Further progress in robot juggling: solvable mirror laws
Abstract
In previous papers we have reported successful laboratory implementations of a family of juggling algorithms. In all but the one degree of freedom case, these empirically successful algorithms have so far resisted our analytical efforts to explain why they work. This is in large measure a consequence of our inability to write down using elementary functions an expression for the closed loop dynamics they induce. We discuss in this paper a modified juggling algorithm whose resulting closed loop dynamics can be written down directly. We offer data establishing the empirical success of the new algorithm. Theoretical analysis of the closed loop dynamics is presently in progress.>
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Guckenheimer, J., & Holmes, P. (1983) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-1140-2 · Cited by 16,144 · see citing works
Raibert, M. H., & Tello, E. R. (1986) · IEEE Expert · doi:10.1109/mex.1986.4307016 · Cited by 2,752 · see citing works
Nonlinear problems in random theory
(1959) · Journal of the Franklin Institute · doi:10.1016/0016-0032(59)90191-7 · Cited by 994 · see citing works
Stable Orbits and Bifurcation of Maps of the Interval
Singer, D. A. (1978) · SIAM Journal on Applied Mathematics · doi:10.1137/0135020 · Cited by 483 · see citing works
Sensitive dependence to initial conditions for one dimensional maps
Guckenheimer, J. M. (1979) · Communications in Mathematical Physics · doi:10.1007/bf01982351 · Cited by 433 · see citing works
AN INTRODUCTION TO CHAOTIC DYNAMICAL SYSTEMS
Manning, A. (1988) · Bulletin of the London Mathematical Society · doi:10.1112/blms/20.4.376 · Cited by 349 · see citing works
Analysis of a Simplified Hopping Robot
Koditschek, D. E., & Bühler, M. (1991) · The International Journal of Robotics Research · doi:10.1177/027836499101000601 · Cited by 272 · see citing works
Self-citationFurther progress in robot juggling: the spatial two-juggle
Rizzi, A. A., & Koditschek, D. E. (2002) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/robot.1993.292261 · Cited by 86 · see citing works
Self-citationProgress in spatial robot juggling
Rizzi, A. A., & Koditschek, D. E. (2003) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/robot.1992.220275 · Cited by 80 · see citing works
Self-citationFrom stable to chaotic juggling: theory, simulation, and experiments
Bühler, M., & Koditschek, D. E. (2002) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/robot.1990.126296 · Cited by 68 · see citing works
Self-citationRobotic tasks with intermittent dynamics
Koditschek, D. E., & Buehler, M. (1990) · Cited by 20 · see citing works
Self-citationPreliminary experiments in spatial robot juggling
Rizzi, A. A., & Koditschek, D. E. (2006) · Springer eBooks · doi:10.1007/bfb0036146 · Cited by 16 · see citing works
Self-citation
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Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors
Ijspeert, A. J., Nakanishi, J., Hoffmann, H., Pástor, P., & Schaal, S. (2012) · Neural Computation · doi:10.1162/neco_a_00393 · Cited by 1,586 · see citing works
The Dynamics of Legged Locomotion: Models, Analyses, and Challenges
Holmes, P. J., Full, R. J., Koditschek, D., & Guckenheimer, J. M. (2006) · SIAM Review · doi:10.1137/s0036144504445133 · Cited by 708 · see citing works
Self-citationDynamic Movement Primitives -A Framework for Motor Control in Humans and Humanoid Robotics
Schaal, S. (2006) · Springer eBooks · doi:10.1007/4-431-31381-8_23 · Cited by 620 · see citing works
Sequential Composition of Dynamically Dexterous Robot Behaviors
Burridge, R. R., Rizzi, A. A., & Koditschek, D. E. (1999) · The International Journal of Robotics Research · doi:10.1177/02783649922066385 · Cited by 446 · see citing works
Self-citationSchaal, S., Peters, J., Nakanishi, J., & Ijspeert, A. J. (2005) · Springer tracts in advanced robotics · doi:10.1007/11008941_60 · Cited by 349 · see citing works
Dynamics systems vs. optimal control — a unifying view
Schaal, S., Mohajerian, P., & Ijspeert, A. (2007) · Progress in Brain Research · doi:10.1016/s0079-6123(06)65027-9 · Cited by 260 · see citing works
Kim, S., Shukla, A., & Billard, A. (2014) · IEEE Transactions on Robotics · doi:10.1109/tro.2014.2316022 · Cited by 220 · see citing works
Learning rhythmic movements by demonstration using nonlinear oscillators
Ijspeort, A. J., Nakanishi, J., & Schaal, S. (2003) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/irds.2002.1041514 · Cited by 183 · see citing works
Robot arm control exploiting natural dynamics
Williamson, M. M., & Brooks, R. A. (1999) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 127 · see citing works
Experiments in hand-eye coordination using active vision
