Dealing with uncertainty is one of the major problems in robotics and one of the main obstacles to populating the world with robots that do something useful. This paper offers a new method for modeling uncertainties that exist in a robotic system, bosed on stochaatic differential equations. The benefit of using such a model is that we axe then able to capture in a analytic mathemgtical structure three key points underlying robot motion: I) the ability to properly express uncertainty within the motion descriptions, 2) the dynamic, changing nature of the task and its constraints, and 3) the idea of establishing a success probability or difficulty index for a taak. This paper is an expansion of these ideas, describing the models used and some initial experimental results for two robotic tasks: planning a velocity profile under force and time constraints, and a simple peg-in-hole task. With respect to the dynsmic nature of robotic motion tasks, the model of the environment uncert~dnty that we propose here is dynamic rather than static; the amount of knowledge about the environment is allowed to change as the robot moves. These results suggest that computetional models traditionMly found in the lower levels in robot systems may have application in the upper planning levels as well.