Single-legged hopping robotics research—A review

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.

[1]  Örjan Ekeberg,et al.  A neuro-mechanical model of legged locomotion: single leg control , 1998, Biological Cybernetics.

[2]  K. D. Maier.  Neural network based control of legged hopping systems , 2001, Proceeding of the 2001 IEEE International Symposium on Intelligent Control (ISIC '01) (Cat. No.01CH37206).

[3]  S. Hyon,et al.  Delayed feedback control of one-legged passive running robot , 2004, SICE 2004 Annual Conference.

[4]  Martin Buehler,et al.  A planar hopping robot with one actuator: design, simulation, and experimental results , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[5]  D. Normand-Cyrot,et al.  Why multirate sampling is instrumental for control design purpose: the example of the one-leg hopping robot , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[6]  Richard W. Longman,et al.  Stable one-legged hopping without feedback and with a point foot , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[7]  Zexiang Li,et al.  Dynamics and optimal control of a legged robot in flight phase , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[8]  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).

[9]  Suzuki Takayuki,et al.  Generation of Suitable Jumping Motion Pattern for Hopping Robot under Genetic Algorithm , 2000 .

[10]  K. Ohnishi,et al.  Variable compliance control based on soft-landing trajectory for hopping robot , 2004, 30th Annual Conference of IEEE Industrial Electronics Society, 2004. IECON 2004.

[11]  Martin Buehler,et al.  Experiments with an Electrically Actuated Planar Hopping Robot , 1993, ISER.

[12]  Takashi Emura,et al.  Quasi-periodic gaits of passive one-legged hopper , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[13]  Matthew D. Berkemeier,et al.  Control of hopping height in legged robots using a neural-mechanical approach , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[14]  Xiaoming Xu,et al.  Motion planning of a novel flip robot: The fastest locomotive trajectory , 2002 .

[15]  Joel W. Burdick,et al.  Designing feedback algorithms for controlling the periodic motions of legged robots , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[16]  Garth Zeglin,et al.  The bow leg hopping robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[17]  Son Kuswadi,et al.  Continuous hopping motion control experiment of one linear actuator robot , 2002, Proceedings of the 41st SICE Annual Conference. SICE 2002..

[18]  A. Schammass,et al.  Control of a one-legged robot with energy savings , 2001 .

[19]  Joel W. Burdick,et al.  Periodic Motions of a Hopping Robot With Vertical and Forward Motion , 1993, Int. J. Robotics Res..

[20]  Kale Harbick,et al.  Robustness Experiments for a Planar Hopping Control System , 2002 .

[21]  Martin Buehler,et al.  Design, modeling and control of a hopping robot , 1993, Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93).

[22]  Christophe Samson,et al.  Running with constant energy , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[23]  Freyr Hardarson.  Locomotion for difficult terrain , 1997 .

[24]  V. Lapshin.  Vertical and Horizontal Motion Control of a One-Legged Hopping Machine , 1992 .

[25]  Xin Jiang,et al.  Passive running of planar 1/2/4-legged robots , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[26]  Mark J. Damborg,et al.  An adaptive controller for a one-legged mobile robot , 1989, IEEE Trans. Robotics Autom..

[27]  Mitsuji Sampei,et al.  Continuous hopping motion experiment of one linear actuator robot with adaptive fuzzy control , 2003, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[28]  J. Barbenel.  The biomechanics of the temporomandibular joint: a theoretical study. , 1972, Journal of biomechanics.

[29]  James E. Bobrow,et al.  Robust balance control of a one-legged, pneumatically-actuated, Acrobot-like hopping robot , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[30]  Wen-Ran Zhang,et al.  Toward a folding-legged uniped that can learn to jump , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[31]  Daniel E. Koditschek,et al.  Preliminary Analysis of a Biologically Inspired 1-DOF "Clock" Stabilized Hopper , 2001 .

[32]  Moshe Kam,et al.  A neural network learning strategy for the control of a one-legged hopping machine , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[33]  B. W. Surgenor,et al.  Jumping height control of an electrically actuated, one-legged hopping robot: modelling and simulation , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[34]  Yu Guo,et al.  Proposing a novel one-legged robot: control via Poincare map , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[35]  Reinhard Blickhan,et al.  A movement criterion for running. , 2002, Journal of biomechanics.

[36]  Evangelos Papadopoulos,et al.  Energy saving passive-dynamic gait for a one-legged hopping robot , 2006, Robotica.

[37]  Kouhei Ohnishi,et al.  A Hopping Height Control for Hopping Robot , 2004 .

