We consider a prototyped walking robot containing a platform and two double-link legs. Thus, it is a five-link mechanism. The front leg models identical motions of the quadruped’s two front legs, and the back leg models identical motions of the quadruped’s two back legs. The legs have passive (uncontrolled) feet that extend in the frontal plane. Because of this the robot is stable in the frontal plane. This robot can be viewed as a “virtual” quadruped. Four DC motors drive the mechanism. Its control system comprises a computer, hardware servo-systems, and power amplifiers. The locomotion of the prototype is planar curvet gait. In the double support our prototype is statically stable and overactuated. In the single support it is an unstable and underactuated system. There is no flight phase. We describe here the scheme of the mechanism, the characteristics of the drives, and the control strategy. The dynamic model of the planar walking is recalled for the double-and single-support phases and for the impact instant. The experiments give results that are close to those of the simulation.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
R. Altendorfer, N. Moore, H. Komsuoglu, M. Buehler, H. B. Brown, Jr., D. McMordie, U. Saranli, R. Full, and D. E. Koditschek, “RHex: A biologically inspired hexapod runner,” J. Autonoumos Robots, 11, 207–213 (2001).
Y. Aoustin and A. M. Formal’sky, “Control strategy for dynamic locomotion design of a walking quadruped,” in: Proc. IFAC Workshop, Motion Control 98 (1998), pp. 401–407.
Y. Aoustin and A. M. Formal’sky, “Control design for a biped: Reference trajectory based on driven angles as functions of the undriven angle,” J. Comput. System Sci., 42, No. 4, 159–176 (2003).
J. Cham, S. A. Bailey, and M. R. Cutkosky, “Robust dynamic locomotion through feedforward-preflex interaction,” in: Proc. ASME Conf. Mechanical Engineers Congress and Exhibition (2000).
C. Chevallereau, G. Abba, Y. Aoustin, F. Plestan, A. R. Westervelt, C. Canudas de Wit, and J. W. Grizzle, “Rabbit: A testbed for advanced control theory,” IEEE Control System Magazine, 23, No. 5, 57–78 (2003).
G. Conte, E. Scaradozzi, A. Suardi, “Control architecture for a prototypal legged robot,” in: Proc. Clawar Conf. (2003), pp. 127–134.
M. De Lasa and M. Buehler, “Dynamic compliant quadruped walking,” in: Proc. IEEE Conf. on Robotics and Automation (2001), pp. 21–26.
J. Estremera, E. Garcia, P. Gonzalez de Santos, “A continuous free crab gait for quadruped robots on irregular terrain,” in: Proc. Int. Conf. on Climbing and Walking Robots (CLAWAR) (2003), pp. 584–592.
A. M. Formal’sky, Locomotion of Anthropomorphic Mechanisms [in Russian], Nauka, Moscow (1982).
A. M. Formal’sky, “Ballistic locomotion of a biped. Design and control of two biped machines,” in: A. Morecki and K. Waldron, eds., Human and Machine Locomotion, CISM, Springer-Verlag, Udine, Italy (1997).
A. M. Formal’sky, C. Chevallereau, B. Perrin, “On ballistic walking locomotion of a quadruped,” Internat. J. Robotics Res., 19, No. 8, 743–761 (2000).
Y. Fukuoka, H. Kimura, A. H. Cohen, “Adaptative dynamic walking of a quadruped robot on irregular terrain based on biological concepts,” Internat. J. Robotics Res., 22, Nos. 3–4, 187–202 (2003).
J. Furusho, A. Sano, M. Sakaguchi, and E. Koizumi, “Realization of bounce gait in a quadruped robot with articular-joint-type legs,” in: Proc. IEEE Conf. on Robotics and Automation (1995), pp. 697–702.
V. S. Gurfinkel, E. V. Gurfinkel, A. Y. Shneider, E. A. Devjanin, A. V. Lensky, and L. G. Shtilman, “Walking robot with supervisory control,” Mechanisms Machines Theory, 16, No. 2, 31–36 (1981).
