Lifelong Robot Recomposition via Persistent Categorical Modeling for Unified Task-Driven Co-Design, Verification, and Planning

Steven Swanbeck; Mitch Pryor

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Lifelong Robot Recomposition via Persistent Categorical Modeling for Unified Task-Driven Co-Design, Verification, and Planning

Steven Swanbeck, Mitch Pryor

arXiv:2608.21676v1Aug 21, 2026cs.RO

TL;DR

Robotic systems are brittle when static design-time assumptions fail during deployment or tasks and environments change. The paper unifies categorical modeling with SMT-based synthesis of heterogeneous hardware, software, and behavior compositions, supporting lifecycle queries and runtime recomposition; it demonstrates this in search and rescue and compares favorably in expressivity and optimization against planner baselines. A practical boundary is that synthesized structural variables are not realizable components, and the demonstrated robot cannot autonomously reconfigure its hardware.

Problem
Static design-then-deploy systems cannot gracefully adapt to changing capabilities, missions, or environments, motivating unified lifecycle reasoning over robot composition.
Method
The framework represents heterogeneous robot components as categorical compositions and uses SMT synthesis to solve parameters, structural variables, and lifecycle reconfiguration queries over a persistent model.
Results
The system synthesizes runtime compositions in a search-and-rescue deployment, reaches the optimum on every optimization row, and expresses lifecycle capabilities that baselines require workarounds or cannot express.
Takeaways & Limitations
The framework provides a mathematical and computational foundation for lifelong robot recomposition across changes in the robot, its tasks, and its environment.
Takeaways & Limitations
Structural free variables specify weakest feasibility conditions rather than realizable components, and the demonstrated robot cannot autonomously reconfigure its own hardware.

Abstract

from arXiv · show

Robotic systems are traditionally designed and deployed in static configurations, with assumptions made at design-time becoming immutable constraints during runtime. This design-then-deploy paradigm produces performant systems under narrow operating conditions, but renders robots brittle when qualities of themselves, their tasks, or their environments unexpectedly change. We address this challenge with a compositional framework that formalizes robotic systems as abstract circuits within a strict symmetric monoidal category, in which design and runtime composition of hardware, software, and behavior are synthesized simultaneously via an SMT-based solver, with monoidal functors projecting the system into lifecycle-specific views and free symbolic variables simultaneously solving for parameters and entire component specifications within larger compositions. This persistent model also supports queries a long-lived system needs beyond plan existence across its entire lifecycle, including mapping Pareto fronts over candidate compositions, diagnosing why a composition has become infeasible, finding its minimal restoration, and reconfiguring with limited change to the deployed system. We evaluate against official implementations of optimal numeric, stream-based, and SMT-based planners all measured onboard a deployed robot and demonstrate the approach end-to-end in a search-and-rescue scenario in which the robot recognizes when it has become unfit and synthesizes and assumes new holistic configurations to restore operation. We release our solver and supporting software open-source.

I. INTRODUCTION

Robotic integration remains difficult because heterogeneous subsystems and disconnected lifecycle stages produce brittle, task-misaligned systems. The paper proposes recompositional robotics, unifying categorical modeling, SMT synthesis, co-design, planning, verification, and runtime reconfiguration.

Heterogeneous robotic subsystems are commonly integrated through ad hoc practices, producing monolithic designs resistant to change.
Static configurations can fail when missions, robot capabilities, or environments change, while separate design actors often produce suboptimal task compromises.
Recompositional robotics dynamically reconfigures heterogeneous hardware, software, and behavior modules throughout a system’s operational lifespan.
The framework models hardware, software, and behavior components as morphisms in a free strict symmetric monoidal category, forming interrogable categorical circuits.
An SMT formulation synthesizes optimal compositions while solving free parametric variables and entire missing components within one composition.
Persistent-model queries cover Pareto-optimal design, infeasibility diagnosis, minimal relaxation, and minimal-change reconfiguration across the robot lifecycle.

