The Furuta pendulum, or rotational inverted pendulum, is a system found in many control labs. It provides a compact yet impressive platform for control demonstrations and draws the attention of the control community as a platform for the development of non-linear control laws. Despite the popularity of the platform there are very few papers which employ the correct dynamics and only one that de...

The dynamics of a bead sliding without friction along a periodically pulsating wire is under consideration. If the arc length of the wire is taken as the relevant coordinate, the motion of the bead is described by a periodic newtonian equation. Sufficient conditions are derived assuring that a given equilibrium is of twist type, a property that implies its nonlinear stability as well as a KAM s...

In this paper, we present a walking approach for the Nao robot that improves the agility and stability of the robot when walking on a flat surface such as the soccer field used in the Standard Platform League. The gait uses the computationally inexpensive model of an inverted pendulum to generate a target trajectory for the center of mass of the robot. This trajectory is adapted using the obser...

The strategies involved in swinging up and balancing the inverted pendulum are discussed. The nonlinear swing-up controller drives the system input according to the energy of the pendulum. The balancing controller is a digital linear quadratic regulator that is based on a model of the plant that has been linearized about the pendulum’s upright equilibrium position. Relays with hysteresis are em...

A classical control approach to stabilizing a dual inverted pendulum system with linear control is presented, along with measured results of the completed system. The emphasis of this work is on both the system’s implementation details and its role in a feedback course at the Massachusetts Institute of Technology. The control method includes a variety of techniques that makes this system not on...

The purpose of this article is to perform an indepth analysis of the classical double inverted pendulum system using the Inverted Pendula Modeling and Control (IPMaC), a Simulink block library designed by the authors of the paper. The custom function blocks included in the IPMaC offer comprehensive program support for the modeling, simulation and control of classical and rotary inverted pendula...

Human beings are highly efficient in maintaining standing balance under the influence of different perturbations. However, biped humanoid robots are far from exhibiting similar skills. This is mainly due to the limitations in the current control and modeling techniques used in humanoid robots. Even though approaches using the Linear Inverted Pendulum Model and the Preview Control schemes have s...

Over the course of a few decades, the pendulum problem has become a prime example in the instruction of many concepts in linear and nonlinear dynamics. Particularly, the inverted pendulum has been illuminating in the areas of dynamical stability and control. Our intent with this dynamics problem was to explore the stability of the inverted state while vertically driving the pivot point. Forcing...

ROTATIONAL DOUBLE INVERTED PENDULUM Name: Li, Bo University of Dayton Advisor: Dr. Raúl Ordóñez The thesis deals with the stabilization control of the Rotational Double Inverted Pendulum (RDIP) System. The RDIP is an extremely nonlinear, unstable, underactuated system of high order. A mathematical model is built for the RDIP with the Euler-Lagrange (E-L) equation. A Linear Quadratic Regulator (...

The approximation of a humanoid robot by an inverted pendulum is one of the most frequently used models to generate a stable walking pattern using a planned zero moment point (ZMP) trajectory. However, on account of the difference between the multibody model of the humanoid robot and the simple inverted pendulum model, the ZMP error might be bigger than the polygon of support and the robot fall...