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In this paper, a robot navigating an environment shared with humans isconsidered, and a cost function that can be exploited in $\text{RRT}^\text{X}$,a randomized sampling-based replanning algorithm that guarantees asymptoticoptimality, to allow for a safe motion is proposed. The cost function is a pathlength weighted by a danger index based on a prediction of human motionperformed using either a linear stochastic model, assuming constantlongitudinal velocity and varying lateral velocity, and a GMM/GMR-based model,computed on an experimental dataset of human trajectories. The proposedapproach is validated using a dataset of human trajectories collected in a realworld setting.

Safe Motion Planning for a Mobile Robot Navigating in Environments Shared with Humans