  This paper presents a neurosymbolic framework to solve motion planning
problems for mobile robots involving temporal goals. The temporal goals are
described using temporal logic formulas such as Linear Temporal Logic (LTL) to
capture complex tasks. The proposed framework trains Neural Network (NN)-based
planners that enjoy strong correctness guarantees when applying to unseen
tasks, i.e., the exact task (including workspace, LTL formula, and dynamic
constraints of a robot) is unknown during the training of NNs. Our approach to
achieving theoretical guarantees and computational efficiency is based on two
insights. First, we incorporate a symbolic model into the training of NNs such
that the resulting NN-based planner inherits the interpretability and
correctness guarantees of the symbolic model. Moreover, the symbolic model
serves as a discrete "memory", which is necessary for satisfying temporal logic
formulas. Second, we train a library of neural networks offline and combine a
subset of the trained NNs into a single NN-based planner at runtime when a task
is revealed. In particular, we develop a novel constrained NN training
procedure, named formal NN training, to enforce that each neural network in the
library represents a "symbol" in the symbolic model. As a result, our
neurosymbolic framework enjoys the scalability and flexibility benefits of
machine learning and inherits the provable guarantees from control-theoretic
and formal-methods techniques. We demonstrate the effectiveness of our
framework in both simulations and on an actual robotic vehicle, and show that
our framework can generalize to unknown tasks where state-of-the-art
meta-reinforcement learning techniques fail.
