本文的亮点在于找到了用贝兹曲线来拟合绝对定位的结果点，从而获得一条比较平滑的曲线，就可以做积分求运动长度等其他应用。
用于在消化道移动的胶囊机器人的一个新型相对位置估计理论
A Novel Relative Position Estimation Method for Capsule Robot Moving in Gastrointestinal Tract [1]
Paper Link
Authors: Min Wang, etc.
2019，Sensors
1. 摘要 Abstract
为了克服这个缺点和提供一个恰当的位置描述理论来匹配这消化道，我们在这儿提出一个相对位置 [2] Paper Link 估计理论用于追踪胶囊机器人，这个理论用机器人沿着消化道的运动距离来表示位置结果。所提出的理论的流程按如下几步：首先，胶囊机器人的绝对位置结果通过磁追踪理论被获得；然后，机器人沿着消化道的运动状态根据运动方向被决定；最后，胶囊机器人的运动轨迹被拟合为贝兹曲线，这样运动距离能够然后使用积分理论被评估。
To overcome this disadvantage and provide a proper position description method to match the GI tract, we here present a relative position [2] Paper Link estimation method for tracking capsule robot, which uses the moving distance of the robot along the GI tract to indicate the position result. The procedure of the proposed method is as followings: firstly, the absolute position results of the capsule robot are obtained with the magnetic tracking method; then, the moving status of the robot along the GI tract is determined according to the moving direction; and finally, the movement trajectory of the capsule robot is fitted with the B e ˊ \acute{e} eˊzier, where the moving distance can then be evaluated using the integral method.
2. 移动距离，曲线拟合 moving distance, curve fitting
为了最小化距离累计的误差和最佳匹配胶囊机器人的运动长度，贝兹曲线被使用来拟合采样点来使得路径更加平滑。
To minimize the error of distance accumulation and better match the moving length of the capsule robot, the B e ˊ \acute{e} eˊizer curve was used to fit the sampling points to make the path smoother.
贝兹曲线能够被看作来产生一条平滑曲线，这条曲线减少由于振荡产生的距离误差。在这篇文章中， B n B_{n} Bn的每一部分都被一片二次方贝兹曲线拟合。每一段曲线的长度然后通过积分每一段拟合曲线被计算。最后，胶囊机器人的运动长度被获得通过累加前进到出口的长度和减去后退的长度。
The B e ˊ \acute{e} eˊizer curve can be seen to produce a smooth curve that reduces distance error due to oscillation. In this paper, every section of B n B_{n} Bn was fitted by a piece of a quadratic B e ˊ \acute{e} eˊizer curve. The length of each curve was then calculated by integrating each fitting curve. Finally, the moving length of the capsule robot was gained by adding the distance of moving toward the exit and subtracting the length moving backward.
二次方贝兹曲线的一般形式被表示为如下：
The general form of the quadratic B e ˊ \acute{e} eˊizer curve is presented as follows:
B t = ( 1 − t ) 2 P 0 + 2 t ( 1 − t ) P 1 + t 2 P 2 \textbf{B}_t=(1-t)^{2}\textbf{P}_{0}+2t(1-t)\textbf{P}_{1}+t^{2}\textbf{P}_{2} Bt=(1−t)2P0+2t(1−t)P1+t2P2
这里的 t ∈ [ 0 , 1 ] t\in[0,1] t∈[0,1]。对于每一个贝兹曲线，每个点的位置 P i , i = 0 , 1 , 2 \textbf{P}_{i}, i=0,1,2 Pi,i=0,1,2能够从绝对追踪结果中被获得。
where t ∈ [ 0 , 1 ] t\in[0,1] t∈[0,1]. For each B e ˊ \acute{e} eˊizer curve, positions of each point P i , i = 0 , 1 , 2 \textbf{P}_{i}, i=0,1,2 Pi,i=0,1,2 can be obtained from the absolute tracking results.
因此，每一段长度能被获得通过积分 B t \textbf{B}_t Bt，为：
Therefore, every segment length can be obtained by integrating B t \textbf{B}_t Bt, which is:
d i s t a n c e = ∫ P 0 P 2 B t d t distance=\int_{\textbf{P}_{0}}^{\textbf{P}_{2}}\textbf{B}_{t}dt distance=∫P0P2Btdt
最后胶囊机器人的移动长度能被得到通过累加贝兹曲线的每一段长度，为：
The final moving length of the capsule robot can be obtained by adding each length of the B e ˊ \acute{e} eˊizer curve, which is:
L = ∑ ( d i s t a n c e + ) − ∑ ( d i s t a n c e − ) L=\sum(distance_{+})-\sum(distance_{-}) L=∑(distance+)−∑(distance−)
[1]: Wang, Min, et al. “A Novel Relative Position Estimation Method for Capsule Robot Moving in Gastrointestinal Tract.” Sensors 19.12 (2019): 2746.
[2]: Xu, Yangxin, and Max Q-H. Meng. “Free Sensor Array Based Relative Localization System for Wireless Capsule Endoscopy.” 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO). IEEE, 2018.