145482 | 39 | … | … | … | … | … | …
145501 | 244 | 130 | … | … | … | 182 | 32
Table 1: continued. HD | EW | EW | EW | EW | EW | EW | EW
---|---|---|---|---|---|---|---
number | (1318 nm) | (1527 nm) | (1561 nm) | (1565 nm) | (1567 nm) | (578.0 nm) | (579.7 nm)
| (mÅ) | (mÅ) | (mÅ) | (mÅ) | (mÅ) | (mÅ) | (mÅ)
145501 | 244 | 130 | … | … | … | 182 | 32
145502 | 226 | … | … | … | 36 | 177 | 36
146331 | 281 | … | … | … | … | … | …
147932 | 284 | … | … | … | … | 207 | 46
148184 | 126 | … | … | … | … | 100 | 53
148379 | 547 | … | … | … | 51 | 427 | 106
148688 | 318 | … | 38 | … | 36 | … | …
148739 | 539 | … | … | … | … | … | …
148937 | 602 | 310 | 50 | … | 52 | 356 | 71
151932 | 247 | … | … | … | … | 336 | …
152235 | 406 | … | 30 | … | 48 | 418 | 101
152270 | … | … | … | … | … | 353 | 66
152386 | 378 | … | 31 | … | 55 | 352 | 70
154811 | 410 | … | … | … | … | … | …
154873 | 385 | 160 | … | … | … | … | …
156134 | 284 | … | 31 | 31 | 33 | 320 | 93
156201 | 306 | … | 29 | 31 | 47 | 318 | 119
156212 | 322 | … | 37 | 37 | 60 | 375 | 133
156738 | 413 | … | 48 | 65 | 57 | 494 | 136
157038 | 560 | … | … | … | 39 | 447 | 124
157778 | … | … | … | … | … | 34 | $<$
157779 | $<$ | $<$ | $<$ | $<$ | … | … | …
159455 | 570 | … | 56 | 58 | 78 | … | …
160065 | 611 | … | 56 | 42 | 65 | … | …
161289 | … | … | … | … | … | … | …
161291 | 543 | … | 38 | 33 | 72 | … | …
162168 | 575 | … | 37 | 45 | 68 | … | …
164438 | 321 | … | 25 | 41 | 35 | 391 | 123
164865 | 485 | … | 32 | 47 | 37 | 383 | 67
165319 | 375 | … | 26 | 29 | 62 | 533 | 191
166734 | 566 | … | … | … | … | 720 | 276
167264 | 123 | … | 12 | 11 | 26 | … | …
167971 | 745 | … | 51 | 57 | 100 | 563 | 158
168607 | 878 | … | 75 | 75 | 100 | 859 | 280
168625 | 809 | … | 100 | 120 | 90 | 842 | 239
168987 | 902 | … | 67 | 100 | 110 | 752 | 146
169034 | 760 | … | 55 | 78 | 60 | 689 | 216
169454 | 528 | … | 24 | 47 | 53 | 482 | 177
169754 | 451 | … | … | 40 | 58 | … | …
170938 | 774 | … | … | 40 | 55 | 476 | 145
171722 | $<$ | … | … | … | … | 20 | $<$
183143 | 629 | … | 69 | 65 | 110 | 807 | 230
188293 | 64 | 48 | … | … | … | … | …
188294 | 37 | … | … | … | … | … | …
303188 | 690 | … | $<$ | $<$ | $<$ | … | …
305529 | … | … | … | … | … | 211 | 49
312980 | 521 | … | 58 | 53 | 61 | … | …
318014 | 998 | … | 58 | 93 | 100 | 675 | 168
319699 | 534 | … | 35 | 33 | 69 | 363 | 87
319702 | 542 | … | 34 | 44 | 50 | 521 | 129

Figure A2: Normalised flux (scaled by the factor shown and offset in the
ordinate for clarity) vs heliocentric velocity for Na i, K i and a handful of
DIBs.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A2: Optical data ctd.

Figure A3: Correlations between equivalent width of DIBs or reddening $E(B-V)$
for which the Pearson correlation coefficient exceeded 0.87, plus some optical
lines. EW is measured in mÅ with reddening in magnitudes. Red points have been
excluded from the correlations. The dashed lines show upper and lower error
bounds obtained byfitting with a second order polynomial.

Figure A3: Correlations ctd.

Figure A3: Correlations ctd.

Figure A3: Correlations ctd.

Figure A3: Correlations ctd.

Figure A3: Correlations ctd.

Figure A3: Correlations ctd.

Figure A3: Correlations ctd.

Figure A3: Correlations ctd.

Figure A3: Correlations ctd.

Figure A3: Correlations ctd.