A. Modular, Reconfigurable, and Self-Reconfigurable Systems

Prior work addresses modular morphology, runtime adaptation, co-design, verification, and planning largely in separate lifecycle stages or restricted configuration spaces. The paper positions recompositional robotics as unified reasoning over heterogeneous black-box components and persistent system queries.

Modular robotics often focuses on physical morphology, whereas this work includes electromechanical hardware, software stacks, and behavior-based task execution.
Recompositional configurations are heterogeneous black-box module compositions defined by interface obligations, with morphology treated as one variable class among many.
Runtime adaptation frameworks commonly enumerate software architecture variants, while this approach synthesizes hardware, software, and behavior configurations beyond predefined candidate sets.
Existing co-design methods optimize within fixed operational envelopes and do not autonomously resynthesize configurations when runtime constraints change.
Computational co-design searches fixed vocabularies of physical primitives, limiting natural expression of software and behavior; interface-based black boxes admit heterogeneous components.
Verification and planning methods generally address restricted models, while the positioning table contrasts their component agency, lifecycle, configuration spaces, and query coverage.

G. Diagnosis, Repair, and Plan Stability

Diagnosis, repair, and stability are established for plans and planning domains, but conventional stages remain decoupled from deployed-system reconfiguration. The proposed unified formulation uses one persistent model to connect failure diagnosis, restoration, and system change.

Existing diagnosis, relaxation, and stability methods operate on plans or planning domains rather than directly on deployed heterogeneous systems.
Because co-design, planning, and verification use separate machinery, planning failure cannot directly trigger hardware or software reconfiguration.
A unified framework can holistically resynthesize structure and capabilities under environmental shifts, hardware failures, and new task objectives.
The persistent categorical model supports diagnosis, relaxation, stability, and design-space queries as one family over a continuously updated system representation.
Categorical circuits use objects and morphisms for types and transformations, with serial and parallel composition governed by category and monoidal laws.
String diagrams represent morphisms as boxes and objects as wires, making physical or informational resource flows and transformations explicit.

B. State Transition Systems

The framework grounds categorical robot compositions in a state transition system for autonomous reasoning. Planning is represented through states, actions, transitions, initial conditions, and goals.

A state transition system is defined as Σ = ⟨S, A, γ⟩, comprising possible states, actions, and a transition function.
The transition function γ maps a state and action to another state, providing the dynamics used to express planning problems.
A planning problem specifies the transition system, an initial state, and a goal-state set; a plan is an action sequence reaching a valid goal state.

IV. APPROACH

The framework models heterogeneous robotic hardware, software, and behavior as a unified categorical state-transition system. System states are resource strings, while morphisms represent composable mutations with preconditions and postconditions.

IV. APPROACH: The robot is represented as an abstract circuit in a strict symmetric monoidal category whose objects encode system states and whose morphisms encode actions.The category supports serial and parallel composition of atomic morphisms across heterogeneous subsystems.
1) Composite Resource Strings as Objects:: System states are tensor products of atomic resources, including grouped hardware, power, ports, compute, and other partial states.The complete state is expressed as the tensor product of these partial states.
1) Composite Resource Strings as Objects:: Because the category is symmetric, permuting atomic resources within a state does not change its representation.This removes dependence on the ordering of resources in the composite state string.
2) Morphisms as Actions:: Morphisms generalize hardware changes, software changes, and plan execution into one action space, with preconditions and postconditions governing applicability and state updates.Composite systems are formed through serial and parallel composition of atomic morphisms.
IV. APPROACH: The synthesis objective is to compose morphisms that transform an initial state into a goal state.The composition uses serial and parallel operators over the action space.

3) Planning Objective:

Lifecycle-specific views reduce the unified categorical model to relevant resources while preserving its compositional structure. The resulting planning problem is translated into SMT, where action activations and additional free variables are solved against initial, transition, and goal constraints.

