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

TL;DR

LTLDoG is a diffusion-based framework that generates long-horizon robot trajectories satisfying complex temporal constraints specified in linear temporal logic, enabling safe and adaptable planning in complex environments.

Contribution

It introduces a novel diffusion-based approach guided by a satisfaction value function for LTL constraints, allowing flexible and generalizable trajectory planning.

Findings

Successfully generates trajectories satisfying obstacle avoidance and visitation constraints.

Demonstrates adaptability to new, unseen instructions at test time.

Effective in robot navigation and manipulation tasks.

Abstract

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 work, we focus on generating long-horizon trajectories that adhere to novel static and temporally-extended constraints/instructions at test time. We propose a data-driven diffusion-based framework, LTLDoG, that modifies the inference steps of the reverse process given an instruction specified using finite linear temporal logic ($\text{LTL}_f$). LTLDoG leverages a satisfaction value function on $\text{LTL}_f$ 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. Code and supplementary material are available online at https://github.com/clear-nus/ltldog.