Hong, W., & Slotine, J.-J. E. (1997) · Lecture Notes in Control and Information Sciences · doi:10.1007/bfb0035204 · Cited by 87 · see citing works
From dynamic movement primitives to associative skill memories
Pástor, P., Kalakrishnan, M., Meier, F., Stulp, F., Buchli, J., Theodorou, E. A., & Schaal, S. (2012) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2012.09.017 · Cited by 70 · see citing works
Comparative Design, Scaling, and Control of Appendages for Inertial Reorientation
Libby, T., Johnson, A. M., Chang-Siu, E., Full, R. J., & Koditschek, D. E. (2016) · IEEE Transactions on Robotics · doi:10.1109/tro.2016.2597316 · Cited by 57 · see citing works
Self-citationEstimating the non-linear dynamics of free-flying objects
Kim, S., & Billard, A. (2012) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2012.05.022 · Cited by 55 · see citing works
Phase Regulation of Decentralized Cyclic Robotic Systems
Klavins, E., & Koditschek, D. E. (2002) · The International Journal of Robotics Research · doi:10.1177/027836402320556430 · Cited by 55 · see citing works
Self-citationCPG modulation for navigation and omnidirectional quadruped locomotion
Santos, C. P., & Matos, V. (2012) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2012.01.004 · Cited by 49 · see citing works
Modeling and control of robotic yo-yo with visual feedback
Hashimoto, K., & Noritsugu, T. (2002) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/robot.1996.506562 · Cited by 43 · see citing works
On the Control of a One Degree-of-Freedom Juggling Robot
Zavala‐Río, A., & Brogliato, B. (1999) · Dynamics and Control · doi:10.1023/a:1008346825330 · Cited by 40 · see citing works
Learning motion dynamics to catch a moving object
Kim, S., Gribovskaya, E., & Billard, A. (2010) · 2010 10th IEEE-RAS International Conference on Humanoid Robots · doi:10.1109/ichr.2010.5686332 · Cited by 39 · see citing works
Design and Analysis of a Blind Juggling Robot
Reist, P., & Raffaello D’andrea, B. (2012) · IEEE Transactions on Robotics · doi:10.1109/tro.2012.2205493 · Cited by 38 · see citing works
Designing rhythmic motions using neural oscillators
Williamson, M. M. (2003) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.1999.813052 · Cited by 33 · see citing works
Toward a dynamical pick and place
Burridge, R. R., Rizzi, A. A., & Koditschek, D. E. (2002) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.1995.526175 · Cited by 33 · see citing works
Self-citationModeling and control of robotic yoyo with visual feedback
Hashimoto, K., & Noritsugu, T. (1996) · Institutional Repositories DataBase (IRDB) · Cited by 31 · see citing works
First-exit model predictive control of fast discontinuous dynamics: Application to ball bouncing
Kulchenko, P., & Todorov, E. V. (2011) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2011.5980196 · Cited by 28 · see citing works
Interactive synthesis of human-object interaction
Jain, S., & Liu, C. K. (2009) · ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA) · doi:10.1145/1599470.1599476 · Cited by 28 · see citing works
Omnidirectional locomotion in a quadruped robot: A CPG-based approach
Matos, V., & Santos, C. P. (2010) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2010.5652667 · Cited by 28 · see citing works
Yoyo Dynamics: Sequence of Collisions Captured by a Restitution Effect
Jin, H., & Zackenhouse, M. (2002) · Journal of Dynamic Systems Measurement and Control · doi:10.1115/1.1485750 · Cited by 28 · see citing works
Realization of flower stick rotation using robotic arm
Aoyama, T., Takaki, T., Miura, T., Gu, Q., & Ishii, I. (2015) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2015.7354179 · Cited by 14 · see citing works
Toward A Systems Theory for the Composition of Dynamically Dexterous Robot Behaviors
Burridge, R. R., Rizzik, A. A., & Koditschek, D. E. (1996) · Springer eBooks · doi:10.1007/978-1-4471-1021-7_17 · Cited by 14 · see citing works
Self-citationRobot Basketball: Ball Dribbling — A Modified Juggling Task
Bätz, G., Sobotka, M., Wollherr, D., & BUSS, M. J. (2009) · Springer eBooks · doi:10.1007/978-3-642-01213-6_29 · Cited by 13 · see citing works
Formal composition of hybrid systems
Culbertson, J. L., Gustafson, P., Koditschek, D. E., & Stiller, P. F. (2020) · Theory and applications of categories · doi:10.70930/tac/8ej2pxy9 · Cited by 11 · see citing works
Self-citationReal-Time Motion Planning for a Volleyball Robot Task Based on a Multi-Agent Technique
Zhang, P.-Y., & Lü, T. (2007) · Journal of Intelligent & Robotic Systems · doi:10.1007/s10846-007-9140-2 · Cited by 11 · see citing works
Return Maps, Parameterization, and Cycle-Wise Planning of Yo-Yo Playing
Jin, H., Ye, Q., & Zacksenhouse, M. (2009) · IEEE Transactions on Robotics · doi:10.1109/tro.2008.2011414 · Cited by 7 · see citing works
Cyclic motion design and analysis for a passive object manipulation using an active plate
