  Autonomous mobile agents often operate in hazardous environments,
necessitating an awareness of safety. These agents can have non-linear,
stochastic dynamics that must be considered during planning to guarantee
bounded risk. Most state of the art methods require closed-form dynamics to
verify plan correctness and safety however modern robotic systems often have
dynamics that are learned from data. Thus, there is a need to perform efficient
trajectory planning with guarantees on risk for agents without known dynamics
models. We propose a "generate-and-test" approach to risk-bounded planning in
which a planner generates a candidate trajectory using an approximate linear
dynamics model and a validator assesses the risk of the trajectory, computing
additional safety constraints for the planner if the candidate does not satisfy
the desired risk bound. To acquire the approximate model, we use a variational
autoencoder to learn a latent linear dynamics model and encode the planning
problem into the latent space to generate the candidate trajectory. The VAE
also serves to sample trajectories around the candidate to use in the
validator. We demonstrate that our algorithm, LaPlaSS, is able to generate
trajectory plans with bounded risk for a real-world agent with learned dynamics
and is an order of magnitude more efficient than the state of the art.