K. Hirai, M. Hirose, Y. Haikawa, and T. Takenaka, “The development of Honda humanoid robot,” in: Proc. IEEE Conf. on Robotics and Automation (1998), pp. 1321–1326.
S. Hirose, and K. Kato, “Study on quadruped walking robot in Tokyo Institute of Technology,” in: Proc. IEEE Conf. on Robotics and Automation (2000), pp. 414–419.
S. Hirose and K. Yoneda, “Toward development of practical quadruped walking vehicles,” J. Robotics Mechatronics, 5, No. 6, 498–504 (1993).
Y. S. Hong, H. K. Lee, S. Y. Yi, and C. W. Lee, “The design and control of a jointed-leg type of a quadrupedal robot for locomotion on irregular ground,” Robotica, 17, No. 4, 383–389 (1999).
M. Kaneko, M. Abe, and K. Tanie, “A hexapod walking machine with decoupled freedoms,” IEEE J. Robotics and Automation, 1, No. 4, 183–190 (1985).
H. Kimura, S. Akiyama, and K. Sakurama, “Realization of dynamic and running of the quadruped using a neural oscillator,” J. Autonoumos Robots, 7, 247–258 (1999).
C. A. Klein and R. L. Briggs, “Use of active compliance in the control of legged vehicles,” IEEE Trans. Systems Man Cybernet., 10, No. 7, 393–400 (2000).
B. T. Krupp, “Preliminary control of a planar robot for quadrupedal locomotion research,” in: Proc. Int. Conf. on Climbing and Walking Robots (CLAWAR) (2003), pp. 95–104.
H. Miura and I. Shimoyama, “Dynamic walk of a biped,” Internat. J. Robotics Res., 3, No. 2, 60–74 (1984).
A. Muraro, C. Chevallereau, and Y. Aoustin, “Optimal trajectories for a quadruped robot with trot, amble, and curvet gaits for two energetic criteria,” Internat. J. Multibody System Dynamics, 9, 39–62 (2003).
B. Perrin, Modelling and Control of a Quadruped for a Dynamically Stable Gait [in French], Ph.D. Thesis, University of Nantes (1999).
I. Poulakakis, J. A. Smith, and M. Buehler, “On the dynamics of bounding and extensions torwards the half-bound and the gallop gaits,” in: Proc. Int. Symp. on Adaptative Motion of Animals and Machines, Kyoto (2003).
G. A. Pratt and M. M. Williamson, “Series elastic actuators,” in: Proc. IEEE Conf. on Intelligent Robots and Systems (1995), pp. 399–406.
U. Saranli, M. Buehler, and D. E. Koditschek, “Rhex: A simple and highly mobile hexapod robot,” Internat. J. Robotics Res., 20, No. 7, 616–631 (2001).
I. E. Sutherland and M. H. Raibert, “Machines that walk,” Scientific American, 248, 44–53 (1983).
S. Talebi, G. Poulakakis, E. Papadopoulos, and M. Buehler, “Quadruped robot running with a bounding gait,” in: D. Rus and S. Singh, eds., Experimental Robotics VII, Lect. Notes Control Information Sci., Vol. 271 (2001), pp. 281–289.
S. H. Ting, R. Blickhan, and R. F. Full, “Dynamic and static stability in hexapedal runners,” J. Experimental Biology, 197, 251–269 (1994).
M. Vukobratovic, B. Borovac, D. Surla, and D. Stokic, Biped Locomotion, Springer (1990).
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 8, pp. 5–28, 2005.
About this article
Cite this article
Aoustin, Y., Formal’sky, A. & Chevallereau, C. Virtual quadruped: Mechanical design, control, simulation, and experimentation. J Math Sci 147, 6552–6568 (2007). https://doi.org/10.1007/s10958-007-0495-5
- Joint Angle
- Reference Trajectory
- Zero Moment Point
- Double Support