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In this work, we address the motion planning problem for autonomous vehicles through a new lattice planning approach, called Feedback Enhanced Lattice Planner (FELP). Existing lattice planners have two major limitations, namely the high dimensionality of the lattice and the lack of modeling of agent vehicle behaviors. We propose to apply the Intelligent Driver Model (IDM) as a speed feedback policy to address both of these limitations. IDM both enables the responsive behavior of the agents, and uniquely determines the acceleration and speed profile of the ego vehicle on a given path. Therefore, only a spatial lattice is needed, while discretization of higher order dimensions is no longer required. Additionally, we propose a directed-graph map representation to support the implementation and execution of lattice planners. The map can reflect local geometric structure, embed the traffic rules adhering to the road, and is efficient to construct and update. We show that FELP is more efficient compared to other existing lattice planners through runtime complexity analysis, and we propose two variants of FELP to further reduce the complexity to polynomial time. We demonstrate the improvement by comparing FELP with an existing spatiotemporal lattice planner using simulations of a merging scenario and continuous highway traffic. We also study the performance of FELP under different traffic densities.