Table 3: Correlation coefficients. The number of sightlines used per correlation is shown in brackets. Both the standard pearson correlation coefficient (top row per parameter) and 95 percent confidence range (second row) for the partial correlation coefficients are presented.  | E(B-V) | FeI | DIB | DIB | DIB | DIB | DIB ) | DIB | DIB | DIB
---|---|---|---|---|---|---|---|---|---|---
|  | (3859.9) | (5074.5) | (5418.9) | (5705.1) | (5711.6) | (5780.5) | (5797.1) | (5849.8) | (6089.9)
E(B-V) | 0.49 (9) | 0.44 (17) | 0.39 (20) | 0.55 (32) | 0.80 (45) | 0.50 (27) | 0.91 (47) | 0.89 (44) | 0.80 (48) | 0.66 (40)
| -0.47$\rightarrow$0.9 | 0.06$\rightarrow$0.83 | -0.06$\rightarrow$0.74 | 0.16$\rightarrow$0.72 | 0.62$\rightarrow$0.87 | 0.29$\rightarrow$0.81 | 0.82$\rightarrow$0.94 | 0.81$\rightarrow$0.94 | 0.65$\rightarrow$0.88 | 0.33$\rightarrow$0.77
Na(3302.4) | 0.84 (30) | -0.31 (23) | 0.73 (13) | 0.05 (26) | 0.74 (26) | -0.01 (39) | 0.79 (20) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.79$\rightarrow$0.95 | -0.64$\rightarrow$0.16 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | -0.27$\rightarrow$0.52 | -0.38$\rightarrow$0.28 | -0.15$\rightarrow$0.7 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
FeI(3859.9) | 0.44 (17) | -0.34 (42) | 0.73 (13) | 0.05 (26) | 0.30 (15) | -0.01 (39) | 0.39 (16) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.06$\rightarrow$0.83 | -0.57$\rightarrow$0.01 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | -0.13$\rightarrow$0.8 | -0.38$\rightarrow$0.28 | -0.11$\rightarrow$0.79 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
CaII(3933.6) | 0.66 (59) | 0.23 (16) | 0.73 (13) | 0.05 (26) | 0.45 (45) | -0.01 (39) | 0.61 (47) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.55$\rightarrow$0.82 | -0.58$\rightarrow$0.48 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | -0.24$\rightarrow$0.38 | -0.38$\rightarrow$0.28 | -0.04$\rightarrow$0.53 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
CaI(4226.7) | 0.57 (44) | 0.49 (15) | 0.73 (13) | 0.05 (26) | 0.47 (39) | -0.01 (39) | 0.55 (37) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.41$\rightarrow$0.79 | -0.42$\rightarrow$0.66 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | -0.05$\rightarrow$0.56 | -0.38$\rightarrow$0.28 | -0.07$\rightarrow$0.56 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
CH+(4232.5) | 0.84 (49) | -0.43 (45) | 0.73 (13) | 0.05 (26) | 0.75 (43) | -0.01 (39) | 0.81 (39) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.73$\rightarrow$0.91 | -0.72$\rightarrow$-0.27 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | -0.11$\rightarrow$0.5 | -0.38$\rightarrow$0.28 | 0.08$\rightarrow$0.65 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
CH(4300.3) | 0.90 (51) | 0.04 (41) | 0.73 (13) | 0.05 (26) | 0.70 (44) | -0.01 (39) | 0.78 (44) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.78$\rightarrow$0.92 | -0.23$\rightarrow$0.4 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | -0.26$\rightarrow$0.36 | -0.38$\rightarrow$0.28 | -0.36$\rightarrow$0.26 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(4726.8) | 0.81 (48) | 0.01 (42) | 0.73 (13) | 0.05 (26) | 0.62 (44) | -0.01 (39) | 0.71 (43) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.67$\rightarrow$0.89 | -0.17$\rightarrow$0.45 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | -0.21$\rightarrow$0.41 | -0.38$\rightarrow$0.28 | -0.28$\rightarrow$0.35 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(4984.8) | 0.49 (36) | 0.34 (29) | 0.73 (13) | 0.05 (26) | 0.34 (33) | -0.01 (39) | 0.25 (31) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.1$\rightarrow$0.66 | -0.26$\rightarrow$0.48 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | -0.44$\rightarrow$0.27 | -0.38$\rightarrow$0.28 | -0.63$\rightarrow$0.04 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(5074.5) | 0.39 (20) | 0.73 (13) | -0.34 (42) | 0.05 (26) | 0.53 (16) | -0.01 (39) | 0.34 (17) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| -0.06$\rightarrow$0.74 | -0.17$\rightarrow$0.84 | -0.57$\rightarrow$0.01 | -0.33$\rightarrow$0.48 | -0.13$\rightarrow$0.83 | -0.38$\rightarrow$0.28 | -0.22$\rightarrow$0.77 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(5418.9) | 0.55 (32) | 0.05 (26) | 0.05 (26) | -0.34 (42) | 0.22 (30) | -0.01 (39) | 0.31 (27) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.16$\rightarrow$0.72 | -0.33$\rightarrow$0.48 | -0.33$\rightarrow$0.48 | -0.57$\rightarrow$0.01 | -0.59$\rightarrow$0.11 | -0.38$\rightarrow$0.28 | -0.62$\rightarrow$0.11 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(5705.1) | 0.80 (45) | 0.30 (15) | 0.53 (16) | 0.22 (30) | -0.34 (42) | -0.01 (39) | 0.91 (41) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.62$\rightarrow$0.87 | -0.13$\rightarrow$0.8 | -0.13$\rightarrow$0.83 | -0.59$\rightarrow$0.11 | -0.57$\rightarrow$0.01 | -0.38$\rightarrow$0.28 | 0.34$\rightarrow$0.78 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(5711.6) | 0.50 (27) | -0.01 (39) | -0.01 (39) | -0.01 (39) | -0.01 (39) | -0.34 (42) | 0.50 (21) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.29$\rightarrow$0.81 | -0.38$\rightarrow$0.28 | -0.38$\rightarrow$0.28 | -0.38$\rightarrow$0.28 | -0.38$\rightarrow$0.28 | -0.57$\rightarrow$0.01 | -0.21$\rightarrow$0.68 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(5780.5) | 0.91 (47) | 0.39 (16) | 0.34 (17) | 0.31 (27) | 0.91 (41) | 0.50 (21) | -0.34 (42) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.82$\rightarrow$0.94 | -0.11$\rightarrow$0.79 | -0.22$\rightarrow$0.77 | -0.62$\rightarrow$0.11 | 0.34$\rightarrow$0.78 | -0.21$\rightarrow$0.68 | -0.57$\rightarrow$0.01 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(5797.1) | 0.89 (44) | -0.01 (37) | -0.01 (37) | -0.01 (37) | -0.01 (37) | -0.01 (37) | -0.01 (37) | -0.34 (42) | 0.19 (24) | -0.01 (42)
| 0.81$\rightarrow$0.94 | -0.31$\rightarrow$0.37 | -0.31$\rightarrow$0.37 | -0.31$\rightarrow$0.37 | -0.31$\rightarrow$0.37 | -0.31$\rightarrow$0.37 | -0.31$\rightarrow$0.37 | -0.57$\rightarrow$0.01 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(5849.8) | 0.80 (48) | 0.19 (24) | 0.19 (24) | 0.19 (24) | 0.19 (24) | 0.19 (24) | 0.19 (24) | 0.19 (24) | -0.34 (42) | -0.01 (42)
| 0.65$\rightarrow$0.88 | -0.38$\rightarrow$0.47 | -0.38$\rightarrow$0.47 | -0.38$\rightarrow$0.47 | -0.38$\rightarrow$0.47 | -0.38$\rightarrow$0.47 | -0.38$\rightarrow$0.47 | -0.38$\rightarrow$0.47 | -0.57$\rightarrow$0.01 | -0.27$\rightarrow$0.36
DIB(6089.9) | 0.66 (40) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.34 (42)
| 0.33$\rightarrow$0.77 | -0.27$\rightarrow$0.36 | -0.27$\rightarrow$0.36 | -0.27$\rightarrow$0.36 | -0.27$\rightarrow$0.36 | -0.27$\rightarrow$0.36 | -0.27$\rightarrow$0.36 | -0.27$\rightarrow$0.36 | -0.27$\rightarrow$0.36 | -0.57$\rightarrow$0.01
DIB(6196.0) | 0.88 (54) | 0.39 (17) | 0.37 (21) | 0.35 (32) | 0.91 (46) | 0.53 (29) | 0.98 (45) | 0.95 (45) | 0.83 (45) | 0.75 (41)
| 0.79$\rightarrow$0.93 | -0.25$\rightarrow$0.71 | -0.26$\rightarrow$0.65 | -0.46$\rightarrow$0.25 | 0.49$\rightarrow$0.82 | 0.02$\rightarrow$0.7 | 0.81$\rightarrow$0.94 | 0.61$\rightarrow$0.87 | 0.36$\rightarrow$0.76 | 0.22$\rightarrow$0.71
DIB(6203.1) | 0.91 (57) | -0.05 (44) | -0.05 (44) | -0.05 (44) | -0.05 (44) | -0.05 (44) | -0.05 (44) | -0.05 (44) | -0.05 (44) | -0.05 (44)
| 0.87$\rightarrow$0.95 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25
DIB(6269.9) | 0.81 (51) | -0.15 (27) | -0.15 (27) | -0.15 (27) | -0.15 (27) | -0.15 (27) | -0.15 (27) | -0.15 (27) | -0.15 (27) | -0.15 (27)
| 0.68$\rightarrow$0.89 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2

