S. Kajita, F. Kanehiro, K. Kaneko, K. Yokoi, and H. Hirukawa, The 3D linear inverted pendulum mode: a simple modeling for a biped walking pattern generation, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180), 2001.
DOI : 10.1109/IROS.2001.973365

S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada et al., Biped walking pattern generation by using preview control of zero-moment point, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422), 2003.
DOI : 10.1109/ROBOT.2003.1241826

P. Wieber, Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations, 2006 6th IEEE-RAS International Conference on Humanoid Robots, 2006.
DOI : 10.1109/ICHR.2006.321375

URL : https://hal.archives-ouvertes.fr/inria-00390462

A. Sherikov, D. Dimitrov, and P. Wieber, Whole body motion controller with long-term balance constraints, 2014 IEEE-RAS International Conference on Humanoid Robots, 2014.
DOI : 10.1109/HUMANOIDS.2014.7041399

URL : https://hal.archives-ouvertes.fr/hal-01418363

C. Brasseur, A. Sherikov, C. Collette, D. Dimitrov, and P. Wieber, A robust linear MPC approach to online generation of 3D biped walking motion, 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), 2015.
DOI : 10.1109/HUMANOIDS.2015.7363423

URL : https://hal.archives-ouvertes.fr/hal-01418355

A. Herdt, N. Perrin, and P. Wieber, Walking without thinking about it, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2010.
DOI : 10.1109/IROS.2010.5654429

URL : https://hal.archives-ouvertes.fr/inria-00567668

H. Hirukawa, S. Hattori, K. Harada, S. Kajita, K. Kaneko et al., A universal stability criterion of the foot contact of legged robots - adios ZMP, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., 2006.
DOI : 10.1109/ROBOT.2006.1641995

H. Dai, A. Valenzuela, and R. Tedrake, Whole-body motion planning with centroidal dynamics and full kinematics, 2014 IEEE-RAS International Conference on Humanoid Robots, 2014.
DOI : 10.1109/HUMANOIDS.2014.7041375

D. E. Orin, A. Goswami, and S. Lee, Centroidal dynamics of a humanoid robot, Autonomous Robots, vol.104, issue.4, 2013.
DOI : 10.1007/978-3-642-16958-8_12

M. Kudruss, M. Naveau, O. Stasse, N. Mansard, C. Kirches et al., Optimal control for whole-body motion generation using COM dynamics for predefined multi-contact configurations, IEEE-RAS Int. Conf. on Humanoid Robotics (ICHR), 2015.
DOI : 10.1109/humanoids.2015.7363428

J. Carpentier, S. Tonneau, M. Naveau, O. Stasse, and N. Mansard, A versatile and efficient pattern generator for generalized legged locomotion, 2016 IEEE International Conference on Robotics and Automation (ICRA), 2016.
DOI : 10.1109/ICRA.2016.7487538

URL : https://hal.archives-ouvertes.fr/hal-01203507

H. Dai and R. Tedrake, Planning robust walking motion on uneven terrain via convex optimization, 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), 2016.
DOI : 10.1109/HUMANOIDS.2016.7803333

B. Ponton, A. Herzog, S. Schaal, and L. Righetti, A convex model of humanoid momentum dynamics for multi-contact motion generation, 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), 2016.
DOI : 10.1109/HUMANOIDS.2016.7803371

I. Mordatch, E. Todorov, and Z. Popovi´cpopovi´c, Discovery of complex behaviors through contact-invariant optimization, ACM Transactions on Graphics, vol.31, issue.4, p.2012
DOI : 10.1145/2185520.2185539

URL : http://homes.cs.washington.edu/~todorov/papers/cio.pdf

P. Zaytsev, Using controllability of simple models to generate maximally robust walking-robot controllers, 2015.

S. Caron, Q. Pham, and Y. Nakamura, ZMP Support Areas for Multicontact Mobility Under Frictional Constraints, IEEE Transactions on Robotics, vol.33, issue.1, 2016.
DOI : 10.1109/TRO.2016.2623338

URL : http://arxiv.org/pdf/1510.03232

H. Audren, J. Vaillant, A. Kheddar, A. Escande, K. Kaneko et al., Model preview control in multi-contact motion-application to a humanoid robot, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2014.
DOI : 10.1109/IROS.2014.6943129

