HZD-based control of a five-link underactuated 3D bipedal robot

This paper presents a within-stride feedback controller that achieves an exponentially stable, periodic, and fast walking gait for a 3D bipedal robot consisting of a torso, revolute knees, and passive (unactuated) point feet. The walking surface is assumed to be rigid and flat; the contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. In addition to the reduced number of actuators, the interest of studying robots with point feet is that the feedback control solution must explicitly account for the robot¿s natural dynamics in order to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics (HZD), a very successful method for planar bipeds, in order to determine a periodic orbit and an autonomous feedback controller that realizes the orbit, for a 3D (spatial) bipedal walking robot. The effect of output selection on the zero dynamics is highlighted and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller.

[1]  Daniel E. Koditschek,et al.  Hybrid zero dynamics of planar biped walkers , 2003, IEEE Trans. Autom. Control..

[2]  Jessy W. Grizzle,et al.  Hybrid Invariant Manifolds in Systems With Impulse Effects With Application to Periodic Locomotion in Bipedal Robots , 2009, IEEE Transactions on Automatic Control.

[3]  A.D. Ames,et al.  Stably Extending Two-Dimensional Bipedal Walking to Three Dimensions , 2007, 2007 American Control Conference.

[4]  Ching-Long Shih,et al.  Asymptotically Stable Walking of a Simple Underactuated 3D Bipedal Robot , 2007, IECON 2007 - 33rd Annual Conference of the IEEE Industrial Electronics Society.

[5]  M.W. Spong,et al.  Reduction-based control with application to three-dimensional bipedal walking robots , 2008, 2008 American Control Conference.

[6]  E. Westervelt,et al.  Feedback Control of Dynamic Bipedal Robot Locomotion , 2007 .

[7]  J. Grizzle,et al.  A Restricted Poincaré Map for Determining Exponentially Stable Periodic Orbits in Systems with Impulse Effects: Application to Bipedal Robots , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[8]  Jun Ho Choi,et al.  Planar bipedal walking with foot rotation , 2005, Proceedings of the 2005, American Control Conference, 2005..

[9]  Christine Chevallereau,et al.  Asymptotically Stable Walking of a Five-Link Underactuated 3-D Bipedal Robot , 2009, IEEE Transactions on Robotics.

[10]  Kevin Warwick,et al.  Control systems : an introduction , 1989 .

[11]  Christine Chevallereau,et al.  RABBIT: a testbed for advanced control theory , 2003 .

[12]  Kazuhito Yokoi,et al.  Biped walking pattern generation by using preview control of zero-moment point , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[13]  Arthur D. Kuo,et al.  Stabilization of Lateral Motion in Passive Dynamic Walking , 1999, Int. J. Robotics Res..

[14]  Franck Plestan,et al.  Stable walking of a 7-DOF biped robot , 2003, IEEE Trans. Robotics Autom..

[15]  Russ Tedrake,et al.  Efficient Bipedal Robots Based on Passive-Dynamic Walkers , 2005, Science.

[16]  E. Westervelt,et al.  Zero Dynamics of Planar Biped Walkers with One Degree of Under Actuation , 2002 .

[17]  Franck Plestan,et al.  Asymptotically stable walking for biped robots: analysis via systems with impulse effects , 2001, IEEE Trans. Autom. Control..

[18]  Mark W. Spong,et al.  Energy Based Control of a Class of Underactuated Mechanical Systems , 1996 .

[19]  Yasuhisa Hasegawa,et al.  Multi-Locomotion Control of Biped Locomotion and Brachiation Robot , 2006 .

[20]  Milos Zefran,et al.  Underactuated dynamic three-dimensional bipedal walking , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[21]  Shuuji Kajita,et al.  Biped Walking Pattern Generator allowing Auxiliary ZMP Control , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[22]  Miomir Vukobratovic,et al.  Zmp: a Review of Some Basic Misunderstandings , 2006, Int. J. Humanoid Robotics.

[23]  Moritz Diehl,et al.  Fast Motions in Biomechanics and Robotics , 2006 .

[24]  A. Isidori.  Nonlinear Control Systems , 1985 .

[25]  Francesco Bullo,et al.  Controlled symmetries and passive walking , 2005, IEEE Transactions on Automatic Control.