Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-18T06:31:43.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Single-legged hopping robotics research—A review

Published online by Cambridge University Press:  01 September 2007

Ajij Sayyad ,
B. Seth  and
P. Seshu
Ajij Sayyad*
Affiliation:
Systems and Control Engineering, IIT Bombay, Mumbai-400 076, India
B. Seth
Affiliation:
Department of Mechanical Engineering, IIT Bombay, Mumbai-400 076, India
P. Seshu
Affiliation:
Department of Mechanical Engineering, IIT Bombay, Mumbai-400 076, India
*
*Corresponding author. E-mail: sayyad@sc.iitb.ac.in
Get access Rights & Permissions [Opens in a new window]

Summary

Inspired by the agility of animal and human locomotion, the number of researchers studying and developing legged robots has been increasing at a rapid rate over the last few decades. In comparison to multilegged robots, single-legged robots have only one type of locomotion gait, i.e., hopping, which represents a highly nonlinear dynamical behavior consisting of alternating flight and stance phases. Hopping motion has to be dynamically stabilized and presents challenging control problems. A large fraction of studies on legged robots has focused on modeling and control of single-legged hopping machines. In this paper, we present a comprehensive review of developments in the field of single-legged hopping robots. We have attempted to cover development of prototype models as well as theoretical models of such hopping systems.

Type
Article
Information
Robotica , Volume 25 , Issue 5 , September 2007 , pp. 587 - 613
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Raibert, M. H., Legged Robots That Balance (MIT Press, Cambridge, 1986).CrossRefGoogle Scholar
2.Hardarson, F., Locomotion for difficult terrain, Technical Report (TRITA-MMK 1998:3, Department of Machine Design, Royal Institute of Technology, Sweden, Apr. 1998).Google Scholar
3.Matsuoka, K., “A Model of Repetitive Hopping Movements in Man,” Proceedings of Fifth World Congress on Theory of Machines and Mechanisms (1979) pp. 1168–1171.Google Scholar
4.Matsuoka, K., “A mechanical model of repetitive hopping movements,” J. Biomech. 5, 251–258 (1980).Google Scholar
5.Raibert, M. H., “Dynamic Stability and Resonance in a One-Legged Hopping Machine,” (Morecki, A., Bianchi, G. and Kedzior, K., eds.) Proceedings of Fourth Symposium on Theory and Practice of Robots and Manipulators (Polish Scientific Publishers, Warsaw, 1981) pp. 352–367.Google Scholar
6.Raibert, M. H. and Brown, H. B., “Experiments in balance with a 2D one-legged hopping machine,” ASME J. Dynam. Syst., Meas. Control 106, 75–81 (Mar. 1984).Google Scholar
7.Raibert, M. H., “Hopping in legged systems-modeling and simulation for the two-dimensional one-legged case,” IEEE Trans. Syst., Man Cybern. 14 (3), 451–463 (May/Jun. 1984).CrossRefGoogle Scholar
8.Raibert, M. H., Brown, H. B. and Chepponis, M., “Experiments in balance with a 3D one-legged hopping machine,” Int. J. Robot. Res. 3 (2), 75–92 (1984).CrossRefGoogle Scholar
9.Raibert, M. H., “Running with symmetry,” Int. J. Robot. Res. 5 (4), 45–61 (1986).CrossRefGoogle Scholar
10.Raibert, M. H., Chepponis, M. and , H. B. Jr.Brown, “Running on four legs as though they were one,” IEEE J. Robot. Autom. 2 (2), 70–82 (Jun. 1986).CrossRefGoogle Scholar
11.Lee, W. and Raibert, M. H., “Control of Hoof Rolling in an Articulated Leg,” Proceedings of IEEE International Conference on Robotics and Automation, Sacramento, USA (Apr. 1991) pp. 1386–1391.Google Scholar
12.MIT Leg Lab, “Leg lab robots,” http://www.ai.mit.edu/projects/leglab/robots/robots-main.html, (Last cited on Feb. 2007).Google Scholar
