This paper presents a robust tracking control algorithm for underactuated biped robots. The biped considered in this work is modeled as a five-link planar robot with four actuators located at hip and knee joints to control the joint angles. The control law is defined based on the sliding mode control approach. The objective of the controller is to generate stable walking based on predefined desired trajectories. The planning of the trajectory in swing phase is discussed while the double support phase is considered to be instantaneous and the impact of the swing leg with the ground is modeled as rigid body contact. In order to formulate the sliding control law, we define four first-order sliding surfaces, based on the number of actuators, as a linear combination of tracking joint positions and velocities. The control approach is shown to guarantee that all trajectories will reach and stay on these surfaces. The surface parameters are then selected to ensure the stability of the surfaces leading to an asymptotically stable control law. Numerical simulation is presented for tracking a multi-step walk of a biped robot.

Volume Subject Area:
Dynamic Systems and Technology
Topics:
Robots, Sliding mode control, Actuators, Algorithms, Computer simulation, Control equipment, Knee, Stability, Tracking control, Trajectories (Physics)
1.
Raibert, M. H., 1986. Legged Robots That Balance. MIT Press, Cambridge, MA.
2.
Vukobratovic, M., Borovac, B., Surla, D., and Stokic, D., 1990. Biped Locomotion. Springer-Verlag, Berlin, Germany.
3.
Mitobe, K., Mori, N., Aida, K., and Nasu, Y., 1995. “Nonlinear feedback control of a biped walking robot.” In Proceedings IEEE International Conference on Robotics and Automation, Vol. 3, pp. 2865–2870.
4.
Tzafestas
S.
,
Raibert
M. H.
, and
Tzafestas
C.
,
1996
. “
Robust sliding-mode control applied to a 5-link biped robot
.”
Journal of Intelligent and Robotic Systems Theory and Applications
,
15
(
1
), pp.
67
–
133
.
5.
Tzafestas
S. G.
,
Krikochoritis
T. E.
, and
Tzafestas
C. S.
,
1997
. “
Robust sliding-mode control of nine-link biped robot walking
.”
Journal of Intelligent and Robotic Systems Theory and Applications
,
20
(
2
), pp.
375
–
402
.
6.
Chang
T. H.
, and
Hurmuzlu
Y.
,
1993
. “
Sliding control without reaching phase and its application to bipedal locomotion
.”
Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME
,
115
(
3
), pp.
447
–
455
.
7.
Goswami, A., Espiau, B., and Keramane, A., 1996. “Limit cycles and their stability in a passive bipedal gait.” In Proceedings of IEEE International Conference on Robotics and Automation, Vol. 1, pp. 246–251.
8.
Grizzle
J.
,
Abba
G.
, and
Plestan
F.
,
2001
. “
Asymptotically stable walking for biped robots: Analysis via systems with impulse effects
.”
IEEE Transactions on Automatic Control
,
46
(
1
), pp.
51
–
64
.
9.
Plestan
F.
,
Grizzle
J. W.
,
Westervelt
E. R.
, and
Abba
G.
,
2003
. “
Stable walking of a 7-dof biped robot
.”
IEEE Transactions on Robotics and Automation
,
19
(
4
), pp.
653
–
668
.
10.
Chevallereau
C.
,
2003
. “
Time-scaling control for an underactuated biped robot
.”
IEEE Transactions on Robotics and Automation
,
19
(
2
), pp.
362
–
368
.
11.
Utkin
V. I.
,
1977
. “
Variable structure systems with sliding modes
.”
IEEE Transactions on Automatic Control
,
22
(
2
), pp.
212
–
222
.
12.
Ashrafiuon, H., and Erwin, R. S., 2004. “Sliding control approach to underactuated multibody systems.” In Proceedings of the American Control Conference, Vol. 2, pp. 1283–1288.
This content is only available via PDF.
Copyright © 2005
 by ASME
You do not currently have access to this content.