URL : https://hal.archives-ouvertes.fr/lirmm-01256511

N. Perrin, D. Lau, and V. Padois, Effective Generation of Dynamically Balanced Locomotion with Multiple Non-coplanar Contacts, The International Symposium on Robotics Research (ISRR), 2015.
DOI : 10.1109/IROS.2008.4651022

URL : https://hal.archives-ouvertes.fr/hal-01388632

N. Perrin, O. Stasse, L. Baudouin, F. Lamiraux, and E. Yoshida, Fast Humanoid Robot Collision-Free Footstep Planning Using Swept Volume Approximations, IEEE Transactions on Robotics, vol.28, issue.2, p.2012
DOI : 10.1109/TRO.2011.2172152

URL : https://hal.archives-ouvertes.fr/hal-00662550

A. Orthey and O. Stasse, Towards reactive whole-body motion planning in cluttered environments by precomputing feasible motion spaces, 2013 13th IEEE-RAS International Conference on Humanoid Robots (Humanoids), 2013.
DOI : 10.1109/HUMANOIDS.2013.7029987

URL : https://hal.archives-ouvertes.fr/hal-00911897

A. Herzog, S. Schaal, and L. Righetti, Structured contact force optimization for kino-dynamic motion generation, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2016.
DOI : 10.1109/IROS.2016.7759420

URL : http://arxiv.org/pdf/1605.08571

K. Fukuda and A. Prodon, Double description method revisited, Conference on Combinatorics and Computer Science, 1996.
DOI : 10.1007/3-540-61576-8_77

A. Escande, A. Kheddar, and S. Miossec, Planning support contact-points for humanoid robots and experiments on HRP-2, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2006.
DOI : 10.1109/IROS.2006.282154

O. Stasse, T. Flayols, R. Budhiraja, K. Giraud-esclasse, J. Carpentier et al., TALOS: A new humanoid research platform targeted for industrial applications, 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids), 2017.
DOI : 10.1109/HUMANOIDS.2017.8246947

URL : https://hal.archives-ouvertes.fr/hal-01485519

J. Carpentier, R. Budhiraja, and N. Mansard, Learning feasibility constraints for multi-contact locomotion of legged robots, Robotics: Science and System (RSS), 2017.
DOI : 10.15607/rss.2017.xiii.031

URL : https://hal.archives-ouvertes.fr/hal-01526200

T. Bretl, Motion Planning of Multi-Limbed Robots Subject to Equilibrium Constraints: The Free-Climbing Robot Problem, The International Journal of Robotics Research, vol.25, issue.4, 2006.
DOI : 10.1177/0278364902021009119

URL : http://robotics.stanford.edu/~latombe/cs326/2007/class14/bretl.pdf

J. Chestnutt, J. Kuffner, K. Nishiwaki, and S. Kagami, Planning biped navigation strategies in complex environments, IEEE-RAS Int. Conf. on Humanoid Robotics, 2003.

R. Deits and R. Tedrake, Footstep planning on uneven terrain with mixed-integer convex optimization, IEEE-RAS Int. Conf. on Humanoid Robotics (ICHR), 2014.
DOI : 10.21236/ada609276

URL : http://www.dtic.mil/dtic/tr/fulltext/u2/a609276.pdf

S. Tonneau, A. Del-prete, J. Pettré, C. Park, D. Manocha et al., An Efficient Acyclic Contact Planner for Multiped Robots, IEEE Transactions on Robotics, vol.34, issue.3, 2018.
DOI : 10.1109/TRO.2018.2819658

URL : https://hal.archives-ouvertes.fr/hal-01267345

J. Mirabel, S. Tonneau, P. Fernbach, A. Seppälä, M. Campana et al., HPP: A new software for constrained motion planning, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2016.
DOI : 10.1109/IROS.2016.7759083

URL : https://hal.archives-ouvertes.fr/hal-01290850

P. Wieber, Holonomy and Nonholonomy in the Dynamics of Articulated Motion, Fast motions in biomechanics and robotics, 2006.
DOI : 10.1007/978-3-540-36119-0_20

A. Herzog, N. Rotella, S. Schaal, and L. Righetti, Trajectory generation for multi-contact momentum control, 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), 2015.
DOI : 10.1109/HUMANOIDS.2015.7363464

Z. Qiu, A. Escande, A. Micaelli, and T. Robert, Human motions analysis and simulation based on a general criterion of stability, International Symposium on Digital Human Modelling, 2011.