3) View-Switching:: Monoidal functors project the full system model into reduced lifecycle views by mapping irrelevant resources to the monoidal unit.This removes associated constraints without changing the underlying composition structure.
3) View-Switching:: Swapping projection functors lets the same model be solved, verified, or optimized for different resource subsets, including hardware, software, or behavior stages.The framework can emulate traditionally decoupled lifecycle stages by narrowing the solver’s focus.
1) The Logic Formula:: A valid planning solution is generated by mapping the categorical model to an SMT problem.The SMT formulation searches over action activations across a finite planning horizon.
1) The Logic Formula:: Boolean activation variables select morphisms over the planning horizon while the formula enforces initial-state, transition, and goal constraints.Each activated action requires its preconditions and applies its postconditions at the next step.
2) Free Variable Synthesis:: SMT reasoning over richer datatypes allows the solver to synthesize missing information that influences the composition alongside Boolean action activations.This extends planning beyond choosing among fully specified actions.

2) Free Variable Synthesis:

The framework jointly solves for parameter values and unspecified component morphisms within a composition. Symbolic domains are grounded at runtime to support open vocabularies while retaining finite satisfiability reasoning.

2) Free Variable Synthesis:: Parametric free variables represent unspecified values in morphism preconditions or postconditions and are solved simultaneously with the composition.For example, a RAM requirement can remain symbolic rather than being fixed in advance.
2) Free Variable Synthesis:: Structural free variables represent entire hypothetical morphisms whose specifications are solved so an otherwise invalid composition can satisfy its constraints.They can therefore identify design targets for components that would make the composition valid.
2) Free Variable Synthesis:: Structural free variables are constrained by the current lifecycle projection.The allowed unspecified component structure depends on F_view.
2) Free Variable Synthesis:: Parametric variables support open symbolic sorts such as String and Set, including runtime names, memory identifiers, and detectable-object classes.The approach grounds each symbolic sort over a finite universe built from problem constants and one reserve element per free variable.
2) Free Variable Synthesis:: Finite grounding preserves satisfiability for the admitted quantifier-free symbolic formulas using equality, disequality, set membership, and single-element set updates.The grounding universe contains the formula’s constants plus one fresh reserve element per free symbolic variable.
2) Free Variable Synthesis:: Runtime grounding means an unseen symbolic value requires a problem-file update rather than re-enumerating or changing the model.The solver can also optimize activations and free variables under hard and soft constraints.
2) Free Variable Synthesis:: The conjunction of labeled constraints supports minimality queries beyond plan existence after a component update changes Φ to Φ′.These queries operate over assignments to action activations, parametric variables, and structural variables.
3) Diagnose: why is the composition infeasible?:: When the updated formula is unsatisfiable, an irreducible subset of constraints identifies conditions jointly necessary for the infeasibility.Removing any one constraint from the subset restores satisfiability, although the subset need not have minimum cardinality.

1) Diagnose: why is the composition infeasible?:

The persistent formulation supports diagnosing infeasibility, minimally restoring feasibility, and recomposing a deployed robot with controlled change. It can prioritize stability or objective optimality through lexicographic optimization.

1) Diagnose: why is the composition infeasible?:: An infeasibility explanation is an irreducible constraint subset in which every constraint is necessary for the updated composition’s unsatisfiability.Such a subset may not be minimum-cardinality, and multiple subsets may exist.
2) Restore: what is the minimal change to restore feasibility?:: Minimal restoration weakens eligible resource requirements with nonnegative slack variables and solves for the smallest required relaxations.For discrete requirements, the solver can return the minimal set whose removal restores feasibility.
2) Restore: what is the minimal change to restore feasibility?:: Minimality is discovered across all eligible requirements simultaneously rather than designated beforehand.This differs from replanning baselines that use a bisection loop for each candidate parameter.
3) Recompose: how much must the deployed system change?:: Recomposition minimizes weighted churn between the deployed component set and a candidate configuration, accounting for practical replacement costs.These costs include hardware mounting, cable connections, software restarts, and behavior-tree modifications.
3) Recompose: how much must the deployed system change?:: Reversing the lexicographic priority instead recovers the cost-optimal solution regardless of the incumbent configuration.The formulation makes the optimality-versus-stability tradeoff an explicit contextual choice.
3) Recompose: how much must the deployed system change?:: Algorithm 1 applies lifelong recomposition based on these diagnostic, restoration, and recomposition queries.The algorithm is used in the paper’s demonstration.

