L. Demougeot, L. Fadiga, T. Pozzo et al., Energy-related optimal control accounts for gravitational load: comparing shoulder, elbow, and wrist rotations, Journal of Neurophysiology, vol.111, issue.1, 2014.
DOI : 10.1152/jn.01029.2012
URL : https://hal.archives-ouvertes.fr/hal-01159573

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

P. Gill, W. Murray, and M. Saunders, SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization, SIAM Review, vol.47, issue.1, pp.99-131, 2005.
DOI : 10.1137/S0036144504446096

J. Gordon, M. Ghilardi, S. Cooper, and C. Ghez, Accuracy of planar reaching movements, Experimental Brain Research, vol.80, issue.1, pp.112-130, 1994.
DOI : 10.1007/BF00241416

G. Gottlieb, D. Corcos, and G. Agarwal, Strategies for the control of voluntary movements with one mechanical degree of freedom, Behavioral and Brain Sciences, vol.14, issue.02, pp.189-250, 1989.
DOI : 10.1037/h0055392

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

M. Guitart-masip, R. Chowdhury, T. Sharot, P. Dayan, E. Duzel et al., Action controls dopaminergic enhancement of reward representations, Proceedings of the National Academy of Sciences, vol.109, issue.19, pp.7511-7516, 2012.
DOI : 10.1073/pnas.1202229109

A. Haith, T. Reppert, and R. Shadmehr, Evidence for Hyperbolic Temporal Discounting of Reward in Control of Movements, Journal of Neuroscience, vol.32, issue.34, pp.11727-11736, 2012.
DOI : 10.1523/JNEUROSCI.0424-12.2012

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

C. Harris and D. Wolpert, The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off, Biological Cybernetics, vol.47, issue.5, 2006.
DOI : 10.1007/s00422-006-0064-x

B. Hoff, A model of duration in normal and perturbed reaching movement, Biological Cybernetics, vol.62, issue.6, pp.481-488, 1994.
DOI : 10.1007/BF00198466

N. Hogan, An organizing principle for a class of voluntary movements, J Neurosci, vol.4, pp.2745-2754, 1984.

C. Howarth, P. Gleeson, and D. Attwell, Updated Energy Budgets for Neural Computation in the Neocortex and Cerebellum, Journal of Cerebral Blood Flow & Metabolism, vol.103, issue.7, pp.1222-1232, 2012.
DOI : 10.1111/j.1471-4159.1977.tb10649.x

H. Huang and A. Ahmed, Is there a reaching speed that minimizes metabolic cost?, Proceedings of the Translational and Computational Motor Control 2012, 2012.

T. Hudson, L. Maloney, and M. Landy, Optimal Compensation for Temporal Uncertainty in Movement Planning, PLoS Computational Biology, vol.186, issue.7, p.1000130, 2008.
DOI : 10.1371/journal.pcbi.1000130.t001

D. Huh, E. Todorov, and T. Sejnowski, Infinite horizon optimal control framework for goal directed movements, Society for Neuroscience Annual Meeting, 2010.

M. Inase, J. Buford, and M. Anderson, Changes in the control of arm position, movement, and thalamic discharge during local inactivation in the globus pallidus of the monkey, J Neurophysiol, vol.75, pp.1087-1104, 1996.

H. Kappen, Optimal control theory and the linear Bellman equation, Bayesian Time Series Models, pp.363-387, 2011.
DOI : 10.1017/CBO9780511984679.018

A. Kardamakis and A. Moschovakis, Optimal Control of Gaze Shifts, Journal of Neuroscience, vol.29, issue.24, pp.7723-7730, 2009.
DOI : 10.1523/JNEUROSCI.5518-08.2009

