K. Akbari-hamed and J. W. Grizzle, Reduced-order framework for exponential stabilization of periodic orbits on parameterized hybrid zero dynamics manifolds: Application to bipedal locomotion, Nonlinear Analysis: Hybrid Systems, vol.25, pp.227-245, 2017.
DOI : 10.1016/j.nahs.2016.08.006

A. D. Ames, K. Galloway, K. Sreenath, and J. W. Grizzle, Rapidly exponentially stabilizing control Lyapunov functions and hybrid zero dynamics. Automatic Control, IEEE Transactions on, vol.59, issue.4, pp.876-891, 2014.
DOI : 10.1109/tac.2014.2299335
URL : http://web.eecs.umich.edu/~grizzle/papers/CFL_Robotics_2012TAC.pdf

C. Byrnes and A. Isidori, Asymptotic stabilization of minimum phase nonlinear systems, IEEE Transactions on Automatic Control, vol.36, issue.10, pp.1122-1159, 1991.
DOI : 10.1109/9.90226

C. Chevallereau, J. W. Grizzle, and C. Shih, Asymptotically stable walking of a five-link underactuated 3D bipedal robot, pp.37-50, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00456192

C. Chevallereau, G. Abba, Y. Aoustin, F. Plestan, E. Westervelt et al., RABBIT: A testbed for advanced control theory, IEEE Control Systems Magazine, vol.23, issue.5, pp.57-79, 2003.
DOI : 10.1109/MCS.2003.1234651
URL : https://hal.archives-ouvertes.fr/hal-00794856

C. Chevallereau and Y. Aoustin, Self-stabilization of 3D walking via vertical oscillations of the hip, 2015 IEEE International Conference on Robotics and Automation (ICRA), pp.5088-5093, 2015.
DOI : 10.1109/ICRA.2015.7139907

C. Chevallereau, J. W. Grizzle, and C. L. Shih, Asymptotically Stable Walking of a Five-Link Underactuated 3-D Bipedal Robot, IEEE Transactions on Robotics, vol.25, issue.1, pp.37-50, 2009.
DOI : 10.1109/TRO.2008.2010366
URL : https://hal.archives-ouvertes.fr/hal-00456192

S. Collins, A. Ruina, R. Tedrake, and M. Wisse, Efficient Bipedal Robots Based on Passive-Dynamic Walkers, Science, vol.307, issue.5712, pp.1082-1085, 2005.
DOI : 10.1126/science.1107799

M. Doi, Y. Hasegawa, and T. Fukuda, 3D dynamic walking based on the inverted pendulum model with two degree of underactuation, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.4166-4171, 2005.
DOI : 10.1109/IROS.2005.1545398

J. Saunders, THE MAJOR DETERMINANTS IN NORMAL AND PATHOLOGICAL GAIT, The Journal of Bone & Joint Surgery, vol.35, issue.3, pp.543-558, 1953.
DOI : 10.2106/00004623-195335030-00003

B. Griffin and J. W. Grizzle, Walking gait optimization for accommodation of unknown terrain height variations, 2015 American Control Conference (ACC), 2015.
DOI : 10.1109/ACC.2015.7172087

B. Griffin and J. Grizzle, Nonholonomic virtual constraints and gait optimization for robust walking control, The International Journal of Robotics Research, vol.136, issue.2
DOI : 10.1109/ICCPS.2014.6843723

J. Grizzle and C. Chevallereau, Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion, 2017.
DOI : 10.1007/978-3-540-74358-3_14
URL : http://www.eecs.umich.edu/~grizzle/papers/Grizzle_Westervelt_HZD_IsidoriFest.pdf

D. G. Hobbelen and M. Wisse, Swing-Leg Retraction for Limit Cycle Walkers Improves Disturbance Rejection, IEEE Transactions on Robotics, vol.24, issue.2, pp.377-389, 2008.
DOI : 10.1109/TRO.2008.917002

Y. Hurmuzlu and D. Marghitu, Rigid Body Collisions of Planar Kinematic Chains With Multiple Contact Points, The International Journal of Robotics Research, vol.431, issue.3, pp.82-92, 1994.
DOI : 10.1098/rspa.1990.0125

J. Jianjuen and . Hu, Stable Locomotion Control of Bipedal Walking Robots: Synchronization with Neural Oscillators and Switching Control, 2000.

