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Natural language instructions often exhibit sequential constraints rather than being simply goal-oriented, for example “go around the lake and then travel north until the intersection”. Existing approaches map these kinds of natural language expressions to Linear Temporal Logic expressions but require an expensive dataset of LTL expressions paired with English sentences. We introduce an approach that can learn to map from English to LTL expressions given only pairs of English sentences and trajectories, enabling a robot to understand commands with sequential constraints. We use formal methods of LTL progression to reward the produced logical forms by progressing each LTL logical form against the groundtruth trajectory, represented as a sequence of states, so that no LTL expressions are needed during training. We evaluate in two ways: on the SAIL dataset, a benchmark artificial environment of 3,266 trajectories and language commands as well as on 10 newly-collected real-world environments of roughly the same size. We show that our model correctly interprets natural language commands with 76.9% accuracy on average. We demonstrate the end-to-end process in real-time in simulation, starting with only a natural language instruction and an initial robot state, producing a logical form from the model trained with trajectories, and finding a trajectory that satisfies sequential constraints with an LTL planner in the environment.

Grounding Language to Non-Markovian Tasks with No Supervision of Task Specifications