The Science of Stick Balancing

Collaborators: John Doyle, Joel Burdick

A human balancing a stick on his or her hand can be modeled as balancing an inverted pendulum on a moving cart. This balancing task is fascinating because although it is a simple dynamical system, it provides useful insights on the fundamental limits of human’s nervous system. Applying the Bode’s integral formula from feedback control theory, interesting predictions can be made such as where a person looks on the stick affects how well he/she can balance the stick. One can easily verify this fact at home by balancing a stick with different gaze locations.

The theoretical work predicts many of the phenomena observed when a person is balancing a stick. With the help of motion capturing system, OptiTrack, I conducted human experiments to demonstrate systematically that the theoretical predictions are observed practice. The most novel finding of these experiments is that gaze location affects the performance significantly – an effect not studied by other researchers in neuroscience. These figures show a schematic of the stick balancing model and the experimental setup.

Inverted Pendulum Inverted Pendulum

Verification of the theoretical results is simple and can be easily done at home using an extensible stick. Hence, human stick balancing is also an ideal case study for learning and teaching robust control theory. For more information about the theoretical framework, refer to this research note.

Before I used the OptiTack system, I built a stereo vision tracking system using webcams.

I also created an interactive data visualization using the preliminary data. It works best on a desktop.


  1. Y. P. Leong and J. C. Doyle, “Understanding robust control theory via stick balancing,” in IEEE Int. Conf. on Decision and Control (CDC), 2016, pp. 1508–1514.
  2. Y. P. Leong, B. Christalin, J. W. Burdick, and J. C. Doyle, The significance of measurement location in human stick balancing, Program No. 794.14. Neuroscience Meeting Planner 2015. Society of Neuroscience, 2015. Online.