  Dynamic movements are ubiquitous in human motor behavior as they tend to be
more efficient and can solve a broader range of skill domains than their
quasi-static counterparts. For decades, robotic juggling tasks have been among
the most frequently studied dynamic manipulation problems since the required
dynamic dexterity can be scaled to arbitrarily high difficulty. However,
successful approaches have been limited to basic juggling skills, indicating a
lack of understanding of the required constraints for dexterous toss juggling.
We present a detailed analysis of the toss juggling task, identifying the key
challenges and formalizing it as a trajectory optimization problem. Building on
our state-of-the-art, real-world toss juggling platform, we reach the
theoretical limits of toss juggling in simulation, evaluate a resulting
real-time controller in environments of varying difficulty and achieve robust
toss juggling of up to 17 balls on two anthropomorphic manipulators.
