V. Acary, Projected event-capturing time-stepping schemes for nonsmooth mechanical systems with unilateral contact and Coulomb???s friction, Computer Methods in Applied Mechanics and Engineering, vol.256, pp.224-250, 2013.
DOI : 10.1016/j.cma.2012.12.012

URL : https://hal.inria.fr/hal-00720747/file/RR-8029.pdf

V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems, Applications in Mechanics and Electronics, Lecture Notes in Applied and Computational Mechanics, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00423530

K. Addi, B. Brogliato, and D. Goeleven, A qualitative mathematical analysis of a class of linear variational inequalities via semi-complementarity problems: applications in electronics, Mathematical Programming, vol.167, issue.1, pp.31-67, 2011.
DOI : 10.1007/s10107-009-0268-7

N. Akhadkar, V. Acary, and B. Brogliato, Analysis of collocated feedback controllers for four-bar planar mechanisms with joint clearances, Multibody System Dynamics, vol.32, issue.1, pp.101-136, 2016.
DOI : 10.1007/s11071-014-1870-7

URL : https://hal.archives-ouvertes.fr/hal-01218531

A. D. Ames, K. Galloway, K. Sreenath, and J. W. Grizzle, Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics, IEEE Transactions on Automatic Control, vol.59, issue.4, pp.876-891, 2014.
DOI : 10.1109/TAC.2014.2299335

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

Y. Aoustin and A. M. Formalskii, Modeling, control and simulation of upward jump of a biped, Multibody System Dynamics, vol.17, issue.7, pp.425-445, 2013.
DOI : 10.1007/s11044-012-9319-6

URL : https://hal.archives-ouvertes.fr/hal-00718175

V. I. Babitsky, Theory of Vibro-Impact Systems and Applications. Foundations of Engineering Mechanics, 1998.
DOI : 10.1007/978-3-540-69635-3

P. Ballard, Formulation and well-posedness of the dynamics of rigid-body systems with perfect unilateral constraints, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.359, issue.1789, pp.2327-2346, 1789.
DOI : 10.1098/rsta.2001.0854

M. Baumann and R. I. Leine, A synchronization-based state observer for impact oscillators using only collision time information, International Journal of Robust and Nonlinear Control, vol.51, issue.1, pp.2542-2563, 2016.
DOI : 10.1002/rnc.3460

URL : https://hal.archives-ouvertes.fr/hal-01326052

D. S. Bernstein, Theory, Facts, and Formulas with Application to Linear Systems Theory, Matrix Mathematics, 2005.

A. Blumentals, B. Brogliato, and F. Bertails-descoubes, The contact problem in Lagrangian systems subject to bilateral and unilateral constraints, with or without sliding Coulomb???s friction: a tutorial, Multibody System Dynamics, vol.30, issue.2, pp.43-76, 2016.
DOI : 10.1007/s11044-013-9352-0

J. M. Bourgeot and B. Brogliato, TRACKING CONTROL OF COMPLEMENTARITY LAGRANGIAN SYSTEMS, International Journal of Bifurcation and Chaos, vol.296, issue.06, pp.1839-1866, 2005.
DOI : 10.1109/JRA.1987.1087120

URL : https://hal.archives-ouvertes.fr/inria-00070619

R. Brammer, Controllability in Linear Autonomous Systems with Positive Controllers, SIAM Journal on Control, vol.10, issue.2, pp.339-353, 1972.
DOI : 10.1137/0310026

B. Brogliato, Absolute stability and the Lagrange???Dirichlet theorem with monotone multivalued mappings, Systems & Control Letters, vol.51, issue.5, pp.343-353, 2004.
DOI : 10.1016/j.sysconle.2003.09.007

URL : https://hal.archives-ouvertes.fr/inria-00071792

B. Brogliato, Inertial couplings between unilateral and bilateral holonomic constraints in frictionless Lagrangian systems, Multibody System Dynamics, vol.2, issue.6, pp.289-325, 2013.
DOI : 10.1007/s11044-012-9317-8

URL : https://hal.archives-ouvertes.fr/hal-00825581

B. Brogliato, Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction, Multibody System Dynamics, vol.8, issue.5, pp.175-216, 2014.
DOI : 10.1007/s11044-013-9392-5

URL : https://hal.archives-ouvertes.fr/hal-00762986

B. Brogliato, Nonsmooth Mechanics. Models, Dynamics and Control, third edn. Communications and Control Engineering, 2016.
DOI : 10.1007/978-3-319-28664-8

