Rocking Stamper and Jumping Snakes from a Dynamical Systems Approach to Artificial Life

Abstract

Dynamical systems offer intriguing possibilities as a substrate for the generation of behavior because of their rich behavioral complexity. However this complexity together with the largely covert relation between the parameters and the behavior of the agent is also the main hindrance in the goal oriented design of a behavior system. This paper presents a general approach to the self-regulation of dynamical systems so that the design problem is circumvented. We consider the controller (a neural network) as the mediator for changes in the sensor values over time and define a dynamics for the parameters of the controller by maximizing the dynamical complexity of the sensorimotor loop under the condition that the consequences of the actions taken are still predictable. This very general principle is given a concrete mathematical formulation and is implemented in an extremely robust and versatile algorithm for the parameter dynamics of the controller. We consider two different applications, a mechanical device called the rocking stamper and the ODE simulations of a "snake" with five degrees of freedom. In these and many other examples studied we observed various behavior modes of high dynamical complexity.

Emergence of Interaction among Adaptive Agents

“…The behavior is changed every few tens of revolutions by an internal reorganization that occurs even in the absence of external stimuli. Furthermore, high-dimensional systems such as snake-or chain-like robots, quadrupeds, and wheeled robots [2] have been successfully controlled, where it is of particular interest that the control algorithm induces a preference for movements with a high degree of coordination among the various degrees of freedom. All the robotic implementations demonstrate the emergence of play-like behavior.…”

“…Based on the concept of homeokinesis [4] and the concept of self-organization, we developed in previous studies a controller [4,1,2] that establishes interesting sensorimotor couplings in a closed loop setup. This is achieved by the simultaneous maximization of the sensitivity with respect to sensory stimuli and the maximization of the predictability of future inputs.…”

“…The capabilities of homeokinetic control become obvious by considering some examples that were realized on various robotic platforms [3]. The "rocking stamper" [2] consists of an inverse pendulum mounted on a bowl-like trunk. It exhibits different rocking modes, preferably at the eigenfrequencies of the system.…”

“…It is considered to be relevant for the ontogenesis of living beings, the generation of behavior in autonomous robots, and the emergence of higher functions in agents. We have shown [1,2], that interesting behaviors can be generated in robotic agents [3] by a self-organizing controller that follows the cybernetic principle of homeokinesis 6 [4]. It combines the maximization of sensitivity with respect to external stimuli and the avoidance of unpredictable behaviors.…”

Homeotaxis: Coordination with Persistent Time-Loops

“…Information-driven self-organisation that relies on dynamics of predictive information [15,10] is related to the search of domain-invariant principles carried out by Der et al [4,7,6,5]. While traditionally an objective function, measuring the distance between the current and a desired behaviour, is provided explicitly by the designers, Der et al consider self-referential adaptive systems: the systems for which the objective function is derived from the dynamics of the system itself, i.e.…”