柔性针的运动学建模及实验研究

Kinematic Modeling and Experimental Study of Flexible Needle

针对带斜尖的柔性针的运动学建模问题,首先简化了WlebsterⅢ等人提出的柔性针非完整约束系统的自行车模型,提出了自行车前、后轮模型.在此基础上,以实际轨迹和误差分析为依据,提出了更符合实际的带返程的自行车模型.采用最小二乘法拟合实验数据,求得模型中各参数.结果表明,带返程的自行车模型远远优于不带返程的模型,其中带返程的前轮模型又优于带返程的后轮模型,且模型的最大误差和误差的均方根都足够小,与实际轨迹吻合度好.

Aiming at the kinematic modeling of bevel-tip flexible needle, this paper simplifies the bicycle model proposed by Webster III et al for the nonholonomic system of the needle, and presents the bicycle front wheel model and back wheel model. Based on this, according to the actual path and the error analysis, a novel bicycle model with retrace is proposed, which is more suitable for the actual condition. The least square method is adopted to fit the experiment data and the model parameters are obtained. Results show that the bicycle model with retrace is much superior to the bicycle model without retrace, and the front wheel model with retrace is superior to the back wheel model with retrace. The maximum error and the root mean square of the model are small enough to fit the actual path well.