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Robust backstepping control of an underactuated one-legged hopping robot in stance phase

Published online by Cambridge University Press:  11 August 2009

Guangping He  and
Zhiyong Geng
Guangping He*
Affiliation:
Department of Mechanical and Electrical Engineering, North China University of Technology, Beijing 100041, People's Republic of China
Zhiyong Geng
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, People's Republic of China
*
*Corresponding author. E-mail: hegp55@126.com
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Summary

Exponentially stabilizing a non-Spring Loaded Inverted Pendulum (SLIP) model-based one-legged hopping robot in stance phase is studied. Differing from the SLIP model systems, the hopping robot with non-SLIP model considered in this paper does not restrict the center of mass of the robot coinciding to the hip joint. A specific underactuated one-legged hopping robot with two actuated arms are selected to investigate the dynamics and control problem. It is shown that the system holds the essential nonlinear prosperities of general systems and belongs to a class of second-order nonholonomic mechanical systems, which cannot be stabilized by any smooth time-invariant state feedback. By using a coordinates transform based on the so-called normalized momentum, a robust backstepping control method is presented for the specific hopping robot system. Both theoretical analysis and numerical simulations show that the robust backstepping controller can stabilize the underactuated one-legged hopping robot to its balance configuration as well as a periodic motion trajectory near to the balance configuration. These results are significative for designing a new non-SLIP model based hopping robot systems with more biological characteristics.

Keywords

Hopping robotsUnderactuationNonholonomyNonlinear control
Type
Article
Information
Robotica , Volume 28 , Issue 4 , July 2010 , pp. 583 - 596
Copyright
Copyright © Cambridge University Press 2009

