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--- robots:armadillo:calibration:welcome [2012/10/10 19:16]
karina [UMB-mark test]
+++ robots:armadillo:calibration:welcome [2021/08/14 04:21] (current)
@@ Line 2: / Line 2: @@
 ===== Odometri constants =====
-It is asumed that the tuningpoint for the belts is the center of the belts.
+It is assumed that the turningpoint for the belts is the center of the belts.
-  cl=0.00348377
+  cl = 0.00348377
-  cr=0.003193242
+  cr = 0.003193242
-  w =1.68336
+  w = 1.68336
 {{:robots:armadillo:calibration:clockwise_graph.png?350|}}
 {{:robots:armadillo:calibration:counterclockwise_graph.png?350|}}
-==== UMB-mark test ====
+===== 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)
-{{:robots:armadillo:calibration:calibration_umb.xlsx|UMB}} (168 KB)
 === BEFORE CALIBRATION ===
@@ Line 18: / Line 30: @@
-r c.g.cw(cm) = 83,43 \\
+$r_{c.g.cw} = 83.43 cm $\\
-r c.g.ccw(cm) = 128,6701986 \\
+$r_{c.g.ccw} = 128.67 cm$ \\
-L=2m \\
+$L = 2 m $\\
 {{:robots:armadillo:calibration:beforecalibration_graph.png?370|}}
-^CLOCKWISE^^^^
+^CLOCKWISE, cw^^^^
 ^	^ϵx [cm]^	^ϵy [cm]^
-|1	|-63	|	|-63,5|
+|1	|-63	|	|-63.5|
-|2	|-50,5	|	|-59|
+|2	|-50.5	|	|-59|
 |3	|-34	|	|-65|
-|4	|-26,5	|	|-78,5|
+|4	|-26.5	|	|-78.5|
-|5	|-41	|	|-91,5|
+|5	|-41	|	|-91.5|
-|Xc.g.=	|-43	|Yc.g.=	|-71,5|
+|X<sub>c.g.</sub>=|-43|Y<sub>c.g.</sub>=|-71.5|
@@ Line 38: / Line 50: @@
 {{:robots:armadillo:calibration:beforecalibration_clockwise_route.png?370|}}
-^COUNTERCLOCKWISE^^^^
+^COUNTERCLOCKWISE, ccw^^^^
 ^	^ϵx [cm]^	^ϵy [cm]^
 |1	|-71	|	|97|
@@ Line 44: / Line 56: @@
 |3	|-74	|	|87|
 |4	|-69	|	|123|
-|5	|-65,5	|	|100,5|
+|5	|-65.5	|	|100.5|
-|Xc.g.=|-75,9	|Yc.g.=	|103,9|
+|X<sub>c.g.</sub>=|-75.9|Y<sub>c.g.</sub>=|103.9|
 {{:robots:armadillo:calibration:beforecalibration_counterclockwise.png?350|}}
@@ Line 52: / Line 64: @@
-== Calculations ==
+=== Calculations ===
+$$\alpha = \frac{x_{c.g.,cw}+x_{c.g.,ccw}}{-4L}\cdot \frac{(180^{\circ})}{\pi}$$
+|α = |851.99 cm|
+|    |8.5199 m |
-$\alpha = \frac{x_{c.g.,cw}+x_{c.g.,ccw}}{-4L}\cdot \frac{(180)}{\pi}$
+$$ \beta = \frac{x_{c.g.,cw}-x_{c.g.,ccw}}{-4L}\cdot \frac{(180^{\circ})}{\pi} $$
-|α = |851,99 cm|
+|β = |-235.7484 cm|
-|    |8,5199 m |
+|    |-2.357 m |
-{{:robots:armadillo:calibration:formula_beta.png?320|}}
-|β = |-235,7484076 cm|
-|    |-2,357 m |
-{{:robots:armadillo:calibration:formula_r.png?170|}}
+$$R = \frac{L/2}{sin(\beta /2)} $$
-|R(m)= |-48,7|
+|R = |-48.7 m|
-{{:robots:armadillo:calibration:formula_ed.png?250|}}
+$$E_d = \frac{D_R}{D_L} = \frac{R+b/2}{R-b/2} $$
 |b = |1.524 m|
-|Ed =|0,9692 |
+|$E_d$ =|0.969 |
-{{:robots:armadillo:calibration:formula_bactual.png?280|}}
+$$b_{actual} = \frac{90^{\circ}}{90^{\circ}-\alpha}\cdot b_{nominal} $$
-|b -actual =|	1,68336|calibrated value of wheelbase|
+|$b_{actual}$ =|1.6834|calibrated value of wheelbase|
 | ::: |1.524|before calibration|
-{{:robots:armadillo:calibration:formula_cl.png?180|}}
+$$c_l = \frac{2}{E_d+1} $$
-{{:robots:armadillo:calibration:formula_cr.png?180|}}
+$$c_r = \frac{2}{(1/E_d)+1} $$
 ^ ^Correction factor ^Before Calibration^After Calibration^
-|cl =|1,0156 |0,0034301|0,00348377 |
+|$c_l$ =|1.0156 |0.00343|0.003484 |
-|cr =|0,9844 |0,003244 |0,003193242|
+|$c_r$ =|0.9844 |0.00324 |0.003193|
@@ Line 84: / Line 97: @@
 $r_{c.g.,cw}=\sqrt{(X_{c.g.,cw})^2+(Y_{c.g.,cw})^2}$
-r c.g.cw(cm) = 4,12 \\
+$r_{c.g.cw} = 4.12 cm$ \\
-r c.g.ccw(cm) = 29,35 \\
+$r_{c.g.ccw} = 29.35 cm$ \\
-^CLOCKWISE^^^^
+^CLOCKWISE, cw^^^^
 ^	^ϵx [cm]^	^ϵy [cm]^
-|1	|-6	|	|-14,5|
+|1	|-6	|	|-14.5|
-|2	|-12,5	|	|-10|
+|2	|-12.5	|	|-10|
-|3	|5,5	|	|8|
+|3	|5.5	|	|8|
-|4	|-5,5	|	|-7|
+|4	|-5.5	|	|-7|
-|5	|2,5	|	|10,5|
+|5	|2.5	|	|10.5|
-|Xc.g.=	|-3,2	|Yc.g.=	|-2,6|
+|X<sub>c.g.</sub>=	|-3.2	|Y<sub>c.g.</sub>=	|-2.6|
 {{:robots:armadillo:calibration:aftercalibration_clockwise.png?350|}}
-^COUNTERCLOCKWISE^^^^
+^COUNTERCLOCKWISE, ccw^^^^
 ^	^ϵx [cm]^	^ϵy [cm]^
-|1	|-38,5	|	|24|
+|1	|-38.5	|	|24|
 |2	|-27	|	|10|
-|3	|-19,5	|	|11|
+|3	|-19.5	|	|11|
-|4	|-22,5	|	|20|
+|4	|-22.5	|	|20|
 |5	|-22	|	|4 |
-|Xc.g.=	|-25,9	|Yc.g.=	|13,8|
+|X<sub>c.g.</sub>=|-25.9|Y<sub>c.g.</sub>=|13.8|
 {{:robots:armadillo:calibration:aftercalibration_counterclockwise.png?350|}}

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