Temporal Planning via Interval Logic Satisfiability for Autonomous Systems

TL;DR

A notion of planning graphs that can account for complex concurrency relations between actions and fluents as a Constraint Programming (CP) model is proposed and demonstrated to outperforms existing PDDL 2.1 planners that capture plans requiring complex concurrent interactions between agents.

Abstract

Many automated planning methods and formulations rely on suitably designed abstractions or simplifications of the constrained dynamics associated with agents to attain computational scalability. We consider formulations of temporal planning where intervals are associated with both action and fluent atoms, and relations between these are given as sentences in Allen's Interval Logic. We propose a notion of planning graphs that can account for complex concurrency relations between actions and fluents as a Constraint Programming (CP) model. We test an implementation of our algorithm on a state-of-the-art framework for CP and compare it with PDDL 2.1 planners that capture plans requiring complex concurrent interactions between agents. We demonstrate our algorithm outperforms existing PDDL 2.1 planners in the case studies. Still, scalability remains challenging when plans must comply with intricate concurrent interactions and the sequencing of actions.

Figures (7)

• Figure 1: An architecture for (semi)-autonomous system, boxes represent physical and/or computational processes, arrows indicate information exchanged between these.
• Figure 2: Refinement of Figure \ref{['fig:semi_autonomous_system_architecture']} in which we identify two new sub-systems in the executive control (supervisor and control) and physical system models (plant and measurement). The diagram also makes explicit the possibility of plans defining the control for multiple autonomous systems that need to act in a co-ordinated manner. See text for details and discussion.
• Figure 3: Global plan timeline, or dateline, and fluent timelines. Each rectangle is an interval. The top row is the intervals or epochs we use to define the temporal extent of actions. The rows below are labeled with the fluents that can be used with them to define TQAs. Intervals may not all be the same size but must satisfy other temporal constraints.
• Figure 4: Truth value assignments to TQAs supported by theories $T_{P,N}$ describe timing diagrams like the above. For each fluent $\varphi_i$, $i=1,2,3$, we set to true TQAs referring to the following intervals shown in Figure \ref{['fig:Dateline_Illustration']}: $I_{\varphi_1,1,1}$, $I_{\varphi_1,0,2}$, $I_{\varphi_1,1,3}$, $I_{\varphi_2,1,1}$, $I_{\varphi_2,0,2}$, $I_{\varphi_2,1,3}$, $I_{\varphi_3,1,2}$, and $I_{\varphi_2,0,3}$. Hatched "bumps" correspond to periods of time the fluent on the left is true. Above each of such periods we write the corresponding IL formula.
• Figure 5: Illustration of the constraints enforcing temporal constraints $\varphi_I \supset \alpha_{I_0}$. From top to bottom, we show four possible ways to decompose $I$ as per Eq. \ref{['eq:timeline_equisat']}. Epochs run in between vertices and selected edges in the planning graph, e.g., the arrow below $I_{t_1}$ connecting the top vertices stands for the decision variable $\varphi_{11}^1$ being set to $1$. Diagonal arrows correspond to a change in the truth value of $\varphi$.

Theorems & Definitions (4)

• Theorem 1
• Remark 1
• Definition 1
• Definition 2