URL : https://hal.archives-ouvertes.fr/hal-01236953

B. Brogliato, R. Lozano, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control, Theory and Applications Communcations and Control Engineering, 2007.
DOI : 10.1007/978-1-84628-517-2

URL : https://hal.archives-ouvertes.fr/hal-01338369

B. Brogliato, M. Mabrouk, and A. Zavala-rio, On the controllability of linear juggling mechanical systems, Systems & Control Letters, vol.55, issue.4, pp.350-367, 2006.
DOI : 10.1016/j.sysconle.2005.08.012

URL : https://hal.archives-ouvertes.fr/inria-00071814

B. Brogliato, S. I. Niculescu, and M. D. Marques, On tracking control of a class of complementary-slackness hybrid mechanical systems, Systems & Control Letters, vol.39, issue.4, pp.255-266, 2000.
DOI : 10.1016/S0167-6911(99)00104-8

B. Brogliato, S. I. Niculescu, and P. Orhant, On the control of finite-dimensional mechanical systems with unilateral constraints, IEEE Transactions on Automatic Control, vol.42, issue.2, pp.200-215, 1997.
DOI : 10.1109/9.554400

B. Brogliato and A. Zavala-rio, On the control of complementary-slackness juggling mechanical systems, IEEE Transactions on Automatic Control, vol.45, issue.2, pp.235-246, 2000.
DOI : 10.1109/9.839946

C. I. Byrnes and A. Isidori, Asymptotic stabilization of minimum phase nonlinear systems, IEEE Transactions on Automatic Control, vol.36, issue.10, pp.1122-1337, 1991.
DOI : 10.1109/9.90226

A. R. Champneys and P. R. Varkonyi, The Painlev?? paradox in contact mechanics, IMA Journal of Applied Mathematics, vol.81, issue.3, pp.538-588, 2016.
DOI : 10.1093/imamat/hxw027

S. L. Chang and L. W. Tsai, On the Redundant-Drive Backlash-Free Robotic Mechanisms, Journal of Mechanical Design, vol.115, issue.2, pp.247-254, 1993.
DOI : 10.1115/1.2919184

URL : http://drum.lib.umd.edu/bitstream/1903/4986/1/TR_90-38.pdf

T. Chang and Y. Hurmuzlu, Sliding Control Without Reaching Phase and Its Application to Bipedal Locomotion, Journal of Dynamic Systems, Measurement, and Control, vol.115, issue.3, pp.447-455, 1993.
DOI : 10.1115/1.2899122

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

C. Chevallereau and Y. Aoustin, Optimal reference trajectories for walking and running of a biped robot, Robotica, vol.19, issue.05, pp.557-569, 2001.
DOI : 10.1017/S0263574701003307

URL : https://hal.archives-ouvertes.fr/hal-00794833

C. Chevallereau, E. R. Westervelt, and J. W. Grizzle, Asymptotically Stable Running for a Five-Link, Four-Actuator, Planar Bipedal Robot, The International Journal of Robotics Research, vol.24, issue.6, pp.431-464, 2005.
DOI : 10.1177/0278364905054929

URL : https://hal.archives-ouvertes.fr/hal-00794892

F. Duarte and J. T. Machado, Describing function of two masses with backlash, Nonlinear Dynamics, vol.27, issue.2???3, pp.409-413, 2009.
DOI : 10.1007/s11071-008-9410-y

F. Facchinei and J. S. Pang, Finite-Dimensional Inequalities and Complementarity Problems, Volume I. Springer Series in Operations Research, 2003.

P. Flores, J. Ambrosio, J. P. Claro, and H. Lankarani, Kinematics and Dynamics of Multibody Systems with Imperfect Joints, Lecture Notes in Applied and Computational Mechanics, vol.34, 2008.

P. Flores, C. Koshy, H. Lankarani, J. Ambrosio, and J. Claro, Numerical and experimental investigation on multibody systems with revolute clearance joints, Nonlinear Dynamics, vol.24, issue.3, pp.383-398, 2011.
DOI : 10.1007/s11071-010-9899-8

URL : https://hal.archives-ouvertes.fr/hal-00649461

S. Galeani, L. Menini, A. Potini, and A. Tornambè, Trajectory tracking for a particle in elliptical billiards, International Journal of Control, vol.24, issue.2, pp.189-213, 2008.
DOI : 10.1103/PhysRevE.64.026212

C. Glocker, Set-Valued Force Laws, Lecture Notes in Applied Mechanics, vol.1, 2001.
DOI : 10.1007/978-3-540-44479-4

C. Glocker, An introduction to impacts Nonsmooth Mechanics of Solids, no, CISM Courses and Lectures, pp.45-102, 2006.

J. Grizzle, G. Abba, and F. Plestan, Asymptotically stable walking for biped robots: analysis via systems with impulse effects, IEEE Transactions on Automatic Control, vol.46, issue.1, pp.51-64, 2001.
DOI : 10.1109/9.898695

