点云曲面最优路径规划研究

Path planning is to find a sequence of location transition actions that transform a start position to a goal position with some constraints. Path planning plays an important role in computer graphics and robotics and other real life applications. Currently plenty of algorithms are presented to solve 2D path planning problems, and many successful applications are achieved. However path planning on 3D point clouds is not researched very much since there exists some technical bottlenecks, including: (1) real-time computing on large scale point clouds is really a challenge; (2) discrete point cloud surfaces lack structure and hierarchical information. In this project, we prepare to study the optimal path planning method on point clouds. We mainly focus on developing a real-time A* path searching algorithm, and using deep neural network to compute well approximated distance filed functions on point clouds, and then many distance relevant path planning tasks can be unified into a distance field related path planning problems. This project can promote the research level of our team, and advance related technical progress. Furthermore, our investigation can generalize some existing path planning algorithms in 2D onto point cloud surfaces, and provide a scientific basis for path computing and path navigation on point clouds.

路径规划旨在设计一条满足某些约束，且连接给定起始和终到位置的路径轨迹，其在计算机图形学和机器人等领域都有广泛的应用。目前已有大量算法被提出并成功解决了许多二维路径规划问题。但是由于大规模三维点云的实时计算存在困难，且点云曲面缺少结构信息，使得三维点云曲面上的路径设计面临巨大挑战。本项目拟研究点云曲面上的最优路径规划方法，其中重点研究点云曲面上的实时A*路径搜索算法和动态点云曲面上基于深度神经网络的快速近似解析距离场函数计算方法，将各种距离相关的路径规划任务统一为基于距离场的最优路径规划问题，减少冗余设计和计算。本项目的开展可以解决点云曲面上距离场函数不存在解析解和路径规划的计算效率问题，能够将二维路径规划方法推广至三维点云曲面上，而且有望设计出新的点云曲面上的路径规划算法，推动点云曲面上路径规划相关技术的发展，为机器人等相关应用提供技术支持，并能够促进团队研究水平的提升。

点云曲面最优路径规划旨在给定的起点和终点之间找到一条满足额外约束的路径曲线，其是自动驾驶、智能制造和机器人等领域的核心技术之一。本项目深入探讨了路径规划技术涉及到的关键问题。从传统的路径规划算法的局限性和缺点入手出发，充分利用已有的技术积累，探索点云曲面上路径规划这一热点问题中的新方法与新技术，从而提出了一系列的相关处理方案。本项目按照计划书展开研究，其成果主要以学术论文和专利体现，在国际著名的期刊（Computer-Aided Design, Physica A: Statistical Mechanics and its Applications，Robotica）上发表4篇SCI论文，同时提交申请专利2项。主要成果概括为：（1）改进传统的RRT路径规划算法，使其能够输出确定性的路径曲线，克服了RRT的弱点；（2）针对现有的路径曲线的曲率不易控制问题，给出了一种基于双调和方程的路径规划方案，此方法较其它方法生成的路径更为光滑；（3）在详细地分析点云曲面结构的基础上，给出了点云曲面上的路径的容许启发函数的定义，从而将A*方法拓展到点云曲面上；（4）给出了两种网格曲面上Dirichlet能量之间的关系，为基于网格化的点云曲面的路径规划提供了一种技术支持。