Studying Sweeps and Swept Volumes Via Differential Equation Approach

主要研究目标是建立一个基于 最近发现的微分方程方法， 解决制造过程中出现的运动相关问题 自动化. 特别令人感兴趣的是， 波及体积理论，这将导致改进的手段， 表示和分析扫描和扫描体积， 数控（NC）加工、机器人操作等。 同样令人感兴趣的是研究 微分方程方法作为表征 扫描体积的交叉点，这导致解决方案， 碰撞检测和其它运动规划问题。 该方法可应用于程序验证和运动控制 数控加工和机器人技术中的规划问题。 这些任务包括 扫描类别的识别， 扫描体积中的奇异性和碰撞检测 障碍（静态和动态）。 该项目将包括工作 将结果用于实际应用。

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.