Analogy between Juggling and Hopping: Active Object Manipulation Approach

Dynamic manipulation of an active object is introduced as a general model of hopping and juggling tasks. In this setting, juggling and hopping are two extreme cases of this general model. Behavioral resemblance of these two tasks is afterwards extended to a detailed mathematical analogy between them. Then the analogy is exploited to develop a unified and abstract planning framework for juggling and hopping. To this end, dynamic manipulation of an active object is decomposed into three distinct phases and two transitions: Carry I, Free flight and Carry II phases. These phases are analogous to Lift off, Free flight and Touch down in hopping. In the next step, a mathematical model for each phase is developed. It is shown that dynamic grasp (in Carry phases of juggling) and foot stability (in Support phases of hopping) conditions share similar sets of dynamic equations. Accordingly, Lift off/Release and Touch down/Catch conditions in hopping/juggling are derived. It is shown that analogous strategies can be developed for Lift off and Release. The analogy is held for Touch down and Catch conditions as well. It is discussed that in the planning framework the initial and the goal configurations of the three phases are set in a model-based and forward manner. To do so, Touch down/Landing time, Free flight duration and robot/object maneuvers during Free flight are used as free parameters for planning in order to ensure foot stability in hopping and dynamic grasp in juggling along with other constraints.

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