Topic

# Inverted pendulum

About: Inverted pendulum is a research topic. Over the lifetime, 8024 publications have been published within this topic receiving 109375 citations.

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TL;DR: The authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model with a model-based fuzzy controller design utilizing the concept of the so-called "parallel distributed compensation" and presents a design methodology for stabilization of a class of nonlinear systems.

Abstract: Presents a design methodology for stabilization of a class of nonlinear systems. First, the authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of the so-called "parallel distributed compensation" is employed. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. The design procedure is conceptually simple and natural. Moreover, the stability analysis and control design problems can be reduced to linear matrix inequality (LMI) problems. Therefore, they can be solved efficiently in practice by convex programming techniques for LMIs. The design methodology is illustrated by application to the problem of balancing and swing-up of an inverted pendulum on a cart.

2,534 citations

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TL;DR: In this article, an analysis is made of the rocking motion of structures of inverted pendulum type during the Chilean earthquakes of May, 1960, and it is shown that there is a scale effect which makes tall slender structures more stable against overturning than might have been expected.

Abstract: During the Chilean earthquakes of May, 1960, a number of tall, slender structures survived the ground shaking whereas more stable appearing structures were severely damaged. An analysis is made of the rocking motion of structures of inverted pendulum type. It is shown that there is a scale effect which makes tall slender structures more stable against overturning than might have been expected, and, therefore, the survival of such structures during earthquakes is not surprising.

1,237 citations

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01 Dec 2006TL;DR: The well-known linear inverted pendulum model is extended to include a flywheel body and it is shown how to compute exact solutions of the capture region for this model, the region on the ground where a humanoid must step to in order to come to a complete stop.

Abstract: It is known that for a large magnitude push a human or a humanoid robot must take a step to avoid a fall. Despite some scattered results, a principled approach towards "when and where to take a step" has not yet emerged. Towards this goal, we present methods for computing capture points and the capture region, the region on the ground where a humanoid must step to in order to come to a complete stop. The intersection between the capture region and the base of support determines which strategy the robot should adopt to successfully stop in a given situation. Computing the capture region for a humanoid, in general, is very difficult. However, with simple models of walking, computation of the capture region is simplified. We extend the well-known linear inverted pendulum model to include a flywheel body and show how to compute exact solutions of the capture region for this model. Adding rotational inertia enables the humanoid to control its centroidal angular momentum, much like the way human beings do, significantly enlarging the capture region. We present simulations of a simple planar biped that can recover balance after a push by stepping to the capture region and using internal angular momentum. Ongoing work involves applying the solution from the simple model as an approximate solution to more complex simulations of bipedal walking, including a 3D biped with distributed mass.

1,049 citations

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29 Oct 2001

TL;DR: Geometric nature of trajectories under the 3D-LIPM and a method for walking pattern generation are discussed, and a simulation result of a walking control using a 12-DOF biped robot model is shown.

Abstract: For 3D walking control of a biped robot we analyze the dynamics of a 3D inverted pendulum in which motion is constrained to move along an arbitrarily defined plane. This analysis yields a simple linear dynamics, the 3D linear inverted pendulum mode (3D-LIPM). Geometric nature of trajectories under the 3D-LIPM and a method for walking pattern generation are discussed. A simulation result of a walking control using a 12-DOF biped robot model is also shown.

1,033 citations

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TL;DR: It is shown that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity.

Abstract: Properties of simple strategies for swinging up an inverted pendulum are discussed. It is shown that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison of energy-based strategies with minimum time strategy gives interesting insights into the robustness of minimum time solutions.

929 citations