Table 3: Correlation coefficients ctd. | E(B-V) | FeI | DIB | DIB | DIB | DIB | DIB ) | DIB | DIB | DIB
---|---|---|---|---|---|---|---|---|---|---
|  | (3859.9) | (5074.5) | (5418.9) | (5705.1) | (5711.6) | (5780.5) | (5797.1) | (5849.8) | (6089.9)
DIB(6283.8) | 0.83 (51) | -0.10 (43) | -0.10 (43) | -0.10 (43) | -0.10 (43) | -0.10 (43) | -0.10 (43) | -0.10 (43) | -0.10 (43) | -0.10 (43)
| 0.7$\rightarrow$0.9 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24
DIB(6376.1) | 0.84 (40) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42)
| 0.66$\rightarrow$0.9 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33
DIB(6439.5) | 0.71 (30) | 0.18 (37) | 0.18 (37) | 0.18 (37) | 0.18 (37) | 0.18 (37) | 0.18 (37) | 0.18 (37) | 0.18 (37) | 0.18 (37)
| 0.46$\rightarrow$0.86 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6
DIB(6614.0) | 0.87 (44) | 0.15 (27) | 0.15 (27) | 0.15 (27) | 0.15 (27) | 0.15 (27) | 0.15 (27) | 0.15 (27) | 0.15 (27) | 0.15 (27)
| 0.74$\rightarrow$0.92 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32
DIB(6993.1) | 0.75 (41) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37)
| 0.6$\rightarrow$0.87 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1
KI(7698.9) | 0.84 (51) | 0.49 (16) | 0.21 (18) | 0.48 (29) | 0.74 (47) | 0.38 (24) | 0.78 (43) | 0.85 (41) | 0.85 (44) | 0.57 (39)
| 0.72$\rightarrow$0.9 | -0.3$\rightarrow$0.7 | -0.53$\rightarrow$0.53 | -0.02$\rightarrow$0.65 | -0.07$\rightarrow$0.51 | -0.32$\rightarrow$0.53 | 0.03$\rightarrow$0.6 | 0.35$\rightarrow$0.78 | 0.4$\rightarrow$0.78 | 0.12$\rightarrow$0.66
DIB(13180) | 0.88 (82) | -0.31 (23) | 0.73 (13) | 0.05 (26) | 0.84 (44) | -0.01 (39) | 0.88 (40) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.85$\rightarrow$0.94 | -0.64$\rightarrow$0.16 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | 0.33$\rightarrow$0.76 | -0.38$\rightarrow$0.28 | 0.38$\rightarrow$0.79 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(15650) | 0.76 (43) | -0.31 (23) | 0.73 (13) | 0.05 (26) | 0.82 (33) | -0.01 (39) | 0.86 (29) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.59$\rightarrow$0.87 | -0.64$\rightarrow$0.16 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | 0.14$\rightarrow$0.71 | -0.38$\rightarrow$0.28 | 0.22$\rightarrow$0.78 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36
DIB(15670) | 0.71 (46) | -0.31 (23) | 0.73 (13) | 0.05 (26) | 0.80 (35) | -0.01 (39) | 0.85 (32) | -0.01 (37) | 0.19 (24) | -0.01 (42)
| 0.59$\rightarrow$0.86 | -0.64$\rightarrow$0.16 | -0.17$\rightarrow$0.84 | -0.33$\rightarrow$0.48 | 0.14$\rightarrow$0.7 | -0.38$\rightarrow$0.28 | 0.19$\rightarrow$0.75 | -0.31$\rightarrow$0.37 | -0.38$\rightarrow$0.47 | -0.27$\rightarrow$0.36

