UniDomain: Unified PDDL Robotics Planning

• UniDomain is a neurosymbolic planning framework that pre-trains a unified PDDL domain from robot manipulation demonstrations to enable zero-shot planning on unseen tasks.
• It employs a three-phase approach—domain pretraining, fusion into task-specific meta-domains, and online planning—using energy-based keyframe extraction and LLM-assisted revisions.
• Empirical results show high success rates and improved plan optimality over LLM-only strategies, emphasizing its practical impact on long-horizon robotic task planning.

UniDomain denotes a framework that pre-trains a unified Planning Domain Definition Language (PDDL) domain from real-world robot manipulation demonstrations and uses that domain for online robotic task planning. In the supplied literature, it is defined by three phases—domain pretraining, domain fusion, and online planning—and is positioned as a response to the limits of LLM- and VLM-only planners on long-horizon, compositional tasks with implicit physical constraints (Ye et al., 29 Jul 2025).

1. Definition and conceptual scope

UniDomain is a neurosymbolic planning framework in which symbolic world knowledge is learned offline from demonstrations rather than handwritten as a fixed domain. Its central object is a unified PDDL domain built from many small “atomic domains,” each corresponding to the symbolic structure extracted from a single robot manipulation demonstration. The resulting symbolic substrate is then specialized into task-class “meta-domains” and used for zero-shot planning on unseen tasks (Ye et al., 29 Jul 2025).

The framework is explicitly motivated by a gap between foundation-model priors and executable long-horizon planning. LLMs and VLMs are described as strong at language and perception but weak at reliable precondition–effect modeling, long-horizon compositionality, and explicit symbolic grounding. UniDomain addresses this by moving domain acquisition into an offline pretraining stage grounded in real robot executions, so that online planning operates over validated symbolic operators and predicates rather than over action structure invented ad hoc from language alone (Ye et al., 29 Jul 2025).

A related but distinct development is UniPlan, which treats a UniDomain-style learned tabletop PDDL domain as a base domain and programmatically extends it to mobile manipulation with navigation, door traversal, bimanual coordination, and action costs. This establishes UniDomain as the symbolic manipulation core rather than a complete mobile-manipulation stack (Ye et al., 9 Feb 2026).

2. Domain pretraining from demonstrations

UniDomain’s pretraining phase begins from 12,393 robot manipulation videos from the DROID dataset. For each demonstration, it performs energy-based keyframe extraction, where frame $t$ is converted to grayscale $I_t \in \mathbb{R}^{W \times H}$ and assigned energy

$E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$

With a sliding window of size $K$, frame $t$ is selected if $E_t$ is a local maximum or minimum within $[t-K, t+K]$. The paper states that this procedure is far cheaper than CLIP/SigLIP embedding-based alternatives and empirically yields better single-pass domain quality (Ye et al., 29 Jul 2025).

From ordered keyframes and the demonstration instruction, a VLM proposes operator names, preconditions, effects, and any new predicates required by each transition. An LLM then revises the resulting grounded domain to ensure syntactic correctness, predicate reuse, naming consistency, and removal of redundant or inconsistent predicates. This revised domain is not accepted directly. UniDomain subjects it to two nested validation loops: a solvability check, where the LLM generates $K$ synthetic test problems and a PDDL planner evaluates whether the domain solves them, and a solution-verification check, where the hardest solvable plan is examined by an LLM for physical plausibility relative to the instruction. The default parameters reported are $K=5$, threshold $\theta=0.6$, and a maximum of $I_t \in \mathbb{R}^{W \times H}$0 refinement iterations (Ye et al., 29 Jul 2025).

Each accepted atomic domain is represented as a bipartite causal graph

$I_t \in \mathbb{R}^{W \times H}$1

where predicate nodes and operator nodes are connected by precondition and effect edges. Aggregating all atomic domains yields a unified symbolic knowledge graph with 3,137 operators, 2,875 predicates, and 16,481 causal edges. The paper states that these operators are grouped into 170 semantic categories and connected through shared predicates such as object-state and spatial relations, which is the basis for compositional generalization (Ye et al., 29 Jul 2025).

