From Abstractions to Grounded Languages for Robust Coordination of Task Planning Robots

TL;DR

The paper introduces a novel framework that treats language as plan-space constraints grounded in temporal-state constraints (TSCs) to coordinate task-planning robots. It formalizes a two-robot coordination problem and defines a coordination language as a minimal set of TSC-based words that express all candidate plans while ensuring RC-free coordination, connecting linguistic abstraction to plan-space reasoning. The key theoretical result is that finding such a minimal language is $NEXP$-complete, and the authors propose an approximate algorithm based on perfect state abstractions to construct compact vocabularies. Empirical evaluations in gridworlds and simulated robotics show that the approach can dramatically reduce communication needs, increase execution flexibility, and improve robustness to dynamic obstacles, albeit with scalability limitations that warrant further research.

Abstract

In this paper, we consider a first step to bridge a gap in coordinating task planning robots. Specifically, we study the automatic construction of languages that are maximally flexible while being sufficiently explicative for coordination. To this end, we view language as a machinery for specifying temporal-state constraints of plans. Such a view enables us to reverse-engineer a language from the ground up by mapping these composable constraints to words. Our language expresses a plan for any given task as a "plan sketch" to convey just-enough details while maximizing the flexibility to realize it, leading to robust coordination with optimality guarantees among other benefits. We formulate and analyze the problem, provide an approximate solution, and validate the advantages of our approach under various scenarios to shed light on its applications.

Figures (9)

• Figure 1: Motivating scenario involving two pathfinding robots, $R_1$ and $R_2$, in a gridworld. Each cell can only accommodate a single robot at a time and the darker cells are obstacles. The robots are tasked to reach their goal locations ($G_1$ and $G_2$), respectively, in the shortest timespan while avoiding collisions. They have a limited sensing range and communication is costly. During plan execution, there may be locations of interest popping up at random places that require one of the robots to visit (denoted by the eye sign).
• Figure 2: Running example where the agents cannot switch locations or stay in the same location in the same time step to avoid collisions. Consider a task for the two robots to switch their locations as shown. Without coordination, each robot may choose any candidate plan for the task and follow the corresponding subplan. In a situation where the plans are chosen differently as shown in the thought bubbles, it would lead to a miscoordination (i.e., a collision).
• Figure 3: Three different plans for the example in Fig. \ref{['fig:motivating']}: the first two plans do not introduce RC: subplan $\pi_1^A$ (black arrows) in $\pi_1$ can be switched with its counterpart ($\pi_2^A$) in $\pi_2$ and recombined with subplan $\pi_2^B$ (blue dashed arrows) without introducing any miscoordinations. Both $\pi_1$ and $\pi_2$, however, introduce RC with $\pi_3$.
• Figure 4: An illustration of a TSC. The top shows the abstract states associated with the TSC and the bottom a plan as a state sequence that satisfies it. The rectangle nodes represent abstract states with their included ground states shown inside.
• Figure 5: Determining $(\alpha^*, \beta^*)$ with two plans (top and bottom) that introduce RC for a given task. When {$I$, $s_1$, $s_2$} (or {$s_3$, $s_4$, $s_5$}) are pair-wisely separated into different abstract states, the two sentences for expressing these two plans will be different since they must represent $s_1$ and $s_2$ (or $s_3$ and $s_4$) as different abstract states with the preceding (or trailing) abstract state shared between the sentences, thus relaxing the RC.

Theorems & Definitions (16)

• Definition 1: Required Coordination (RC)
• Proposition 1
• Definition 2: Temporal-State Constraint (TSC)
• Definition 3: Language
• Definition 4: Coordination Language
• Definition 5: State Abstraction
• Theorem 1
• Lemma 1
• Theorem 2
• Theorem 3