[38]  H. Benjamin Brown,et al.  Experiments in Balance with a 3D One-Legged Hopping Machine , 1984 .

[39]  Mark R. Cutkosky,et al.  Dynamic Stability of Open-Loop Hopping , 2007 .

[40]  Daniel E. Koditschek,et al.  Analysis of a Simplified Hopping Robot , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[41]  F. ur-Rehman.  Steering control of a hopping robot model during the flight phase , 2005 .

[42]  Martin Buehler,et al.  Stable control of a simulated one-legged running robot with hip and leg compliance , 1997, IEEE Trans. Robotics Autom..

[43]  Martin Buehler,et al.  Vertical motion control of a hopping robot , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[44]  Daniel E. Koditschek,et al.  Stability of coupled hybrid oscillators , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[45]  Clay M. Thompson,et al.  Passive Dynamic Running , 1989, ISER.

[46]  V. B. Larin.  Control of the hopping apparatus , 2001, ITSC 2001. 2001 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.01TH8585).

[47]  Sang-Ho Hyon,et al.  Dynamics-based control of a one-legged hopping robot , 2003 .

[48]  Marc H. Raibert,et al.  Running With Symmetry , 1986 .

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

[50]  Martin Buehler,et al.  Design, control, and energetics of an electrically actuated legged robot , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[51]  S. K. Singh,et al.  Intelligent control of autonomous systems using a constrained optimal control approach , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

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

[53]  Evangelos Papadopoulos,et al.  On increasing energy autonomy for a one-legged hopping robot , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[54]  K. Ohnishi,et al.  Motion control in the support phase for a one-legged hopping robot , 2004, The 8th IEEE International Workshop on Advanced Motion Control, 2004. AMC '04..

[55]  Jing-Sin Liu,et al.  A rank condition for /spl rho/-exponential stabilization of dynamic Caplygin systems , 2004, IEEE Conference on Robotics, Automation and Mechatronics, 2004..

[56]  Mark R. Cutkosky,et al.  SEE LABS RUN: A DESIGN-ORIENTED LABORATORY FOR TEACHING DYNAMIC SYSTEMS , 2001 .

[57]  Moshe Kam,et al.  Control of hopping height for a one-legged hopping machine , 1993, Other Conferences.

[58]  Alexander F. Vakakis,et al.  Chaotic motions in the dynamics of a hopping robot , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[59]  Daniel E. Koditschek,et al.  Characterization of monoped equilibrium gaits , 1997, Proceedings of International Conference on Robotics and Automation.

[60]  Marc H. Raibert,et al.  Experiments in Balance With a 2D One-Legged Hopping Machine , 1984 .

[61]  정완균,et al.  Take-off Motion of Legged Robot Hopping , 2003 .

[62]  K. Uno,et al.  A hopping robot with impulsive actuator , 2002, Proceedings of the 41st SICE Annual Conference. SICE 2002..

[63]  Takashi Emura,et al.  Energy-preserving control of a passive one-legged running robot , 2004, Adv. Robotics.

[64]  Tao Geng,et al.  A novel one-legged robot: cyclic gait inspired by a jumping frog , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

[65]  M. Kam,et al.  Adaptive control of a legged robot using an artificial neural network , 1989, IEEE 1989 International Conference on Systems Engineering.

[66]  Evangelos Papadopoulos,et al.  Single Actuator Control Analysis of a Planar 3DOF Hopping Robot , 2005, Robotics: Science and Systems.

[67]  Moshe Kam,et al.  Control algorithms for a vertically-constrained one-legged hopping machine , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[68]  Marc H. Raibert,et al.  Legged Robots That Balance , 1986, IEEE Expert.

[69]  Martin Buehler,et al.  A control strategy for stable passive running , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[70]  Mitsuji Sampei,et al.  Feedback error learning control using adaptive fuzzy network to control one linear actuator hopping robot , 2002, Asia-Pacific Conference on Circuits and Systems.

[71]  Yongji Wang,et al.  Nonholonomic motion planning: a polynomial fitting approach , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[72]  M. Kam,et al.  Vertical control for a mechanical model of the one-legged hopping machine , 1992, [Proceedings 1992] The First IEEE Conference on Control Applications.

[73]  Teodor Akinfiev,et al.  Vertical Movement of Resonance Hopping Robot with Electric Drive and Simple Control System , 2003 .

[74]  Marc H. Raibert,et al.  Running on four legs as though they were one , 1986, IEEE J. Robotics Autom..

