Neurosymbolic Motion and Task Planning for Linear Temporal Logic Tasks

This article 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 bounded linear temporal logic (LTL) and co-safe 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, temporal logic formula, and errors in the dynamical models of the robot) is not available 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 NNs 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 NN 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 unseen tasks where state-of-the-art meta-reinforcement learning techniques fail.