V. APPLICATIONS

The applications span design-time component selection, symbolic behavior completion, runtime grounding, and autonomous recomposition for search and rescue. The persistent model turns these stages into queries over shared hardware, software, and behavior compositions.

A. Design-Time Component Engineering: The search-and-rescue application combines solver-generated hardware, software, and behavior components to recognize and adapt to changing mission conditions.The mission requires unmapped traversal, person detection, approach, condition assessment, and communication to a remote operator.
A. Design-Time Component Engineering: The solver designs STT and VLM subcompositions against the deployment computer’s resource constraints, evaluating GPU usage, latency, and a hybrid assessment-quality metric.Five Whisper variants and eleven VLM variants were represented symbolically for Pareto analysis.
A. Design-Time Component Engineering: The model grounds hardware reconfiguration into human-readable instructions while autonomously producing software compose and parameter YAML updates.In the demonstration, hardware instructions are delivered through an augmented-reality headset and executed by a human teammate.
A. Design-Time Component Engineering: 20 of 55 STT–VLM compositions are Pareto-optimal, leading to deployment of Whisper Small and Gemma4 26B.All 55 candidate subcompositions were feasible; the remaining 35 were dominated by another composition.
A. Design-Time Component Engineering: A structural variable µ completes an initially UNSAT behavior composition by supplying the missing image source for PromptVLM.The resulting interaction is stored as a VLMInteraction component, whose runtime parameters θ are grounded into an executable behavior tree.

B. Runtime Recomposition in a Search-and-Rescue Mission

In the search-and-rescue mission, the robot detects when its current composition becomes UNSAT and synthesizes replacements that restore SAT operation as task, state, and environmental conditions change.

B. Runtime Recomposition in a Search-and-Rescue Mission: The robot starts UNSAT for the search-and-rescue objective and autonomously generates hardware interfaces, software components, and a task-aligned behavior tree.The resulting composition includes LiDAR-based localization and YOLOE-based person detection.
B. Runtime Recomposition in a Search-and-Rescue Mission: Exceeding the 10 m teammate-range constraint triggers a new behavior tree that returns the robot to communication range.A teammate then attaches a long-range radio, significantly extending the communication range for further exploration.
B. Runtime Recomposition in a Search-and-Rescue Mission: In darkness, loss of RGB-based person detection makes the composition UNSAT, prompting an RGB-to-thermal camera swap and corresponding software and behavior changes.The updated composition restores SAT operation and enables another person to be detected, approached, and assessed.
B. Runtime Recomposition in a Search-and-Rescue Mission: Across the demonstration, the robot autonomously identifies UNSAT conditions caused by task, state, or environmental changes and grounds new compositions into actionable updates.Hardware updates require teammate action, while software and behavior recomposition are autonomous.

VI. EVALUATION

The evaluation treats lifelong recomposition as multiple queries over one persistent model rather than only single-plan generation. It compares the approach with established planning formalisms onboard the deployed robot and examines adaptation, diagnosis, restoration, and reconfiguration capabilities.

