Stable Walking and Running Robots Without Feedback

In this paper we give an overview of our previous work on open-loop stable walking and running robots. The concept of open-loop control implies that all actuators of a robot receive purely periodic pre-calculated torque or force inputs that are never altered by any feedback interference. Passive-dynamic robots can be considered as a special case with zero actuation for which a stabilization is much easier due to the possibility of time shifts. We have developed a numerical method that optimizes the open-loop stability of solutions of periodic optimal control problems with discontinuities. Using this method, we were able to find a number of open-loop stable one- and two-legged robot configurations and motions.

[1]  Richard W. Longman,et al.  Human-like actuated walking that is asymptotically stable without feedback , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[2]  M. Coleman,et al.  Prediction of stable walking for a toy that cannot stand. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Richard W. Longman,et al.  Open-loop stable running , 2005, Robotica.

[4]  K. Mombaur,et al.  Open‐loop stable solutions of periodic optimal control problems in robotics , 2005 .

[5]  Roger D. Quinn,et al.  Design of a 5-cm monopod hopping robot , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[6]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

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

[8]  Jay C. Hsu,et al.  Modern Control Principles and Applications , 1968 .

[9]  M. Coleman,et al.  An Uncontrolled Walking Toy That Cannot Stand Still , 1998 .

[10]  Robert Ringrose,et al.  Self-stabilizing running , 1997, Proceedings of International Conference on Robotics and Automation.

[11]  Martin Buehler.  Dynamic locomotion with one, four and six-legged robots (特集「ロコモーション」) , 2002 .

[12]  Masahiro Fujita,et al.  Four-Legged Robot League , 2002 .

[13]  Richard W. Longman,et al.  Self-stabilizing somersaults , 2005, IEEE Transactions on Robotics.

[14]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[15]  Jerry E. Pratt,et al.  Exploiting inherent robustness and natural dynamics in the control of bipedal walking robots , 2000 .