Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are incorporated into the planning problem to provide probabilistic safety guarantees by imposing an upper bound on the collision probability of the planned trajectory. Yet, this results in overly conservative behavior on the grounds that the gap between the obtained risk and the specified upper limit is not explicitly restricted. To address this issue, we propose a real-time capable approach to quantify the risk associated with planned trajectories obtained from multiple probabilistic planners, running in parallel, with different upper bounds of the acceptable risk level. Based on the evaluated risk, the least conservative plan is selected provided that its associated risk is below a specified threshold. In such a way, the proposed approach provides probabilistic safety guarantees by attaining a closer bound to the specified risk, while being applicable to generic uncertainties of moving obstacles. We demonstrate the efficiency of our proposed approach, by improving the performance of a state-of-the-art probabilistic planner, in simulations and experiments using a mobile robot in an environment shared with humans.
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