13.Zeglin, G., Uniroo: A one legged dynamic hopping robot, B.S. Thesis (Massachusetts Institute of Technology, Cambridge, May 1991).Google Scholar
14.Papantoniou, K. V., “Electromechanical Design for an Electrically Powered, Actively Balanced One Leg Planar Robot,” Proceedings of IROS, Workshop on Intelligence for Mechanical Systems, Osaka, Japan (Nov. 1991) pp. 1553–1560.Google Scholar
15.Prosser, J. and Kam, M., “Vertical Control for a Mechanical Model the One-Legged Hopping Machine,” Proceedings of First IEEE Conference on Control Applications, Dayton, USA (Sep. 1992) pp. 136–141.Google Scholar
16.Prosser, J. and Kam, M., “Control of Hopping Height for a One-Legged Hopping Machine,” Proceedings of Mobile Robots VII, SPIE, Boston, USA (Nov. 1992) pp. 604–612.CrossRefGoogle Scholar
17.Lebaudy, A., Prosser, J. and Kam, M., “Control Algorithms for a Vertically-Constrained One-Legged Hopping Machine,” Proceedings of IEEE Conference on Decision and Control, San Antonio, USA (Dec. 1993) pp. 2688–2693.Google Scholar
18.Ambulatory, R obotics Lab, “Centre for intelligent machines,” http://www.cim.mcgill.casimarlweb/robots.html, (Last cited on Feb. 2007).Google Scholar
19.Rad, H., Gregorio, P. and Buehler, M., “Design, Modeling and Control of a Hopping Robot,” Proceedings of IROS, Yokohama, Japan (Jul. 1993) pp. 1778–1785.Google Scholar
20.Gregorio, P., Design, C ontrol and Energy Minimization Strategies for an Electrically Actuated Legged Robot, Master Thesis (McGill University, Aug. 1994).Google Scholar
21.Gregorio, P., Ahmadi, M. and Buehler, M., “Experiments With an Electrically Actuated Planar Hopping Robot,” Lecture Notes in Control and Information Sciences 200, Experimental Robotics III (Yoshikawa, T. and Miyazaki, F., eds.) (Springer-Verlag, New York, 1994) pp. 269–281.Google Scholar
22.Ahmadi, M. and Buehler, M., “Preliminary Experiments With an Actively Tuned Passive Dynamic Running Robot,” International Symposium on Experimental Robots V (Casals, A. and Almeida, A.T. de, eds.) (Springer-Verlag, New York, 1997) pp. 249–260.Google Scholar
23.Gregorio, P., Ahmadi, M. and Buehler, M., “Design, control, and energetics of an electrically actuated legged robot,” IEEE Trans. Syst., Man, Cybern. 27 (4), 626–634 (Aug. 1997).CrossRefGoogle ScholarPubMed
24.Ahmadi, M. and Buehler, M., “The ARL Monopod II Running Robot: Control and Energetics,” Proceedings of IEEE International Conference on Robotics and Automation, Detroit, USA (May 1999) pp. 1689–1694.Google Scholar
25.Mehrandezh, M., Surgenor, B. W. and Dean, S. R. H., “Jumping Height Control of an Electrically Actuated, One-Legged Hopping Robot: Modelling and Simulation,” Proceedings of IEEE International Conference on Decision and Control, New Orleans, USA (Dec. 1995) pp. 1016–1020.Google Scholar
26.Okubo, O. H., Nakano, E. and Handa, M., “Design of a Jumping Machine Using Self-Energizing Spring,” Proceedings of IROS, Osaka, Japan (Nov. 1996) pp. 186–191.Google Scholar
27.Ringrose, R., Self-stabilizing running, Ph.D. Thesis (Massachusetts Institute of Technology, Cambridge, Feb. 1997).Google Scholar
28.Ringrose, R., “Self-Stabilizing Running,” Proceedings of IEEE International Conference on Robotics and Automation, Albuquerque, USA (Apr. 1997) pp. 487–493.Google Scholar
29.Zhang, W., Wang, G., Chambers, T. and Simon, W. E., “Toward a Folding-Legged Uniped That Can Learn to Jump,” Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, Florida, USA (Oct. 1997) pp. 4315–4319.Google Scholar
