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The Foucault Pendulum is a Spherical Pendulum of fixed length with two angular degrees of freedom, attached to a suspension which rotates once a day around the Earth axis at a distance essentially set by Earth radius and the geodetic…
This study introduces an analytically tractable and computationally efficient model of the legged robot dynamics associated with locomotion on a dynamic rigid surface (DRS), and develops a real-time motion planner based on the proposed…
A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be…
The one-dimensional nonlinear oscillations of a magnet attached to a spring and interacting with a set of magnets are analyzed theoretically and experimentally. The equation of motion is solved numerically using the Euler method in a…
Soft robots, distinguished by their inherent compliance and continuum structures, present unique modeling challenges, especially when subjected to significant external loads such as gravity and payloads. In this study, we introduce an…
Aerial manipulators (AM) exhibit particularly challenging, non-linear dynamics; the UAV and the manipulator it is carrying form a tightly coupled dynamic system, mutually impacting each other. The mathematical model describing these…
New method of analysing the free and heavy symmetric tops using Euler's equations to perform extraction from the body frame to the lab frame. Subsequent to extraction, the lab frame equations are solved by space phasor method.
This paper introduces a simulation study of fluid actuated multi-driven closed system as spherical mobile robot called "RollRoller". Robot's mechanism design consists of two essential parts: tubes to lead a core and mechanical controlling…
A new Lagrangian formulation with complex currents is developed and yields a direct and simple method for modeling three-phase permanent-magnet and induction machines. The Lagrangian is the sum a mechanical one and of a magnetic one. This…
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…
Exact solutions are found for Euler's equations of rigid body motion for general asymmetrical bodies under the influence of torque by using Jacobi elliptic functions. Differential equations are determined for the amplitudes and the…
In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance…
Control of compliant mechanical systems is increasingly being researched for several applications including flexible link robots and ultra-precision positioning systems. The control problem in these systems is challenging, especially with…
Being able to effectively locate saddle (and other fixed) points in dynamical systems holds tremendous implications in a number of applications in engineering and science, among which the study of rare events in molecular simulations stands…
This study evaluates the application of a discrete action space reinforcement learning method (Q-learning) to the continuous control problem of robot inverted pendulum balancing. To speed up the learning process and to overcome technical…
This paper addresses reinforcement learning based, direct signal tracking control with an objective of developing mathematically suitable and practically useful design approaches. Specifically, we aim to provide reliable and easy to…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…
Soft robots are made of compliant materials and perform tasks that are challenging for rigid robots. However, their continuum nature makes it difficult to develop model-based control strategies. This work presents a robust model-based…
Most of the advanced control systems use sensor-based feedback for robust control. Tilt angle estimation is key feedback for many robotics and mechatronics applications in order to stabilize a system. Tilt angle cannot be directly measured…