D. Kirk, Optimal control theory: An Introduction, 1970.

M. Klein-flügge, S. Kennerley, A. Saraiva, W. Penny, and S. Bestmann, Behavioral Modeling of Human Choices Reveals Dissociable Effects of Physical Effort and Temporal Delay on Reward Devaluation, PLOS Computational Biology, vol.6, issue.3, p.1004116, 2015.
DOI : 10.1371/journal.pcbi.1004116.s010

S. Kobayashi and W. Schultz, Influence of Reward Delays on Responses of Dopamine Neurons, Journal of Neuroscience, vol.28, issue.31, pp.7837-7846, 2008.
DOI : 10.1523/JNEUROSCI.1600-08.2008

R. Krampe, M. Doumas, A. Lavrysen, and M. Rapp, The costs of taking it slowly: Fast and slow movement timing in older age., Psychology and Aging, vol.25, issue.4, pp.980-990, 2010.
DOI : 10.1037/a0020090

M. Kushmerick, Energetics of muscle contraction. Comprehensive Physiology, p.32, 1983.

S. Laughlin, Energy as a constraint on the coding and processing of sensory information, Current Opinion in Neurobiology, vol.11, issue.4, pp.475-480, 2001.
DOI : 10.1016/S0959-4388(00)00237-3

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

P. Lennie, The Cost of Cortical Computation, Current Biology, vol.13, issue.6, pp.493-497, 2003.
DOI : 10.1016/S0960-9822(03)00135-0

D. Liu and E. Todorov, Evidence for the Flexible Sensorimotor Strategies Predicted by Optimal Feedback Control, Journal of Neuroscience, vol.27, issue.35, pp.9354-9368, 2007.
DOI : 10.1523/JNEUROSCI.1110-06.2007

P. Mazzoni, A. Hristova, and J. Krakauer, Why Don't We Move Faster? Parkinson's Disease, Movement Vigor, and Implicit Motivation, Journal of Neuroscience, vol.27, issue.27, pp.7105-7116, 2007.
DOI : 10.1523/JNEUROSCI.0264-07.2007

J. Mink and W. Thach, Basal ganglia motor control. iii. pallidal ablation: normal reaction time, muscle cocontraction, and slow movement, J Neurophysiol, vol.65, pp.330-351, 1991.

K. Mombaur, A. Truong, and J. Laumond, From human to humanoid locomotion???an inverse optimal control approach, Autonomous Robots, vol.24, issue.5, 2009.
DOI : 10.1007/s10514-009-9170-7

J. Myerson and L. Green, Discounting of delayed rewards: Models of individual choice, Journal of the Experimental Analysis of Behavior, vol.64, issue.3, pp.263-276, 1995.
DOI : 10.1901/jeab.1995.64-263

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

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

Y. Niv, N. Daw, J. D. Dayan, and P. , Tonic dopamine: opportunity costs and the control of response vigor, Psychopharmacology, vol.13, issue.7, pp.507-520, 2007.
DOI : 10.1007/s00213-006-0502-4

F. Nori and R. Frezza, Linear optimal control problems and quadratic cost functions estimation, 12th Mediterranean Conference on Control and Automation, MED'04, 2004.

C. Papaxanthis, T. Pozzo, K. Popov, and J. Mcintyre, Hand trajectories of vertical arm movements in one- G and zero- G environments, Experimental Brain Research, vol.120, issue.4, pp.496-502, 1998.
DOI : 10.1007/s002210050423

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

H. Ralston, Energy-speed relation and optimal speed during level walking, Internationale Zeitschrift f??r Angewandte Physiologie Einschliesslich Arbeitsphysiologie, vol.109, issue.4, pp.277-283, 1958.
DOI : 10.1007/BF00698754

A. Rao, D. Benson, C. Darby, M. Patterson, C. Francolin et al., Algorithm 902, ACM Transactions on Mathematical Software, vol.37, issue.2, pp.1-39, 2010.
DOI : 10.1145/1731022.1731032

M. Richardson and T. Flash, Comparing smooth arm movements with the two-thirds power law and the related segmented-control hypothesis, J Neurosci, vol.22, pp.8201-8211, 2002.

