Graceful connections in dynamical systems – an approach to gait transitions in robotics

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Memon, Abdul Basit
Verriest, Erik I.
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Gaits have become an integral part of the design method of robots heading to complex terrains. But research into optimal ways to transition between different gaits is still lacking, and is the primary motivation behind this research. An essential characteristic of gaits is periodicity, and considering that a novel notion of graceful transition is proposed: a graceful transition is one that has maximally persisting periodicity. This particular notion of persistence in the characteristic behavior can be generalized. Therefore, a comprehensive framework for the general problem of connecting any two trajectories of a dynamical system, with an underlying characteristic behavior, over a finite time interval and in a manner that the behavior persists maximally during the transition, is developed and presented. This transition is called the Gluskabi Raccordation, and the characteristic behavior is defined by a kernel representation. Along with establishing this framework, the kernel representations for some interesting characteristic behaviors are also identified. The problem of finding the Gluskabi Raccordations is then solved for different combinations of characteristic behaviors and dynamical systems, and compact widely applicable results are obtained. Lastly, the problem of finding graceful gait transitions is treated within this newly established broader framework, and these graceful gait transitions are obtained for the case of a two-piece worm model.
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