Modeling and Analysis of Stochastic Dynamics and Emergent Phenomena in Swarm Robotic Systems Using the Fokker-Planck Formalism

2010 ◽  
Author(s):  
Manish Kumar ◽  
Subramanian Ramakrishnan
Keyword(s):  
Stochastic Dynamics ◽  
Robotic Systems ◽  
Modeling And Analysis ◽  
Emergent Phenomena ◽  
Fokker Planck

Maneuverability and Heading Control of a Quadruped Robot Utilizing Tail Dynamics

2017 ◽  
Author(s):  
Wael Saab ◽  
Pinhas Ben-Tzvi
Keyword(s):  
High Speed ◽  
Sufficient Conditions ◽  
Quadruped Robot ◽  
Robotic Systems ◽  
Improve Performance ◽  
Modeling And Analysis ◽  
System Sensitivity ◽  
Proposed Model ◽  
Heading Control ◽  
Heading Angle

This paper presents modeling and analysis of a quadruped robot that utilizes tail dynamics to control its heading angle. The tail is envisioned to assist locomotion as a means separate from its legs to generate forces and moments to improve performance in terms maneuverability. Tail motion is analyzed for both low and high-speed tail actuation to derive sufficient conditions to maintain equilibrium and formulate maneuverability relations that result in rotation and translation of the robotic system. Sensitivity analysis is presented to select optimal tail mass and length ratios to maximize the change of the heading angle. A heading controller is then proposed and simulated to achieve a desired heading angle utilizing tail dynamics. Results of this research will assist in the design, modeling, and analysis of robotic systems sharing similar topologies to the proposed model, such as mobile robots with wheeled, tracked, multi-legged, or articulated-body based locomotion with swinging extremities such as tails, torsos, and limbs.

Random Vibration of Thermally Buckled Plates: II Nonzero Temperature Gradient Across the Plate Thickness

1997 ◽  
Vol 50 (11S) ◽  
pp. S105-S116 ◽  
Author(s):  
John Lee
Keyword(s):  
Temperature Gradient ◽  
Random Vibration ◽  
Stochastic Dynamics ◽  
Plate Thickness ◽  
Composite Plates ◽  
Single Mode ◽  
Large Temperature ◽  
Plate Temperature ◽  
Planck Distribution ◽  
Fokker Planck

As a theoretical tool, we use the single-mode Fokker-Planck distribution for an isotropic plate to describe the random vibration of thermally buckled composite plates. The Fokker-Plank distribution becomes singular as uniform plate temperature far exceeds, say, 20 times the critical buckling temperature. Then the asymptotic high-temperature moments depend only on the snap-through displacement, testifying that stochastic dynamics has degenerated into a static snap-through problem in the limit of high plate temperature and large temperature gradient across the plate thickness. Otherwise, it is nonsingular and bimodal for low and moderate plate temperatures. From the nonsingular Fokker-Planck distribution, we have deduced peak scaling by the standard deviation of displacement distribution and derived a functional form for strain distribution by using the quadratic relation between strain and displacement. They have been validated by the displacement histograms of numerical simulations and the strain histograms of thermally buckled plate experiments.

Characterization with Fokker–Planck theory of the nonlinear stochastic dynamics of a class of two-state continuous bioreactors

2021 ◽  
Vol 102 ◽  
pp. 66-84
Author(s):  
Roberto Baratti ◽  
Jesus Alvarez ◽  
Stefania Tronci ◽  
Massimilano Grosso ◽  
Alexander Schaum
Keyword(s):  
Stochastic Dynamics ◽  
Nonlinear Stochastic Dynamics ◽  
Fokker Planck

scholarly journals Space-Time Inversion of Stochastic Dynamics

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 839
Author(s):  
Massimiliano Giona ◽  
Antonio Brasiello ◽  
Alessandra Adrover
Keyword(s):  
Stochastic Dynamics ◽  
Exit Time ◽  
Planck Equation ◽  
Space Time ◽  
Langevin Equations ◽  
Time Inversion ◽  
Stochastic Thermodynamics ◽  
Wiener Processes ◽  
Fokker Planck Equation ◽  
Fokker Planck

This article introduces the concept of space-time inversion of stochastic Langevin equations as a way of transforming the parametrization of the dynamics from time to a monotonically varying spatial coordinate. A typical physical problem in which this approach can be fruitfully used is the analysis of solute dispersion in long straight tubes (Taylor-Aris dispersion), where the time-parametrization of the dynamics is recast in that of the axial coordinate. This allows the connection between the analysis of the forward (in time) evolution of the process and that of its exit-time statistics. The derivation of the Fokker-Planck equation for the inverted dynamics requires attention: it can be deduced using a mollified approach of the Wiener perturbations “a-la Wong-Zakai” by considering a sequence of almost everywhere smooth stochastic processes (in the present case, Poisson-Kac processes), converging to the Wiener processes in some limit (the Kac limit). The mathematical interpretation of the resulting Fokker-Planck equation can be obtained by introducing a new way of considering the stochastic integrals over the increments of a Wiener process, referred to as stochastic Stjelties integrals of mixed order. Several examples ranging from stochastic thermodynamics and fractal-time models are also analyzed.

The Application of Bioinspired Jumping Locomotion Principles to Mobile Robots: Modeling and Analysis

2011 ◽  
Author(s):  
Omar Gilani ◽  
Pinhas Ben-Tzvi
Keyword(s):  
Mathematical Model ◽  
Energy Storage ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Robotic Systems ◽  
Modeling And Analysis ◽  
Unstructured Environments ◽  
Model Based ◽  
High Magnitude ◽  
Jumping Robot

Nature provides various alternative locomotion strategies which could be applied to robotic systems. One such strategy is that of jumping, which enables centimeter to millimeter-scaled insects to traverse highly unstructured environments quickly and efficiently. These insects generate the required high magnitude power through specialized structures which store and rapidly release large amounts of energy. This paper presents an investigation into the morphology of natural jumpers and derives a generalized mathematical model based on them. The model describes mathematically the relationships present in a jumping system which uses a pause-and-leap jumping strategy. The use of springs as energy storage elements for such a jumping system is assessed. The discussion is then further extended to another bioinspired approach that can be applied to a jumping robot: that of gliding using foldable wings. The developed jumping and gliding mobility paradigm is analyzed and its feasibility for mobile robot applications is discussed.

scholarly journals Dynamic Modeling and Analysis of Propulsion effect of 3 DoF robot

2013 ◽  
Vol 1 (2) ◽  
pp. 30-38
Author(s):  
Ahmet Shala ◽  
Xhevahir Bajrami
Keyword(s):  
Dynamic Modeling ◽  
Vertical Direction ◽  
Robotic Systems ◽  
Dynamical Modeling ◽  
Modeling And Analysis ◽  
Working Model ◽  
Earth Gravity ◽  
Modeling Analysis ◽  
3D Software ◽  
And Control

Dynamical Modeling of robots is commonly first important step of Modeling, Analysis and Control of robotic systems. This paper is focused on using Denavit-Hartenberg (DH) convention for kinematics and Newton- Euler Formulations for dynamic modeling of 3 DoF - Degree of Freedom of 3D robot. The process of deriving of dynamical model is done using Software Maple. Simulations are done using Matlab/Simulink for analysis of propulsion effect under Earth gravity when First Link rotates with 1000 rpm, second Link can move free in vertical direction and Third Link can rotates free around their rotations axle. Simulations results shows very good propulsion of proposed 3 DoF robot. Results are verified-compared with constructed model of 3 DoF robot using Working Model 3D Software.

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