S. Caron, Q. Pham, and Y. Nakamura, Leveraging Cone Double Description for Multi-contact Stability of Humanoids with Applications to Statics and Dynamics, Robotics: Science and Systems XI, 2015.
DOI : 10.15607/RSS.2015.XI.028

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

P. Wieber, Viability and predictive control for safe locomotion, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2008.
DOI : 10.1109/IROS.2008.4651022

URL : https://hal.archives-ouvertes.fr/inria-00390555

A. Herdt, H. Diedam, P. Wieber, D. Dimitrov, K. Mombaur et al., Online Walking Motion Generation with Automatic Footstep Placement, Advanced Robotics, vol.18, issue.5-6, 2010.
DOI : 10.1002/rnc.1251

H. Hirukawa, S. Hattori, S. Kajita, K. Harada, K. Kaneko et al., A Pattern Generator of Humanoid Robots Walking on a Rough Terrain, Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007.
DOI : 10.1109/ROBOT.2007.363644

B. Ponton, A. Herzog, A. Del-prete, S. Schaal, and L. Righetti, On time optimization of centroidal momentum dynamics, IEEE-RAS Int. Conf. on Robotics and Automation (ICRA), 2018.

A. Winkler, D. Bellicoso, M. Hutter, and J. Buchli, Gait and Trajectory Optimization for Legged Systems Through Phase-Based End-Effector Parameterization, IEEE Robotics and Automation Letters, vol.3, issue.3, 2018.
DOI : 10.1109/LRA.2018.2798285

S. Caron, A. Kheddar, D. Serra, C. Brasseur, A. Sherikov et al., Multi-contact walking pattern generation based on model preview control of 3D COM accelerations A newton method with always feasible iterates for nonlinear model predictive control of walking in a multi-contact situation, IEEE-RAS Int. Conf. on Humanoid Robotics (ICHR) IEEE-RAS Int. Conf. on Humanoid Robotics (ICHR), 2016.

S. Lengagne, J. Vaillant, E. Yoshida, and A. Kheddar, Generation of whole-body optimal dynamic multi-contact motions, The International Journal of Robotics Research, vol.6, issue.2, p.2013
DOI : 10.1145/1276377.1276396

URL : https://hal.archives-ouvertes.fr/lirmm-00819250

J. Pitman, Occupation measures for markov chains, Advances in Applied Probability, 1977.

J. B. Lasserre, D. Henrion, C. Prieur, and E. Trélat, Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations, SIAM Journal on Control and Optimization, vol.47, issue.4, 2008.
DOI : 10.1137/070685051

URL : https://hal.archives-ouvertes.fr/hal-00136032

E. Parzen, On Estimation of a Probability Density Function and Mode, The annals of mathematical statistics, 1962.
DOI : 10.1214/aoms/1177704472

C. M. Bishop, Pattern recognition and machine learning, 2006.

A. Dempster, N. Laird, and D. Rubin, Maximum likelihood from incomplete data via the em algorithm, Journal of the royal statistical society. Series B, 1977.

J. Hershey and P. Olsen, Approximating the Kullback Leibler Divergence Between Gaussian Mixture Models, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07, 2007.
DOI : 10.1109/ICASSP.2007.366913

Y. Or and E. Rimon, Characterization of frictional multi-legged equilibrium postures on uneven terrains The Int, Journal of Robotics Research, p.2017

Y. Tian, Q. Jin, and Z. Deng, Quadratic optimization over a polyhedral cone, Journal of Industrial and Management Optimization, vol.12, issue.1, 2016.
DOI : 10.3934/jimo.2016.12.269