Table 3: continued. | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB
---|---|---|---|---|---|---|---|---|---|---|---
| (6196.0) | (6203.1) | (6269.9) | (6283.8) | (6376.1) | (6439.5) | (6614.0) | (6993.1) | (13180) | (15650) | (1567)
E(B-V) | 0.88 (54) | 0.91 (57) | 0.81 (51) | 0.83 (51) | 0.84 (40) | 0.71 (30) | 0.87 (44) | 0.75 (41) | 0.88 (82) | 0.76 (43) | 0.71 (46)
| 0.79$\rightarrow$0.93 | 0.87$\rightarrow$0.95 | 0.68$\rightarrow$0.89 | 0.7$\rightarrow$0.9 | 0.66$\rightarrow$0.9 | 0.46$\rightarrow$0.86 | 0.74$\rightarrow$0.92 | 0.6$\rightarrow$0.87 | 0.85$\rightarrow$0.94 | 0.59$\rightarrow$0.87 | 0.59$\rightarrow$0.86
Na(3302.4) | 0.81 (30) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.11 (31) | -0.11 (31) | -0.11 (31)
| 0.21$\rightarrow$0.76 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.49$\rightarrow$0.24 | -0.49$\rightarrow$0.24 | -0.49$\rightarrow$0.24
FeI(3859.9) | 0.39 (17) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.31 (23) | -0.31 (23) | -0.31 (23)
| -0.25$\rightarrow$0.71 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.64$\rightarrow$0.16 | -0.64$\rightarrow$0.16 | -0.64$\rightarrow$0.16
CaII(3933.6) | 0.67 (54) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.60 (48) | 0.34 (32) | 0.20 (34)
| -0.01$\rightarrow$0.51 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.05$\rightarrow$0.51 | -0.39$\rightarrow$0.35 | -0.55$\rightarrow$0.12
CaI(4226.7) | 0.63 (44) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.42 (39) | 0.27 (28) | 0.42 (31)
| 0.15$\rightarrow$0.65 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.35$\rightarrow$0.3 | -0.52$\rightarrow$0.26 | -0.25$\rightarrow$0.49
CH+(4232.5) | 0.80 (47) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.43 (45) | -0.43 (45) | -0.43 (45)
| 0.04$\rightarrow$0.58 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.72$\rightarrow$-0.27 | -0.72$\rightarrow$-0.27 | -0.72$\rightarrow$-0.27
CH(4300.3) | 0.76 (47) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.04 (41) | 0.04 (41) | 0.04 (41)
| -0.27$\rightarrow$0.32 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.23$\rightarrow$0.4 | -0.23$\rightarrow$0.4 | -0.23$\rightarrow$0.4
DIB(4726.8) | 0.74 (46) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.01 (42) | 0.01 (42) | 0.01 (42)
| -0.11$\rightarrow$0.48 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.17$\rightarrow$0.45 | -0.17$\rightarrow$0.45 | -0.17$\rightarrow$0.45
DIB(4984.8) | 0.34 (35) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.34 (29) | 0.34 (29) | 0.34 (29)
| -0.51$\rightarrow$0.16 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.26$\rightarrow$0.48 | -0.26$\rightarrow$0.48 | -0.26$\rightarrow$0.48
DIB(5074.5) | 0.37 (21) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.73 (13) | 0.73 (13) | 0.73 (13)
| -0.26$\rightarrow$0.65 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.17$\rightarrow$0.84 | -0.17$\rightarrow$0.84 | -0.17$\rightarrow$0.84
DIB(5418.9) | 0.35 (32) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.05 (26) | 0.05 (26) | 0.05 (26)
| -0.46$\rightarrow$0.25 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.33$\rightarrow$0.48 | -0.33$\rightarrow$0.48 | -0.33$\rightarrow$0.48
DIB(5705.1) | 0.91 (46) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.84 (44) | 0.82 (33) | 0.80 (35)
| 0.49$\rightarrow$0.82 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | 0.33$\rightarrow$0.76 | 0.14$\rightarrow$0.71 | 0.14$\rightarrow$0.7
DIB(5711.6) | 0.53 (29) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.01 (39) | -0.01 (39) | -0.01 (39)
| 0.02$\rightarrow$0.7 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.38$\rightarrow$0.28 | -0.38$\rightarrow$0.28 | -0.38$\rightarrow$0.28
DIB(5780.5) | 0.98 (45) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.88 (40) | 0.86 (29) | 0.85 (32)
| 0.81$\rightarrow$0.94 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | 0.38$\rightarrow$0.79 | 0.22$\rightarrow$0.78 | 0.19$\rightarrow$0.75
DIB(5797.1) | 0.95 (45) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.01 (37) | -0.01 (37) | -0.01 (37)
| 0.61$\rightarrow$0.87 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.31$\rightarrow$0.37 | -0.31$\rightarrow$0.37 | -0.31$\rightarrow$0.37
DIB(5849.8) | 0.83 (45) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.19 (24) | 0.19 (24) | 0.19 (24)
| 0.36$\rightarrow$0.76 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.38$\rightarrow$0.47 | -0.38$\rightarrow$0.47 | -0.38$\rightarrow$0.47
DIB(6089.9) | 0.75 (41) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.01 (42) | -0.01 (42) | -0.01 (42)
| 0.22$\rightarrow$0.71 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.27$\rightarrow$0.36 | -0.27$\rightarrow$0.36 | -0.27$\rightarrow$0.36
DIB(6196.0) | -0.34 (42) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | 0.81 (47) | 0.80 (34) | 0.80 (36)
| -0.57$\rightarrow$0.01 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | 0.26$\rightarrow$0.71 | 0.07$\rightarrow$0.67 | 0.14$\rightarrow$0.7
DIB(6203.1) | -0.05 (44) | -0.34 (42) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.05 (44) | -0.05 (44) | -0.05 (44)
| -0.36$\rightarrow$0.25 | -0.57$\rightarrow$0.01 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25 | -0.36$\rightarrow$0.25
DIB(6269.9) | -0.15 (27) | -0.15 (27) | -0.34 (42) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.15 (27) | -0.15 (27) | -0.15 (27)
| -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2 | -0.57$\rightarrow$0.01 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2 | -0.56$\rightarrow$0.2

