For a mobile robot to travel as rapidly as possible through a large-scale environment, it must rely upon stored knowledge of that portion of the environment that is occluded or otherwise beyond sensor range. Yet low mechanical accuracy and consequent positioning errors characteristic of mobile robots make it difficult in practice for a mobile robot to acquire an accurate metrical description of large scale space or accurately track a trajectory expressed in a global coordinate frame. Hence, methods for generating optimal feedforward control are not practical for application to high speed control of an autonomous mobile robot. This paper addresses the problem of acquiring and applying approximate information about environment geometry for high speed control of a mobile robot in circumstances of limited positioning accuracy. The robot combines relatively accurate information about the layout of nearby obstacles from current sensor information with approximate knowledge of the relative position of learned safe trajectory targets to travel to a goal at high speed. This method enables the robot to anticipate obstacle geometry beyond sensor range, yet can cope with substantial position estimation errors, disturbances, and minor changes in the environment.