Abstract: This paper pursues multi-goal motion planning, where the overall set of goals is divided into k groups and the virtual agent needs to visit at least one goal per group. We have developed a combined task and motion-planning approach which can work with ground and aerial vehicles whose motions are simulated by differential equations or by physics-based game engines. The proposed approach is based on a hybrid search, where the expansion of a motion tree in the continuous state space is guided by heuristic costs and generalized traveling salesman tours computed over a discrete abstraction. The discrete abstraction is obtained via a probabilistic roadmap constructed over a low-dimensional configuration space resulting from a simplified problem setting. By capturing the connectivity of the free configuration space and connecting the goals, the roadmap provides generalized traveling salesman tours that effectively guide the motion-tree expansion. Experiments demonstrate that the approach not only improves previous methodologies in terms of runtime and solution length but also that it is scalable with respect to both the number of goals and groups.