The sensorimotor loop as a dynamical system: How regular motion primitives may emerge from self-organized limit cycles

TL;DR

This paper models a simple robot's sensorimotor loop as a dynamical system, revealing how regular motion primitives emerge from self-organized limit cycles influenced by control parameters and bifurcations.

Contribution

It demonstrates the emergence of stable limit cycles and diverse motion types in a simple robot model through dynamical systems analysis, highlighting self-organization and bifurcation phenomena.

Findings

Multiple stable limit cycles exist for the same parameters.

Limit cycle stability is affected by fold bifurcations.

Symmetry-breaking behaviors can be generated through timing control.

Abstract

We investigate the sensorimotor loop of simple robots simulated within the LPZRobots environment from the point of view of dynamical systems theory. For a robot with a cylindrical shaped body and an actuator controlled by a single proprioceptual neuron we find various types of periodic motions in terms of stable limit cycles. These are self-organized in the sense, that the dynamics of the actuator kicks in only, for a certain range of parameters, when the barrel is already rolling, stopping otherwise. The stability of the resulting rolling motions terminates generally, as a function of the control parameters, at points where fold bifurcations of limit cycles occur. We find that several branches of motion types exist for the same parameters, in terms of the relative frequencies of the barrel and of the actuator, having each their respective basins of attractions in terms of initial conditions. For low drivings stable limit cycles describing periodic and drifting back-and-forth motions are found additionally. These modes allow to generate symmetry breaking explorative behavior purely by the timing of an otherwise neutral signal with respect to the cyclic back-and-forth motion of the robot.