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...

Exact feedback linearization converts any system into appropriate form such that the controller design becomes convenient for the system. In this technique, control algorithm is developed based on exact feedback linearization through energy control. This approach is applicable to under actuated in which single control input, acceleration of cart, controlled the angle and position of cart. This ...

In this paper, we report on a new stability analysis for hybrid legged locomotion systems based on factorization of return maps. We apply this analysis to a family of models of the Spring Loaded Inverted Pendulum (SLIP) with different leg recirculation strategies. We obtain a necessary condition for the asymptotic stability of those models, which is formulated as an exact algebraic expression d...

This paper presents an interactive locomotion controller using motion capture data and an inverted pendulummodel (IPM). The motion data of a character is decomposed into those of upper and lower bodies, which are then dimension-reduced via what we call hierarchical Gaussian process dynamical model (H-GPDM). The locomotion controller receives the desired walking direction from the user. It is in...

To use numerical investigation of functional differential equations it is very important to know if difference analogues of the considered differential equations have the reliability to preserve some general properties of these equations, in particular, property of stability. This problem is considered here by investigation of a difference analogue of the linear mathematical inverted pendulum. ...

In order to explore the essence of structural controllability, structural controllability of inverted pendulum is analyzed in this presented study and a sufficient controllability condition of a class of perturbed linear system is obtained, which is essential to prove the structural controllability for the perturbed inverted pendulum. Two different structured models of inverted pendulum are con...

It is shown how to obtain asymptotic stability in second-order undamped systems using time-delay action in the feedback of position. The effect of the delay is similar to derivative feedback in modifying the behavior of the system. Results are given on the selection of the controller parameters both in the absence and the presence of additional delay in the feedback path. The time-lag position ...

We present a comparison of a LQR controller and Q-learning on a simulation of a triple inverted pendulum. While the LQR controller was able to balance the pendulum, Qlearning was unable due to memory and computing limitations. We examine the strengths and weaknesses of each method and compare their abilities.

This paper investigates the design and analysis of three controllers used to stabilize an inverted pendulum on a cart. This is accomplished by decomposing each control algorithm into two separate phases: swing-up control and stabilization control. A classical, H2, and H∞ design are each considered to stabilize a nominal linearized model of the inverted pendulum on a cart in the upward vertical ...

Model Predictive Control (MPC) is used to improve the performance of energy control for swinging up a pendulum. A new MPC method is developed in continuous time, but it explicitly considers its digital implementation letting the control signal be piecewise constant. The stability properties of the algorithm are analyzed in terms of the free MPC design parameters. The achieved performance improv...