The design and implementation of theoretically-sound robot motion planning algorithms is challenging. Within the framework of resolution-exact algorithms, it is possible to exploit soft predicates for collision detection. The design of soft predicates is a balancing act between their implementability and their accuracy/effectivity.

In this paper, we focus on the class of planar polygonal rigid robots with arbitrarily complex geometry. We exploit the remarkable decomposability property of soft collision-detection predicates of such robots. We introduce a general technique to produce such a decomposition. If the robot is an m-gon, the complexity of this approach scales linearly in m. This contrasts with the $O(m^3)$ complexity known for exact planners. It follows that we can now routinely produce soft predicates for any rigid polygonal robot. This results in resolution-exact planners for such robots within the general Soft Subdivision Search (SSS) framework. This is a significant advancement in the theory of sound and complete planners for planar robots.

We implemented such decomposed predicates in our open-source Core Library. The experiments show that our algorithms are effective, perform in real time on non-trivial environments, and can outperform many sampling-based methods.

理论上合理的机器人运动计划算法的设计和实现具有挑战性。在精确分辨率算法的框架内，可以利用软谓词进行碰撞检测。软谓词的设计是其可实现性与准确性/有效性之间的平衡。

在本文中，我们将重点放在具有任意复杂几何形状的平面多边形刚性机器人上。我们利用此类机器人的软碰撞检测谓词的显着可分解性。我们介绍了产生这种分解的通用技术。如果机器人是m边形，则此方法的复杂性以m线性扩展。这与$Ø（{米}^3）$确切的计划者知道的复杂性。因此，我们现在可以常规地为任何刚性多边形机器人生成软谓词。这样就可以在常规的“软细分搜索”（SSS）框架内为此类机器人制定精确的计划制定者。这是平面机器人声音和完整计划者理论的重大进步。

我们在开源核心库中实现了此类分解谓词。实验表明，我们的算法有效，可以在非平凡的环境下实时执行，并且可以胜过许多基于采样的方法。