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<h1 class="index-header">
<a href="/2022/03/21/2022-03-21-camera-model/" target="_self">
相机投影模型总结
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</h1>
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<div>
相机投影模型总结 本文旨在总结各种不同的相机投影模型，对于具体建模原理没有涉及。 对于以下的投影操作，此处首先假设已经获得一个待投影的3d点在相机坐标系下的三维坐标[x,y,z]⊤[x,y,z]^{\top}[x,y,z]⊤，接下来通过相机投影后获得的二维像素坐标为[u,v]⊤[u,v]^{\top}[u,v]⊤。 针孔模型——pinhole 针孔相机模型一般有四个参数，记为[fx,fy,cx
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2022-03-21
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<a href="/2021/08/30/2021-08-30-hand-eye-calib/" target="_self">
手眼标定
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<div>
手眼标定 基本原理 手眼标定其实是一种用于标定多传感器之间外参的有效方式。核心方程为 \[ AX = XB \] 此处假设有两种传感器C与I，其中： \(A = T_{C_2}^{C_1}\)是传感器C在1时刻与2时刻之间的相对位姿变换； \(B=T_{I_2}^{I_1}\)是传感器I在1时刻与2时刻之间的相对位姿变换； \(X=T_{I_2}^{C_2} = T_{I_1}^{C_1}\)是
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2021-08-30
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<img src="/img/one-piece/one-piece45.jpg" srcset="/img/loading.gif" lazyload alt="多传感器时间同步方法">
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<h1 class="index-header">
<a href="/2021/08/21/2021-08-21-multi-sensor-time-calib/" target="_self">
多传感器时间同步方法
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</h1>
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多传感器时间同步方案 硬件方案 举个例子 开机fpga便依靠自身的晶振时钟对imu和视觉进行分频触发，保证了imu与视觉的时间同步； 1pps信号输入fpga时间同步板； 当1pps信号出现时，a. fpga会进入中断记录此时自身的时间戳；b. 从gnss接收机获得当前1pps触发时的gnss时间戳;c. 得到fpga与gnss的时间差，完成gnss与vio的时间同步； 此处需要强调
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2021-08-21
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<a href="/2021/06/28/2021-06-28-wheel-sensor/" target="_self">
轮式里程计原理与状态传播数学推导
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轮速计原理 磁电式轮速传感器是由永磁性磁芯和线圈组成。磁力线从磁芯的一极出来，穿过齿圈和空气，返回到磁芯的另一极。由于传感器的线圈圈绕在磁芯上，因此，这些磁力线也会穿过线圈。当车轮旋转时，与车轮同步的齿圈（转子）随之旋转，齿圈上的齿和间隙依次快速经过传感器的磁场，其结果是改变了磁路的磁阻，从而导致线圈中感应电势发生变化，产生一定幅值、频率的电势脉冲。 光电式轮速传感器：轮子转一圈打4096个光电
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零空间投影
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零空间投影 slam中的问题描述 在MSCKF更新模块中，系统的误差方程为 \[ \tilde{z} = z - h(X,P) \approx H_x \tilde{x} + H_f \tilde{p}_f \] 其中X为系统滑窗中的帧集合状态，P为参与更新的3d点集合。此处测量误差其实使用的是重投影误差。因为是一开始使用了系统滑窗帧状态对视觉特征进行三角化得到了3d路标，然后利用这些3d路标投影
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<a href="/2021/06/04/2021-06-04-lagrangian-multipliers/" target="_self">
<img src="/img/one-piece/one-piece42.png" srcset="/img/loading.gif" lazyload alt="拉格朗日乘子法--带约束的最优化问题求解">
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拉格朗日乘子法--带约束的最优化问题求解
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实际工程场景与带约束最小化问题建模 一般情况下，我们通常会遇到这样一种情况，对于一个状态x，我们会对其有很多形如\(f_i(x)=0\)的观测，同时状态x，其本身满足\(g(x)=0\)这样的约束条件。我们想要求解的是在如上已知条件下状态x的最优估计。好了，既然已经有了问题，那么我们需要对其进行一个精确的数学建模。首先，无论如何最后求解得到的状态x是需要满足 \[ g(x) = 0 \] 同时，对
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关于旋转或姿态的扰动求导问题总结
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下面1，2两节都是在哈密顿形式的姿态上进行讨论的，第三节开始涉及JPL与哈密顿的区别。 1 对于可加法因变量的扰动求导 因为加法本身是无向的（左右等价），所以没有左右扰动的概念。但是对于旋转矩阵群，左乘和右乘是不等价的，因此左右扰动的概念仅仅在不适用加法的群上存在。 1.1 左扰动雅克比 \[ \begin{aligned} \frac{\partial(\boldsymbol{R} \b
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机器人领域常用数学转换总结
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向量与其反对称矩阵之间的转换 \[ \lfloor\mathbf{v}\times\rfloor = \begin{bmatrix} 0 & -v_3 & v_2 \\ v_3 & 0 & -v_1 \\ -v_2 & v_1 & 0 \end{bmatrix} \] 向量->反对称矩阵 12345inline Eigen::Matrix&l
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关于Ax=b形式的矩阵分解与求解问题
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对于一个线性方程\(Ax=b\)，其中A的维度为\(m\times n， m \geq n\)，\(x\)的维度为\(n\times 1\)，b的维度为\(m \times 1\)，则在A满秩的情况下，\(x\)有解且唯一。 对于高斯牛顿法，我们一般求解的是\(J^T J x = J^T b\)，其中\(J\)为残差\(b\)对状态\(x\)的雅克比矩阵，维度为\(m*n\)，这样的话其实更加简
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线性系统的误差状态的维护 在基于滤波方法的状态估计问题中，需要实时维护系统的误差状态（也就是系统变量的协方差矩阵），本文主要对系统的误差状态进行分析。 对于线性系统，从k时刻到k+1时刻的状态传播转移 \[ \hat{\boldsymbol{x}}_{k+1}=\boldsymbol{A}_{k} \hat{\boldsymbol{x}}_{k}+ \boldsymbol{B}_k \bo
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