Learning and Optimizing the Efficacy of Spatio-Temporal Task Allocation under Temporal and Resource Constraints

TL;DR

This work formalizes Spatio-Temporal Efficacy-optimized Allocation for Multi-robot systems (STEAM), addressing how to maximize coalition-task performance while respecting a makespan constraint. It introduces E-ITAGS, an interleaved graph-search algorithm guided by the Normalized Allocation Cost (NAC) and Time Budget Overrun (TBO) heuristics, and a convex combination via the Time-Extended Metric (TETAM) to balance efficacy and scheduling. A realizability-aware active learning module learns trait-efficacy maps that relate aggregated robot traits to task performance using a GP-UCB framework with realizability projections, yielding sample-efficient learning. Theoretical suboptimality bounds are established, showing favorable guarantees when $\alpha$ is chosen away from 1, and extensive RoboCup Rescue experiments demonstrate higher allocation efficacy under strict time budgets, with robust data efficiency and practical scalability.

Abstract

Complex multi-robot missions often require heterogeneous teams to jointly optimize task allocation, scheduling, and path planning to improve team performance under strict constraints. We formalize these complexities into a new class of problems, dubbed Spatio-Temporal Efficacy-optimized Allocation for Multi-robot systems (STEAM). STEAM builds upon trait-based frameworks that model robots using their capabilities (e.g., payload and speed), but goes beyond the typical binary success-failure model by explicitly modeling the efficacy of allocations as trait-efficacy maps. These maps encode how the aggregated capabilities assigned to a task determine performance. Further, STEAM accommodates spatio-temporal constraints, including a user-specified time budget (i.e., maximum makespan). To solve STEAM problems, we contribute a novel algorithm named Efficacy-optimized Incremental Task Allocation Graph Search (E-ITAGS) that simultaneously optimizes task performance and respects time budgets by interleaving task allocation, scheduling, and path planning. Motivated by the fact that trait-efficacy maps are difficult, if not impossible, to specify, E-ITAGS efficiently learns them using a realizability-aware active learning module. Our approach is realizability-aware since it explicitly accounts for the fact that not all combinations of traits are realizable by the robots available during learning. Further, we derive experimentally-validated bounds on E-ITAGS' suboptimality with respect to efficacy. Detailed numerical simulations and experiments using an emergency response domain demonstrate that E-ITAGS generates allocations of higher efficacy compared to baselines, while respecting resource and spatio-temporal constraints. We also show that our active learning approach is sample efficient and establishes a principled tradeoff between data and computational efficiency.

Figures (11)

• Figure 1: E-ITAGS performs spatio-temporal task allocation for heterogeneous multi-robot teams by optimizing collective performance while respecting spatio-temporal and resource constraints. The realizability-aware active learning module explicitly models, actively learns, and optimizes trait-efficacy maps that approximate the effects of collective capabilities on task performance, with more details in Secs. \ref{['sec:mainapproach']} and \ref{['subsec:active_learning_approach']}, and in Figs. \ref{['fig:sampling_relaxation']}. and \ref{['fig:active_learning_pipeline']}.
• Figure 3: The proposed realizability-aware active learning pipeline. We illustrate our idea using the convex hull-constrained strategy in a simple scenario with 3 robots, each characterized by 2 traits. The box-constrained strategy shares the same pipeline except for its allowable region to sample the candidates. On a 2D plane denoting the trait space, the pink region is encircled by the convex hull of all directly realizable trait combinations in $\mathcal{Y}_{ \boldsymbol{Q} }$ (the dark blue dots). Red points within the convex hull are randomly sampled candidates, with each candidate's neighborhood shown as a yellow circle. Note that all neighborhoods are initialized to be the same size, while adaptively shrunk by the zooming mechanism as reflected by smaller yellow circles in the "Adaptive Sampler". The UCB-based selector picks the candidate, shown as the dashed circle, followed by the projector projecting it to the nearest neighbor in $\mathcal{Y}_{ \boldsymbol{Q} }$. The realizable sample is fed into the simulated evaluator for label, which is leveraged to train the trait-efficacy map.
• Figure 4: The layout of a RoboCup search and rescue scenario. Black obstacles indicate that pathways are (partially) obstructed. Green dots represent alive civilians waiting for rescue. The red dots are fire brigades, blue dots are police forces, and white dots are ambulance vehicles.
• Figure 5: Comparison of E-ITAGS' allocation efficacy, makespan, and computation time against ITAGS. E-ITAGS consistently generates solutions of superior efficacy (left) while simultaneously ensuring that its makespan is better than or equal to that of ITAGS (middle). Green dots indicate E-ITAGS performs better than ITAGS and grey dots indicate E-ITAGS and ITAGS perform equally. Larger allocation efficacy and smaller makespan are desirable. Red dots indicate that E-ITAGS' benefits over ITAGS comes at the cost of slightly worse computation time (right).
• Figure 6: We compare the runtime of E-ITAGS and ITAGS across three crucial modules: task allocation, scheduling, and motion planning. The increase in total runtime can be attributed to E-ITAGS spending more time searching through the task allocation graph.

Theorems & Definitions (1)

• Theorem 1