30.De Man, H., Lefeber, D. and Vermeulen, J., “Control on Irregular Terrain of a Hopping Robot With One Articulated Leg,” Proceedings of International Conference on Advanced Robotics: Workshop II: New Approaches on Dynamic Walking and Climbing Machines, Monterey, USA (1997) pp. 72–76.Google Scholar
31.Zdravko, T., Lefeber, D., Vermeulen, J. and Man, H. De, “Setting Objective Parameters of a Hopping Robot Based on Power Consumption,” Proceedings of International Conference on Climbing and Walking Robots, Brussels, Belgium (Nov. 1998) pp. 297–302.Google Scholar
32.De Man, H., Lefeber, D. and Vermeulen, J., “Design and Control of a Robot with One Articulated Leg for Locomotion on Irregular Terrain,” (Morecki, A., Bianchi, G. and Wojtyra, M., eds.) Proceedings 12th Symposium on Theory and Practice of Robots and Manipulators (Springer Wien New York, 1998) pp. 417–424.Google Scholar
33.Vermeulen, J., Lefeber, D. and De Man, H., “A Control Strategy for a Robot With One Articulated Leg Hopping on Irregular Terrain,” Proceedings of International Conference on Climbing and Walking Robots, Madrid, USA (Oct. 2000) pp. 399–406.Google Scholar
34.Brown, B. and Zeglin, G., “The Bow Leg Hopping Robot,” Proceedings of IEEE International Conference on Robotics and Automation, Leuven, Belgium (May 1998) pp. 781–786.Google Scholar
35.Zeglin, G. and Brown, B., “Control of a Bow Leg Hopping Robot,” Proceedings of IEEE International Conference on Robotics and Automation, Leuven, Belgium (May 1998) pp. 793–798.Google Scholar
36.Zeglin, G., The bow leg hopping robot, Ph.D. Thesis (Pittsburgh: Carnegie Mellon University, Oct. 1999).Google Scholar
37.Zeglin, G. and , H. B. Jr. Brown, “First Hops of the 3D Bow Leg,” Proceedings of International Conference on Climbing and Walking Robots, Paris, France (Sep. 2002) pp. 357–364.Google Scholar
38.The robotics Institute, “Bow leg hopping robot,” http://www.cs.cmu.edu/garthz/research/bowleg/, (Last cited on Feb. 2007).Google Scholar
39.Berkemeier, M. D. and Desai, K. V., “A comparison of three approaches for the control of hopping height in legged robots,” (submitted to Int. J. Robot. Res., 1998).Google Scholar
40.Berkemeier, M. D. and Desai, K. V., “Control of Hopping Height in Legged Robots Using a Neural-Mechanical Approach,” Proceedings of International Conference on Robotics and Automation, Michigan, USA (May 1999) pp. 1695–1701.Google Scholar
41.Wei, T. E., Nelson, G. M., Quinn, R. D., Verma, H. and Garverick, S. L., “Design of a 5-cm Monopod Hopping Robot,” Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, USA (Apr. 2000) pp. 2828–2833.Google Scholar
42.Sandia, Lab News, “Lab News Release–Hop to it: Sandia hoppers leapfrog conventional wisdom about robot mobility,” 52 (21), (Oct. 2000), http://www.sandia.gov/LabNews/LN10-20-00/hop/story.html, (Last cited on Feb. 2007).Google Scholar
43.Peck, M. A., “Dynamics of a gyroscopic hopping rover,” Advances in the Astronautical Sciences. 108 (2), 1369–1390 (February, 2001).Google Scholar
44.Albro, J. V. and Bobrow, J. E., “Optimal Motion Primitives for a 5 DOF Experimental Hopper,” Proceedings of IEEE International Conference on Robotics and Automation, Seoul, Korea (May 2001) pp. 3630–3635.Google Scholar
45.Cham, J. G., Stafford, B. and Cutkosky, M. R., “See Labs Run: A Design-Oriented Laboratory for Teaching Dynamic Systems,” Proceedings of 2001 ASME International Mechanical Engineering Congress and Exposition, New York, USA (Nov. 2001) pp. 1–8.Google Scholar
46.Cham, J. G. and Cutkosky, M. R., “Dynamic stability of open-loop hopping,” (submitted to ASME J. Dynam. Syst., Meas. Control, 2004.Google Scholar