Table 2: continued. | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB
---|---|---|---|---|---|---|---|---|---|---|---
| (6196.0) | (6203.1) | (6269.9) | (6283.8) | (6376.1) | (6439.5) | (6614.0) | (6993.1) | (13180) | (15650) | (1567)
DIB(6283.8) | -0.10 (43) | -0.10 (43) | -0.10 (43) | -0.34 (42) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.10 (43) | -0.10 (43) | -0.10 (43)
| -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.57$\rightarrow$0.01 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24 | -0.38$\rightarrow$0.24
DIB(6376.1) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.01 (42) | -0.34 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.01 (42) | -0.01 (42) | -0.01 (42)
| -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.57$\rightarrow$0.01 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33 | -0.3$\rightarrow$0.33
DIB(6439.5) | 0.18 (37) | 0.18 (37) | 0.18 (37) | 0.18 (37) | 0.18 (37) | -0.34 (42) | 0.15 (27) | -0.22 (37) | 0.18 (37) | 0.18 (37) | 0.18 (37)
| -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.57$\rightarrow$0.01 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6 | -0.01$\rightarrow$0.6
DIB(6614.0) | 0.15 (27) | 0.15 (27) | 0.15 (27) | 0.15 (27) | 0.15 (27) | 0.15 (27) | -0.34 (42) | -0.22 (37) | 0.15 (27) | 0.15 (27) | 0.15 (27)
| -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.57$\rightarrow$0.01 | -0.53$\rightarrow$0.1 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32 | -0.47$\rightarrow$0.32
DIB(6993.1) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.22 (37) | -0.34 (42) | -0.22 (37) | -0.22 (37) | -0.22 (37)
| -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.57$\rightarrow$0.01 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1 | -0.53$\rightarrow$0.1
KI(7698.9) | 0.81 (49) | 0.78 (52) | 0.75 (52) | 0.75 (53) | 0.71 (40) | 0.64 (29) | 0.81 (41) | 0.65 (44) | 0.67 (47) | 0.50 (33) | 0.52 (35)
| 0.25$\rightarrow$0.7 | -0.06$\rightarrow$0.49 | 0.05$\rightarrow$0.57 | -0.05$\rightarrow$0.49 | 0.24$\rightarrow$0.72 | -0.$\rightarrow$0.66 | 0.4$\rightarrow$0.8 | 0.03$\rightarrow$0.59 | -0.32$\rightarrow$0.28 | -0.42$\rightarrow$0.3 | -0.26$\rightarrow$0.44
DIB(13180) | 0.81 (47) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.34 (42) | -0.08 (25) | -0.15 (28)
| 0.26$\rightarrow$0.71 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.57$\rightarrow$0.01 | -0.39$\rightarrow$0.44 | -0.26$\rightarrow$0.51
DIB(15650) | 0.80 (34) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.08 (25) | -0.34 (42) | -0.15 (28)
| 0.07$\rightarrow$0.67 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.39$\rightarrow$0.44 | -0.57$\rightarrow$0.01 | -0.26$\rightarrow$0.51
DIB(15670) | 0.80 (36) | -0.05 (44) | -0.15 (27) | -0.10 (43) | -0.01 (42) | 0.18 (37) | 0.15 (27) | -0.22 (37) | -0.15 (28) | -0.15 (28) | -0.34 (42)
| 0.14$\rightarrow$0.7 | -0.36$\rightarrow$0.25 | -0.56$\rightarrow$0.2 | -0.38$\rightarrow$0.24 | -0.3$\rightarrow$0.33 | -0.01$\rightarrow$0.6 | -0.47$\rightarrow$0.32 | -0.53$\rightarrow$0.1 | -0.26$\rightarrow$0.51 | -0.26$\rightarrow$0.51 | -0.57$\rightarrow$0.01

