Consider the problem of planning collision-free motion of n objects movable through contact with a robot that can autonomously translate in the plane and that can move a maximum of \(m \le n\) objects simultaneously. This represents the abstract formulation of a general class of manipulation planning problems that are proven to be decidable in this paper. The tools used for proving decidability of this simplified manipulation planning problem are, in fact, general enough to handle the decidability problem for the wider class of systems characterized by a stratified configuration space. These include, e.g., problems of legged and multi-contact locomotion, bi-manual manipulation. In addition, the approach described does not restrict the dynamics of the manipulation system modeled.

考虑规划通过与机器人接触可移动的n个对象的无碰撞运动的问题，该机器人可以在平面中自主平移，并且最多可以同时移动\（m \ le n \）个对象。这代表了一般类别的操纵计划问题的抽象表述，在本文​​中证明是可以确定的。实际上，用于证明此简化的操纵计划问题的可判定性的工具足够通用，可以处理以分层配置空间为特征的更广泛的系统类别的可判定性问题。这些包括，例如，腿式和多触点运动，双向操纵的问题。另外，所描述的方法不限制建模的操纵系统的动力学。