Examination of Balancing in a Real-World Inverted Pendulum

Motor adaptation is typically studied using simplified virtual tasks. Here, we investigated how humans learn to stabilize a physically unstable, underactuated system, and how participants cope with changes in the system’s dynamics. Twelve right-handed adults balanced a real inverted pendulum by moving a cart along a linear rail. Study 1 characterized the passive mechanical properties of three pendulums (short, medium, and long) using free-oscillatory decay and fall to ±30° trials, after their release from the upright position. Longer rods exhibited slower decay and lower natural frequencies, as well as a longer duration before falling, indicating greater passive stability. Study 2 assessed human motor control of the pendulum to maintain balance. Human participants trained with the medium pendulum (30 trials) and were then tested with all three pendulums (20 trials each). During training, balance performance improved significantly, with time to failure increasing over trials. During testing, performance scaled with pendulum length, and longer rods were easier to balance. Similar peak cart velocities were observed across conditions, suggesting equivalent actuation effort. Additionally, as expected, pendulum angular velocities decreased with rod length, reflecting underlying inertial differences. Pendulum passive dynamics closely matched behavioral performance, supporting a strong link between intrinsic system properties and balancing outcomes. These findings show that motor learning in physically unstable environments is not only shaped by feedback and effort, but also by the alignment of human control strategies and abilities with the natural dynamics of the plant. We note that in this study, we used a modified pendulum rig previously employed to examine control engineering approaches to modelling balance, thereby generating a dataset that can later be used to compare human performance with real-time computer control implementations of the same tasks.