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Discovering State and Action Abstractions for Generalized Task and Motion Planning
Aidan Curtis, Tom Silver, Joshua B. Tenenbaum, Tomas Lozano-Perez, Leslie Pack Kaelbling
TL;DR
Robotic TAMP generalizes to novel tasks but is difficult to scale because each problem entails large combinatorial and continuous search. GENTAMP learns task-specific abstract policies from a few plans and uses them to guide TAMP search, increasing search speed in large domains. Its abstract plans cannot be executed greedily step by step when geometric or physical constraints make earlier choices obstruct later ones.
Problem
TAMP generalizes to novel environments and tasks, but its large combinatorial and continuous search makes scaling difficult.
Source: Introduction · p. 1Method
GENTAMP learns task-specific abstract policies from example plans and compiles them into action and ordering constraints that guide TAMP search.
Source: Introduction · p. 2, Background · p. 3Results
GENTAMP’s simple learned policies increase TAMP search speed in large domains, supporting more scalable and generalizable long-horizon robotic planning.
Source: Conclusion · p. 8Takeaways & Limitations
The learned policies apply to problems with arbitrary numbers of objects and initial states from only a few example plans.
Source: Conclusion · p. 7Abstract plans cannot be executed greedily step by step because geometric and physical constraints can make earlier placements obstruct later ones.
Source: Background · p. 3
Abstract
from arXiv · showhide
Generalized planning accelerates classical planning by finding an algorithm-like policy that solves multiple instances of a task. A generalized plan can be learned from a few training examples and applied to an entire domain of problems. Generalized planning approaches perform well in discrete AI planning problems that involve large numbers of objects and extended action sequences to achieve the goal. In this paper, we propose an algorithm for learning features, abstractions, and generalized plans for continuous robotic task and motion planning (TAMP) and examine the unique difficulties that arise when forced to consider geometric and physical constraints as a part of the generalized plan. Additionally, we show that these simple generalized plans learned from only a handful of examples can be used to improve the search efficiency of TAMP solvers.
Introduction
Robotic TAMP must account for geometric and physical constraints, but its combinatorial and continuous search makes scaling difficult. GENTAMP brings generalized planning to continuous robotics by learning task-specific plans from examples.
Introduction
- GENTAMP’s abstract LOAD policy repeats picking and placing objects on the tray until it is full or none remain, then grasps the tray.Figure 1 illustrates this task-specific policy.Source: Figure 1 · p. 1
- TAMP’s combinatorial and continuous search limits its scalability, despite its generalizability to novel environments and tasks.Robotic planning also needs to account for geometric and physical constraints while selecting goal-directed actions.Source: Introduction · p. 1
- Generalized planning learns compact, reusable plans from a few examples to avoid repeating costly searches across problem instances.The plans can cover instances with varying numbers of objects, but existing discrete methods do not handle continuous features such as capacity or collision constraints.Source: Introduction · pp. 1–2
- GENTAMP applies generalized planning to continuous robotic domains, where plans may require complex continuous features.The paper presents a framework for learning and executing generalized plans in mixed discrete-continuous environments.Source: Introduction · p. 2
- The paper proposes learning features and abstractions from examples, then using them to form generalized plans for continuous TAMP.Its stated contributions also include formulating generalized TAMP and executing learned plans on unseen problems.Source: Introduction · p. 2
Background
The paper formulates generalized TAMP over tasks described by logical specifications of possible initial states and goals. Since geometry and physics constrain execution, it uses per-task constrained domains to guide TAMP search rather than executing abstract plans greedily.
Task and motion planning
- TAMP extends planning with sampled entities and certified predicates from continuous spaces, adding samples during search until a classical planner can achieve the goal.The paper uses PDDLSTREAM as its implementation basis while noting that the overall approach is compatible with other TAMP methods.Source: Background · p. 3
Generalized Task and Motion Planning
- Generalized TAMP tasks specify sets of possible initial states and goals through quantified logical expressions, allowing instances with arbitrary numbers of entities.Task demonstrations convey the task’s logical description, which is not known in advance.Source: Background · p. 3
- A generalized TAMP planner constructs a constrained domain for each task so a TAMP solver can find ground plans efficiently for conforming instances.The constraints encode the abstract plan’s action and ordering requirements.Source: Background · p. 3
- Unlike classical generalized planning, generalized TAMP uses one lifted domain across tasks and includes continuous geometric and physical parameters in task specifications.Because abstract plans cannot be executed greedily under geometry and physics constraints, the paper evaluates search speed across test instances.Source: Background · p. 3
Working example
- The working LOAD domain represents object placement and collision-free relationships with predicates, while its task requires placing objects on a tray or filling it.An optimal policy repeatedly picks and places an object until the tray is full, then picks up the tray.Source: Background · p. 3
GENTAMP Training
GENTAMP learns generalized policies by extracting candidate features from example TAMP plans, selecting an approximately valid abstraction, and planning over its abstract states and actions. Its feature grammar combines symbolic predicates with sampled geometric entities, while continuous-state sampling limits guarantees of correctness.