J. B. Hiriat-urruty and C. Lemaréchal, Fundamentals of Convex Analysis. Grundlehren text Editions, 2000.

Y. Hurmuzlu, F. Génot, and B. Brogliato, Modeling, stability and control of biped robots???a general framework, Automatica, vol.40, issue.10, pp.1647-1664, 2004.
DOI : 10.1016/j.automatica.2004.01.031

URL : https://hal.archives-ouvertes.fr/inria-00072297

C. Koshy, P. Flores, and H. Lankarani, Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches, Nonlinear Dynamics, vol.224, issue.6, pp.325-338, 2013.
DOI : 10.1007/s11071-013-0787-x

A. Krinner and T. Thümmel, Non-smooth Behaviour of a Linkage Mechanism with Revolute Clearance Joints, New Advances in Mechanisms, Transmissions and Applications. Proceedings of the Second Conference MeTrApp 2013, Mechanisms and Machine Science, pp.233-241, 2014.
DOI : 10.1007/978-94-007-7485-8_29

A. Lagerberg and B. Egardt, Backlash Estimation With Application to Automotive Powertrains, IEEE Transactions on Control Systems Technology, vol.15, issue.3, pp.483-493, 2007.
DOI : 10.1109/TCST.2007.894643

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

V. Lampaert, J. Swevers, and F. Bender, Modification of the Leuven integrated friction model structure, IEEE Transactions on Automatic Control, vol.47, issue.4, pp.683-687, 2002.
DOI : 10.1109/9.995050

P. Lancaster and M. Tismenetsky, The Theory of Matrices, 1985.

R. I. Leine and N. Van-de-wouw, Stability and Convergence of Mechanical Systems with Unilateral Constraints, Lecture Notes in Applied and Computational Mechanics, vol.36, 2008.
DOI : 10.1007/978-3-540-76975-0

A. Lewis, Simple mechanical control systems with constraints, IEEE Transactions on Automatic Control, vol.45, issue.8, pp.1420-1436, 2000.
DOI : 10.1109/9.871752

P. Li, W. Chen, D. Li, and R. Yu, A novel transition model for lubricated revolute joints in planar multibody systems, Multibody System Dynamics, vol.9, issue.3, pp.279-294, 2016.
DOI : 10.1007/s11044-015-9484-5

P. Liljebäck, K. Y. Pettersen, O. Stavdhal, and J. T. Gravdhal, Hybrid Modelling and Control of Obstacle-Aided Snake Robot Locomotion, IEEE Transactions on Robotics, vol.26, issue.5, pp.781-799, 2010.
DOI : 10.1109/TRO.2010.2056211

K. Lynch and C. Black, Recurrence, controllability, and stabilization of juggling, IEEE Transactions on Robotics and Automation, vol.17, issue.2, pp.113-124, 2001.
DOI : 10.1109/70.928557

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

M. Mata-jimenez and B. Brogliato, Analysis of PD and nonlinear control of mechanical systems with dynamic backlash, Journal of Vibration and Control, vol.9, issue.1, pp.119-156, 2003.

N. Mcclamroch and D. Wang, Feedback stabilization and tracking of constrained robots, IEEE Transactions on Automatic Control, vol.33, issue.5, pp.419-426, 1988.
DOI : 10.1109/9.1220

L. Menini, C. Possieri, and A. Tornambé, On the computation of the continuous-time reference trajectory for mechanical juggling systems, 2015 54th IEEE Conference on Decision and Control (CDC), pp.145-150, 2015.
DOI : 10.1109/CDC.2015.7402100

L. Menini and A. Tornambé, State estimation of (otherwise unobservable) linear mechanical systems through the use of non-smooth impacts: the case of two mating gears, Automatica, vol.38, issue.10, pp.1823-1826, 2002.
DOI : 10.1016/S0005-1098(02)00065-1

L. Menini and A. Tornambé, Velocity observers for non-linear mechanical systems subject to non-smooth impacts, Automatica, vol.38, issue.12, pp.2169-2175, 2002.
DOI : 10.1016/S0005-1098(02)00164-4

L. Menini and A. Tornambè, Control of (otherwise) uncontrollable linear mechanical systems through non-smooth impacts, Systems & Control Letters, vol.49, issue.4, pp.311-322, 2003.
DOI : 10.1016/S0167-6911(03)00101-4