Table 4: Correlation coefficients for single cloud dominated sightlines. The number of sightlines used per correlation is shown in brackets. Both the standard pearson correlation coefficient (top row per parameter) and 95 percent confidence range (second row) for the partial correlation coefficients are presented. Blank cells correspond to datasets with less than 5 datapoints. | E(B-V) | FeI | DIB | DIB | DIB | DIB | DIB ) | DIB | DIB | DIB
---|---|---|---|---|---|---|---|---|---|---
|  | (3859.9) | (5074.5) | (5418.9) | (5705.1) | (5711.6) | (5780.5) | (5797.1) | (5849.8) | (6089.9)
E(B-V) | 0.90 (12) |  | 0.84 (6) | 0.78 (7) | 0.92 (10) | 0.59 (7) | 0.95 (12) | 0.92 (12) | 0.84 (10) | 0.75 (9)
| 0.75$\rightarrow$0.99 |  | -0.8$\rightarrow$0.99 | 0.36$\rightarrow$1. | -0.01$\rightarrow$0.94 | 0.02$\rightarrow$0.99 | 0.44$\rightarrow$0.96 | 0.89$\rightarrow$0.99 | 0.22$\rightarrow$0.96 | -0.38$\rightarrow$0.92
Na(3302.4) | 0.99 (7) | -0.52 (5) |  |  |  | 0.35 (9) |  | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.36$\rightarrow$1. | -1.$\rightarrow$1. |  |  |  | -0.77$\rightarrow$0.74 |  | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
FeI(3859.9) |  | 0.21 (10) |  |  |  | 0.35 (9) |  | 0.39 (11) | 0.44 (5) | 0.41 (12)
|  | -0.92$\rightarrow$0.15 |  |  |  | -0.77$\rightarrow$0.74 |  | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
CaII(3933.6) | 0.83 (16) |  | 0.74 (6) | 0.46 (7) | 0.79 (11) | 0.35 (9) | 0.73 (13) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.18$\rightarrow$0.88 |  | -0.93$\rightarrow$0.98 | -0.9$\rightarrow$0.87 | -0.49$\rightarrow$0.79 | -0.77$\rightarrow$0.74 | -0.6$\rightarrow$0.66 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
CaI(4226.7) | 0.80 (13) |  | 0.75 (6) | 0.34 (7) | 0.82 (9) | 0.35 (9) | 0.90 (11) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.17$\rightarrow$0.92 |  | -0.95$\rightarrow$0.97 | -0.73$\rightarrow$0.95 | 0.05$\rightarrow$0.96 | -0.77$\rightarrow$0.74 | 0.09$\rightarrow$0.93 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
CH+(4232.5) | 0.88 (12) | 0.10 (13) | 0.50 (5) | 0.69 (7) | 0.73 (10) | 0.35 (9) | 0.85 (10) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.85$\rightarrow$0.99 | -0.65$\rightarrow$0.54 | -1.$\rightarrow$1. | -0.96$\rightarrow$0.65 | -0.88$\rightarrow$0.36 | -0.77$\rightarrow$0.74 | -0.86$\rightarrow$0.59 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
CH(4300.3) | 0.94 (12) | 0.63 (10) | 0.77 (5) | 0.80 (7) | 0.79 (10) | 0.35 (9) | 0.83 (12) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.81$\rightarrow$0.99 | 0.1$\rightarrow$0.95 | -1.$\rightarrow$1. | -0.96$\rightarrow$0.65 | -0.84$\rightarrow$0.48 | -0.77$\rightarrow$0.74 | -0.86$\rightarrow$0.3 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(4726.8) | 0.80 (12) | 0.27 (11) | 0.52 (6) | 0.77 (7) | 0.63 (10) | 0.35 (9) | 0.56 (10) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.46$\rightarrow$0.96 | -0.46$\rightarrow$0.8 | -0.99$\rightarrow$0.87 | -0.96$\rightarrow$0.68 | -0.81$\rightarrow$0.55 | -0.77$\rightarrow$0.74 | -0.88$\rightarrow$0.51 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(4984.8) | 0.87 (7) | 0.23 (8) |  | 0.85 (7) | 0.79 (6) | 0.35 (9) | 0.68 (6) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| -0.6$\rightarrow$0.97 | -0.88$\rightarrow$0.7 |  | -0.64$\rightarrow$0.97 | -0.99$\rightarrow$0.9 | -0.77$\rightarrow$0.74 | -0.87$\rightarrow$0.99 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(5074.5) | 0.84 (6) |  | 0.21 (10) |  |  | 0.35 (9) |  | 0.39 (11) | 0.44 (5) | 0.41 (12)
| -0.8$\rightarrow$0.99 |  | -0.92$\rightarrow$0.15 |  |  | -0.77$\rightarrow$0.74 |  | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(5418.9) | 0.78 (7) |  |  | 0.21 (10) | 0.70 (6) | 0.35 (9) | 0.89 (6) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.36$\rightarrow$1. |  |  | -0.92$\rightarrow$0.15 | -0.7$\rightarrow$1. | -0.77$\rightarrow$0.74 | -1.$\rightarrow$-1. | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(5705.1) | 0.92 (10) |  |  | 0.70 (6) | 0.21 (10) | 0.35 (9) | 0.94 (9) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| -0.01$\rightarrow$0.94 |  |  | -0.7$\rightarrow$1. | -0.92$\rightarrow$0.15 | -0.77$\rightarrow$0.74 | 0.5$\rightarrow$0.99 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(5711.6) | 0.59 (7) | 0.35 (9) | 0.35 (9) | 0.35 (9) | 0.35 (9) | 0.21 (10) | 0.48 (5) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.02$\rightarrow$0.99 | -0.77$\rightarrow$0.74 | -0.77$\rightarrow$0.74 | -0.77$\rightarrow$0.74 | -0.77$\rightarrow$0.74 | -0.92$\rightarrow$0.15 | -1.$\rightarrow$1. | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(5780.5) | 0.95 (12) |  |  | 0.89 (6) | 0.94 (9) | 0.48 (5) | 0.21 (10) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.44$\rightarrow$0.96 |  |  | -1.$\rightarrow$-1. | 0.5$\rightarrow$0.99 | -1.$\rightarrow$1. | -0.92$\rightarrow$0.15 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(5797.1) | 0.92 (12) | 0.39 (11) | 0.39 (11) | 0.39 (11) | 0.39 (11) | 0.39 (11) | 0.39 (11) | 0.21 (10) | 0.44 (5) | 0.41 (12)
| 0.89$\rightarrow$0.99 | -0.78$\rightarrow$0.51 | -0.78$\rightarrow$0.51 | -0.78$\rightarrow$0.51 | -0.78$\rightarrow$0.51 | -0.78$\rightarrow$0.51 | -0.78$\rightarrow$0.51 | -0.92$\rightarrow$0.15 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(5849.8) | 0.84 (10) | 0.44 (5) | 0.44 (5) | 0.44 (5) | 0.44 (5) | 0.44 (5) | 0.44 (5) | 0.44 (5) | 0.21 (10) | 0.41 (12)
| 0.22$\rightarrow$0.96 | -1.$\rightarrow$1. | -1.$\rightarrow$1. | -1.$\rightarrow$1. | -1.$\rightarrow$1. | -1.$\rightarrow$1. | -1.$\rightarrow$1. | -1.$\rightarrow$1. | -0.92$\rightarrow$0.15 | -0.08$\rightarrow$0.89
DIB(6089.9) | 0.75 (9) | 0.41 (12) | 0.41 (12) | 0.41 (12) | 0.41 (12) | 0.41 (12) | 0.41 (12) | 0.41 (12) | 0.41 (12) | 0.21 (10)
| -0.38$\rightarrow$0.92 | -0.08$\rightarrow$0.89 | -0.08$\rightarrow$0.89 | -0.08$\rightarrow$0.89 | -0.08$\rightarrow$0.89 | -0.08$\rightarrow$0.89 | -0.08$\rightarrow$0.89 | -0.08$\rightarrow$0.89 | -0.08$\rightarrow$0.89 | -0.92$\rightarrow$0.15
DIB(6196.0) | 0.93 (16) |  | 0.87 (6) | 0.50 (7) | 0.91 (10) | 0.72 (7) | 0.98 (12) | 0.97 (12) | 0.91 (10) | 0.92 (9)
| 0.66$\rightarrow$0.96 |  | -0.97$\rightarrow$0.95 | -0.73$\rightarrow$0.95 | -0.15$\rightarrow$0.92 | -1.$\rightarrow$-1. | 0.45$\rightarrow$0.96 | 0.01$\rightarrow$0.9 | -0.23$\rightarrow$0.91 | 0.66$\rightarrow$0.99
DIB(6203.1) | 0.96 (15) | 0.28 (13) | 0.28 (13) | 0.28 (13) | 0.28 (13) | 0.28 (13) | 0.28 (13) | 0.28 (13) | 0.28 (13) | 0.28 (13)
| 0.9$\rightarrow$0.99 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58
DIB(6269.9) | 0.90 (13) | 0.30 (7) | 0.30 (7) | 0.30 (7) | 0.30 (7) | 0.30 (7) | 0.30 (7) | 0.30 (7) | 0.30 (7) | 0.30 (7)
| 0.56$\rightarrow$0.97 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92

