Task Assistance Planning (TAP) involves coordinating an assisting robot to support a task robot executing a predefined trajectory, with the goal of maximizing the duration of effective assistance to the task robot. This coordination may be critical in diverse applications such as providing a communication relay in search-and-rescue missions. While existing approaches optimally solve TAP on static, precomputed discrete roadmaps, they scale poorly to continuous configuration spaces because committing to a fixed roadmap can either omit optimal solutions or incur prohibitive preprocessing delays. Furthermore, a naive anytime extension that interleaves continuous roadmap densification with optimal discrete solvers introduces cyclic temporal dependencies that render the problem computationally intractable. To address this gap, we introduce Directed Acyclic Roadmap for TAP (DART), an anytime algorithmic framework designed for continuous TAP. DART restricts the incrementally constructed roadmap to a Directed Acyclic Graph (DAG). This key architectural shift eliminates cyclic temporal dependencies, drastically reducing the combinatorial search space evaluated during path optimization. We evaluate DART on both low-dimentional simulated real-world problem and high-dimentional synthetic problem and demonstrate empirically that DART achieves computational speedups of up to three orders of magnitude compared to undirected baseline methods, allowing for rapid incremental updates and the discovery of higher-quality assistance trajectories within a given time budget.
