Discovering the symbols and rules that can be used in long-horizon planning from a robot's unsupervised exploration of its environment and continuous sensorimotor experience is a challenging task. The previous studies proposed learning symbols from single or paired object interactions and planning with these symbols. In this work, we propose a system that learns rules with discovered object and relational symbols that encode an arbitrary number of objects and the relations between them, converts those rules to Planning Domain Description Language (PDDL), and generates plans that involve affordances of the arbitrary number of objects to achieve tasks. We validated our system with box-shaped objects in different sizes and showed that the system can develop a symbolic knowledge of pick-up, carry, and place operations, taking into account object compounds in different configurations, such as boxes would be carried together with a larger box that they are placed on. We also compared our method with the state-of-the-art methods and showed that planning with the operators defined over relational symbols gives better planning performance compared to the baselines.

翻译：从机器人在其环境中的无监督探索和连续感觉运动经验中发现可用于长期规划的符号和规则是一项具有挑战性的任务。以往的研究提出了从单个或成对物体交互中学习符号并进行规划的方法。在本工作中，我们提出了一种系统，该系统利用发现的对象符号和关系符号学习规则，这些符号可编码任意数量的对象及其之间的关系，并将这些规则转换为规划领域描述语言（PDDL），生成涉及任意数量对象可供性以实现任务的规划。我们使用不同尺寸的盒状物体验证了该系统，结果表明该系统能够开发拾取、搬运和放置操作的符号化知识，同时考虑不同配置下的物体组合（例如放置在较大盒子上的盒子会随较大盒子一起被搬运）。我们还与最先进的方法进行了比较，结果表明，使用基于关系符号定义的算子进行规划，相比基线方法具有更优的规划性能。