Neuro-Symbolic Embodied Task Planning

• The paper demonstrates that integrating symbolic planning with neural policies yields high success rates (90-95%) in robotic tasks with few demonstrations.
• The framework abstracts continuous sensorimotor data into symbolic representations, using STRIPS-based operators to enable clear, interpretable task decomposition.
• The integrated planning loop combines high-level discrete reasoning with low-level neural execution, enhancing adaptability and interpretability in embodied robotic environments.

A neuro-symbolic framework for embodied task planning integrates discrete symbolic abstractions with learned neural components for skill execution, thereby leveraging the compositional generalization and interpretability of symbolic planning and the data-driven adaptability of deep learning. These frameworks support the automatic discovery of symbolic representations, efficient task decomposition, robust high-level planning, and the grounding of plans via neural policies in robotic environments.

1. Symbolic Abstraction and State Representation

The foundation of the neuro-symbolic approach is the abstraction of the agent's continuous sensorimotor state and actions into a symbolic space. Let $\mathcal{S}$ denote the continuous state space (e.g., concatenated object features), $\mathcal{A}$ the continuous action space, $\mathcal{T}$ the set of object types, and $\mathcal{O}$ the set of current objects. The framework introduces a finite set of first-order predicates $\mathcal{P}$ of the form $$p: \Theta_p \rightarrow \{\mathsf{True}, \mathsf{False}\}$$, where each $\Theta_p\subseteq\mathcal{T}^k$.

The abstraction mapping $\psi$ transforms a physical state $s \in \mathcal{S}$ into its symbolic state $$\bar{s} = \psi(s, \mathcal{P}) = \{p(o_1,\dots,o_k) \mid p \in \mathcal{P},\ o_i \in \mathcal{O},\ p(o_1,\dots,o_k) \text{ holds in } s\}$$. Trajectories are abstracted by retaining time points where any predicate changes value, reducing the information to the symbolic transitions relevant for planning (Keller et al., 27 Mar 2025).

2. Operator Learning and Symbolic Planning

From demonstrations, the framework learns a collection of symbolic operators $\Sigma$, each in STRIPS form: $$\langle \mathrm{pre}_+, \mathrm{pre}_-, \mathrm{eff}_+, \mathrm{eff}_- \rangle$$. Operators define preconditions for applicability and effects for state transitions. The symbolic planning module formulates the task in PDDL and solves the abstract planning problem $(\bar{s}_0, \bar{s}_g, \Sigma)$, with start state $\bar{s}_0$ and goal $\bar{s}_g$, using off-the-shelf classical planners such as Fast Downward.

Symbolic plans are validated against demonstrations by selecting the top-$K$ plans and using a similarity metric (e.g., Levenshtein distance) to abstraction sequences from the dataset for increased robustness. The planner relies on the grounding provided by the discovered symbolic representation to ensure logical coherence and generalizability of plans (Keller et al., 27 Mar 2025).

3. Neural Skill Learning for Action Grounding

For each symbolic operator $\sigma_i \in \Sigma$, the framework learns a neuro-symbolic skill $\pi^i = (g^i, f^i)$, where $g^i$ is a subgoal sampler proposing continuous targets consistent with the operator's effects, and $f^i$ is a subgoal-conditioned neural policy mapping current (transformed) state features and the subgoal to a low-level action.

Demonstrations are segmented according to symbolic transitions, and for each applicable segment, tuples of ($s$, $a$, subgoal) are stored in operator-specific datasets. Controllers $f^i_\theta$ are trained via behavior cloning with a squared error loss, while subgoal samplers $g^i$ employ non-parametric density estimation over observed goal embeddings. This design supports efficient skill acquisition and ensures that neural execution remains tightly aligned with symbolic task structure (Keller et al., 27 Mar 2025).

4. Integrated Planning and Execution Loop

The system interleaves symbolic planning and neural skill execution:

1. A full symbolic plan $$\pi_\text{sym} = (\hat{\sigma}_1, \dots, \hat{\sigma}_n)$$ is produced.
2. For each symbolic action $\hat{\sigma}_i$:
   • The relevant state features are extracted, and a subgoal $s^{(i)}_g$ is sampled.
   • While the operator’s effects are unmet in the current state, the neural controller $f^i_\theta$ acts towards the subgoal.
   • If the neural policy fails to make progress within a threshold, the system triggers replanning.

At each layer, interfaces handle the conversion between symbolic object arguments and their corresponding neural features (e.g., relative poses), ensuring consistent symbolic-to-neural grounding (Keller et al., 27 Mar 2025).

5. Empirical Evaluation and Generalization

The neuro-symbolic framework has been validated extensively in simulated robotics (MuJoCo/robosuite), tackling tasks such as block stacking, pouring, and painting with a Panda manipulator. Experimental conditions included novel initial poses, new goal permutations, and increased object counts beyond the training set.

Key results show that with only 100 demonstrations, the approach achieves $\sim90\%$ success rates across all test scenarios; at 300 demonstrations, success rates exceed $95\%$, significantly outperforming both pure neural (hierarchical neural net) and purely symbolic (predicate selection ablation) baselines. Additionally, the approach supports interpretable plan inspection—both at the predicate and operator level—via human-readable PDDL and visual overlay of learned predicates, facilitating interpretability and diagnostics (Keller et al., 27 Mar 2025).

6. Interpretability, Data Efficiency, and Limitations

The explicit structure of the symbolic abstraction allows not only interpretability of learned plans and skills but also provides strong generalization to novel compositions and configurations due to compositionality and logical reasoning. Data efficiency stems from the ability of the symbolic planner to synthesize unseen behavior through recombination of learned abstractions. However, limitations include reliance on accurate abstraction/discovery from demonstrations, potential brittleness to poor predicate induction, and the complexity of grounding symbolic-state transitions in high-dimensional, noisy environments.

Future directions entail tighter integration of predicate learning with visual-LLMs, online abstraction refinement, and automatic operator naming and schema discovery to increase scalability and robustness, especially for settings with greater perceptual aliasing or partial observability (Keller et al., 27 Mar 2025).