3. Fusion into task-specific meta-domains

The unified domain is intentionally broad, but the paper characterizes it as too large and somewhat noisy for direct planning. UniDomain therefore retrieves a set of relevant atomic domains for a target task class and fuses them into a compact meta-domain. In the reported experiments, retrieval is manual but lightweight: for a given evaluation domain, 40 demonstrations are selected whose descriptions and scenes resemble the target tasks (Ye et al., 29 Jul 2025).

Fusion is hierarchical. Given retrieved atomic domains $I_t \in \mathbb{R}^{W \times H}$2, UniDomain builds a binary tree and recursively merges sibling domains via

$I_t \in \mathbb{R}^{W \times H}$3

Predicate merging uses MPNet text embeddings and cosine similarity

$I_t \in \mathbb{R}^{W \times H}$4

with candidate pairs filtered below $I_t \in \mathbb{R}^{W \times H}$5 before LLM equivalence checking. Operator merging proceeds after predicate alignment, again using embedding similarity on operator names with threshold $I_t \in \mathbb{R}^{W \times H}$6, followed by LLM judgment on names, preconditions, and effects (Ye et al., 29 Jul 2025).

When two operators are judged functionally equivalent, the merged operator typically uses unioned constraints:

$I_t \in \mathbb{R}^{W \times H}$7

The paper presents this as a way to preserve completeness while improving causal connectivity. For the reported benchmarks, fusion from 40 retrieved demonstrations produced a meta-domain with 78 predicates and 61 operators, a substantial reduction from the unified domain while retaining cross-task compositional structure (Ye et al., 29 Jul 2025).

A key negative result is that direct LLM fusion without the structured predicate/operator alignment procedure fails completely in the reported ablations: the fused domains contain structural or syntax errors and are unusable. Likewise, using only individual atomic domains without fusion yields only 19% task success, which the paper interprets as evidence that compositional generalization depends on the fused symbolic layer rather than mere retrieval (Ye et al., 29 Jul 2025).

4. Planning pipeline and symbolic filtering

Online planning in UniDomain is performed with a task image, an instruction $I_t \in \mathbb{R}^{W \times H}$8, and a fused meta-domain $I_t \in \mathbb{R}^{W \times H}$9. The LLM/VLM first proposes an initial problem

$E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$0

from which the set of predicates used in the initial and goal states, $E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$1, is extracted. UniDomain then filters operators by relevance using the causal graph structure. It defines

$E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$2

$E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$3

and sets

$E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$4

A refined problem is then generated as

$E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$5

and solved by a classical planner, specifically Fast Downward in the reported implementation (Ye et al., 29 Jul 2025).

The paper also states that predicates are pre-organized into four semantic groups: object category descriptors, state/attribute predicates, spatial relations, and affordance-related predicates. This grouping is not decorative; ablation results show that removing grouping hurts performance, especially on the Combination domain, while removing filtering sharply reduces success on long-horizon domains such as BlockWorld (Ye et al., 29 Jul 2025).

The planning formalism remains classical. A planning instance is written as $E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$6, with domain $E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$7 and problem $E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$8. UniDomain relies on deterministic STRIPS-style operators, fully observed states, and PDDL 1.0 expressivity. The paper explicitly notes that there is no support for explicit temporal constraints, numeric fluents, or uncertainty, and suggests PDDL 2.1, PPDDL, and RDDL as future directions (Ye et al., 29 Jul 2025).

5. Empirical performance and relation to UniPlan

UniDomain is evaluated on 100 long-horizon tasks across four unseen domains: BlockWorld, Desktop, Kitchen, and Combination. The reported metrics are Success Rate, Success-weighted Path Length,

$E(I_t) = \sum_{i=1}^W \sum_{j=1}^H I_t(i,j)^2.$9

and Optimality Rate,

$K$0

Against LLM/VLM-only baselines such as Code-as-Policies, ReAct, and VLM-CoT, and LLM+PDDL baselines such as ISR-LLM, VLM-PDDL, and BoN-iVML, UniDomain reports 85% Success Rate and 83% $K$1. The paper summarizes the overall gain as up to 58% higher task success and 160% improvement in plan optimality over state-of-the-art LLM and LLM-PDDL baselines (Ye et al., 29 Jul 2025).

