Highly under-actuated dynamic manipulation: Dice stacking is mostly open-loop

Humans ability to grasp and dynamically manipulate objects with their hands is unmatched by current robots. To better understand human dynamic manipulation, we studied dice stacking, a task in which humans form a vertical stack of dice from a set of initially unstacked playing dice using an overturned cup and the surface of a table. This task is high dimensional and under-actuated, so it may superficially seem an incredible feat of state estimation and feedback control, but we show that this task is amenable to open-loop strategies. We simulated a cup with dice oscillated by fixed arm movement patterns using two different computer simulation frameworks with different contact models. These simulations showed that, for a range of arm and wrist movements, the dice naturally stack without any dice state feedback. We verified the predictions of these simulations with a physical robot. Thus, we have added dice stacking to the small list of dynamic manipulation tasks that can be robustly performed open-loop. We speculate that, for highly under-actuated tasks, humans may be biased to learn open-loop strategies over state feedback strategies. Future work could investigate the presence of such a bias in humans and its potential value for reinforcement learning algorithms.