A Value Function Space Approach for Hierarchical Planning With Signal Temporal Logic Tasks

Signal Temporal Logic (STL) has emerged as an expressive formal language for reasoning intricate task planning objectives. However, existing STL-based methods often assume full observation and known dynamics of the system, which imposes constraints on real-world applications. To address this challenge, we propose a hierarchical planning framework that starts by constructing the Value Function Space (VFS) for state and action abstraction, which embeds functional information about affordances of the low-level skills. Subsequently, we utilize a neural network to approximate the dynamics in the VFS and employ sampling based optimization to synthesize high-level skill sequences that maximize the robustness measure of the given STL tasks in the VFS. Then those skills are executed in the low-level environment. Empirical evaluations in the Safety Gym and ManiSkill environments demonstrate that our method accomplish the STL tasks without further training in the low-level environments, substantially reducing the training burdens.