[Matlab six-degree-of-freedom robot] Explanation of the double-variable function atan2(x,y)

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【Main line】

1. Build a robot model
2. Correct solution of kinematics
3. Construction of workspace based on Monte Carlo Method

【Supplementary explanation】

1. Understanding of Flexible Workspaces and Accessible Workspaces
2. Detailed establishment steps of modified DH parameters (modified Denavit-Hartenberg)
3. Questions about parameterization of rotation (Euler angles, attitude angles, quaternions)

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About the atan2() function

Using the bivariate function $Atan2(y,x)$计算$The\; advantage\; of\; arctan(y/x)$ is that it uses the signs of x and y, so it candetermine the quadrant of the resulting angle。

For example:
$Atan2(-2.0,-2.0)=-135°$

rad2deg(atan2(-2.0,-2.0))

$Atan2(2.0,2.0)=45°$

rad2deg(atan2(2.0,2.0))

However , the two angles cannot be distinguished using the univariate arctangent function

For example:
$Atan(2.0/2.0)=45°$

rad2deg(atan(2.0/2.0))

Then $Atan(-2.0/-2.0)=45°$

rad2deg(atan(-2.0/-2.0))```

Since the range we set when calculating the angle is usually $360°$ , so the Atan2() function is used. The advantage of the two-variable arctangent function is also known as the "4-quadrant arctangent" function, which is specified in some libraries, such asmatlab. Finally, it is stipulated that when both variables are zero,$Atan2(0,0)=0$