The ablations sharpen the interpretation of these gains. Removing LLM revision increases refinement iterations from about 0.49 to about 1.36; removing solvability checking leaves syntactically valid but often unsolvable domains; removing solution verification permits physically implausible plans; removing all closed-loop feedback produces very poor domains. In the one-shot setting, the paper reports 28% success for energy-based keyframes and 15% for CLIP-like similarity keyframes, with 47.8s versus 0.6s per demonstration, respectively, in computation time (Ye et al., 29 Jul 2025).

UniPlan extends this lineage from tabletop manipulation to long-horizon mobile manipulation. It takes a UniDomain-style base domain $K$2 and systematically augments it by AST-based rewriting. The extension injects predicates such as rob_at_node ?r ?n and obj_at_node ?o ?n, appends move_robot and open_door, lifts hand_free ?r and holding ?r ?o to hand-indexed variants, and introduces $K$9 with (:metric minimize (total-cost)). This makes UniDomain the symbolic manipulation backbone, while UniPlan adds the “world around the table” together with navigation, door modeling, and bimanual coordination (Ye et al., 9 Feb 2026).

6. Terminological divergence across the supplied literature

The supplied sources use the string “UniDomain” or closely related terminology in several unrelated research areas. The robotics framework is the only source in which “UniDomain” is the formal name of a system. In the other cases, the supplied material uses the term as an interpretive label for distinct notions.

Source	Field	Meaning in the supplied material
(Nietz, 2014)	Magnetism	A unidomain ferromagnet: a single magnetic domain with spatially uniform magnetization
(Jong et al., 2024)	Univalent foundations	A suggested “univalent domain theory” reconstruction of continuous and algebraic domains
(Chang et al., 2017)	Commutative algebra	Graded integral domains that are UMT-domains
(Fagella et al., 2017)	Complex dynamics	A suggested “UniDomain” reading as a univalent wandering domain
(Ye et al., 29 Jul 2025)	Robotics	A framework for pretraining a unified PDDL domain from demonstrations
(Ye et al., 9 Feb 2026)	Robotics	A mobile-manipulation planner that explicitly builds on UniDomain-style base domains

In ferromagnetism, the relevant term is “unidomain ferromagnet,” meaning a sample that remains in a single magnetic domain throughout the process, so that the phase transition and driven dynamics proceed via coherent rotation of a uniform magnetization vector rather than via domain nucleation or wall motion (Nietz, 2014). In univalent foundations, the supplied exposition treats “UniDomain” as a shorthand for a predicative, constructive reconstruction of continuous and algebraic domain theory in HoTT/UF, including continuity via ind-completion, small bases, ideal completion, and Scott’s $K$3 as an algebraic dcpo with a small basis (Jong et al., 2024).

In commutative algebra, the related object is not “UniDomain” but graded integral domains that are UMT-domains, with characterizations involving homogeneous maximal $K$4-ideals, quasi-Prüfer localizations, valuation domains, and PvMD criteria (Chang et al., 2017). In complex dynamics, the supplied discussion uses “UniDomain” to suggest a wandering Fatou component whose entire forward orbit is mapped univalently; the cited result constructs an entire function in class $K$5 with a wandering domain $K$6 such that $K$7 is univalent for all $K$8, while each component in the orbit is bounded and surrounded by the postcritical set (Fagella et al., 2017).

A common misconception would be to treat these usages as a single concept. The supplied literature does not support that. What it does support is terminological overlap across fields, with the robotics framework providing the formal system named “UniDomain,” and the remaining cases supplying unrelated notions built around “unidomain,” “domain theory,” “UMT-domains,” or “univalent wandering domains” (Ye et al., 29 Jul 2025).