This paper reviews certain theoretical results in robot task planning and control obtained with the support of NSF Research Initiation Grant DMC-8505160. The “natural control” paradigm is reviewed and detailed attention is focused upon the specific task of robot navigation in a cluttered environment. The paper concludes with some comments concerning the problems which remain before this approach to robot command and control can be made practicable in a real manufacturing environment. A summary of formal results presented in the paper now follows. The class of “navigation functions” simultaneously encodes the task of navigating amidst obstacles and automatically generates correct feedback control laws for this purpose as well. We show that the topology of navigation tasks precludes any stronger class of controllers (with respect to convergence properties). On the other hand we demonstrate that a member of this class must exist for any environment. Finally, we construct controllers for an increasingly realistic catalogue of environments by recourse to “deformation” of the true environment into a computationally simpler but topologically equivalent model.