Walking and steering control for a 3D biped robot considering ground contact and stability

This paper presents a stable walking control method for a 3D bipedal robot with 14 joint actuators. The overall control law consists of a ZMP (zero moment point) controller, a swing ankle rotation controller and a partial joint angles controller. The ZMP controller guarantees that the stance foot remains in flat contact with the ground. The swing ankle rotation controller ensures a flat foot impact at the end of the swinging phase. Each of these controllers creates 2 constraints on joint accelerations. As a consequence, the partial joint angles controller is implemented to track only 10 independent outputs. These outputs are defined as a linear combination of the 14 joint angles. The most important question addressed in this paper is how this linear combination can be defined in order to ensure walking stability. The stability of the walking gait under closed loop control is evaluated with the linearization of the restricted Poincare map of the hybrid zero dynamics. As a result, the robot can achieve an asymptotically stable and periodic walking along a straight line. Finally, another feedback controller is supplemented to adjust the walking direction of the robot and some examples of the robot steered to walk along different paths with mild curvature are given.

[1]  Wisama Khalil,et al.  Modeling, Identification and Control of Robots , 2003 .

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

[3]  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.

[4]  Atsuo Kawamura,et al.  The direction control of a biped robot using gyro sensor feedback , 2010, 2010 11th IEEE International Workshop on Advanced Motion Control (AMC).

[5]  J. Grizzle.  Remarks on Event-Based Stabilization of Periodic Orbits in Systems with Impulse Effects , 2006 .

[6]  D Tlalolini,et al.  Human-Like Walking: Optimal Motion of a Bipedal Robot With Toe-Rotation Motion , 2011, IEEE/ASME Transactions on Mechatronics.

[7]  Christine Chevallereau,et al.  Stability analysis and time-varying walking control for an under-actuated planar biped robot , 2011, Robotics Auton. Syst..

[8]  B. Brogliato,et al.  Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics , 2008 .

[9]  Masayuki Inaba,et al.  Online humanoid walking control system and a moving goal tracking experiment , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[10]  Joao P. Ferreira,et al.  Neuro-fuzzy ZMP control of a biped robot , 2006 .

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

[12]  M. van de Panne,et al.  Generalized biped walking control , 2010, ACM Trans. Graph..

[13]  Christine Chevallereau,et al.  Stable Bipedal Walking With Foot Rotation Through Direct Regulation of the Zero Moment Point , 2008, IEEE Transactions on Robotics.

[14]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[15]  Miomir Vukobratović,et al.  Biped Locomotion: Dynamics, Stability, Control and Application , 1990 .

[16]  Kazuhisa Mitobe,et al.  Control of walking robots based on manipulation of the zero moment point , 2000, Robotica.

[17]  Shuuji Kajita,et al.  Real-time 3D walking pattern generation for a biped robot with telescopic legs , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[18]  Christine Chevallereau,et al.  A Path-Following Approach to Stable Bipedal Walking and Zero Moment Point Regulation , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[19]  Vladimir J. Lumelsky,et al.  Synthesis of turning pattern trajectories for a biped robot in a scene with obstacles , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

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

[21]  Robert D. Gregg,et al.  Reduction-based Control of Three-dimensional Bipedal Walking Robots , 2010, Int. J. Robotics Res..

[22]  J. Y. S. Luh,et al.  On-Line Computational Scheme for Mechanical Manipulators , 1980 .

[23]  Hirochika Inoue,et al.  Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[24]  Yannick Aoustin,et al.  Design of a walking cyclic gait with single support phases and impacts for the locomotor system of a thirteen-link 3D biped using the parametric optimization , 2009 .

[25]  Franck Plestan,et al.  A penalty-based approach for contact forces computation in bipedal robots , 2009, 2009 9th IEEE-RAS International Conference on Humanoid Robots.

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

[27]  Jun-Ho Oh,et al.  Experimental realization of dynamic walking of the biped humanoid robot KHR-2 using zero moment point feedback and inertial measurement , 2006, Adv. Robotics.

[28]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

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

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

[31]  Takashi Matsumoto,et al.  Real time motion generation and control for biped robot -1st report: Walking gait pattern generation- , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[32]  Christine Chevallereau,et al.  Steering of a 3D bipedal robot with an underactuated ankle , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[33]  Hiroki Takeuchi,et al.  Development of "MEL HORSE" , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[34]  M. Omizo,et al.  Modeling , 1983, Encyclopedic Dictionary of Archaeology.

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

[36]  Takashi Matsumoto,et al.  Real time motion generation and control for biped robot -2nd report: Running gait pattern generation- , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[37]  Ryo Kurazume,et al.  The sway compensation trajectory for a biped robot , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[38]  Kazuhito Yokoi,et al.  Balance control of a piped robot combining off-line pattern with real-time modification , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[39]  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).