Versine Curve Acc/Dec Snap Continuous Control Algorithm
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摘要: 针对传统的加减速算法如S型曲线加加速度不连续、正弦型曲线加加加速度(snap)不连续导致进给过程中存在柔性冲击等问题,提出snap连续的全类型非对称七段式正矢曲线加减速控制算法。通过利用系统最优机械性能,分析最大加、减速度和最大速度的可达性,规划17种速度曲线类型;针对给定轨迹段长度小于系统从起点速度运动到终点速度所需最短轨迹段长的问题,给出该算法下基于给定轨迹段长约束的起点速度和终点速度的可达性校验方法,同时采用盛金公式修正起点速度和终点速度。在自主开发的多轴运动控制器验证所提出的snap连续的全类型非对称七段式正矢曲线加减速控制算法。实验结果表明:在保证snap连续以提高系统柔性及最大加、减速度和最大速度不超限情况下,该算法可规划出17种速度曲线类型;在给定轨迹段长度较短系统无法从起点速度运动到终点速度的情形下,该算法解决起点速度和终点速度的可达性校验及修正问题。Abstract: For the traditional acceleration and deceleration algorithms such as S-curve jerk discontinuity, sinusoidal curve snap discontinuity leads to flexible impact in the feed process, an acceleration & deceleration snap continuous control algorithm with asymmetric seven-segment versine curve is proposed in this paper. Considering the optimal mechanical performance of the system, by analyzing the maximum acceleration, maximum deceleration and maximum speed accessibility, 17 types of speed curves are planned; Aiming at the problem that the length of a given trajectory segment is smaller than the shortest trajectory segment length required for the system to move from the starting velocity to the ending velocity, a method for verifying the reachability of the starting velocity and the ending velocity based on the length constraint of the given trajectory segment is proposed. Meanwhile, the Shengjin formula is used to correct the starting speed and the ending speed. The self-developed multi-axis motion controller verifies the proposed all-type asymmetric seven-segment versine curve acceleration & deceleration snap continuous control algorithm. The experimental results show that the algorithm can plan 17 types of speed curves under the condition that the snap is continuous to improve system flexibility and the maximum acceleration, the maximum deceleration and the maximum speed are not exceeded. The problem of reachability check and correction of starting speed and ending speed under constraint of a given trajectory length can be solved.
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Key words:
- versine curve /
- asymmetric /
- seven-segment /
- Shengjin formula /
- reachability checking /
- jerk
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表 1 简易运动控制系统平台相关系数
核心部件 型号 相关参数 主运动控制器 DSP(TMS32C6655) 主频1.5GHz; CCS7.2.0 从运动控制器 DSP(TMS32C6713) 主频200MHz; CCS3.3 FIFO FPGA XILINX XC3S400A:16bit*32 DPRAM FPGA Altera CYCLONE V 5CEFA4F23C8N 四轴运动控制器 FPGA Altera CYCLONE III EP3C40F484C8 伺服驱动器 松下A4(MADDT1205003) 三环控制:位置、速度、转矩 伺服电机 松下A4(MSMD012P1U) 额定转速3 000 r/min; 2 500脉冲/转; 滚珠丝杠 —— 导程4 mm 表 2 17种类型参数曲线的轨迹参数
实验组别 参数曲线类型 轨迹段长/mm 起点速度/(mm·s-1) 终点速度/(mm·s-1) 最大速度/(mm·s-1) 1 1 4.000 20.000 60.000 60.000 2 2 10.000 20.000 60.000 60.000 3 3 70.000 20.000 300.000 300.000 4 4 120.000 20.000 300.000 300.000 5 5 4.000 60.000 20.000 60.000 6 6 10.000 60.000 20.000 60.000 7 7 70.000 300.000 20.000 300.000 8 8 120.000 300.000 20.000 300.000 9 9 10.000 20.000 30.000 60.000 10 10 100.000 20.000 120.000 240.000 11 11 100.000 120.000 20.000 240.000 12 12 110.000 20.000 30.000 240.000 13 13 20.000 20.000 30.000 60.000 14 14 140.000 20.000 120.000 240.000 15 15 140.000 120.000 20.000 240.000 16 16 140.000 20.000 30.000 240.000 17 17 10.000 20.000 20.000 20.000 表 3 17种类型轨迹参数加减速控制各运动段运动时间
组别 线型 七个运动段时间/ms T1 T2 T3 T4 T5 T6 T7 1 1 0.068 0 0.068 0 0 0 0 2 2 0.100 0 0.100 0.033 0 0 0 3 3 0.200 0.100 0.200 0. 0 0 0 4 4 0.200 0.150 0.200 0.107 0 0 0 5 5 0 0 0 0 0.067 0 0.067 6 6 0 0 0 0.041 0.094 0 0.094 7 7 0 0 0 0 0.200 0.080 0.200 8 8 0 0 0 0.127 0.200 0.111 0.200 9 9 0.081 0 0.081 0 0.060 0 0.060 10 10 0.200 0.042 0.200 0 0.144 0 0.144 11 11 0.153 0 0.153 0 0.200 0 0.200 12 12 0.200 0.058 0.200 0 0.200 0.018 0.200 13 13 0.100 0 0.100 0.078 0.082 0 0.082 14 14 0.200 0.075 0.200 0.081 0.163 0 0.163 15 15 0.173 0 0.173 0.083 0.200 0.044 0.200 16 16 0.200 0.075 0.200 0.082 0.200 0.033 0.200 17 17 0 0 0 0.500 0 0 0 -
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