COLIN: Planning with Continuous Linear Numeric Change (1401.5857v1)

Abstract: 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.

• The paper's main contribution is a forward-chaining heuristic planner that uses linear programming to integrate continuous linear numeric change with duration-dependent effects.
• It introduces a Temporal Relaxed Planning Graph that assesses continuous change over time, enhancing the evaluation of both numeric and temporal planning constraints.
• Benchmark tests in domains like Satellite and Rovers demonstrate COLIN's scalability and efficiency, highlighting its potential for real-world autonomous systems and energy management.

Insightful Overview of "COLIN: Planning with Continuous Linear Numeric Change"

This paper presents "COLIN," a forward-chaining heuristic search planner that introduces significant advancements in reasoning capabilities for planning with continuous linear numeric change and duration-dependent effects. These advances are established within the Planning Domain Definition Language (PDDL) framework, specifically PDDL2.1, and push forward the state-of-the-art in managing planning problems that require tightly integrated numeric and temporal reasoning.

Key Innovations

The authors elevate the handling of continuous and duration-dependent numeric effects in planning. Two critical innovations stand out:

1. Integration of Numeric and Temporal Constraints: COLIN adeptly handles the intersection of numeric changes that vary with time. By employing linear programming (LP) to identify and constrain these intersections at each planning state, COLIN ensures consistency in action applicability and searches for an optimal planning path.
2. Temporal Relaxed Planning Graph: An advancement over existing heuristics, the Temporal Relaxed Planning Graph extends to accommodate continuous change directly. This extension considers the ongoing effects of actions over time, allowing COLIN to assess the impacts of continuous changes continuously.

System Architecture and Techniques

COLIN builds on the architecture of CRIKEY3, employing FF-style forward search, but introducing enhancements that allow reasoning about variables and plans as continuous processes. The implemented LP computes variable bounds, effectively narrowing down action considerations. This allows COLIN to maintain a consistent representation of states, facilitating state progression with both discrete and continuous effects.

Benchmarking and Results

The authors develop an array of benchmark domains to quantify and validate COLIN's performance against planning scenarios integrating continuous dynamic effects, such as Rovers, Satellite, AUV, and Airplane Landing domains. Notably:

• Scalability and Efficiency: The results highlight the planner’s scalability and efficiency, particularly in domains where continuous numeric effects and temporal constraints are deeply integrated, like energy management and robotic motion coordination.
• Post Optimization: Employing mixed integer programming as a final optimization step, COLIN tends towards reducing plan cost further post-solution, although preserving feasibility remains the focus.

Theoretical and Practical Implications

The paper implies shifts in both theory and application:

1. Theoretical Implications: COLIN's approach validates the utility of LP in combining temporal and numeric constraints beyond traditional discrete settings. This has extensive implications for how future planners might integrate more complex dynamic systems, potentially extending into nonlinear numeric planning.
2. Practical Implications: From an application standpoint, COLIN has potential in real-world domains such as autonomous systems, energy management, and operations planning, where continuous process interactions are relevant and impactful.

Future Directions

Building upon this groundwork, future research could explore non-linear continuous changes, potentially integrating near-real-time adaptability in dynamic environments. Further consideration of metrics for optimization beyond makespan, including energy efficiency and resource utility, remains a compelling avenue.

In conclusion, the COLIN planner represents a substantial step forward in the planning community, providing a bridge between classical goal-oriented planning and more nuanced models that consider time-dependent change deeply. It stands as a benchmark for future explorations in temporal-numeric planning domains.