====== Armadillo Calibration ======

===== Odometri constants =====
It is assumed that the turningpoint for the belts is the center of the belts.

  cl = 0.00348377
  cr = 0.003193242
  w = 1.68336
{{:robots:armadillo:calibration:clockwise_graph.png?350|}}
{{:robots:armadillo:calibration:counterclockwise_graph.png?350|}}
===== UMB-mark test =====

{{:robots:armadillo:calibration:calibration_umb.xlsx|UMB test}} (168 KB) Data and calculation showed in this page

Where am I? Sensors and Methods for Mobile Robot Positioning: \\
{{:robots:armadillo:calibration:pos96rep.pdf|Download book from University of Michigan}} (12.2 MB)\\
Chapter 5 is used as the base for these calculation. The two following articles describe the process in greater detail.

Measurement and Correction of Systematic, Odometry Errors in Mobile Robots:\\ 
{{:robots:armadillo:calibration:paper58.pdf|Download Paper 58}} (803 KB)

Correction of Systematic Odometry Errors in Mobile Robots:\\ 
{{:robots:armadillo:calibration:paper59.pdf|Download Paper 59}} (177 KB)



=== BEFORE CALIBRATION ===

$r_{c.g.,cw}=\sqrt{(X_{c.g.,cw})^2+(Y_{c.g.,cw})^2}$


$r_{c.g.cw} = 83.43 cm $\\
$r_{c.g.ccw} = 128.67 cm$ \\
$L = 2 m $\\

{{:robots:armadillo:calibration:beforecalibration_graph.png?370|}}

^CLOCKWISE, cw^^^^
^	^ϵx [cm]^	^ϵy [cm]^
|1	|-63	|	|-63.5|
|2	|-50.5	|	|-59|
|3	|-34	|	|-65|
|4	|-26.5	|	|-78.5|
|5	|-41	|	|-91.5|
|X<sub>c.g.</sub>=|-43|Y<sub>c.g.</sub>=|-71.5|


{{:robots:armadillo:calibration:beforecalibration_clockwise.png?350|}}

{{:robots:armadillo:calibration:beforecalibration_clockwise_route.png?370|}}

^COUNTERCLOCKWISE, ccw^^^^
^	^ϵx [cm]^	^ϵy [cm]^
|1	|-71	|	|97|
|2	|-100	|	|112|
|3	|-74	|	|87|
|4	|-69	|	|123|
|5	|-65.5	|	|100.5|
|X<sub>c.g.</sub>=|-75.9|Y<sub>c.g.</sub>=|103.9|

{{:robots:armadillo:calibration:beforecalibration_counterclockwise.png?350|}}

{{:robots:armadillo:calibration:beforecalibration_counterclockwise_route.png?370|}}


=== Calculations ===

$$\alpha = \frac{x_{c.g.,cw}+x_{c.g.,ccw}}{-4L}\cdot \frac{(180^{\circ})}{\pi}$$
|α = |851.99 cm|
|    |8.5199 m |

$$ \beta = \frac{x_{c.g.,cw}-x_{c.g.,ccw}}{-4L}\cdot \frac{(180^{\circ})}{\pi} $$
|β = |-235.7484 cm|
|    |-2.357 m |


$$R = \frac{L/2}{sin(\beta /2)} $$
|R = |-48.7 m|

$$E_d = \frac{D_R}{D_L} = \frac{R+b/2}{R-b/2} $$
|b = |1.524 m|
|$E_d$ =|0.969 |

$$b_{actual} = \frac{90^{\circ}}{90^{\circ}-\alpha}\cdot b_{nominal} $$
|$b_{actual}$ =|1.6834|calibrated value of wheelbase|
| ::: |1.524|before calibration|

$$c_l = \frac{2}{E_d+1} $$

$$c_r = \frac{2}{(1/E_d)+1} $$
^ ^Correction factor ^Before Calibration^After Calibration^
|$c_l$ =|1.0156 |0.00343|0.003484 |
|$c_r$ =|0.9844 |0.00324 |0.003193|


=== AFTER CALCULATION ===
$r_{c.g.,cw}=\sqrt{(X_{c.g.,cw})^2+(Y_{c.g.,cw})^2}$

$r_{c.g.cw} = 4.12 cm$ \\
$r_{c.g.ccw} = 29.35 cm$ \\

^CLOCKWISE, cw^^^^
^	^ϵx [cm]^	^ϵy [cm]^
|1	|-6	|	|-14.5|
|2	|-12.5	|	|-10|
|3	|5.5	|	|8|
|4	|-5.5	|	|-7|
|5	|2.5	|	|10.5|
|X<sub>c.g.</sub>=	|-3.2	|Y<sub>c.g.</sub>=	|-2.6|

{{:robots:armadillo:calibration:aftercalibration_clockwise.png?350|}}

^COUNTERCLOCKWISE, ccw^^^^
^	^ϵx [cm]^	^ϵy [cm]^
|1	|-38.5	|	|24|
|2	|-27	|	|10|
|3	|-19.5	|	|11|
|4	|-22.5	|	|20|
|5	|-22	|	|4 |
|X<sub>c.g.</sub>=|-25.9|Y<sub>c.g.</sub>=|13.8|

{{:robots:armadillo:calibration:aftercalibration_counterclockwise.png?350|}}