B. G. Buss, K. Akbari-hamed, and J. W. Grizzle, Exponentially stabilizing continuous-time controllers for periodic orbits of hybrid systems: Application to bipedal locomotion with ground height variations, The International Journal of Robotics Research, vol.35, issue.8, pp.977-999, 2015.

S. Kajita, F. Kanehiro, K. Kaneko, K. Yokoi, and H. Hirohisa, 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), pp.239-246, 2001.
DOI : 10.1109/IROS.2001.973365

T. Koolen, T. De-boer, J. Rebula, J. Goswami, and . Pratt, Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models, The International Journal of Robotics Research, vol.1, issue.9, pp.1094-1113, 2012.
DOI : 10.1145/1275808.1276509

T. Mcgeer, Passive Dynamic Walking, The International Journal of Robotics Research, vol.2, issue.4, pp.62-82, 1990.
DOI : 10.1109/JRA.1986.1087060

T. Mcgeer, Passive walking with knees, Proceedings., IEEE International Conference on Robotics and Automation, pp.1640-1645, 1990.
DOI : 10.1109/ROBOT.1990.126245

B. Morris and J. W. Grizzle, Hybrid Invariant Manifolds in Systems With Impulse Effects With Application to Periodic Locomotion in Bipedal Robots, IEEE Transactions on Automatic Control, vol.54, issue.8, pp.1751-1764, 2009.
DOI : 10.1109/TAC.2009.2024563

N. Pateromichelakis, A. Mazel, M. A. Hache, R. Gelin, T. Koumpogiannis et al., Head-eyes system and gaze analysis of the humanoid robot Romeo, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.1374-1379, 2014.
DOI : 10.1109/IROS.2014.6942736

. Ames, Mechanics-based design of underactuated robotic walking gaits: Initial experimental realization, 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pp.981-986, 2016.

H. Razavi, A. M. Bloch, C. Chevallereau, and J. W. Grizzle, Restricted discrete invariance and self-synchronization for stable walking of bipedal robots, 2015 American Control Conference (ACC), pp.4818-4824, 2015.
DOI : 10.1109/ACC.2015.7172088

H. Razavi, A. M. Bloch, C. Chevallereau, and J. W. Grizzle, Symmetry in legged locomotion: a new method for designing stable periodic gaits, Autonomous Robots, vol.21, issue.3, pp.1119-1142, 2017.
DOI : 10.1109/TRO.2004.838030
URL : https://hal.archives-ouvertes.fr/hal-01398837

R. Seyed-hamed, Symmetry Method for Limit Cycle Walking of Legged Robots, 2016.

C. Shih, J. W. Grizzle, and C. Chevallereau, From stable walking to steering of a 3D bipedal robot with passive point feet, Robotica, vol.30, issue.07, pp.119-1130, 2012.
DOI : 10.1017/S0263574708005079
URL : https://hal.archives-ouvertes.fr/hal-00794633

M. W. Spong and F. Bullo, Controlled symmetries and passive walking, IEEE Transactions on Automatic Control, vol.50, issue.7, pp.1025-1031, 2005.
DOI : 10.1109/TAC.2005.851449
URL : http://motion.me.ucsb.edu/pdf/2001n-sb.pdf

P. Van-zutven and H. Nijmeijer, Foot Placement Indicator for Balance of Planar Bipeds with Point Feet, International Journal of Advanced Robotic Systems, vol.3, issue.1, pp.1-11, 2013.
DOI : 10.1109/ICRA.2013.6631257

E. R. Westervelt, J. W. Grizzle, and D. E. 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

R. Eric, . Westervelt, W. Jessy, C. C. Grizzle, H. Choi et al., Feedback Control of Dynamic Bipedal Robot Locomotion, 2007.

C. Z. , L. Elyaaqoubi, N. Abba, and G. , Optimized 3D stable walking of a bipedal robot with line-shaped massless feet and sagittal underactuation, Robotics and Autonomous Systems, vol.83, pp.203-216, 2016.