Q-ITAGS: Quality-Optimized Spatio-Temporal Heterogeneous Task Allocation with a Time Budget

TL;DR

This work forms a new class of spatiotemporal heterogeneous task allocation problems that formalize these complexities and contributes a novel framework, named Quality-Optimized Incremental Task Allocation Graph Search (Q-ITAGS), to solve such problems.

Abstract

Complex multi-objective missions require the coordination of heterogeneous robots at multiple inter-connected levels, such as coalition formation, scheduling, and motion planning. The associated challenges are exacerbated when solutions to these interconnected problems need to simultaneously maximize task performance and respect practical constraints on time and resources. In this work, we formulate a new class of spatiotemporal heterogeneous task allocation problems that formalize these complexities. We then contribute a novel framework, named Quality-Optimized Incremental Task Allocation Graph Search (Q-ITAGS), to solve such problems. Q-ITAGS offers a flexible interleaved framework that i) explicitly models and optimizes the effect of the collective capabilities on task performance via learnable trait-quality maps, and ii) respects both resource and spatiotemporal constraints including a user-specified time budget (i.e. maximum makespan). In addition to algorithmic contributions, we derive theoretical suboptimality bounds in terms of task performance that varies as a function of a single hyperparameter. Detailed experiments involving a simulated emergency response task and a real-world video game dataset reveal that i) Q-ITAGS results in superior team performance compared to a state-of-the-art method, while also respecting complex spatiotemporal and resource constraints, ii) Q-ITAGS efficiently learns trait-quality maps to enable effective trade-off between task performance and resource constraints, and iii) Q-ITAGS suboptimality bounds consistently hold in practice.

Figures (4)

• Figure 1: Q-ITAGS performs spatio-temporal task allocation for heterogeneous multi-robot teams by optimizing collective performance while respecting spatio-temporal and resource constraints. It explicitly models, actively learns, and optimizes trait-quality maps that approximate the effects of collective capabilities on task performance.
• Figure 2: Comparison of Q-ITAGS' allocation quality, makespan, and computation time against ITAGS. Q-ITAGS consistently generates solutions of superior quality (left) while simultaneously ensuring that its makespan is better than or equal to that of ITAGS (middle). Green dots indicate Q-ITAGS performs better than ITAGS and grey dots indicate Q-ITAGS and ITAGS perform equally. Larger allocation quality and smaller makespan are desirable. Red dots indicate that Q-ITAGS' benefits over ITAGS comes at the cost of slightly worse computation time (right).
• Figure 3: The theoretical bound consistently holds for varying values of $\alpha$. A value of $0$ for a normalized optimality gap represents an optimal allocation, and a value of $1$ represents the worst possible allocation seen within the experiments.
• Figure 4: Q-ITAGS' active learning module consistently outperforms a uniform-sampling baseline in terms of sample efficiency and accuracy when learning trait-quality maps from real-world data. We show prediction errors (RMSE) as a function of number of training samples. Solid orange curve is the average error of the baseline across 20 random seeds, and the shaded region denotes the maximum and minimum errors.

Theorems & Definitions (2)

• theorem thmcountertheorem
• proof