Robustness in Human Manipulation of Dynamically Complex Objects Through Control Contraction Metrics

Control and manipulation of objects with underactuated dynamics remains a challenge for robots. Due to their typically nonlinear dynamics, it is computationally taxing to implement model-based planning and control techniques. Yet humans can skillfully manipulate such objects, seemingly with ease. More insight into human control strategies may inform how to enhance control strategies in robots. This study examined human control of objects that exhibit complex - underactuated and nonlinear - dynamics. We hypothesized that humans seek to make their trajectories exponentially stable to achieve robustness in the face of external perturbations. A stable trajectory is also robust to the high levels of noise in the human neuromotor system. Motivated by the task of carrying a cup of coffee, a virtual implementation of transporting a cart-pendulum system was developed. Subjects interacted with the virtual system via a robotic manipulandum that provided a haptic and visual interface. Human subjects were instructed to transport this simplified system to a target position as fast as possible without `spilling coffee,' while accommodating different visible perturbations that could be anticipated. To test the hypothesis of exponential convergence, tools from the framework of control contraction metrics were leveraged to analyze human trajectories. Results showed that with practice the trajectories indeed became exponentially stable, selectively around the perturbation. While these findings are agnostic about the involvement of feedback and feedforward control, they do support the hypothesis that humans learn to make trajectories stable, consistent with achieving predictability.