Conditional Timed Partial Orders: An Expressive and Interpretable Framework for Robot Task Specification and Planning

2026-09-07

AI Summary

本文提出条件时序偏序(cTPOs)扩展了时序偏序(TPOs)，增加了相对时间约束和基于环境的条件事件激活，通过分解算法解决由此产生的大规模MILP问题，提高了任务规划效率。

Abstract

Timed Partial Orders (TPOs), originally proposed for workflows, provide an interpretable framework for robot task specification with planning algorithms based on mixed-integer linear programming (MILP). However, TPOs are limited in expressivity, capturing only partial-order events with simple timing constraints. In this paper, we introduce Conditional TPOs (cTPOs), which extend TPOs with richer relative-timing constraints and conditional event activations based on environmental conditions. We show that planning for cTPOs also reduces to an MILP problem; however, the added expressivity results in significantly larger MILPs that can become computationally intractable. To address this challenge, we propose a decomposition algorithm that partitions a cTPO into smaller sub-TPOs, yielding a sequence of smaller MILP problems. We prove that this decomposition is complete and preserves plan optimality while improving the interpretability of complex tasks. Experimental results demonstrate the effectiveness of cTPOs as a task specification framework and the efficiency of our decomposition approach, achieving up to four orders of magnitude speedup over the monolithic MILP.

Problem

• Conditional Timed Partial Orders
• expressivity
• relative-timing constraints
• conditional event activations

Innovation

• Conditional Timed Partial Orders
• relative-timing constraints
• conditional event activations
• decomposition algorithm
• mixed-integer linear programming