47.Hyon, S. H. and Mita, T., “Development of a Biologically Inspired Hopping Robot–“Kenken”, Proceedings of IEEE International Conference on Robotics and Automation, Washington, USA (May 2002) pp. 3984–3991.Google Scholar
48.Hyon, S. H., Emura, T. and Mita, T., “Dynamics-based control of a one-legged hopping robot,” Proc. IME, J. Syst. Control Eng. 217 (2) Part I, 83–98 (Apr. 2003).Google Scholar
49.Takeuchi, K., Kuswadi, S., Nakaura, S. and Sampei, N., “Continuous Hopping Motion Control Experiment of One Linear Actuator Robot,” Proceedings of 41st SICE Annual Conference, Osaka, Japan (Aug. 2002) pp. 232–237.Google Scholar
50.Kuswadi, S., Takahashi, A., Ohnishi, A., Sampei, N. and Nakaura, S., “Feedback Error Learning Control Using Adaptive Fuzzy Network to Control One Linear Actuator Hopping Robot,” Proceedings of Asia-Pacific Conference on Circuits and Systems, Singapore (Oct. 2002), pp. 37–41.Google Scholar
51.Kuswadi, S., Sampei, M. and Nakaura, S., “One Linear Actuator Hopping Robot Control: Model Reference Adaptive Fuzzy Control Approach,” Proceedings of IECI Japan Workshop, Chofu Bunka Kaikan Tazukuri, Japan (Apr. 2003), pp. 1–7.Google Scholar
52.Kuswadi, S., Sampei, M. and Nakaura, S., “Model Reference Adaptive Fuzzy Control for One Linear Actuator Hopping Robot,” Proceedings of 12th IEEE International Conference on Fuzzy Systems, St. Louis, USA (May 2003) pp. 254–259.Google Scholar
53.Funato, T., Kuswadi, S., Sampei, M. and Nakaura, S., “Continuous Hopping Motion Experiment of One Linear Actuator Robot With Adaptive Fuzzy Control,” Proceedings of SICE Annual Conference, Fukui, Japan (Aug. 2003) pp. 2506–2511.Google Scholar
54.Kuswadi, S., Takahashi, A., Ohnishi, A., Sampei, M. and Nakaura, S., “A One Linear Actuator Hopping Robot: Modelling and Control,” Adv. Robot. 17 (8), 709–713 (Dec. 2003).CrossRefGoogle Scholar
55.Singapore robotic games, “A self-stabilizing hopping robot,” Open Category Competition in the Singapore Robotic Games, (May 2003), http://www.eng.nus.edu.sg/research/2003/2003C3/038.htm, (Last cited on Feb. 2007).Google Scholar
56.Uno, K., Ohmori, M. and Kondo, R. A., “A Hopping Robot With Impulsive Actuator,” Proceedings of 41st SICE Annual Conference, Osaka, Japan (Aug. 2002) pp. 2831–2832.Google Scholar
57.Akinfiev, T., Armada, M. and Montes, H., “Vertical Movements of Resonance Hopping Robot With Electric Drive and Simple Control System,” Proceedings of IEEE 11th Mediterranean Conference on Control and Automation, Rodas, Gracia (Jun. 2003).Google Scholar
58.Leavitt, J., Bobrow, J. E. and Sideris, A., “Robust Balance Control of a One-Legged, Pneumatically-Actuated, Acrobot-Like Hopping Robot,” Proceedings of IEEE International Conference on Robotics and Automation, New Orleans, USA (Apr./May 2004), pp. 4240–4245.CrossRefGoogle Scholar
59.Sato, A. and Buehler, M., “A Planar Hopping Robot With One Actuator: Design, Simulation, and Experimental Results,” Proceedings of IROS, Sendai, Japan (Sep./Oct. 2004) pp. 3540–3545.Google Scholar
60.Koditschek, D. E. and Buhler, M., Analysis of a simplified hopping robot, Technical Report (8804, Department of Electrical Engineering, Yale University, Princeton, NJ, 1988).Google Scholar
61.Koditschek, D. E. and Buehler, M., “Analysis of a simplified hopping robot,” Int. J. Robot. Res. 10 (6), 587–605 (1991).CrossRefGoogle Scholar
62.Vakakis, A. F. and Burdick, J. W., “Chaotic Motions in the Dynamics of a Hopping Robot,” Proceedings of IEEE International Conference on Robotics and Automation, Cincinnati, USA (May 1990) pp. 1464–1469.Google Scholar
