# COLIN: Planning with Continuous Linear Numeric Change

arXiv: https://arxiv.org/abs/1401.5857 · HTML: https://mlsanity.com/paper/1401.5857/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2014.

## Built on by (most cited first, 10 of 10)

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- [Gradient-Based Mixed Planning with Symbolic and Numeric Action Parameters](https://mlsanity.com/paper/2110.10007/) (2021)
- [A Domain-Independent Agent Architecture for Adaptive Operation in Evolving Open Worlds](https://mlsanity.com/paper/2306.06272/) (2023)
- [When Prolog meets generative models: a new approach for managing knowledge and planning in robotic applications](https://mlsanity.com/paper/2309.15049/) (2023)
- [Efficient Temporal Piecewise-Linear Numeric Planning with Lazy Consistency Checking](https://mlsanity.com/paper/2105.10176/) (2021)
- [Improving Search by Utilizing State Information in OPTIC Planners Compilation to LP](https://mlsanity.com/paper/2106.07924/) (2021)
- [System Resilience through Health Monitoring and Reconfiguration](https://mlsanity.com/paper/2208.14525/) (2022)
- [A Metric Hybrid Planning Approach to Solving Pandemic Planning Problems with Simple SIR Models](https://mlsanity.com/paper/2409.11631/) (2024)
- [A User Study on Contrastive Explanations for Multi-Effector Temporal Planning with Non-Stationary Costs](https://mlsanity.com/paper/2409.13427/) (2024)
- [From Kinematics to Dynamics: Learning to Refine Hybrid Plans for Physically Feasible Execution](https://mlsanity.com/paper/2604.12474/) (2026)

## Abstract (arXiv)

In this paper we describe COLIN, a forward-chaining heuristic search planner, capable of reasoning with COntinuous LINear numeric change, in addition to the full temporal semantics of PDDL. Through this work we make two advances to the state-of-the-art in terms of expressive reasoning capabilities of planners: the handling of continuous linear change, and the handling of duration-dependent effects in combination with duration inequalities, both of which require tightly coupled temporal and numeric reasoning during planning. COLIN combines FF-style forward chaining search, with the use of a Linear Program (LP) to check the consistency of the interacting temporal and numeric constraints at each state. The LP is used to compute bounds on the values of variables in each state, reducing the range of actions that need to be considered for application. In addition, we develop an extension of the Temporal Relaxed Planning Graph heuristic of CRIKEY3, to support reasoning directly with continuous change. We extend the range of task variables considered to be suitable candidates for specifying the gradient of the continuous numeric change effected by an action. Finally, we explore the potential for employing mixed integer programming as a tool for optimising the timestamps of the actions in the plan, once a solution has been found. To support this, we further contribute a selection of extended benchmark domains that include continuous numeric effects. We present results for COLIN that demonstrate its scalability on a range of benchmarks, and compare to existing state-of-the-art planners.