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 (ICRA), 2003.

J. Pratt, J. Carff, S. Drakunov, and A. Goswami, Capture Point: A Step toward Humanoid Push Recovery, 6th IEEE-RAS International Conference on Humanoid Robots, 2006.

I. Mordatch, E. Todorov, and Z. Popovi?, Discovery of complex behaviors through contact-invariant optimization, ACM Trans. on Graph, vol.31, issue.4, pp.1-43, 2012.

R. Deits and R. Tedrake, Footstep planning on uneven terrain with mixed-integer convex optimization, Humanoid Robots (Humanoids), 14th IEEE-RAS Int. Conf. on, 2014.

M. Posa, C. Cantu, and R. Tedrake, A direct method for trajectory optimization of rigid bodies through contact, The Int. Journal of Robot. Research (IJRR), vol.33, issue.1, pp.69-81, 2014.

A. W. Winkler, C. 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, pp.1-1, 2018.

T. Bretl, Motion planning of multi-limbed robots subject to equilibrium constraints: The free-climbing robot problem, The Int. Journal of Robot. Research (IJRR), vol.25, issue.4, pp.317-342, 2006.

K. Hauser, T. Bretl, and J. Latombe, Non-gaited humanoid locomotion planning, Humanoid Robots, 2005 5th IEEE-RAS Int. Conf. on, 2005, pp.7-12

A. Escande, A. Kheddar, and S. Miossec, Planning contact points for humanoid robots, Robotics and Autonomous Systems, vol.61, issue.5, pp.428-442, 2013.
URL : https://hal.archives-ouvertes.fr/lirmm-00800829

M. X. Grey, A. D. Ames, and C. K. Liu, Footstep and motion planning in semi-unstructured environments using randomized possibility graphs, 2017 IEEE International Conference on Robotics and Automation (ICRA), pp.4747-4753, 2017.

P. Kaiser, C. Mandery, A. Boltres, and T. Asfour, Affordance-based multi-contact whole-body pose sequence planning for humanoid robots in unknown environments, IEEE International Conference on Robotics and Automation, 2018.

T. Koolen, T. Boer, J. R. Rebula, A. Goswami, and J. E. Pratt, Capturability-based analysis and control of legged locomotion, part 1: Theory and application to three simple gait models, I. J. Robotics Res, vol.31, issue.9, pp.1094-1113, 2012.

J. E. Pratt, T. Koolen, T. Boer, J. R. Rebula, S. Cotton et al., Capturability-based analysis and control of legged locomotion, part 2: Application to m2v2, a lower-body humanoid, I. J. Robotics Res, vol.31, issue.10, pp.1117-1133, 2012.

A. Del-prete, S. Tonneau, and N. Mansard, Zero Step Capturability for Legged Robots in Multi Contact, Accepted on IEEE Trans on Robotics, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01574687

J. Carpentier and N. Mansard, Multicontact locomotion of legged robots, IEEE Transactions on Robotics, vol.34, issue.6, pp.1441-1460, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01859108

A. Herzog, N. Rotella, S. Schaal, and L. Righetti, Trajectory generation for multi-contact momentum-control, Humanoid Robots (Humanoids), 15h IEEE-RAS Int. Conf. on, 2015.

H. Dai, A. Valenzuela, and R. Tedrake, Whole-body motion planning with centroidal dynamics and full kinematics, Humanoid Robots (Humanoids), 14th IEEE-RAS Int. Conf. on, pp.295-302, 2014.

S. Caron, A. Escande, L. Lanari, and B. Mallein, Capturabilitybased analysis, optimization and control of 3d bipedal walking, 2018.

B. Ponton, A. Herzog, S. Schaal, and L. Righetti, A convex model of humanoid momentum dynamics for multi-contact motion generation, Proceedings of the 2016 IEEE-RAS International Conference on Humanoid Robots, 2016.

G. Mesesan, J. Englsberger, C. Ott, and A. Albu-schffer, Convex properties of center-of-mass trajectories for locomotion based on divergent component of motion, IEEE Robotics and Automation Letters, vol.3, issue.4, pp.3449-3456, 2018.

