Several planners have been developed to compute dynamically feasible, collision-free robot paths from an initial to a goal configuration. A key assumption in these works is that the goal region is reachable; an assumption that often fails in practice when environments are disconnected. Motivated by this limitation, we consider known 3D environments comprising objects, also called blocks, that form distinct navigable support surfaces (planes), and that are either non-movable (e.g., tables) or movable (e.g., boxes). These surfaces may be mutually disconnected due to height differences, holes, or lateral separations. Our focus is on tasks where the robot must reach a goal region residing on an elevated plane that is unreachable. Rather than declaring such tasks infeasible, an effective strategy is to enable the robot to interact with the environment, rearranging movable objects to create new traversable connections; a problem known as Navigation Among Movable Objects (NAMO). Existing NAMO planners typically address 2D environments, where obstacles are pushed aside to clear a path. These methods cannot directly handle the considered 3D setting; in such cases, obstacles must be placed strategically to bridge these physical disconnections. We address this challenge by developing BRiDGE (Block-based Reconfiguration in Disconnected 3D Geometric Environments), a sampling-based planner that incrementally builds trees over robot and object configurations to compute feasible plans specifying which objects to move, where to place them, and in what order, while accounting for a limited number of movable objects. To accelerate planning, we introduce non-uniform sampling strategies. We show that our method is probabilistically complete and we provide extensive numerical and hardware experiments validating its effectiveness.

翻译：已有多种规划器被开发用于计算机器人从初始构型到目标构型的动态可行且无碰撞的路径。这些工作的一个关键假设是目标区域可达；然而，当环境非连通时，这一假设在实践中常常不成立。受此局限性的启发，我们研究已知的三维环境，该环境包含构成不同可导航支撑面（平面）的物体（也称为块体），这些物体可以是不可移动的（例如桌子）或可移动的（例如箱子）。这些支撑面可能由于高度差、孔洞或横向分离而相互不连通。我们的研究重点在于机器人必须到达位于一个无法抵达的升高平面上的目标区域的任务。与其宣布此类任务不可行，一种有效的策略是使机器人能够与环境交互，重新排列可移动物体以创建新的可穿越连接；这一问题被称为可移动物体间导航（NAMO）。现有的NAMO规划器通常处理二维环境，通过推开障碍物来清理路径。这些方法无法直接处理所考虑的三维场景；在这种情况下，必须策略性地放置障碍物以弥合这些物理上的不连通性。我们通过开发BRiDGE（非连通三维几何环境中的基于块体的重配置），一种基于采样的规划器，来应对这一挑战。该规划器在机器人和物体构型上增量地构建树，以计算可行的规划，指定移动哪些物体、将其放置于何处以及以何种顺序进行，同时考虑可移动物体的数量限制。为了加速规划，我们引入了非均匀采样策略。我们证明了我们的方法是概率完备的，并提供了大量的数值和硬件实验来验证其有效性。