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References

1.Raibert, M. H., Legged Robots That Balance (MIT Press, Boston, 1986).CrossRefGoogle Scholar
2.Seipel, J. E. and Holmes, P., “Running in three dimensions: Analysis of a point-mass sprung-leg model,” Int. J. Robot. Res., 24 (8), 657–674 (2005).CrossRefGoogle Scholar
3.Poulakakis, I., Papadopoulos, E. and Buhler, M., “On the stability of the passive dynamics of quadrupedal running with a bounding gait,” Int. J. Robot. Res., 25 (7), 669–687 (2006).CrossRefGoogle Scholar
4.Raibert, M. H., “Hopping in legged systems-modeling and simulation for the two-dimensional one-legged case,” IEEE Trans. Syst. Man Cybern., SMC-14 (3), 451–463 (1984).Google Scholar
5.Raibert, M. H., Benjamin Brown, H. Jr., and Cheppoins, Michael, “Experiments in balance with 2 3D one-legged hopping machine,” Int. J. Robot. Res., 3 (2), 75–92 (1984).Google Scholar
6.Raibert, M. H., Chepponis, M. and Brown, H. B. Jr., “Running on four legs as though they were one,” IEEE J. Robot. Autom., RA-2 (2), 70–82 (1986).CrossRefGoogle Scholar
7.Hodgins, J. K. and Raibert, M. H., “Biped gymnastics,” Int. J. Robot. Res., 9 (2), 115–132 (1990).Google Scholar
8.Hodgins, J. K. and Raibert, M. H., “Adjusting step length for rough terrain locomotion,” IEEE Trans. Robot. Autom., 7 (3), 289–298 (1991).Google Scholar
9.Hyon, S. H. and Mita, T., “Development of a Biologically Inspired Hopping Robots-Kenken,” IEEE International Conference on Robotics and Automation, Washington, DC (2002) pp. 3984–3991.Google Scholar
10.Zeglin, G. J., Uniroo: A One-Legged Dynamic Hopping Robot BS thesis (Boston, MA: Department of Mechanical Engineering, Massachusetts Institute of Technology, 1991).Google Scholar
11.Isidori, A., Nonlinear Control Systems (Springer-Verlag, Berlin, 1995).Google Scholar
12.Sastry, S., Nonlinear Systems Analysis, Stability and Control (Springer-Verlag, New York, 1999).Google Scholar
13.Olfati-Saber, R., Nonlinear Control of Underactuated Mechanical Systems with Application to Robotics and Aerospace Vehicles Doctoral Dissertation (Massachusetts Institute of Technology, Cambridge, 2001).Google Scholar
14.Samson, C., “Control of chained systems application to path following and time-vary point-stabilization of mobile robots,” IEEE Trans. Autom. Control, 40 (1), 64–77 (1995).Google Scholar
15.Lucibello, P. and Oriolo, G., “Robust stabilization via iterative state steering with an application to chained-form systems,” Automatica, 37, 71–79 (2001).CrossRefGoogle Scholar
16.Marchand, N. and Alamir, M., “Discontinuous exponential stabilization of chained form systems,” Automatica, 39, 343–348 (2003).CrossRefGoogle Scholar
17.Oriolo, G. and Vendittelli, M., “A framework for the stabilization of general nonholonomic systems with an application to the plate-ball mechanism,” IEEE Trans. Robot., 21 (2), 162–175 (2005).Google Scholar
18.Spong, M. W., “The swing up control problem for the acrobot,” IEEE Control Syst. Mag., 15, 49–55 (1995).Google Scholar
19.Kristić, M., Kanellakopoulos, I. and Kokotović, P., Nonlinear and Adaptive Control Design (John Wiley & Sons San Francisco, 1995).Google Scholar
20.Freeman, R. A. and Kokotović, P. V., Robust Nonlinear Control Design: State-Space and Lyapunov Techniques (Birkhäuser, Boston, 1996).CrossRefGoogle Scholar
21.Bloch, A. M., Baillieul, J., Crouch, P. and Marsden, J., Nonholonomic Mechanics and Control (Springer-Verlag, New York, 2003).Google Scholar
22.Do, K. D., Jiang, Z. P. and Pan, J.. “Universal controllers for stabilization and tracking of underactuated ships,” Syst. Control Lett., 47, 299–317 (2002).Google Scholar
23.Luca, A. D., Mattone, R. and Oriolo, G., “Stabilization of an underactuated planar 2R manipulator,” Int. J. Robust Nonlinear Control, 10, 181–198 (2000).3.0.CO;2-X>CrossRefGoogle Scholar
24.Murray, R. M., Zexiang, Li and Sastry, S. Shankar, A Mathematical Introduction to Robotics Manipulation (CRC Press, Boca Raton, 1994).Google Scholar
25.Brockett, R. W., “Asymptotic Stability and Feedback Stabilization,” In: Differential Geometric Control Theory (Brockett, R. W., Millman, R. S. and Sussmann, H. J., eds.) (Birkhauser, Boston, 1983) pp. 181–191.Google Scholar
26.Luca, A. D. and Oriolo, G., “Trajectory planning and control for planar robots with passive last joint,” Int. J. Robot. Res., 21 (5–6), 575–590 (2002).CrossRefGoogle Scholar
27.Fliess, M., Lévine, J., Martin, P. and Rouchon, P., “Flatness and defect of nonlinear systems: Introductory theory and examples,” Int. J. Control, 61 (6), 1327–1361 (1995).CrossRefGoogle Scholar
28.Mazenc, F. and Praly, L., “Adding integrations, saturated controls, and stabilization for feedforward systems,” IEEE Trans. Autom. Control, 40, 1559–1578 (1996).Google Scholar
29.Papadopoulos, E. and Cherouvim, N., “On Increasing Energy Autonomy for a One-Legged Hopping Robot,” IEEE International Conference on Robotics & Automation, New Orleans (2004) pp. 4645–4650.Google Scholar
30.He, G.-P., Tan, X.-L., Zhang, X.-H. and Lu, Z., “Modeling, motion planning, and control of one-legged hopping robot actuated by two arms,” Mech. Mach. Theory, 43 (1), 33–49 (2008).Google Scholar
31.Ahmadi, M. and Buhler, M., “Controlled passive dynamic running experiments with the ARL-Monopod II,” IEEE Trans. Robot., 22 (2), 974–986 (2006).Google Scholar