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.32, issue.9, pp.1104-1119, 2013.
URL : https://hal.archives-ouvertes.fr/lirmm-00819250

S. Tonneau, A. D. 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, pp.586-601, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01267345

P. Fernbach, S. Tonneau, and M. Taïx, Croc: Convex resolution of centroidal dynamics trajectories to provide a feasibility criterion for the multi contact planning problem, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018.
URL : https://hal.archives-ouvertes.fr/hal-01726155

K. Fukuda and A. Prodon, Double description method revisited, pp.91-111, 1996.

D. E. Orin, A. Goswami, and S. Lee, Centroidal dynamics of a humanoid robot, Autonomous Robots, vol.35, issue.2, pp.161-176, 2013.

Z. Qiu, A. Escande, A. Micaelli, and T. Robert, Human motions analysis and simulation based on a general criterion of stability, Int. Symposium on Digital Human Modeling, 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, 2015.

A. Del-prete, S. Tonneau, and N. Mansard, Fast Algorithms to Test Robust Static Equilibrium for Legged Robots, 2016 IEEE International Conference on Robotics and Automation (ICRA), 2016.
URL : https://hal.archives-ouvertes.fr/hal-01201060

S. Tonneau, A. D. Prete, J. Pettré, and N. Mansard, 2PAC: Two Point Attractors for Center of Mass Trajectories in Multi Contact Scenarios, Trans. on Graphics, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01609055

J. , Is the cross product of two bezier curves a bezier curve, Mathematics Stack Exchange, issue.10, pp.2017-2029

F. Farshidian, M. Neunert, A. W. Winkler, G. Rey, and J. Buchli, An efficient optimal planning and control framework for quadrupedal locomotion, Robotics and Automation (ICRA, pp.93-100, 2017.

R. Budhiraja, J. Carpentier, and N. Mansard, Dynamics consensus between centroidal and whole-body models for locomotion of legged robots, ICRA 2019-IEEE International Conference on Robotics and Automation, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01875031

F. Gao, W. Wu, Y. Lin, and S. Shen, Online safe trajectory generation for quadrotors using fast marching method and bernstein basis polynomial, 2018 IEEE International Conference on Robotics and Automation (ICRA), pp.344-351, 2018.

W. Sun, G. Tang, and K. Hauser, Fast UAV trajectory optimization using bilevel optimization with analytical gradients, CoRR, 2018.

A. Makhorin, Glpk, 2008.

J. Carpentier, A. 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, p.3, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01543060

J. Mirabel, S. Tonneau, P. Fernbach, A. K. Seppälä, M. Campana et al., Hpp: A new software for constrained motion planning, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp.383-389, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01290850

J. Carpentier, R. Budhiraja, and N. Mansard, Learning Feasibility Constraints for Multi-contact Locomotion of Legged Robots, Robotics: Science and Systems, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01526200

R. Orsolino, M. Focchi, C. Mastalli, H. Dai, D. G. Caldwell et al., Application of wrench based feasibility analysis to the online trajectory optimization of legged robots, IEEE Robotics and Automation Letters, pp.1-1, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02086079

V. Samy, S. Caron, K. Bouyarmane, and A. Kheddar, Post-impact adaptive compliance for humanoid falls using predictive control of a reduced model, 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids), pp.655-660, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01569819

, His research interest include motion planning and robotics, with a focus on motion and contact planning for locomotion of legged robots in multicontact scenario, Pierre Fernbach is in a post-doctoral research position in the Gepetto team at LAAS-CNRS, 2018.

, He defended his Phd in 2015 after 3 years in the INRIA/IRISA Mimetic research team, and pursued a post-doc in robotics at LAAS-CNRS in Toulouse, within the Gepetto team. His research focuses on motion planning based on the biomechanical analysis of motion invariants

O. Stasse, Intelligent Systems from the University of Paris 6, and the French Habilitation to Supervise Research (HDR) in Robotics (2013) from the University of Toulouse III, he was at the Joint French-Japanese Robotics Laboratory (JRL) between the CNRS and the AIST in Tsukuba, 2000.