Interleaving Scheduling and Motion Planning with Incremental Learning of Symbolic Space-Time Motion Abstractions

TL;DR

This work proposes a novel solution framework that interleaves off-the-shelf schedulers and motion planners in an incremental learning loop to generate valid plans under complex temporal and spatial constraints, where synchronized motion is critical.

Abstract

Task and Motion Planning combines high-level task sequencing (what to do) with low-level motion planning (how to do it) to generate feasible, collision-free execution plans. However, in many real-world domains, such as automated warehouses, tasks are predefined, shifting the challenge to if, when, and how to execute them safely and efficiently under resource, time and motion constraints. In this paper, we formalize this as the Scheduling and Motion Planning problem for multi-object navigation in shared workspaces. We propose a novel solution framework that interleaves off-the-shelf schedulers and motion planners in an incremental learning loop. The scheduler generates candidate plans, while the motion planner checks feasibility and returns symbolic feedback, i.e., spatial conflicts and timing adjustments, to guide the scheduler towards motion-feasible solutions. We validate our proposal on logistics and job-shop scheduling benchmarks augmented with motion tasks, using state-of-the-art schedulers and sampling-based motion planners. Our results show the effectiveness of our framework in generating valid plans under complex temporal and spatial constraints, where synchronized motion is critical.

Figures (5)

• Figure 1: SAMP schedule of robots ($r_1$, $r_2$) performing overlapping move–pick–drop tasks. Intervals [$t_i$, $t_j$] indicate start and end times. Robots travel from start locations ($s_1$, $s_2$) to pick components ($c_1$, $c_2$) at ($l_1$, $l_2$) and deliver them to ($d_1$, $d_2$), parallelizing tasks when possible.
• Figure 2: Our framework. Given a SAMP problem $\psi$, the scheduler sends a candidate schedule $\rho$ to the motion planner. If invalid, the planner returns geometric (unreachable configurations $\Sigma$ and obstacles $\Omega$) and temporal (new delays $\overline{d}$ and durations $\overline{\delta}$) refinements until a valid SAMP schedule $\pi$ is found (with trajectories $\tau$), if one exists.
• Figure 3: Parallel motion groups $\mathcal{P}(\pi) = \{\mathcal{G}_1, \mathcal{G}_2, \mathcal{G}_3\}$.
• Figure 4: Temporal refinement for $\mathcal{G}=\{a,b,c\}$, starting at $s_{\min}$ (start of $a$). The motion planner delays the start of $b$ (from $\delta_b$ to $\overline{\delta}_b$) and increases its duration (from $d_b$ to $\overline{d}_b$).
• Figure 5: A logistics scenario with two robots ($r_0, r_1$) delivering two items ($c_0, c_1$) from $l_0$ and $l_1$. The first schedule is infeasible as $\Sigma=\{l_0,l_1\}$ is blocked by $\Omega=\{\text{door}\}$ (Layer 1, RRT). The second schedule is geometrically feasible but trajectories need updated delays $\overline{\delta}$ and durations $\overline{d}$ (Layer 2, ST-RRT*). Such motion planning's feedback leads to a final valid SAMP schedule.

Theorems & Definitions (25)

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