C. I. Morarescu and B. Brogliato, Trajectory Tracking Control of Multiconstraint Complementarity Lagrangian Systems, IEEE Transactions on Automatic Control, vol.55, issue.6, pp.1300-1313, 2010.
DOI : 10.1109/TAC.2010.2042231

URL : https://hal.archives-ouvertes.fr/hal-00756307

J. J. Moreau, Unilateral Contact and Dry Friction in Finite Freedom Dynamics, Nonsmooth Mechanics and Applications, no. 302 in CISM Courses and Lectures, pp.1-82, 1988.
DOI : 10.1007/978-3-7091-2624-0_1

A. Müller, Internal Preload Control of Redundantly Actuated Parallel Manipulators—Its Application to Backlash Avoiding Control, IEEE Transactions on Robotics, vol.21, issue.4, pp.668-677, 2005.
DOI : 10.1109/TRO.2004.842341

N. Nguyen and B. Brogliato, Multiple Impacts in Dissipative Granular Chains, Lecture Notes in Applied and Computational Mechanics, vol.72, 2014.
DOI : 10.1007/978-3-642-39298-6

URL : https://hal.archives-ouvertes.fr/hal-00908612

M. Nordin, J. Galic, and P. Gutman, New models for backlash and gear play, International Journal of Adaptive Control and Signal Processing, vol.11, issue.1, pp.49-63, 1997.
DOI : 10.1002/(SICI)1099-1115(199702)11:1<49::AID-ACS394>3.0.CO;2-X

M. Nordin and P. Gutman, Controlling mechanical systems with backlash???a survey, Automatica, vol.38, issue.10, pp.1633-1649, 2002.
DOI : 10.1016/S0005-1098(02)00047-X

H. B. Oza, Y. V. Orlov, and S. K. Spurgeon, Finite time stabilization of a perturbed double integrator with unilateral constraints, Removal of singularities in the inverse dynamics of parallel robots. Mechanism and Machine Theory, pp.200-212, 2014.
DOI : 10.1016/j.matcom.2012.02.011

B. Paden and R. Panja, Globally asymptotically stable ???PD+??? controller for robot manipulators, International Journal of Control, vol.6, issue.6, pp.1697-1712, 1988.
DOI : 10.1115/1.3139651

L. Paoli, Vibro-Impact Problems with Dry Friction---Part I: Existence Result, SIAM Journal on Mathematical Analysis, vol.47, issue.5, pp.3285-3313, 2015.
DOI : 10.1137/140988899

L. Paoli, Vibro-Impact Problems with Dry Friction---Part II: Tangential Contacts and Frictional Catastrophes, SIAM Journal on Mathematical Analysis, vol.48, issue.2, pp.1272-1296, 2016.
DOI : 10.1137/140988905

L. Paoli and M. Schatzman, Penalty Approximation for Non-smooth Constraints in Vibroimpact, Journal of Differential Equations, vol.177, issue.2, pp.375-418, 2001.
DOI : 10.1006/jdeq.2001.4027

URL : https://hal.archives-ouvertes.fr/hal-00127048

L. Paoli and M. Schatzman, Penalty approximation for dynamical systems submitted to multiple nonsmooth constraints, Multibody System Dynamics, vol.8, issue.3, pp.347-366, 2002.

C. Pereira, A. Ramalho, and J. Ambrosio, A critical overview of internal and external cylinder contact force models, Nonlinear Dynamics, vol.220, issue.3, pp.681-697, 2011.
DOI : 10.1007/s11071-010-9830-3

URL : https://hal.archives-ouvertes.fr/hal-00624469

C. M. Pereira, A. L. Ramalho, and J. A. Ambrosio, Applicability domain of internal cylindrical contact force models. Mechanism and Machine Theory 78, pp.141-157, 2014.

F. Pfeiffer and C. Glocker, Multibody Dynamics with Unilateral Contacts. Nonlinear Science, 1996.

M. Posa, M. Tobenkin, and R. Tedrake, Stability Analysis and Control of Rigid-Body Systems With Impacts and Friction, IEEE Transactions on Automatic Control, vol.61, issue.6, pp.1423-1437, 2016.
DOI : 10.1109/TAC.2015.2459151

M. Reyhanoglu, A. Van-der-schaft, N. Mcclamroch, and I. Kolmanovsky, Dynamics and control of a class of underactuated mechanical systems, IEEE Transactions on Automatic Control, vol.44, issue.9, pp.1663-1671, 1999.
DOI : 10.1109/9.788533