63.Li, Z. and He, J., “An Energy Perturbation Approach to Limit Cycle Analysis in Legged Locomotion Systems,” Proceedings of 29th IEEE Conference on Decision and Control, Honolulu, USA (Dec. 1990) pp. 1989–1994.CrossRefGoogle Scholar
64.Vakakis, A. F., Burdick, J. W. and Caughey, T. K., “An “interesting” strange attractor in the dynamics of a hopping robot,” Int. J. Robot. Res. 10 (6), 587–605 (Dec. 1991).CrossRefGoogle Scholar
65.Ostrowski, J. P. and Burdick, J. W., “Designing Feedback Algorithms for Controlling the Periodic Motions of Legged Robots,” Proceedings of IEEE International Conference on Robotics and Automation, Georgia, USA (May 1993) pp. 260–266.Google Scholar
66.M'Closkey, R. T. and Burdick, J. W., “Periodic motions of a hopping robot with vertical and forward motion,” Int. J. Robot. Res. 12 (3), 197–218 (Jun. 1993).CrossRefGoogle Scholar
67.Helferty, J. J., Collins, J. B. and Kam, M., “A Neural Network Learning Strategy for the Control of a One-Legged Hopping Machine,” Proceedings of IEEE International Conference on Robotics and Automation, Scottsdale, USA (May 1989) pp.1604–1609.Google Scholar
68.Helferty, J. J. and Kam, M., “Adaptive Control of a Legged Robot Using an Artificial Neural Network,” Proceedings of IEEE International Conference on Systems Engineering, Dayton, USA (Aug. 1989) pp. 165–168.CrossRefGoogle Scholar
69.Michalska, H., Ahmadi, M. and Buehler, M., “Vertical Motion Control of a Hopping Robot,” Proceedings of IEEE International Conference on Robotics and Automation, Minneapolis, USA (Apr. 1996) pp. 2712–2717.Google Scholar
70.Yoshida, Y., Kamano, T., Yasuno, T., Suzuki, T., Harada, H. and Kataoka, Y., “Generation of suitable jumping motion pattern for hopping robot under genetic algorithm,” Trans. IEE Jpn. 120-c (10), 1365–1371 (Oct. 2000).Google Scholar
71.Komsuoglu, H. and Koditschek, D. E., “Preliminary Analysis of a Biologically Inspired 1-DOF Clock' Stabilized Hopper,” Proceedings of World Multi-Conference on Systemics, Cybernetics and Informatics, Orlando, USA (Jul. 2000) pp. 670–675.Google Scholar
72.Klavins, E. and Koditschek, D. E., “Stability of Coupled Hybrid Oscillators,” Proceedings of IEEE International Conference on Robotics and Automation, Seoul, Korea (May 2001) pp. 4200–4207.Google Scholar
73.Kusano, Y. and Tsutsumi, K., “Hopping Height Control of an Active Suspension Type Leg Module Based on Reinforcement Learning and a Neural Network,” Proceedings of IROS, Lausanne, Switzerland (Sep./Oct. 2002) pp. 2672–2677.Google Scholar
74.Harbick, K. and Sukhatme, G., Height control for a one-legged hopping robot using a one-dimensional mode, Technical Report (IRIS-01-405, Institute for Robotics and intelligent Systems, USC, 2001).Google Scholar
75.Harbick, K. and Sukhatme, G., Height control for a one-legged hopping robot using a two-dimensional mode, Technical Report (IRIS-01-406, Institute for Robotics and intelligent Systems, USC, 2001).Google Scholar
76.Harbick, K. and Sukhatme, G., “Controlling Hopping Height of a Pneumatic Monopod,” Proceedings of International Conference on Robotics and Automation, Washington, USA (May 2002) pp. 3998–4003.Google Scholar
77.Harbick, K. and Sukhatme, G., Speed control of a pneumatic monopod using a neural network, Technical Report (IRIS-02-413, Institute for Robotics and intelligent Systems, USC, 2002).Google Scholar
78.Harbick, K. and Sukhatme, G., “Robustness Experiments for a Planar Hopping Control System,” Proceedings of International Conference on Climbing and Walking Robots (Sep. 2002) pp. 349–356.Google Scholar
79.Francois, C. and Samson, C., “Running with constant energy,” International Conference on Robotics and Automation, San Diego, USA (May 1994) pp. 131–136.Google Scholar
