Technical solution of vision and manipulator calibration system

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One  、 Two cases of hand eye calibration

          First, let's talk about industrial applications , Hands and eyes （ The camera ） Two positional relationships , The first is to put the camera （ eye ） Fixed on the manipulator （ hand ） above , Move your eyes with your hands ; The second is the camera （ eye ） And manipulator （ hand ） Separate , The position of the eye is fixed relative to the hand , Here are two pictures on the Internet to illustrate ：

  Case one ： Camera movement

The second case ： The camera is fixed

As can be seen from the above two schematic diagrams , In the first case, we require the transformation relationship between the camera coordinate system and the manipulator coordinate system ; In the second case, the relationship between the camera coordinate system and the basic coordinate system is required ; The following describes the solution process .

Two 、 When the camera moves , Calibration solution process

          In the derivation , We'll use four coordinate systems , They are the basic coordinate system , Manipulator coordinate system , Camera coordinate system , And the coordinate system of the calibration object , The following is a schematic diagram ：

among baseHcal Represents the transformation relationship from the basic coordinate system to the calibration object coordinate system , Including rotation matrix and translation vector ;camHtool Represents the transformation relationship from camera coordinate system to manipulator coordinate system ; These two transformation relations remain unchanged during the movement of the manipulator ;camHcal It can be calculated by camera calibration ;baseHtool Can be derived from the robot system .

Next, control the robot hand from the position 1 Move to location 2：

base = baseHtool （1）* tool（1）

tool（1） = inv（camHtool）*cam（1）

cam（1） = camHcal（1）*obj

Combine the above three formulas ：

base = baseHtool （1）* inv（camHtool）* camHcal（1）*obj

Move to the robot position 2 after ：

base = baseHtool （2）* inv（camHtool）* camHcal（2）*obj

because base and obj It's fixed, so ：

baseHtool （1）* inv（camHtool）* camHcal（1）=baseHtool （2）* inv（camHtool）* camHcal（2）

Only one camHtool It's an unknown quantity , The specific solution process will be put in the next article .

3、 ... and 、 When the camera is fixed , Calibration solution process

In the case of a fixed camera , Or control the manipulator from the position 1 Move to location 2：

obj（1） = inv（camHcal(1)) *cam

cam = camHbase *base

base = baseHtool（1） * tool(1)

Combine the above three formulas ：

obj（1） = inv（camHcal(1))  * camHbase* baseHtool（1） *tool（1）

Move to location 2 after ：

obj（2） = inv（camHcal(2))  * camHbase* baseHtool（2） *tool（2）

because obj and tool The relative position of is constant , So no matter how you move ：

inv（camHcal(1))  * camHbase* baseHtool（1）= inv（camHcal(2))  * camHbase* baseHtool（2）

There are only variables camHbase, That's what we're asking for .

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