A. Rodic, M. Vukobratovic, K. Addi, and G. Dalleau, Contribution to the modeling of nonsmooth multipoint contact dynamics of biped locomotion?theory and experiments, Robotica, vol.26, pp.157-175, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00919720

S. Saperstone, Global Controllability of Linear Systems with Positive Controls, SIAM Journal on Control, vol.11, issue.3, pp.417-423, 1973.
DOI : 10.1137/0311034

S. Saperstone and J. Yorke, Controllability of Linear Oscillatory Systems Using Positive Controls, SIAM Journal on Control, vol.9, issue.2, pp.253-262, 1971.
DOI : 10.1137/0309019

D. Serra, A. C. Satici, F. Ruggiero, V. Lippiello, and B. Siciliano, An Optimal Trajectory Planner for a Robotic Batting Task: The Table Tennis Example, Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics, pp.90-101, 2016.
DOI : 10.5220/0005982000900101

M. W. Spong, R. Kelly, and R. Ortega, Comments on "Adaptive manipulator control: a case study" by J. Slotine and W. Li, IEEE Transactions on Automatic Control, vol.35, issue.6, pp.761-762, 1990.
DOI : 10.1109/9.53565

C. Studer, Numerics of Unilateral Contacts and Friction Modeling and Numerical Time Integration in Non-Smooth Dynamics, Lecture Notes in Applied and Computational Mechanics, vol.47, 2009.

A. Tanwani, B. Brogliato, and C. Prieur, Observer Design for Unilaterally Constrained Lagrangian Systems: A Passivity-Based Approach, IEEE Transactions on Automatic Control, vol.61, issue.9, pp.2386-2401, 2016.
DOI : 10.1109/TAC.2015.2492098

URL : https://hal.archives-ouvertes.fr/hal-01113344

T. Thuemmel and M. Rossner, Introduction to modelling and parameter identification methodology of linkages by measurements and simulation, Proceedings of 13rd World Congress in Mechanisms and Machine Science, pp.19-25, 2011.

T. Thümmel and L. Ginzinger, Measurements and simulations of a crank and rocker mechanism including friction, clearance and impacts, Proceedings of IXth Intern. Conf. on the Theory of Machines and Mechanisms, 2004.

S. Varedi, H. Daniali, M. Dardel, and A. Fathi, Optimal dynamic design of a planar slider-crank mechanism with a joint clearance, Mechanism and Machine Theory, vol.86, pp.191-200, 2015.
DOI : 10.1016/j.mechmachtheory.2014.12.008

E. Westervelt, J. Grizzle, and D. Koditschek, Hybrid zero dynamics of planar biped walkers, IEEE Transactions on Automatic Control, vol.48, issue.1, pp.42-56, 2003.
DOI : 10.1109/TAC.2002.806653

P. B. Wieber and C. Chevallereau, Online adaptation of reference trajectories for the control of walking systems, Robotics and Autonomous Systems, vol.54, issue.7, pp.559-566, 2006.
DOI : 10.1016/j.robot.2006.04.007

URL : https://hal.archives-ouvertes.fr/inria-00070702

M. Wojtyra, Modeling of static friction in closed-loop kinematic chains???Uniqueness and parametric sensitivity problems, Multibody System Dynamics, vol.83, issue.4, pp.10-1007, 2016.
DOI : 10.1115/DETC2013-12591

N. Van-de-wouw and R. I. Leine, Attractivity of Equilibrium Sets of Systems with Dry Friction, Nonlinear Dynamics, vol.35, issue.1, pp.19-39, 2008.
DOI : 10.1023/B:NODY.0000017482.61599.86

H. Xiao, Y. Shao, and M. Brennan, On the contact stiffness and nonlinear vibration of an elastic body with a rough surface in contact with a rigid flat surface, European Journal of Mechanics - A/Solids, vol.49, pp.315-328, 2015.
DOI : 10.1016/j.euromechsol.2014.08.005

S. Yan, W. Xiang, and L. Zhang, A comprehensive model for 3D revolute joints with clearances in mechanical systems, Nonlinear Dynamics, vol.24, issue.1, pp.309-328, 2015.
DOI : 10.1007/s11071-014-1870-7

A. Zavala-rio and B. Brogliato, On the control of a one degree-of-freedom juggling robot, Dynamics and Control, vol.9, issue.1, pp.67-90, 1999.
DOI : 10.1023/A:1008346825330

A. Zavala-rio and B. Brogliato, Direct adaptive control design for one-degree-of-freedom complementary-slackness jugglers, Automatica, vol.37, issue.7, pp.1117-1123, 2001.
DOI : 10.1016/S0005-1098(01)00061-9