基于泰勒级数的3D匀速运动控制算法及误差分析

在高强度聚焦超声（HIFU）治疗肿瘤过程中,需要针对肿瘤形状制定最有效的照射轨迹,在最短时间内最精确地按照预定轨迹对肿瘤组织进行理疗.文中以一阶泰勒级数为插补算法基础,提出了具有实际意义的“曲线线速度”概念,并对任意参数曲线线速度误差进行改进,同时保证插补的步长误差与弦高误差在允许范围内.特别以空间椭圆螺旋线为例,详细推导了插补算法并分析插补误差.在S3C44B0X单片机控制的三维移动机构上,利用μC/OSⅡ RTOS内核控制运动,实现了包括直线、椭圆、空间螺旋线等匀速运动.实验结果表明,本算法能有效控制线速度的稳定性并同时保证步长误差和弦高误差在允许范围内.

3D Uniform Motion Control Method Based on Taylor Series and Accuracy Analysis

In the process of using high intensity focused ultrasound (HIFU) system to ablate tumor tissue, the irradiation trajectory needs to be optimized based on tumor’s shape. So the tumor can be effectively treated in the shortest time. Based on the first-order-Taylor series interpolation algorithm, the actual "linear velocity" concept was proposed, and the linear velocity error was improved for any kind of movement along parametric curves. The new control method can also effectively maintain the step-size shift and chord deviation within the permitted range. Particularly, the derivative of interpolation algorithm for spatial spiral trajectory was explained in details and its accuracy was analyzed. The μC/OS II RTOS kernel was used to control the movement, and some movement, such as straight line, ellipse, spirals, etc., were realized to validate the proposed interpolation method and accuracy evaluation method. The experiments show that the stability of the linear velocity is also verified and it can also effectively maintain the step-size shift and chord deviation within the permitted range.