We have developed a formalism for describing and analyzing a very simple representative of a class of robotic tasks which involve repeated robot-environment interactions, among then the task of juggling. We review our empirical success to date with a new class of control algorithms for this task domain that we call “mirror algorithms.” These new nonlinear feedback algorithms were motivated strongly by experimental insights after the failure of local controllers based upon a linearized analysis. We offer here a proof that a suitable mirror algorithm is correct with respect to the local version of the specified task — the “vertical one-juggle” — but observe that the resulting ability to place poles of the local linearized system does not achieve noticeably superior transient performance in experiments. We discuss the further analysis and experimentation that should provide a theoretical basis for improving performance. For more information: Kod*Lab