Fast Task Planning with Neuro-Symbolic Relaxation

TL;DR

Flax tackles long-horizon robotic planning under large object sets by coupling a Graph Neural Network-based object-importance predictor with a symbolic relaxation and corrective complementation pipeline. The method quickly prunes the task, then uses a rule-relaxed rough plan to recover potentially important objects, and finally applies complementary rules to restore consistency, enabling reliable planning within strict time budgets. Empirical results on MazeNamo, Isaac Sim, and real-world trials show Flax improves average success rate and reduces planning time relative to previous neuro-symbolic baselines, with especially large gains on harder tasks and successful sim-to-real transfer without additional fine-tuning. This approach offers a practical path toward fast, scalable, long-horizon planning in complex, real-world environments.

Abstract

Real-world task planning requires long-horizon reasoning over large sets of objects with complex relationships and attributes, leading to a combinatorial explosion for classical symbolic planners. To prune the search space, recent methods prioritize searching on a simplified task only containing a few ``important" objects predicted by a neural network. However, such a simple neuro-symbolic (NeSy) integration risks omitting critical objects and wasting resources on unsolvable simplified tasks. To enable Fast and reliable planning, we introduce a NeSy relaxation strategy (Flax), combining neural importance prediction with symbolic expansion. Specifically, we first learn a graph neural network to predict object importance to create a simplified task and solve it with a symbolic planner. Then, we solve a rule-relaxed task to obtain a quick rough plan, and reintegrate all referenced objects into the simplified task to recover any overlooked but essential elements. Finally, we apply complementary rules to refine the updated task, keeping it both reliable and compact. Extensive experiments are conducted on both synthetic and real-world maze navigation benchmarks where a robot must traverse through a maze and interact with movable obstacles. The results show that Flax boosts the average success rate by 20.82\% and cuts mean wall-clock planning time by 17.65\% compared with the state-of-the-art NeSy baseline. We expect that Flax offers a practical path toward fast, scalable, long-horizon task planning in complex environments.

Figures (6)

• Figure 1: Flax achieves high success rates and fast planning on MazeNamo tasks. The chart shows that Flax significantly outperforms Fast Downward (Pure Plan)helmert2006fast and PLOIsilver2021planning in both success rate and planning speed for expert-level tasks.
• Figure 2: A typical maze navigation instance and automatically synthesized plan. Heavy boxes (push-only): blue squares; Light boxes (push/pick-and-place): yellow squares; Walls: grey squares (cannot be manipulated); Empty space: black squares; Goal: green cell; Robot: red triangle. Each snapshot shows the state immediately after the labelled operator executes.
• Figure 3: Flax pipeline.Pre-processing: convert the task to PDDL and encode it as a relational graph $\mathcal{G}$. Training: a symbolic planner provides an optimal plan; objects in the plan are labeled 1 as important, others 0. A GNN learns these labels from $\mathcal{G}$ with BCE loss. Planning (budget $B$): planning runs in three steps. Step 1: keep objects with importance $>q$ to form $\tau_{\mathcal{O}_1}$; lower $q$ until a plan $\mu$ is found or time $\Delta t_1$ expires. Step 2: if Step 1 fails, solve a rule-relaxed task within $\Delta t_2$ to obtain rough plan $\mu_r$; merge its objects with $\mathcal{O}_1$ to get $\mathcal{O}_2$. Step 3: lightweight rules restore consistency, yielding $\mathcal{O}_3$. Remaining time plans on $\tau_{\mathcal{O}_3}$; the plan is then validated on the original task.
• Figure 4: Importance set progression: pruning in Step 1 keeps $\{p_{15},p_{19}\}$, then lowering $\tau$ adds $\{p_{21}, o_{22}\}$; the rough plan injects $p_{20}$ into $\mathcal{O}_{1}$ to form $\mathcal{O}_{2}$; symbolic complementation adds $o_{21}$, yielding $\mathcal{O}_{3}$ that defines the solvable simplified task.
• Figure 5: IsaacSim Experiments. (a) Scene abstraction in a robotics environment. Obstacles and positions are mapped to symbols. (b)(c)(d) IsaacSim tasks involving different actions.