Motion planning is a difﬁcult and widely studied problem in robotics. Current research aims not only to ﬁnd feasible paths, but to ensure paths have certain properties, e.g., shortest or safest paths. This is difﬁcult for current state-of-the-art sampling-based techniques as they typically focus on simply ﬁnding any path. Despite this difﬁculty, sampling-based techniques have shown great success in planning for a wide range of applications. Among such planners, Rapidly-Exploring Random Trees (RRTs) search the planning space by biasing exploration toward unexplored regions. This paper introduces a novel RRT variant, Medial Axis RRT (MARRT), which biases tree exploration to the medial axis of free space by pushing all conﬁgurations from expansion steps towards the medial axis. We prove that this biasing increases the tree’s clearance from obstacles. Improving obstacle clearance is useful where path safety is important, e.g., path planning for robots performing tasks in close proximity to the elderly. Finally, we experimentally analyze MARRT, emphasizing its ability to effectively map difﬁcult passages while increasing obstacle clearance, and compare it to contemporary RRT techniques.