Table 4: continued.  | E(B-V) | FeI | DIB | DIB | DIB | DIB | DIB ) | DIB | DIB | DIB
---|---|---|---|---|---|---|---|---|---|---
|  | (3859.9) | (5074.5) | (5418.9) | (5705.1) | (5711.6) | (5780.5) | (5797.1) | (5849.8) | (6089.9)
DIB(6283.8) | 0.92 (12) | 0.65 (11) | 0.65 (11) | 0.65 (11) | 0.65 (11) | 0.65 (11) | 0.65 (11) | 0.65 (11) | 0.65 (11) | 0.65 (11)
| 0.39$\rightarrow$0.96 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86
DIB(6376.1) | 0.88 (8) | 0.52 (10) | 0.52 (10) | 0.52 (10) | 0.52 (10) | 0.52 (10) | 0.52 (10) | 0.52 (10) | 0.52 (10) | 0.52 (10)
| 0.15$\rightarrow$0.98 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88
DIB(6439.5) | 0.81 (5) | 0.37 (10) | 0.37 (10) | 0.37 (10) | 0.37 (10) | 0.37 (10) | 0.37 (10) | 0.37 (10) | 0.37 (10) | 0.37 (10)
| -1.$\rightarrow$1. | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81
DIB(6614.0) | 0.92 (12) |  | 0.92 (5) | 0.55 (7) | 0.90 (8) | 0.66 (6) | 0.97 (9) | 0.96 (9) | 0.96 (9) | 0.88 (7)
| 0.57$\rightarrow$0.97 |  | -1.$\rightarrow$1. | -0.73$\rightarrow$0.95 | -0.12$\rightarrow$0.97 | -1.$\rightarrow$-1. | 0.54$\rightarrow$0.99 | -0.39$\rightarrow$0.91 | 0.15$\rightarrow$0.97 | 0.37$\rightarrow$1.
DIB(6993.1) | 0.96 (8) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10)
| 0.3$\rightarrow$0.99 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75
KI(7698.9) | 0.90 (12) |  |  | 0.79 (6) | 0.89 (11) | 0.58 (5) | 0.85 (10) | 0.95 (10) | 0.98 (9) | 0.66 (10)
| 0.75$\rightarrow$0.99 |  |  | -1.$\rightarrow$-1. | -0.3$\rightarrow$0.86 | -1.$\rightarrow$1. | -0.53$\rightarrow$0.82 | -0.29$\rightarrow$0.9 | -0.03$\rightarrow$0.96 | -0.66$\rightarrow$0.74
DIB(13180) | 0.80 (15) | -0.52 (5) |  | 0.69 (5) | 0.84 (9) | 0.35 (9) | 0.90 (8) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| -0.14$\rightarrow$0.87 | -1.$\rightarrow$1. |  | -1.$\rightarrow$1. | -0.21$\rightarrow$0.94 | -0.77$\rightarrow$0.74 | -0.08$\rightarrow$0.97 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(15650) | 0.96 (5) | -0.52 (5) |  |  | 0.84 (5) | 0.35 (9) |  | 0.39 (11) | 0.44 (5) | 0.41 (12)
| -1.$\rightarrow$1. | -1.$\rightarrow$1. |  |  | -1.$\rightarrow$1. | -0.77$\rightarrow$0.74 |  | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89
DIB(15670) | 0.88 (8) | -0.52 (5) |  |  | 0.87 (6) | 0.35 (9) | 0.86 (6) | 0.39 (11) | 0.44 (5) | 0.41 (12)
| 0.11$\rightarrow$0.98 | -1.$\rightarrow$1. |  |  | -0.7$\rightarrow$1. | -0.77$\rightarrow$0.74 | -0.99$\rightarrow$0.86 | -0.78$\rightarrow$0.51 | -1.$\rightarrow$1. | -0.08$\rightarrow$0.89

