We have recently developed an algorithm for generating complex dynamically-feasible maneuvers for autonomous vehicles traveling at high speeds over large distances. Our approach is based on performing anytime incremental search on a multi-resolution, dynamically-feasible lattice state space. It has been implemented on an autonomous passenger vehicle that competed in, and won, the Urban Challenge. Much of the speed and robustness of our approach owes to the clever design and use of grid-based cost maps that were used throughout the planning process. In this paper, we explain the design and use of these various grid-based cost maps.