Persistent Passive Hopping and Juggling is Possible Even With Plastic Collisions
- 2 July 2002
- journal article
- research article
- Published by SAGE Publications in The International Journal of Robotics Research
- Vol. 21 (7), 621-634
- https://doi.org/10.1177/027836402322023213
Abstract
We describe simple one-dimensional models of passive (no energy input, no control), generally dissipative, vertical hopping and one-ball juggling. The central observation is that internal passive system motions can conspire to eliminate collisions in these systems. For hopping, two point masses are connected by a spring and the lower mass has inelastic collisions with the ground. For juggling, a lower point-mass hand is connected by a spring to the ground and an upper point-mass ball is caught with an inelastic collision and then re-thrown into gravitational free flight. The two systems have identical dynamics. Despite inelastic collisions between non-zero masses, these systems have special symmetric energy-conserving periodic motions where the collision is at zero relative velocity. Additionally, these special periodic motions have a non-zero sized, one-sided region of attraction on the higher-energy side. For either very large or very small mass ratios, the one-sided region of attraction is large. These results persist for mildly non-linear springs and non-constant gravity. Although non-collisional damping destroys the periodic motions, small energy injection makes the periodic motions stable, with a two-sided region of attraction. The existence of such special energy conserving solutions for hopping and juggling points to possibly useful strategies for both animals and robots. The lossless motions are demonstrated with a table-top experiment.Keywords
This publication has 18 references indexed in Scilit:
- Control of a bow leg hopping robotPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Small slope implies low speed for McGeer's passive walking machinesDynamics and Stability of Systems, 2000
- Stable control of a simulated one-legged running robot with hip and leg complianceIEEE Transactions on Robotics and Automation, 1997
- Planning and Control of Robotic Juggling and Catching TasksThe International Journal of Robotics Research, 1994
- Band-edge localization as intermittent chaosPhysical Review B, 1993
- Walking Without Impacts as a Motion/Force Control ProblemJournal of Dynamic Systems, Measurement, and Control, 1992
- Vertical and Horizontal Motion Control of a One-Legged Hopping MachineThe International Journal of Robotics Research, 1992
- Analysis of a Simplified Hopping RobotThe International Journal of Robotics Research, 1991
- Passive bipedal runningProceedings of the Royal Society of London. B. Biological Sciences, 1990
- Three Uses for Springs in Legged LocomotionThe International Journal of Robotics Research, 1990