1 research outputs found
Synchronization of a class of cyclic discrete-event systems describing legged locomotion
It has been shown that max-plus linear systems are well suited for
applications in synchronization and scheduling, such as the generation of train
timetables, manufacturing, or traffic. In this paper we show that the same is
true for multi-legged locomotion. In this framework, the max-plus eigenvalue of
the system matrix represents the total cycle time, whereas the max-plus
eigenvector dictates the steady-state behavior. Uniqueness of the
eigenstructure also indicates uniqueness of the resulting behavior. For the
particular case of legged locomotion, the movement of each leg is abstracted to
two-state circuits: swing and stance (leg in flight and on the ground,
respectively). The generation of a gait (a manner of walking) for a multiple
legged robot is then achieved by synchronizing the multiple discrete-event
cycles via the max-plus framework. By construction, different gaits and gait
parameters can be safely interleaved by using different system matrices. In
this paper we address both the transient and steady-state behavior for a class
of gaits by presenting closed-form expressions for the max-plus eigenvalue and
max-plus eigenvector of the system matrix and the coupling time. The
significance of this result is in showing guaranteed robustness to
perturbations and gait switching, and also a systematic methodology for
synthesizing controllers that allow for legged robots to change rhythms fast.Comment: Submitte