80.Schwind, W. J. and Koditschek, D. E., “Control of Forward Velocity for a Simplified Planar Hopping Robot,” Proceedings of IEEE International Conference on Robotics and Automation, Aichi, Japan (May 1995) pp. 691–696.Google Scholar
81.Maier, K. D., “Neural Network Based Control of Legged Hopping Systems,” Proceedings of IEEE International Symposium on Intelligent Control, Mexico (Sep. 2001) pp.115–120.Google Scholar
82.Seyfarth, A., Geyer, H., Gunther, M. and Blickhan, R., “A movement criterion for running,” J. Biomech. 35 (5), 649–655 (May 2002).Google ScholarPubMed
83.Papadopoulos, E. and Cherouvim, N., “On Increasing Energy Autonomy for a One-Legged Hopping Robot,” Proceedings of IEEE International Conference on Robotics and Automation, New Orieans, USA (Apr./May 2004) pp. 4645–4650.CrossRefGoogle Scholar
84.Cherouvim, N. and Papadopoulos, E., “Energy saving passive-dynamic gait for a one-legged hopping robot,” Robotica. 24 (4), 491–498 (July 2006).Google Scholar
85.Shanmuganathan, P. V., Dynamics and stabilization of under-actuated monopedal hopping, Ph.D. Thesis (Bombay, India: Indian Institute of Technology, Jul. 2002).Google Scholar
86.Sznaier, M. and Domborg, M. J., “An adaptive controller for a one-legged mobile robot,” IEEE Trans. Robot. Autom. 5 (2), 253–259 (Apr. 1989).CrossRefGoogle Scholar
87.Lapshin, V. V., “Motion control of a legged machine in the supportless phase of hopping,” Int. J. Robot. Res. 10 (4), 327–337 (Aug. 1991).CrossRefGoogle Scholar
88.Lapshin, V. V., “Vertical and horizontal motion control of a one-legged hopping machine,” Int. J. Robot. Res. 11 (5), 491–498 (Oct. 1992).CrossRefGoogle Scholar
89.Cherouvim, N. and Papadopoulos, E., “Single actuator control analysis of a planar 3 DOF hopping robot,” In: Chapter in Robotics: Science and Systems I (Thrun et al., eds.) (MIT Press, Cambridge, Massachusetts, 2005).Google Scholar
90.Tedrake, R. and Seung, H. S., “Improved Dynamic Stability Using Reinforcement Learning,” Proceedings of 5th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, Paris, France (Sep. 2002) pp. 341–348.Google Scholar
91.Li, Z. and Montgomery, R., “Dynamics and Optimal Control of a Legged Robot in Flight Phase,” Proceedings of IEEE International Conference on Robotics and Automation, Cincinnati, USA (May 1990) pp. 1816–1821.Google Scholar
92.Rehman, F. U. and Michalska, H., “Geometric Approach to Feedback Stabilization of a Hopping Robot in the Flight Phase,” Proceedings of 8th International Conference on Advanced Robotics, Monterey, USA (Jul. 1997) pp. 551–556.Google Scholar
93.Rehman, F., “Discontinuous Feedback Stabilization of a Hopping Robot in Flight Phase,” Proceedings of IEEE International Multi-Topic Conference, Technology for the 21st Century, Lahore, Pakistan (Dec. 2001) pp. 190–194.Google Scholar
94.Rehman, F. U., “Steering Control of a Hopping Robot Model During the Flight Phase,” Proc. IEE Control Theory Appl. 152 (6), 645–653 (Nov. 2005).CrossRefGoogle Scholar
95.Chelouah, P., Di, Giamberardino, Monaco, S. and Normand–Cyrot, D., “Digital Control of Nonholonomic Systems Two Case Studies,” Proceedings of 32nd IEEE Conference on Decision and Control, San Antonio, USA (Dec. 1993) pp. 2664–2669.Google Scholar
96.Di Giamberardino, P., Monaco, S. and Normand-Cyrot, D., “Why Multirate Sampling is Instrumental for Control Design Purpose: The Example of the One-Leg Hopping Robot,” Proceedings of IEEE Conference on Decision and Control, Las Vegas, USA (Dec. 2002) pp. 3249–3254.Google Scholar
