A program of research in robotics that seeks to encode abstract tasks in a form that simultaneously affords a control scheme for the torque-actuated dynamical systems, as well as a proof that the resulting closed-loop behavior will correctly achieve the desired goals, is reviewed. Two different behaviors that require dexterity and might plausibly connote 'intelligence' - navigating in a cluttered environment and juggling a number of otherwise freely falling objects - are examined with regard to similarities in problem representation, method of solution, and causes of success. The central theme concerns the virtue of global stability mechanisms. At the planning level they lend autonomy, that is, freedom from dependence upon some 'higher' intelligence. They encourage the design of canonical procedures for model problems, which may then be instantiated in particular settings by a change of coordinates. The procedures developed result in provably autonomous behavior. Simulation results and physical experimental studies suggest the practicability of these methods.