This article develops a formalism for describing and analyzing a very simple representative class of robotic tasks that require “dynamical dexterity” – among them, the task of juggling. The authors review their empirical success, to date, with a new class of control algorithms for this task domain, called “mirror algorithms.” The formalism for representing the task domain and encoding within it the desired robot behavior enables them to prove that a suitable mirror algorithm is correct with respect to a specified task.