97.Kumar, A. and Singh, S. K., “Intelligent Control of Autonomous Systems Using a Constrained Optimal Control Approach,” Proceedings of 32nd IEEE Conference on Decision and Control, San Antonio, USA (Dec. 1993) pp. 1252–1257.Google Scholar
98.Liu, J. S., Wang, L. S. and Tsai, L. S., “A Nonlinear Programming Approach to Nonholonomic Motion Planning With Obstacle Avoidance,” Proceedings of IEEE International Conference on Robotics and Automation, San Diego, USA (May 1994) pp. 70–75.Google Scholar
99.Wang, Y., “Nonholonomic Motion Planning: a Polynomial Fitting Approach,” Proceedings of IEEE International Conference on Robotics and Automation, Minneapolis, USA (Apr. 1996) pp. 2956–2961.Google Scholar
100.Lee, T. C. and Liu, J. S., “A Rank Condition for rho-Exponential Stabilization of Dynamic Caplygin Systems,” Proceedings of IEEE Conference on Robotics, Automation and Mechatronics, Singapore (Dec. 2004) pp. 1020–1025.Google Scholar
101.Mombaur, K. D., Bock, H. G., Schloder, J. P., Winckler, M. J. and Longman, R. W., “Open-Loop Stable Control of Running Robots a Numerical Method for Studying Stability in the Context of Optimal Control Problems,” Proceedings of International Conference on Climbing and Walking Robots, Brussels, Belgium (Nov. 1998) pp. 89–94.Google Scholar
102.Mombaur, K. D., Longman, R. W., Bock, H. G. and Schloder, J. P., “Stable One-Legged Hopping Without Feedback and With a Point Foot,” Proceedings of IEEE International Conference on Robotics and Automation, Washington, USA (May 2002) pp. 3978–3983.Google Scholar
103.Mombaur, K. D., Longman, R. W., Bock, H. G. and Schloder, J. P., “Open loop stable running,” Robotica 23 (1), 21–33 (Jan. 2005).CrossRefGoogle Scholar
104.Larin, V. B., “Control of the Hopping Apparatus,” Proceedings of IEEE Intelligent Transportation Systems, Oakland, USA (Aug. 2001) pp. 385–390.Google Scholar
105.Larin, V. B., “Control By Non-Stationary Driving of the Hopping Apparatus,” Proceedings of the 4th World Congress on Intelligent Control and Automation, Shanghai, China (Jun. 2002) pp. 2822–2830.Google Scholar
106.Thompson, C. M. and Raibert, M. H., “Passive dynamic running,” In: International Symposium of Experimental Robotics I (Hayward, V. and Khatib, O., eds.) (Springer-Verlag, New York, Jun. 1989) pp. 74–83.Google Scholar
107.Ahmadi, M. and Buehler, M., “A Control Strategy for Stable Passive Running,” Proceedings of Intelligent Robots and Systems, Pittsburgh (Aug. 1995) pp. 152–157.Google Scholar
108.Ahmadi, M. and Buehler, M., “Stable control of a simulated one-legged running robot with hip and leg compliance,” IEEE Trans. Robot. Autom. 13 (1), 96–104 (Feb. 1997).CrossRefGoogle Scholar
109.Francois, C. and Samson, C., “New approach to the control of the planar one-legged hopper,” Int. J. Robot. Res. 17 (11), 1150–1166 (Nov. 1998).CrossRefGoogle Scholar
110.Schammass, A., Caurin, G. A. P. and Valente, C. M. O., “Control of a one-legged robot with energy savings,” J. Brazilian Soc. Mech. Sci. 3 (1), 41–48 (Jan. 2001).CrossRefGoogle Scholar
111.Hyon, S. H. and Emura, T., “Quasi-Periodic Gaits of Passive One-Legged Hopper,” Proceedings of Intelligent Robots and Systems, Lausanne, Switzerland (Sep./Oct. 2002) pp. 2625–2630.Google Scholar
112.Hyon, S. H. and Emura, T., “Energy-preserving control of a passive one-legged running robot,” Adv. Robot. 18 (4), 357–381 (May 2004).CrossRefGoogle Scholar
113.Hyon, S. H., Emura, T. and Ueta, T., “Delayed Feedback Control of One-Legged Passive Running Robot,” Proceedings of Annual SICE Conference, Teine-ku, Sapporo, Japan (Aug. 2004) pp. 949–954.Google Scholar
114.Hyon, S. H., Jiang, X., Emura, T. and Ueta, T., “Passive Running of Planar 1/2/4-Legged Robots,” Proceedings of Intelligent Robots and Systems, Sendai, Japan (Sep./Oct. 2004) pp. 3532–3539.Google Scholar
