This paper advances a mathematical formulation which, when combined with appropriate operator and sensor inputs, can be used to generate the control functions necessary for short, autonomous periods of remote manipulation under human supervision. It is shown that all manipulation tasks belong to one of four basic categories which are a function of the spatial variability of the task and its dynamic state. Techniques for both describing and executing tasks in each category are given and the relation between these techniques and previous efforts are discussed. Additionally, methods for measuring and tracking the task motion as a function of position, velocity and acceleration are considered.