GENTAMP Training
- The selected features and an initial state define an abstract FOND problem whose solution is a policy that returns an abstract action from feature evaluations.The learned policy can then be applied to novel instances, including those with varying numbers of entities.Source: GENTAMP Training · pp. 4, 6
- Features map states to Boolean values or qualitative numeric values, forming abstract states and actions that can be planned over with a nondeterministic planner.Decreasing a numeric feature can abstractly either reach zero or remain positive, making derived actions nondeterministic.Source: GENTAMP Training · pp. 4, 6
- Because TAMP state spaces are continuous, high-dimensional, and nonlinear, abstractions are learned from sampled transitions rather than exhaustively verified across every reachable transition.Correctness of features quantifying over continuous variables is not guaranteed for finite samples; under uniform sampling, evaluations are correct in the limit of infinite samples.Source: GENTAMP Training · pp. 4–5
- A TAMP solver supplies example plans whose transitions are used to build a pool of candidate features, including features mixing symbolic predicates and sampled geometric entities.The grammar supports high-arity predicates and alternating quantifiers; candidates are bounded by a complexity limit.Source: GENTAMP Training · pp. 4–5
- The feature grammar builds per-entity logical expressions from predicates, named variables, negation, conjunction, implication, and chained quantifiers.The resulting numeric feature counts entities satisfying a quantified concept, such as objects that fit on a tray without collision.Source: GENTAMP Training · p. 5, Table 1 · p. 5
- A weighted Max-SAT solver selects a low-complexity feature subset intended to satisfy soundness, completeness, and goal-distinguishability on the example transitions.Evaluating numeric features over all example transitions makes SAT-theory construction typically the slowest learning stage.Source: GENTAMP Training · pp. 4–5
Using a Generalized Task and Motion Plan
GENTAMP embeds a learned abstract policy into TAMP by constraining operator order and abstract preconditions and effects. The resulting search jointly considers action skeletons and continuous-parameter bindings.
Using a Generalized Task and Motion Plan
- Directly choosing feasible ground actions with matching abstract effects is insufficient because geometric and physical constraints also govern execution.In LOAD, the constrained specification excludes placing an object on the table when the policy requires increasing the number of objects on the tray.Source: Using a Generalized Task and Motion Plan · p. 6
- To execute a generalized plan, GENTAMP builds planning operators encoding its action ordering and abstract preconditions and effects, then supplies them to PDDLSTREAM.This supports concurrent search over plan skeletons and continuous-parameter bindings.Source: Using a Generalized Task and Motion Plan · p. 6
Experiments
GENTAMP is evaluated on four continuous robotic TAMP tasks with policies learned from examples. Its execution speed greatly exceeds a state-of-the-art TAMP algorithm, with the speed difference increasing exponentially with object count.
Experiments
- For Unstack, the learned policy repeatedly moves a clear block onto the table until no stacked blocks remain.The task is to remove all stacked blocks and place them on the table.Source: Experiments · p. 6
- For Sort, the learned policy places green objects in the green region before red objects in the red region, although no example plan used that order.The task is to sort objects into similarly colored regions.Source: Experiments · p. 6
- For Clutter, the learned policy moves objects blocking access to a target until it can be reached, avoiding task-specific engineering described as previously needed for large problems.Features from small examples guide search toward objects blocking trajectories.Source: Experiments · p. 6
- For Transport, the learned policy fills a tray until its physical capacity is reached, carries it to the destination, and unloads it.The plan reasons about object geometry to determine whether more objects fit on the tray.Source: Experiments · p. 6
- GENTAMP greatly outperforms a state-of-the-art TAMP algorithm in execution speed, and the speed difference increases exponentially with object count.Figure 3 compares planning speed with standard TAMP and partial skeleton across four tasks.Source: Experiments · p. 6
Related work
Prior generalized-planning work primarily addresses discrete symbolic domains, while robotics learning approaches have limited generalization from few examples to varied object counts and geometric configurations. Other TAMP acceleration methods reduce or bias search, whereas GENTAMP targets tasks where all objects, operators, and state-space regions may matter.
