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We present a new sampling-based algorithm for complete motion planning. Our algorithm relies on computing a star-shaped roadmap of the free space. We partition the free space into star-shaped regions such that a single point, called the guard, can see every point in the star-shaped region. The resulting set of guards capture the intraregion connectivity—the connectivity between points belonging to the same star-shaped region. We capture the inter-region connectivity by computing connectors that link guards of adjacent regions. The guards and connectors are combined to obtain the star-shaped roadmap. We present an efficient algorithm to compute the roadmap in a deterministic manner without explicit computation of the free space. We show that the star-shaped roadmap captures the connectivity of the free space, thereby enabling us to perform complete motion planning. Our approach is relatively simple to implement