  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.