L. Rigoux and E. Guigon, A Model of Reward- and Effort-Based Optimal Decision Making and Motor Control, PLoS Computational Biology, vol.8, issue.10, p.1002716, 2012.
DOI : 10.1371/journal.pcbi.1002716.g007

L. Schmidt, B. Arc, G. Lafargue, D. Galanaud, V. Czernecki et al., Disconnecting force from money: effects of basal ganglia damage on incentive motivation, Brain, vol.131, issue.5, pp.1303-1310, 2008.
DOI : 10.1093/brain/awn045
URL : https://hal.archives-ouvertes.fr/hal-00333398

N. Schouppe, J. Demanet, C. Boehler, K. Ridderinkhof, and W. Notebaert, The Role of the Striatum in Effort-Based Decision-Making in the Absence of Reward, Journal of Neuroscience, vol.34, issue.6, pp.2148-2154, 2014.
DOI : 10.1523/JNEUROSCI.1214-13.2014

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

R. Shadmehr, Control of movements and temporal discounting of reward, Current Opinion in Neurobiology, vol.20, issue.6, pp.726-730, 2010.
DOI : 10.1016/j.conb.2010.08.017

R. Shadmehr and J. Krakauer, A computational neuroanatomy for motor control, Experimental Brain Research, vol.163, issue.Pt 3, pp.359-381, 2008.
DOI : 10.1007/s00221-008-1280-5

R. Shadmehr, J. Orban-de-xivry, M. Xu-wilson, and T. Shih, Temporal Discounting of Reward and the Cost of Time in Motor Control, Journal of Neuroscience, vol.30, issue.31, pp.10507-10516, 2010.
DOI : 10.1523/JNEUROSCI.1343-10.2010

R. Stengel, Optimal Control and Estimation Dover books on advanced mathematics, 1986.

R. Sutton and A. Barto, Reinforcement Learning, 1998.
DOI : 10.1007/978-1-4615-3618-5
URL : https://hal.archives-ouvertes.fr/hal-00764281

H. Tanaka, J. Krakauer, and N. Qian, An Optimization Principle for Determining Movement Duration, Journal of Neurophysiology, vol.95, issue.6, pp.3875-3886, 2006.
DOI : 10.1152/jn.00751.2005

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

E. Todorov, Optimal control theory, chapter 12, Bayesian Brain: Probabilistic Approaches to Neural Coding, Doya K (ed), pp.269-298, 2006.

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

R. Turner and M. Desmurget, Basal ganglia contributions to motor control: a vigorous tutor, Current Opinion in Neurobiology, vol.20, issue.6, pp.704-716, 2010.
DOI : 10.1016/j.conb.2010.08.022

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-beers, Saccadic Eye Movements Minimize the Consequences of Motor Noise, PLoS ONE, vol.83, issue.4, p.2070, 2008.
DOI : 10.1371/journal.pone.0002070.g005

R. Van-beers, P. Haggard, and D. Wolpert, The Role of Execution Noise in Movement Variability, Journal of Neurophysiology, vol.91, issue.2, 2004.
DOI : 10.1152/jn.00652.2003

F. Van-der-helm and L. Rozendaal, Musculoskeletal Systems with Intrinsic and Proprioceptive Feedback, Biomechanics and neural control of posture and movement, pp.164-174, 2000.
DOI : 10.1007/978-1-4612-2104-3_11

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

D. Wolpert and M. Landy, Motor control is decision-making, Current Opinion in Neurobiology, vol.22, issue.6, pp.996-1003, 2012.
DOI : 10.1016/j.conb.2012.05.003

S. Young, J. Pratt, and T. Chau, Target-Directed Movements at a Comfortable Pace: Movement Duration and Fitts's Law, Journal of Motor Behavior, vol.41, issue.4, pp.339-346, 2009.
DOI : 10.3200/JMBR.41.4.339-346