The inverted pendulum: history and survey of open and current problems in control theory and robotics

Abstract

The inverted pendulum is a classical problem in dynamics and control theory widely used as a fundamental system for testing emerging control algorithms. In spite of its very simple structure appropriate for developing real-time implementation, the inverted-pendulum model is considered the richest one among common robotic benchmarks. Not only it can describe many engineering problems but also it can explain several biological examples. Various mathematical models and experimental designs for the inverted pendulum exist offering an attractive tool for education and research. The objective of this survey is to present an overview of the available varieties of such system, highlighting the richness of its dynamics and then providing an overall picture of different control design approaches and trendy robotic problems related to its simple structure. In total, 300 references in the open literature, dating back to Galileo's first experiments written in 1602, are compiled to provide an overall picture of historical, current and challenging developments based on the stabilization principle of the inverted pendulum.