Related work
- Prior generalized-planning approaches include testing plans across instances, merging example plans, searching generalized-plan spaces, and learning feature-based abstractions in symbolic domains [1, 2, 3].GENTAMP follows the feature-and-abstraction strategy while applying it to continuous geometric domains through a TAMP solver.Source: Related work · p. 7
- The cited imitation- and offline-reinforcement-learning approaches are described as limited to visual or simulated-dynamics changes, with no known method generalizing from a few examples to arbitrary object counts and geometric configurations.The passage also notes reinforcement learning's sample complexity and need for thousands of example interactions.Source: Related work · p. 7
- TAMP acceleration methods reduce search spaces, learn constraints or partial grounding, or bias continuous sampling; GENTAMP instead targets settings where all objects, operators, and state-space regions may be relevant.The cited approaches include identifying goal-irrelevant objects [1], learning constraints [2], partial grounding [3], and sampling scores [4].Source: Related work · p. 7
Conclusion
The paper defines generalized TAMP and presents an algorithm that learns task-specific abstract policies from a few example plans. These policies increase TAMP search speed in large domains, supporting more scalable and generalizable long-horizon robotic planning.
Conclusion
- The paper introduces a generalized TAMP problem definition for learning generalizable and scalable policies for continuous robotics tasks.Source: Conclusion · p. 7
- Its algorithm learns task-specific abstract policies that apply across arbitrary numbers of objects and initial states from a few example plans.Source: Conclusion · p. 7
- The learned policies increase TAMP solver search speed in large domains, leading to more scalable and generalizable long-horizon robotic planning.Source: Conclusion · p. 8
Appendix
The appendix fragment specifies an input-output form for a TAMP procedure and steps for constructing a new action from action-related conditions and effects.
Appendix
- The procedure takes ⟨SN, IN, AN, GN⟩ = PN, πφ, F as input and outputs a valid TAMP plan.Source: Appendix · p. 9
- The plan is represented as a sequence of action-state pairs, (a1, s1), (a2, s2), . . . , (an, sn).Source: Appendix · p. 9
- The action-construction steps add ordering conditions to NewAction using the action's preconditions and effects.Source: Appendix · p. 9
16 I.add part(Order(Ia))
The supplied passage labels this section as GENTAMP policy execution.
16 I.add part(Order(Ia))
- The section is titled “Algorithm 2: GENTAMP Policy Execution.”Source: §16 · p. 9
Experimental Details
The experiments use common PDDLSTREAM search settings for GENTAMP, unguided TAMP, and Oracle Skeleton, with policy-learning complexity and compute resources specified. Reported execution times cover GENTAMP after learning; policy-learning runtime is given separately in an appendix table.
Experimental Details
- GENTAMP, Unguided TAMP, and Oracle Skeleton use PDDLSTREAM with the same search control strategy and greedy best-first search using the hAdd heuristic.Source: Experimental Details · p. 9
- All abstraction learning uses a maximum feature complexity of 5, and each experiment container has 1 CPU and 4 GB of memory.Experiments ran in Docker containers on Google Cloud Kubernetes Engine using an e2-standard-16 machine.Source: Experimental Details · p. 9
- Reported experimental results include GENTAMP execution time only after policy learning, while policy-learning runtime breakdown appears in Appendix Table 1.Source: Experimental Details · p. 9
Valid Abstraction Definitions
A valid abstraction requires sound abstract actions, complete action coverage, and features that distinguish goal from non-goal states.
Valid Abstraction Definitions
- Soundness requires every transition enabled by an abstract action to have a concrete action with the same qualitative abstract-state effects.The condition applies across problem instances where the abstract action’s preconditions hold.Source: Valid Abstraction Definitions · p. 9
- Completeness requires an applicable abstract action whenever any concrete action is applicable in a state.Source: Valid Abstraction Definitions · p. 9
- Goal-distinguishability requires at least one feature to differ between every non-goal state and goal state; validity combines this with soundness and completeness.Source: Valid Abstraction Definitions · p. 9
SAT Theory Description
The section describes the SAT feature-selection theory, the training and testing instances, and the resulting task-specific abstractions.
SAT Theory Description
- The SAT theory uses a transition database D and goal-satisfying subset G to produce a binary feature-selection label.Its listed constraints relate state-pair distinctions to transition-pair distinctions and distinguish goal from non-goal states.Source: SAT Theory Description · p. 9
Training/Testing Problems
- Training and testing cover Unstack, Sort, Clutter, and Transport, with object counts and task configurations varied across instances.Unstack trains with 8 blocks and tests 2–16; Sort tests equal red/green counts from 1–8. Clutter trains at 2, 5, and 8 distractors and tests 2–16 in steps of 2; Transport tests 2–16 objects at tray capacity 2.Source: Training/Testing Problems · pp. 9–10
Learned Abstractions
- The learned abstractions use task-specific features and qualitative actions, including holding, placement, region, trajectory, and collision relations.The listed feature definitions include holding and quantified object relations, as well as tray/stove and collision-related conditions.Source: Learned Abstractions · pp. 10–11