LTLDoG: Satisfying Temporally-Extended Symbolic Constraints for Safe Diffusion-Based Planning

Operating effectively in complex environments while complying with specified constraints is crucial for the safe and successful deployment of robots that interact with and operate around people. In this letter, we focus on generating long-horizon trajectories that adhere to static and temporally-extended constraints/instructions at test time. We propose a data-driven diffusion-based framework, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LTLDoG</small>, that modifies the inference steps of the reverse process given an instruction specified using finite linear temporal logic (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text {LTL}_{f}$</tex-math></inline-formula>). <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LTLDoG</small> leverages a satisfaction value function on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text {LTL}_{f}$</tex-math></inline-formula> and guides the sampling steps using its gradient field. This value function can also be trained to generalize to new instructions not observed during training, enabling flexible test-time adaptability. Experiments in robot navigation and manipulation illustrate that the method is able to generate trajectories that satisfy formulae that specify obstacle avoidance and visitation sequences.