Hybrid Dynamic Modelling and Bioinspired Control Based on Central Pattern Generator of Biped Robotic Gait

This chapter presents the theoretical foundations and methodology to develop a bioinspired hybrid control architecture for a biped robotic device that reproduces gait and human motor control strategies with the ability to adapt the trajectory to environmental conditions. The objective is to design robotic devices (such as exoskeletons), through the functional integration of hybrid dynamic system modeling (event-driven and continuous dynamics) with efficient and robust conventional control techniques and bioinspired control algorithms, with a near-natural human gait pattern. The human gait cycle is modeled as a hybrid dynamic using a finite state machine (FSM). The gait trajectories are to be generated in such a way that they will be capable of adapting to disturbances in the path followed by the robotic device; this will be achieved using a neuronal oscillator that simulates the behavior of a central pattern generator (CPG).

A Model of Growth Trajectory Bifurcation in Animals Ontogeny

The aim of this study was to formulate and analyse a model of ontogenetic growth cessation in pigs. The cessation of growth when an animal reaches its species-specific size in ontogeny is still a problem. Systemic factors that contribute to this process are unknown. The focus of the research is an analysis of the growth dynamic that explains some aspects of the problem. The method applied to meet the purpose of the study was mathematical modelling. To enhance the understanding of the growth trajectories in ontogeny an analytical model of growth in pigs was built. The model was formulated as a hybrid dynamic system with discrete-time and continuum equations. The novelty of the study is a concept of ontogenetic growth in the pig. Both a new modelling technique, and new variables are introduced. A central theme of the study is an analysis of the growth trajectory bifurcation, and a description of the two emerged growth trajectories. A reading of a normal form of bifurcation applied to the growth trajectory bifurcation has been offered. The results suggest that ontogenetic growth in pigs is not continuous. The growth trajectory has bifurcation at the point the animals attain their individual maximum weight. At this point, two new growth trajectories emerge. On one trajectory, animals continue to grow till a species maximum weight is reached. On other trajectory, animals continue to live till obtainable life span is attained. The emerged trajectories are genetic channels that open the way to grow for the certain phenotypes. Ontogenetic growth stops when the feed conversion coefficient grows into infinity.

A Mathematical Modelling for Workflows

A mathematical heuristic model was proposed to analyze the flow of information in administrative workflows. The model starts from a conceptual analysis from the perspective of probabilistic systems, information theory, and information entropy. The main parameters of the analysis are to identify theoretically a workflow as a hybrid dynamic system where the probabilistic distribution of the information, the time of information processing, and the precision with which the workflow is executed are caused by the cognitive performance of agents within a complex adaptive system. The model of analysis provides support for the search for empirical evidence in workflow investigations, highlighting the presence or absence of agent ad hoc methods and their influence on firm’s productivity.

A Multibody Toolbox for Hybrid Dynamic System Modeling Based on Nonholonomic Symbolic Formalism

This paper proposes a hybrid multibody dynamics formalism with a symbolical multibody toolbox developed in MATLAB Environment. The toolbox can generate the dynamic model of a multibody system with hybrid and nonholonomic dynamic properties. The framework and software structure of the toolbox are briefly demonstrated. The paper discusses the recursive kinematics and modular modeling theories that help improve the modeling performance and offer accessibility into the dynamic elements. The formalism that offers a symbolic solution to nonholonomic and constrained dynamics is explained in detail. The toolbox also provides design tools and auto-compilation of hybrid automata. Two exemplary models and their simulations are presented to verify the feasibility of the formalism and demonstrate the performance of the toolbox.