Sleiman Safaoui, Tyler H Summers, ICRA 2024.
Keywords: Risk-based planning, Wasserstein-based ambiguity set, DR-CVaR, Uncertain environments
Overview
Planning a trajectory for an autonomous robot in the presence of dynamics obstacles is a challenging problem. It involves having to predict how the obstacles will move and choosing a collision-free path.
Modern motion planning solutions (e.g. ones based on machine learning) can, to some extent, capture the intention of the dynamic obstacles when generating a motion plan. However, these motion plans generally do not provide hard safety guarantees.
To address this issue, we propose the usage of a safety filter before passing down the reference trajectory from the motion planner to the controller, as shown in the figure below. The safety filter is an optimization-based module that makes corrections to the reference trajectory to enforce the satisfaction of safety requirements.
We assume that the safety filter has access to a motion prediction module that generates sample trajectories for the obstacle vehicles. These sample trajectories capture some of the uncertainty in the obstacles’ motion. However, since these trajectories are only samples and do not capture the true distribution of the uncertainty, we rely on tools from distributionally robust optimization (DRO) to account for that.
In particular, we formulate an empirical distribution from the samples and consider a Wasserstein-based ambiguity set around the empirical distribution. This ambiguity set consists of all distributions that are within some epsilon distance of the empirical distribution where the distance is measured using the Wasserstein metric.
The notion of safety we use in this work is the CVaR risk metric: the conditional value-at-risk. CVaR is a metric that measures the average of the worst cases. Thus, CVaR not only limits the probability of unsafe events, but also puts a bound on the level of danger or risk in the worst cases.
By computing the CVaR with respect to the ambiguity set, we get a DR-CVaR safety constraint that ensures that the corrected trajectory is safe even when the distribution is unknown.
Through numerical simulations, we show that the proposed safety filtering solution can run in real time and ensure the safety of the ego vehicle even in edge cases. An example of that is shown in the figure below where the ego vehicle (in blue) navigates around the other three obstacles and safely reaches its goal on the right side.
For more details, check out our paper on arXiv! (the ICRA24 version will soon be on IEEE Xplore as well.)