# Brown Bag Seminar

### Drive-Based Motivation for Coordination of Limit Cycle Behaviors

### Abstract

Navigation is often be considered a prototypical behavior for a robotic system. Constructing robots capable of complex behaviors requires developing a method for switching among possible behaviors, for example using a hybrid automaton. Recent work has developed an alternative approach using continuous dynamical systems that use an internal drive state to select the desired behavior. In one particular result, authors developed drive dynamics that result in trajectories where the robot repeatedly flows to one point attractor and then another, yielding a limit cycle where the robot patrols between two points. A further level of complexity arises when one seeks to create a system that switches between these basic limit cycles instead of the original point attractors. This work outlines the problem using the recently-developed drive-based dynamical framework. As a proof-of-concept we demonstrate the existence of an attracting set consisting of orbits that repeatedly flow between two canonical limit cycles (e.g., Hopf oscillators). This attracting set connecting limit cycle behaviors arises from a bifurcation depending on a family of parameters which is analogous to the bifurcation that produces the limit cycle connecting two point-attractor behaviors in previously-published system. Implications and next-steps in the case of arbitrary limit cycles are discussed.