The motion planning problem of a single autonomous vehicle having a minimum turn radius constraint, visiting an ordered sequence of targets in an environment with polygonal obstacles, is addressed. Two types of vehicles are considered: aerial/ground vehicle - described by the Dubins/Reeds-Shepp vehicle models, respectively. The problem is posed in the form of a search tree by using the obstacles’ vertices, vehicle’s initial configuration, and the set of target points as nodes. The tree’s arcs are represented by the Dubins/Reed-Shepp paths without terminal angle constraint (relaxed paths) connecting two adjacent nodes. These relaxed paths - connecting an initial configuration and a destination, are calculated using a feedback algorithm. Due to the computational complexity of the problem a genetic algorithm is proposed. Additionally, two deterministic search algorithms are presented. A quick heuristic greedy algorithm which uses the visibility graph distances for estimating the remaining vehicle path and an exhaustive algorithm which provides optimal solution trajectories. The performance of the algorithms is demonstrated and compared through sample runs and a Monte Carlo study. Results confirm that the heuristic algorithm provides relatively good solution for a small radius turn vehicle, while the genetic algorithm offers a good trade-off between computational load and performance. © 2017, Springer Science+Business Media B.V.