论文标题
平面环境中有效的距离束缚路径计划：工作区凸度
Efficient Distance-Optimal Tethered Path Planning in Planar Environments: The Workspace Convexity
论文作者
论文摘要
本文的主要贡献是证明Omni方向连接机器人工作空间的凸度（即，所有绑带长度可加入的机器人配置的集合）以及一组距离距离的距离绑带的路径计划计划算法，这些算法利用工作空间convexexity。该工作空间在拓扑上被证明是一个简单连接的子集，并且在几何上是所有配置集的凸子集。作为一个直接的结果，两种配置之间的束缚长度可加入的最佳路径被证明是通过局部无碰撞的局部最短路径，这是由给定配置的串联曲线串联所指定的同置最短路径，这可以简单地通过在2D环境中执行未固定的路径缩短过程来构建，而不是在搜索过程中执行未经束缚的路径缩短过程。 凸度是束缚机器人运动学的固有特性，因此对所有高级距离距离最佳的束缚的路径计划任务都有普遍的影响：最耗时的工作空间预估算（WP）过程被取代了目标配置（GCP）过程（GCP）过程，并以途径进行了途径。自然提出了受工作空间凸度的激励，有效解决以下问题的有效算法：（a）最佳的束缚重新配置（TR）计划问题是通过局部不受欢迎的路径缩短（UPS）过程来解决的，（ups）过程（b）在启动的位置（tp）的启动位置（b）在某个方面（tp）的范围（tp）求解（tp）是从一个启动的位置来解决的（tp），从而解决了一个目标（tp），从而解决了一个目标（tp）的求解（b）流程和$ n $ ups流程，其中$ n $是访问目标位置的绑定长度亚受欢迎的配置的数量，（c）最佳的束缚动作，访问多个目标位置的序列，称为
The main contribution of this paper is the proof of the convexity of the omni-directional tethered robot workspace (namely, the set of all tether-length-admissible robot configurations), as well as a set of distance-optimal tethered path planning algorithms that leverage the workspace convexity. The workspace is proven to be topologically a simply-connected subset and geometrically a convex subset of the set of all configurations. As a direct result, the tether-length-admissible optimal path between two configurations is proven exactly the untethered collision-free locally shortest path in the homotopy specified by the concatenation of the tether curve of the given configurations, which can be simply constructed by performing an untethered path shortening process in the 2D environment instead of a path searching process in the pre-calculated workspace. The convexity is an intrinsic property to the tethered robot kinematics, thus has universal impacts on all high-level distance-optimal tethered path planning tasks: The most time-consuming workspace pre-calculation (WP) process is replaced with a goal configuration pre-calculation (GCP) process, and the homotopy-aware path searching process is replaced with untethered path shortening processes. Motivated by the workspace convexity, efficient algorithms to solve the following problems are naturally proposed: (a) The optimal tethered reconfiguration (TR) planning problem is solved by a locally untethered path shortening (UPS) process, (b) The classic optimal tethered path (TP) planning problem (from a starting configuration to a goal location whereby the target tether state is not assigned) is solved by a GCP process and $n$ UPS processes, where $n$ is the number of tether-length-admissible configurations that visit the goal location, (c) The optimal tethered motion to visit a sequence of multiple goal locations, referred to as