URL : http://www.aimsciences.org/journals/doIpChk.jsp?paperID=11082&mode=full

F. John, Extremum problems with inequalities as subsidiary conditions Studies and Essays Presented to R. Courant on his 60th Birthday, 1948.
DOI : 10.1007/978-3-0348-0439-4_9

M. Diehl, H. G. Bock, H. Diedam, and P. Wieber, Fast Direct Multiple Shooting Algorithms for Optimal Robot Control, Fast motions in biomechanics and robotics, 2006.
DOI : 10.1007/978-3-540-36119-0_4

URL : https://hal.archives-ouvertes.fr/inria-00390435

E. M. Gertz and S. J. Wright, Object-oriented software for quadratic programming, ACM Transactions on Mathematical Software, vol.29, issue.1, 2003.
DOI : 10.1145/641876.641880

URL : http://pages.cs.wisc.edu/~swright/ooqp/ooqp-paper.pdf

D. Leineweber, I. Bauer, H. G. Bock, and J. P. Schlöder, An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: theoretical aspects, Computers & Chemical Engineering, vol.27, issue.2, 2003.
DOI : 10.1016/S0098-1354(02)00158-8

L. Saab, O. E. Ramos, F. Keith, N. Mansard, P. Soù et al., Dynamic Whole-Body Motion Generation Under Rigid Contacts and Other Unilateral Constraints, IEEE Transactions on Robotics, vol.29, issue.2, p.2013
DOI : 10.1109/TRO.2012.2234351

URL : https://hal.archives-ouvertes.fr/lirmm-00831097

K. Nishiwaki and S. Kagami, High frequency walking pattern generation based on preview control of ZMP, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., 2006.
DOI : 10.1109/ROBOT.2006.1642104

K. H. Koch, K. Mombaur, and P. Soù-eres, Optimization-based walking generation for humanoid robot, IFAC Symposium on Robot Control (SYROCO), 2012.
DOI : 10.3182/20120905-3-HR-2030.00189

D. Clever, M. Harant, K. Mombaur, M. Naveau, O. Stasse et al., COCoMoPL: A Novel Approach for Humanoid Walking Generation Combining Optimal Control, Movement Primitives and Learning and its Transfer to the Real Robot HRP-2, IEEE Robotics and Automation Letters (RAL), 2017.
DOI : 10.1109/LRA.2017.2657000

URL : https://hal.archives-ouvertes.fr/hal-01459840

Y. Tassa, T. Erez, and E. Todorov, Synthesis and stabilization of complex behaviors through online trajectory optimization, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2012.
DOI : 10.1109/IROS.2012.6386025

URL : http://homes.cs.washington.edu/~todorov/papers/MPCGetUp.pdf

Y. Tassa, N. Mansard, and E. Todorov, Control-limited differential dynamic programming, 2014 IEEE International Conference on Robotics and Automation (ICRA), 2014.
DOI : 10.1109/ICRA.2014.6907001

URL : http://homes.cs.washington.edu/%7Evikash/Projects/Hddn/Manipulation_RSS_13.pdf

P. Gill, W. Murray, and M. Saunders, User's guide for qpopt 1.0: A fortran package for quadratic programming, 1995.

R. Orsolino, M. Focchi, C. Mastalli, H. Dai, D. Caldwell et al., A feasibility metric for trajectory optimization of legged robots using wrench polytopes, 2017.

J. Carpentier, A. Del-prete, S. Tonneau, T. Flayols, F. Forget et al., Multi-contact Locomotion of Legged Robots in Complex Environments ? The Loco3D project, RSS Workshop on Challenges in Dynamic Legged Locomotion, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01543060

A. Del-prete, F. Nori, G. Metta, and L. Natale, Prioritized motion???force control of constrained fully-actuated robots: ???Task Space Inverse Dynamics???, Robotics and Autonomous Systems, vol.63, 2015.
DOI : 10.1016/j.robot.2014.08.016

J. Carpentier, M. Benallegue, N. Mansard, and J. Laumond, Center-of-Mass Estimation for a Polyarticulated System in Contact???A Spectral Approach, IEEE Transactions on Robotics, vol.32, issue.4, p.2016
DOI : 10.1109/TRO.2016.2572680

URL : https://hal.archives-ouvertes.fr/hal-01182734