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方法的框架来解决制造自动化中出现的运动相关问题。在扫描体积理论方面取得进展是特别有趣的，这将导致在数控（NC）加工、机器人操作等中出现的扫描和扫描体积的表示和分析的改进方法。同样令人感兴趣的是研究微分方程方法作为表征扫描体相交的工具的全部潜力，这将导致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中的程序验证和运动规划问题。任务包括识别扫描的类别，扫描体积中的奇点特征以及检测与障碍物的碰撞（包括静态和动态）。该项目将包括将结果用于实际应用的工作。

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.