Experimental Validation of a Framework for the Design of Controllers that Induce Stable Walking in Planar Bipeds

In this paper we present the experimental validation of a framework for the systematic design, analysis, and performance enhancement of controllers that induce stable walking in N -link underactuated planar biped robots. Controllers designed via this framework act by enforcing virtual constraints—holonomic constraints imposed via feedback—on the robot’s configuration, which create an attracting two-dimensional invariant set in the full walking model’s state space. Stability properties of resulting walking motions are easily analyzed in terms of a two-dimensional subdynamic of the full walking model. A practical introduction to and interpretation of the framework is given. In addition, in this paper we develop the ability to regulate the average walking rate of the biped to a continuum of values by modification of within-stride and stride-boundary characteristics, such as step length.

[1]  W. Goldsmith,et al.  Impact: the theory and physical behaviour of colliding solids. , 1960 .

[2]  A. Isidori.  Nonlinear Control Systems: An Introduction , 1986 .

[3]  J. Furusho,et al.  Control of a Dynamical Biped Locomotion System for Steady Walking , 1986 .

[4]  Marc H. Raibert,et al.  Legged Robots That Balance , 1986, IEEE Expert.

[5]  M. Vukobratovic,et al.  Biped Locomotion , 1990 .

[6]  Akihito Sano,et al.  Sensor-Based Control of a Nine-Link Biped , 1990, Int. J. Robotics Res..

[7]  Akihito Sano,et al.  Realization of natural dynamic walking using the angular momentum information , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[8]  Shuuji Kajita,et al.  Dynamic walking control of a biped robot along a potential energy conserving orbit , 1992, IEEE Trans. Robotics Autom..

[9]  Jessy W. Grizzle,et al.  Interpolation and numerical differentiation for observer design , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[10]  Dan B. Marghitu,et al.  Rigid Body Collisions of Planar Kinematic Chains With Multiple Contact Points , 1994, Int. J. Robotics Res..

[11]  A. Michel,et al.  Stability theory for hybrid dynamical systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[12]  Bernard Espiau,et al.  Limit cycles and their stability in a passive bipedal gait , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[13]  S. Kajita,et al.  Experimental study of biped dynamic walking , 1996 .

[14]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[15]  Daniel E. Koditschek,et al.  Spring loaded inverted pendulum running: a plant model , 1998 .

[16]  Jerry E. Pratt,et al.  Intuitive control of a planar bipedal walking robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[17]  G. W. Howell,et al.  Simple controllable walking mechanisms which exhibit bifurcations , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[18]  Jong H. Park,et al.  Biped robot walking using gravity-compensated inverted pendulum mode and computed torque control , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[19]  T. Takenaka,et al.  The development of Honda humanoid robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

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

[21]  Kazuhito Yokoi,et al.  A high stability, smooth walking pattern for a biped robot , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[22]  Ambarish Goswami,et al.  Postural Stability of Biped Robots and the Foot-Rotation Indicator (FRI) Point , 1999, Int. J. Robotics Res..

[23]  Atsuo Takanishi,et al.  Development of a bipedal humanoid robot-control method of whole body cooperative dynamic biped walking , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[24]  Atsuo Takanishi,et al.  Control to realize human-like walking of a biped humanoid robot , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[25]  A. Kuo,et al.  Active control of lateral balance in human walking. , 2000, Journal of biomechanics.

[26]  A. Ruina,et al.  Efficiency, speed, and scaling of two-dimensional passive-dynamic walking , 2000 .

[27]  Chee-Meng Chew,et al.  Virtual Model Control: An Intuitive Approach for Bipedal Locomotion , 2001, Int. J. Robotics Res..

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

[29]  Kazuhito Yokoi,et al.  A realtime pattern generator for biped walking , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[30]  J.W. Grizzle,et al.  Event-based PI control of an underactuated biped walker , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[31]  Carlos Canudas de Wit,et al.  Switching and PI control of walking motions of planar biped walkers , 2003, IEEE Trans. Autom. Control..

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

[33]  E. Westervelt,et al.  Toward a coherent framework for the control of planar biped locomotion , 2003 .

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

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