Construction of bifurcating multi-behavioral dynamical systems for coordination of resource-constraint robot collectives
Date
2024
Authors
Baxevani, Kleio
Journal Title
Journal ISSN
Volume Title
Publisher
University of Delaware
Abstract
This dissertation expands the class of planar mutli-behavioral dynamical systems that generate different behaviors via the same model without involving switching between distinct vector fields. Instead, the different behaviors are being invoked by blending continuously selected vector fields and triggering bifurcations in the resulting composite continuously time-varying dynamical system. The contribution of this work is a set of new analytical conditions on the system parameters that ensure the existence of the necessary bifurcations. While building recent advances that are biologically inspired, drawing conceptual connections to bee colony behaviors, and which formally introduce motivation and value dynamics as an efficient means of designing unique dynamical systems that can exhibit a range of distinct behaviors. One way in which these advances are further extended in this dissertation is by lifting some of the existing restrictions on what kind of planar vector fields can be combined to produce bifurcations. This relaxation enriches the class of dynamical systems that such an approach applies and gives rise to new behaviors. ☐ The constructive process that yields the said multi-behavioral dynamical systems facilitates tractable theoretical study and stability analysis since all behavior modes are traced back to the same set of suitably parameterized differential equations. One way to utilize this theoretical construction in the domain of robotics is to use the resulting vector fields as reference motion for mobile robots. The robots may operate in isolation or in large groups and adjust their motion in a feedback fashion to follow the reference vector fields. This way robot groups of arbitrary dimensions can be steered and made behave as a group without either centralized coordination or local interaction. This motion planning strategy is particularly suitable for resource-constraint robot collectives, members of which can neither sense nor communicate with each other. The theoretical predictions from the mathematical analysis in this dissertation are verified through a series of numerical simulations. In addition, experimental implementation of key aspects of the motion planning methodology in the context of robot-assisted play-based pediatric rehabilitation confirm the applicability and efficacy of the proposed methods in real-world applications. ☐ While the bifurcation-based multi-behavioral system design approach is limited to a subset of planar dynamical systems, the class of applicable problems is rich and includes many instances of ground or marine vehicle coordination. A possible future direction could be to lift some of these limitations allowing the synthesis of a greater span of dynamical systems that can capture a greater spectrum of possible applications.
Description
Keywords
Behaviors, Bifurcations, Resource-constraints, Motion planning, Pediatric rehabilitation