From Durations to Dynamics: Translating Temporal Planning into PDDL+

Opening — Why this matters now

Planning systems sit quietly at the heart of many modern AI applications: logistics scheduling, robotic control, workflow automation, and industrial optimization. Yet the moment time enters the equation, planning becomes dramatically harder.

Temporal planning—where actions last for intervals rather than occurring instantaneously—introduces complications that classical planners were never designed to handle. Durations must be tracked. Conditions must hold during execution. Numeric resources may change continuously.

For years, the AI planning community has used PDDL 2.1 to represent such temporal problems. But planners that handle it efficiently remain limited. Meanwhile, a more expressive language—PDDL+—has existed for nearly two decades, designed to model hybrid systems with events and processes.

The catch? No practical bridge between the two.

This paper finally provides one.

The authors present the first fully specified compilation from temporal planning with durative actions into PDDL+, showing that temporal planning problems can be systematically rewritten into a PDDL+ formulation without losing correctness. In practice, this means we can leverage a different class of planners—and sometimes solve problems faster.

In other words: instead of building better temporal planners, we can sometimes translate the problem into a language that already has better tooling.

A classic engineering move.

Background — Two languages, two views of time

To appreciate the contribution, we need to understand the conceptual difference between PDDL 2.1 and PDDL+.

PDDL 2.1: Actions with duration

Temporal planning in PDDL 2.1 models actions that last over time. Each action has:

A plan therefore becomes a schedule of actions on a timeline. The planner must ensure actions do not interfere with each other and that all temporal constraints remain satisfied.

While expressive, this formulation forces planners to reason directly about overlapping durations—a computationally expensive task.

PDDL+: Systems that evolve

PDDL+ models time differently. Instead of durative actions, the world evolves through three mechanisms:

Rather than scheduling durations, the system simulates dynamic processes and triggered events. In many cases, this representation aligns better with hybrid-system reasoning used in control theory.

The key observation—known informally for years—is that a durative action could theoretically be expressed as a combination of start events, processes, and end events.

What the literature lacked was a rigorous compilation showing how to do this correctly and efficiently.

Implementation — Turning durative actions into processes

The compilation strategy essentially decomposes every durative action into three pieces:

Two variants appear depending on whether the duration is fixed or flexible:

The compiled model introduces additional helper variables to ensure the semantics remain correct. These include:

The system also introduces lock predicates that prevent conflicting actions from executing simultaneously.

This lock mechanism enforces the “no moving target” rule in temporal planning: two actions cannot simultaneously read and modify the same variable.

Conceptually, the compilation works like a carefully engineered simulation layer that recreates the semantics of temporal planning inside the PDDL+ execution model.

The authors prove three key properties:

Importantly, the resulting plan length increases by at most a constant factor.

So the translation remains computationally manageable.

Findings — When translation beats native planning

Theory aside, the authors test their compilation on several temporal-numeric planning domains.

Each domain contains 20 benchmark instances, including problems where numeric and temporal reasoning interact strongly.

Domains evaluated

The compiled problems are solved using the ENHSP PDDL+ planner, and results are compared with several native temporal planners.

Coverage results

The surprising outcome: the compiled PDDL+ approach often outperforms specialized temporal planners, particularly on problems where numeric reasoning interacts with time.

Temporal planners still perform better on purely temporal domains. But once numeric dynamics enter the picture, the PDDL+ formulation becomes highly competitive.

This suggests something deeper about the structure of planning problems: sometimes the difficulty lies less in the problem itself and more in how it is represented.

Implications — Representation as a competitive advantage

This work reinforces a recurring lesson in AI system design: representation matters as much as algorithms.

Rather than building ever more specialized planners, the authors demonstrate that translating problems into a richer modeling language can unlock existing solver capabilities.

For practitioners building planning systems—robotics, industrial scheduling, autonomous operations—this insight carries practical implications.

Strategic takeaways

More broadly, this research hints at a future where planning systems become interoperable across modeling languages. Instead of committing to a single planner architecture, engineers could dynamically translate problems to whichever formalism yields the best performance.

In effect, planning could evolve toward something resembling a compiler ecosystem rather than a monolithic solver.

Conclusion — Planning by translation

The paper provides the first rigorous and practical compilation from temporal planning in PDDL 2.1 into PDDL+. Beyond theoretical elegance, the experiments show that this translation can improve performance on complex temporal-numeric tasks.

It is a reminder that innovation in AI often comes not from entirely new algorithms, but from reframing problems in a language that machines understand better.

Sometimes the smartest solution is simply to translate.

Cognaptus: Automate the Present, Incubate the Future.