[75]  Gaurav S. Sukhatme,et al.  Speed Control of a Pneumatic Monopod using a Neural Network , 2002 .

[76]  Faizan Ur Rehman.  Discontinuous feedback stabilization of a hopping robot in flight phase , 2001, Proceedings. IEEE International Multi Topic Conference, 2001. IEEE INMIC 2001. Technology for the 21st Century..

[77]  Alexander F. Vakakis,et al.  An "Interesting" Strange Attractor in the Dynamics of a Hopping Robot , 1991, Int. J. Robotics Res..

[78]  Daniel E. Koditschek,et al.  Analysis of a Simplified Hopping Robot , 1991, Int. J. Robotics Res..

[79]  Daniel E. Koditschek,et al.  Control of forward velocity for a simplified planar hopping robot , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[80]  Philip Holmes,et al.  Stability Analysis of a Clock-Driven Rigid-Body SLIP Model for RHex , 2004, Int. J. Robotics Res..

[81]  D. Lefeber,et al.  A Control Strategy for a Robot with One Articulated Leg Hopping on Irregular Terrain , 2003 .

[82]  M. Mehrandezh,et al.  Low energy body design and nonlinear control of balance in a one legged robot , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[83]  Martin Buehler,et al.  The ARL monopod II running robot: control and energetics , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[84]  Marc H. Raibert,et al.  Hopping in legged systems — Modeling and simulation for the two-dimensional one-legged case , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[85]  Martin Buehler,et al.  Preliminary Experiments with an Actively Tuned Passive Dynamic Running Robot , 1997, ISER.

[86]  Mitsuji Sampei,et al.  A one linear actuator hopping robot: modeling and control , 2003, Adv. Robotics.

[87]  Hiroki Okubo,et al.  Design of a jumping machine using self-energizing spring , 1996, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS '96.

[88]  Garth Zeglin,et al.  Uniroo--a one legged dynamic hopping robot , 1991 .

[89]  Matthew D. Berkemeier,et al.  Low-energy control of a one-legged robot with 2 degrees of freedom , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[90]  Garth Zeglin,et al.  Control of a bow leg hopping robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[91]  Daniel E. Koditschek,et al.  Toward the control of a multi-jointed, monoped runner , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[92]  V. V. Lapshin,et al.  Motion Control of a Legged Machine in the Supportless Phase of Hopping , 1991, Int. J. Robotics Res..

[93]  Xiaowen Zhang,et al.  Designing ballistic flipping gait for a one-legged robot , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[94]  Jing-Sin Liu,et al.  A nonlinear programming approach to nonholonomic motion planning with obstacle avoidance , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[95]  A. Chelouah,et al.  Digital control of nonholonomic systems two case studies , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[96]  Hannah Michalska,et al.  Geometric approach to feedback stabilization of a hopping robot in the flight phase , 1997, 1997 8th International Conference on Advanced Robotics. Proceedings. ICAR'97.

[97]  Ronald S. Fearing,et al.  Sliding and hopping gaits for the underactuated Acrobot , 1998, IEEE Trans. Robotics Autom..

[98]  Kouhei Ohnishi,et al.  Attitude control of hopping robot using angular momentum , 2003, IEEE International Conference on Industrial Technology, 2003.

[99]  Mitsuji Sampei,et al.  Model reference adaptive fuzzy control for one linear actuator hopping robot , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[100]  Tsutomu Mita,et al.  Development of a biologically inspired hopping robot-"Kenken" , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[101]  Claude Samson,et al.  A New Approach to the Control of the Planar One-Legged Hopper , 1998, Int. J. Robotics Res..

[102]  Gaurav S. Sukhatme,et al.  Controlling hopping height of a pneumatic monopod , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[103]  Gaurav S. Sukhatme,et al.  Height Control for a One-Legged Hopping Robot using a One-Dimensional Model , 2001 .

[104]  Zexiang Li,et al.  An energy perturbation approach to limit cycle analysis in legged locomotion systems , 1990, 29th IEEE Conference on Decision and Control.

[105]  K. V. Papantoniou.  Electromechanical design for an electrically powered, actively balanced one leg planar robot , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[106]  Vladimir B. Larin.  Control by non-stationary driving of the hopping apparatus , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

[107]  Y. Kusano,et al.  Hopping height control of an active suspension type leg module based on reinforcement learning and a neural network , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[108]  James E. Bobrow,et al.  Optimal motion primitives for a 5 DOF experimental hopper , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[109]  Marc Raibert,et al.  Control of hoof rolling in an articulated leg , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.