Aoyama, T., Harada, Y., Gu, Q., Takaki, T., & Ishii, I. (2015) · Advanced Robotics · doi:10.1080/01691864.2015.1024737 · Cited by 6 · see citing works
Sufficiently Accurate Model Learning
Zhang, C., Khan, A., Paternain, S., & Ribeiro, A. (2020) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra40945.2020.9197502 · Cited by 5 · see citing works
Observer-Based Visual Servoing
Hashimoto, K. (1999) · Elsevier eBooks · doi:10.1016/b978-012281845-5/50003-1 · Cited by 4 · see citing works
Dynamic systems: brain, body, and imitation
Schaal, S. (2006) · Cambridge University Press eBooks · doi:10.1017/cbo9780511541599.007 · Cited by 3 · see citing works
Control of robotic yoyo with energy compensation based on an integrated model of a robot and a yoyo
Nemoto, T., Noguchi, Y., Miyakawa, H., & Iwase, M. (2015) · Journal of Advanced Simulation in Science and Engineering · doi:10.15748/jasse.2.329 · Cited by 3 · see citing works
Geometric Trap Design for Automatic Part Feeders
Berretty, R.-P., Goldberg, K., Overmars, M. H., & van der Stappen, A. F. (2000) · Springer eBooks · doi:10.1007/978-1-4471-0765-1_17 · Cited by 3 · see citing works
Reciprocal excitation between biological and robotic research
Schaal, S., Sternad, D., Dean, W. J., Kotosaka, S., Osu, R., & Kawato, M. (2000) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.403706 · Cited by 3 · see citing works
VolleyBot: A competative framework for AI and UAV research and development
Shoval, S. (2016) · IEEE Convention of Electrical and Electronics Engineers in Israel · doi:10.1109/icsee.2016.7806185 · Cited by 2 · see citing works
Flower Stick Manipulation Based on the High-speed Visual Feedback Control of a Dual Robotic Arm
Aoyama, T., Matsuba, K., Takaki, T., Ishii, I., & Hasegawa, Y. (2018) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2018.11.543 · Cited by 2 · see citing works
Oscillator-based yoyo control: implementation and comparison with model-based control
Jin, H., & Zacksenhouse, M. (2005) · International Conference on Advanced Robotics (ICAR) · doi:10.1109/.2005.1507406 · Cited by 2 · see citing works
Control scheme of nongrasping manipulation based on virtual connecting constraint
Aoyama, T., Takaki, T., Gu, Q., & Ishii, I. (2016) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2016.7487571 · Cited by 1 · see citing works
Rotating Manipulation of Flower Stick Based on Only Consideration of Kinematic Constraint
Aoyama, T., Takaki, T., Miura, T., & Ishii, I. (2017) · Journal of the Robotics Society of Japan · doi:10.7210/jrsj.35.258 · Cited by 1 · see citing works
Toward obstacle avoidance in intermittent dynamical environments
Burridge, R. R., Rizzi, A. A., & Koditschek, D. E. (1997) · Lecture notes in control and information sciences · doi:10.1007/bfb0035197 · Cited by 1 · see citing works
Self-citationCoordination learning of robot movements with vision processes
Burdet, E., & Luthiger, J. (1999) · Robotica · doi:10.1017/s0263574799001344 · Cited by 1 · see citing works
Posture angle manipulation of passive object using active plate
Aoyama, T., Harada, Y., Takaki, T., & Ishii, I. (2014) · IEEE International Conference on Robotics and Biomimetics (ROBIO) · doi:10.1109/robio.2014.7090538
Position and inclination control of a passive disk based on cyclic motion generation
Aoyama, T., Gu, Q., Takaki, T., & Ishii, I. (2017) · ROBOMECH Journal · doi:10.1186/s40648-016-0071-1
Robotic Yoyo Based on Visual Feedback
Hashimoto, K., & Noritsugu, T. (1996) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)57802-7
Inertial Reorientation for Aerial and Terrestrial Legged Maneuverability
Libby, T. (2017) · eScholarship (California Digital Library)
(2002) · Cited by 200 · see citing works
- Authors
- Rizzi, A. A., & Koditschek, D. E.
- Affiliations
- University of Michigan (US)
- ORCID
- Koditschek, D.E.
- Venue
- Proceedings of the 1994 IEEE International Conference on Robotics and Automation
- Publisher
- IEEE Comput. Soc. Press
- Published
- 2002-12-17
- Pages
- 2935-2940
- ISSN
- 1050-4729 (ISSN-L)
- OpenAlex
- W2164094201
- Cited by
- 50
- References
- 12
- Citations by year
- 2020: 1 · 2018: 1 · 2017: 3 · 2016: 3 · 2015: 3 · 2014: 2 · 2012: 5
- FWCI
- 3.26
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Proceedings - IEEE International Conference on Robotics and Automation/Proceedings (publishedVersion)
- ScholarlyCommons (University of Pennsylvania) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Dynamics and Control of Mechanical Systems
- Physical Sciences › Engineering › Biomedical Engineering › Robotic Locomotion and Control
- Life Sciences › Neuroscience › Cognitive Neuroscience › Motor Control and Adaptation
- Keywords
- closed-loop dynamics, analytical dynamics, robot manipulators, one degree of freedom
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