Uncertainty in the executin of robot motion plans must be accounted for in the geometric computations from which plans are obtained, especially in the case where position sensing is inaccurate. We give an $O(n^{2} log n)$ algorithm to find a single commanded motion direction which will guarantee a successful motion in the plane from a specified start to a specified goal whenever such a one-step motion is possible. The plans account for uncertainty in the start position and in robot control, and anticipate that the robot may stick on or slide along obstacle surfaces with which it comes in contact. This bound improves on the best previous bound by a quadratic factor, and is achieved in part by a new analysis of the geometric complexity of the backprojection of the goal as a function of commanded motion direction.