Applications of Chaotic Dynamics in Robotics

Abstract

This article presents a summary of applications of chaos and fractals in robotics. Firstly, basic concepts of deterministic chaos and fractals are discussed. Then, fundamental tools of chaos theory used for identifying and quantifying chaotic dynamics will be shared. Principal applications of chaos and fractal structures in robotics research, such as chaotic mobile robots, chaotic behaviour exhibited by mobile robots interacting with the environment, chaotic optimization algorithms, chaotic dynamics in bipedal locomotion and fractal mechanisms in modular robots will be presented. A brief survey is reported and an analysis of the reviewed publications is also presented.

Design and Implementation of a Microcontroller Based Active Controller for the Synchronization of the Petrzela Chaotic System

“…There are many possible options for the selection of the gains k 1 , k 2 and k 3 that allows us to control the speed of convergence and to make stabilization of the system possible (11). By using the characteristic matrix of the closed Computation 2019, 7, 40 5 of 16 loop system, the gains can be selected in such a way that all the eigenvalues are negative real parts as shown in (12).…”

“…In recent decades, chaotic systems have been studied due to their nonlinear dynamic properties and for the possible applications they have in different fields of science. This began due to the work of references [1,2] in which they showed that synchronization of chaotic systems is possible; this development has been utilized in areas such as secure communications [3][4][5], cryptography [6,7], medical applications, mechanisms, and robotics [8][9][10][11][12][13][14][15]. Some of the synchronization schemes that have been successfully developed and applied include linear and nonlinear feedback control [16][17][18][19][20][21][22][23][24][25], where a Lyapunov candidate function V is proposed in such a way that the control law selected from the first derivative of V must be defined as negative [25].…”

“…In search and rescue applications (natural disasters), the robot must navigate in highly irregular and erratic environments, using chaotic motion planning techniques to ensure a quick search in the entire workspace. Therefore, the possibility of proposing navigation paths based on chaotic systems and their implementation in analog and embedded electronic systems remains open [12][13][14].…”

Nonlinear dynamics modeling and simulation of two-wheeled self-balancing vehicle

“…When the Lyapunov exponents are greater than 0, the system is unstable or chaotic. 22,23 When the Lyapunov exponent is 0, the phase trajectory is periodic motion. 24 When the Lyapunov exponent of all states of the system is less than 0, the phase orbit of the system is attracted to a stable fixed point, and the whole system is stable.…”

Multi-Agent Cooperative Control Consensus: A Comparative Review

“…Owing to the ability to handle abundant computational resources that are embedded in an autonomous agent enables it to enhance operational effective capabilities through a cooperative teamwork of multi-agent in military and civilian applications [1]. So by using multi-agent systems, certain global objectives can be achieved through sensing, exchange of information using communication, computation and their control [2,3].…”