VI. EVALUATION: The evaluation tests single feasible or optimal composition planning before measuring lifelong-recomposition properties.The additional properties concern model modification, diagnosis of unsatisfiability, minimal restoration, and required recomposition.
VI. EVALUATION: The persistent model supports queries for why a composition is unsatisfiable, which minimal changes restore satisfiability, and how much recomposition is required.These queries extend evaluation beyond whether a single plan exists.
VI. EVALUATION: Comparisons use official implementations of PDDL 2.1 with ENHSP, PDDLStream with Fast Downward, and SMTPlan+ with Z3.Each baseline receives a best-faith encoding, and negative results are treated as correct outputs rather than encoding failures.
VI. EVALUATION: All approaches are measured onboard the same NVIDIA Jetson AGX Orin, with reported solve times given as medians over 10 trials.Interquartile ranges are below 0.6 s except for one reported result of 1.26 s.
VI. EVALUATION: Table II reports SAT and OPT solve times across the search-and-rescue deployment and three microbenchmarks, distinguishing feasible, optimal, suboptimal, and infeasible outcomes.PDDLStream lacks an authored encoding for the full-scale search-and-rescue model, so its corresponding entries are marked N/E.

B. Planning Performance

The evaluation compares recompositional planning with numeric, stream-based, and SMT-based baselines under initial planning and mission-time changes. The solver reaches optimal solutions while supporting onboard recomposition and broader lifelong queries, including diagnosis, restoration, and low-churn reconfiguration.

Initial planning: Our solver reaches the optimum on every optimization row by co-optimizing free variables in a single query.PDDLStream reaches the optimum only when hand-authored streams encode the solution structure, while satisficing SMTPlan+ returns SUBOPT solutions.
Initial planning: 4.9 s to 6.7 s: full search-and-rescue problems solve onboard the edge device within the event-driven recomposition budget.Recomposition is triggered when the robot becomes UNSAT rather than at every control step.
Absorbing change during deployment: 0 model edits: across four mission-time modifications, our approach recovers SAT and OPT results while most baselines require 22–34 edits or produce UNSAT or SUBOPT results.The modifications include a GPU upgrade, changed objective, increased sensing precision, and an open-vocabulary operator request.
Queries beyond plan existence: 500 USD versus 20,000 USD: the budget-cut query identifies the LiDAR cost as the sole cause of unsatisfiability in 0.08 s.ENHSP reports only that the problem is unsolvable, while SMTPlan+ cannot certify infeasibility or explain it.
Queries beyond plan existence: 19,860 USD: the solver finds the minimal budget increase restoring feasibility in 11.4 s without being told which parameter to relax.An ENHSP bisection workaround needs 22 full iterations and 19.6 s, while requiring the parameter to relax as input.
Queries beyond plan existence: Churn 0 preserves the deployed configuration at slightly higher cost, unlike the cost-optimal baseline solution with churn 4.The explicit cost-versus-stability tradeoff allows the solver to choose stability rather than only minimizing total financial cost.

E. Expressivity Summary

The persistent categorical model expresses lifelong recomposition capabilities that fixed-model planners cannot directly represent, while supporting co-optimization and deployment-oriented queries. The evaluation demonstrates this framework in search and rescue, subject to modeling, hardware, metric, and benchmark limitations.

The formalism supports minimality queries over one persistent categorical model and simultaneously co-optimizes all free variables, whereas baselines require workarounds, re-encoding, or cannot express these capabilities.The comparison covers hand-encoded requirements, free-variable classes, and co-optimized variable types.
Reasoning quality depends on an ontology that explicitly captures semantic differences between components with otherwise similar data types.RGB and thermal streams are treated equivalently for person detection in the demonstrated task but are not generally interchangeable for lower-contrast objects.
Structural free variables identify weakest feasibility conditions rather than realizable designs, so practical matching or implementation remains external to the solver.The paper notes that catalog matching is possible but not implemented.
The deployment and evaluation scope remains bounded by human-enacted hardware changes, point-estimate quality assumptions, and comparisons against planners designed for fixed models.The paper also reports no established benchmark for component-based lifelong recomposition, requiring author-created variants and baseline encodings.
The framework uses one categorical model for Pareto-optimal pre-deployment compositions and runtime queries about feasibility, restoration costs, and minimal operational changes.These queries span changes in system capabilities, tasks, and environments.
Its search-and-rescue demonstration spans pre-deployment component and subcomposition design through runtime recomposition of hardware, software, and behavior.