115.Berkemeier, M. D. and Fearing, R. S., “Sliding and hopping gaits for the underactuated acrobot,” IEEE Trans. Robot. Autom. 14 (4), 629–634 (Aug. 1998).Google Scholar
116.Geng, T., Yang, Y. and Xu, X., “A Novel One-Legged Robot: Cyclic Gait Inspired by a Jumping Frog,” Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, Tucson, USA (Oct. 2001) pp. 1412–1417.Google Scholar
117.Geng, T., Xu, X., Yang, Y., Li, X. and Zhang, X., “Designing Ballistic Flipping Gait for a One-Legged Robot,” Proceedings of Intelligent Robots and Systems, Maui, USA (Oct. Nov. 2001) pp. 716–721.Google Scholar
118.Geng, T., Xiong, G., Li, X., Yang, Y., Guo, Y. and Ma, Q., “Proposing a Novel One-Legged Robot: Control via Poincar'Map,” Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, USA (Dec. 2001) pp. 4184–4185.Google Scholar
119.Geng, T. and Xu, X., “Motion planning of a novel flip robot: The fastest locomotive trajectory,” Eur. J. Mech. Eng. 47 (2), 91–98 (2002).Google Scholar
120.Morita, Y. and Ohnishi, K., “Attitude Control of Hopping Robot Using Angular Momentum,” Proceedings of IEEE International Conference on Industrial Technology, Maribor, Slovenia (Dec. 2003) pp. 173–178.Google Scholar
121.Ohnishi, K. and Ohashi, E., “Motion Control in the Support Phase for a One-Legged Hopping Robot,” Proceedings of 8th IEEE International Workshop on Advanced Motion Control, Kawasaki, Japan (Mar. 2004) pp. 259–262.Google Scholar
122.Ohashi, E. and Ohnishi, K., “A hopping height control for hopping robot,” IEEJ Trans. Ind. Appl. 124-D (7), 660–665 (Jul. 2004).Google Scholar
123.Ohashi, E. and Ohnishi, K., “Variable Compliance Control Based on Soft-Landing Trajectory for Hopping Robot,” Proceedings of 30th Annual Conference of IEEE Industrial Electronics Society, Busan, South Korea (Nov. 2004) pp. 117–122.Google Scholar
124.Nji, K. and Mehrandezh, M., “Low Energy Body Design and Nonlinear Control of Balance in a One Legged Robot,” Proceedings of 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas (Dec. 2004) pp. 311–316.CrossRefGoogle Scholar
125.Dummer, R. and Berkemeier, M., “Low-Energy Control of a One-Legged Robot With 2 Degrees of Freedom,” Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, USA (Apr. 2000) pp. 2815–2821.Google Scholar
126.Schwind, W. J. and Koditschek, D. E., “Characterization of Monoped Equilibrium Gaits,” Proceedings of IEEE International Conference on Robotics and Automation, Albuquerque, USA (Apr. 1997) pp. 1986–1992.Google Scholar
127.Saranli, U., Schwind, W. J. and Koditschek, D. E., “Toward the Control of a Multi-Jointed, Monoped Runner,” Proceedings of IEEE International Conference on Robotics and Automation, Leuven, Belgium (May 1998) pp. 2676–2682.Google Scholar
128.Sung, S. H. and Youm, Y., “Take-Off Motion of Legged Robot Hopping,” Proceedings of International Conference on Mechatronics and Information Technology, Jecheon, Korea (Dec. 2003) pp. 730–735.Google Scholar
129.Wadden, T. and Ekeberg, O. E., “A neuro-mechanical model of legged locomotion: Single leg control,” Biol. Cybern. 79 (2), 161–173 (Aug. 1998).Google ScholarPubMed
130.Rummel, J., Seyfarth, A. and Iida, F., “Stable Locomotion of Feedforward Controlled One-Legged Robot,” Proceedings of XXth Congress of the International Society of Biomechanics, Cleveland, USA (Aug. 2005).Google Scholar
131.Altendorfer, R., Koditschek, D. E. and Holmes, P., “Stability analysis of a clock-driven rigid-body SLIP model for Rhex,” Int. J. Robot. Res. 23 (10–11)1001–1012, (Oct. Nov. 2004).CrossRefGoogle Scholar