# Modeling and Computation Seminar

### Motivational dynamics: a dynamical systems approach for prioritizing control tasks

### Abstract

Mobile robots are becoming increasingly ubiquitous due to technological advances in sensing, actuation, and computation. However, devising control strategies to ensure that robots perform their assigned tasks in unpredictable real-world environments remains a challenge. An approach that has proved useful in practice is to encode tasks as point attractors of dynamical systems, e.g., design vector fields that steer a vehicle to a desired location. To encode richer behaviors, one can develop methods to switch among low-level point-attractor controllers; this is often done by developing an automaton that discretely switches between available controllers, yielding a hybrid dynamical system. The hybrid system approach is powerful because automatons can be automatically synthesized based on high-level task specifications, but has the inherent weakness of requiring the discretization of the system model, which reduces robustness of the resulting controller. In this work, we develop an alternative approach based on a dynamical systems mechanism for making decisions, i.e., choosing controllers. We show that this approach can encode tasks where an agent must repeatedly carry out several behaviors in sequence, i.e., as a limit cycle. Restricting to a specific case, we derive conditions under which this limit cycle must exist. We conclude the talk with some speculation as to future directions of this work, including connections to programming languages and the topology of attracting sets of dynamical systems.