Studying Sweeps and Swept Volumes Via Differential Equation Approach

主要的研究目标是开发一个基于最近发现的微分方程式方法的框架，用于解决制造自动化中出现的与运动相关的问题。特别感兴趣的是在扫描体理论中产生进步，这将导致表示和分析在数控(NC)加工、机器人操作等中出现的扫描体和扫描体的改进的手段。还感兴趣的是研究作为表征扫描体的交点的工具的微分方程式方法的全部潜力，这导致了碰撞检测和其他运动规划问题的解决方案。该方法将应用于数控加工和机器人领域中的程序验证和运动规划问题。这些任务包括识别扫掠类别、表征扫掠体的奇异性以及检测与障碍物(静态和动态)的碰撞。该项目将包括将成果落实到实际应用中的工作。

The primary research objective is to develop a framework based on the recently discovered differential equation approach for solving motion related problems that arise in manufacturing automation. It is of particular interest to produce an advance in the theory of swept volumes, which will lead to improved means of representing and analyzing sweeps and swept volumes that occur in numerically controlled (NC) machining, robot manipulation, etc. Also of interest is to investigate the full potential of the differential equation approach as a tool for characterizing intersections of swept volumes, which leads to solutions for collision detection and other motion planning problems. The method will be applied to program verification and motion planning problems in NC machining and robotics. The tasks include identification of classes of sweeps, characterization of singularities in swept volumes and detection of collision with obstacles (both static and dynamic). The project will include work on implementing the results for practical applications.