Energy-Based Limit Cycle Compensation for Dynamically Balancing Wheeled Inverted Pendulum Machines

In this paper we present an energy-based algorithm to minimize limit cycles in dynamically balancing wheeled inverted pendulum (IP) machines. Because the algorithm is not based on absolute values of parameters, the performance is robust and accounts for mechanical reconfiguration and wear. The effects of phenomena such as drive-train friction, rolling friction, backlash and sensor bandwidth are well known, causing either limit cycles or instabilities in IP balancing machines and yet compensation or control design to mitigate these effects are not well known. The effects of these non-linearities can be observed in the energy behavior of IP balancing machines, hence, as a broader goal we seek to establish an energy-based framework for the investigation of non-linearities in this class of machines. We successfully demonstrate the effectiveness of our algorithm on a two-wheeled IP balancing machine, “Charlie”, developed in our laboratory. As an example we show a reduction in the amplitude of limit cycles over a 10 second period from 220 degrees in wheel angle and 15 degrees in pitch to 9.9 degrees and 1.3 degrees respectively.