Table 4: continued. | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB
---|---|---|---|---|---|---|---|---|---|---|---
| (6196.0) | (6203.1) | (6269.9) | (6283.8) | (6376.1) | (6439.5) | (6614.0) | (6993.1) | (13180) | (15650) | (1567)
E(B-V) | 0.93 (16) | 0.96 (15) | 0.90 (13) | 0.92 (12) | 0.88 (8) | 0.81 (5) | 0.92 (12) | 0.96 (8) | 0.80 (15) | 0.96 (5) | 0.88 (8)
| 0.66$\rightarrow$0.96 | 0.9$\rightarrow$0.99 | 0.56$\rightarrow$0.97 | 0.39$\rightarrow$0.96 | 0.15$\rightarrow$0.98 | -1.$\rightarrow$1. | 0.57$\rightarrow$0.97 | 0.3$\rightarrow$0.99 | -0.14$\rightarrow$0.87 | -1.$\rightarrow$1. | 0.11$\rightarrow$0.98
Na(3302.4) | 0.89 (7) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.90 (6) | 0.21 (10) | 0.12 (7) | 0.12 (7) | 0.12 (7)
| -0.94$\rightarrow$0.79 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.93$\rightarrow$0.98 | -0.65$\rightarrow$0.75 | -0.95$\rightarrow$0.73 | -0.95$\rightarrow$0.73 | -0.95$\rightarrow$0.73
FeI(3859.9) |  | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) |  | 0.21 (10) | -0.52 (5) | -0.52 (5) | -0.52 (5)
|  | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 |  | -0.65$\rightarrow$0.75 | -1.$\rightarrow$1. | -1.$\rightarrow$1. | -1.$\rightarrow$1.
CaII(3933.6) | 0.83 (16) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.81 (12) | 0.21 (10) | 0.83 (10) | 0.74 (5) | 0.55 (7)
| -0.41$\rightarrow$0.63 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.5$\rightarrow$0.73 | -0.65$\rightarrow$0.75 | -0.58$\rightarrow$0.8 | -1.$\rightarrow$1. | -0.9$\rightarrow$0.86
CaI(4226.7) | 0.91 (13) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.92 (10) | 0.21 (10) | 0.52 (9) | 0.59 (5) | 0.69 (7)
| 0.25$\rightarrow$0.93 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.16$\rightarrow$0.92 | -0.65$\rightarrow$0.75 | -0.74$\rightarrow$0.76 | -1.$\rightarrow$1. | -0.93$\rightarrow$0.8
CH+(4232.5) | 0.77 (12) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.74 (11) | 0.21 (10) | 0.10 (13) | 0.10 (13) | 0.10 (13)
| -0.6$\rightarrow$0.65 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.68$\rightarrow$0.64 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.54 | -0.65$\rightarrow$0.54 | -0.65$\rightarrow$0.54
CH(4300.3) | 0.80 (12) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.81 (10) | 0.21 (10) | 0.63 (10) | 0.63 (10) | 0.63 (10)
| -0.83$\rightarrow$0.28 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.86$\rightarrow$0.44 | -0.65$\rightarrow$0.75 | 0.1$\rightarrow$0.95 | 0.1$\rightarrow$0.95 | 0.1$\rightarrow$0.95
DIB(4726.8) | 0.66 (12) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.61 (10) | 0.21 (10) | 0.27 (11) | 0.27 (11) | 0.27 (11)
| -0.82$\rightarrow$0.32 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.83$\rightarrow$0.51 | -0.65$\rightarrow$0.75 | -0.46$\rightarrow$0.8 | -0.46$\rightarrow$0.8 | -0.46$\rightarrow$0.8
DIB(4984.8) | 0.53 (7) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.56 (7) | 0.21 (10) | 0.23 (8) | 0.23 (8) | 0.23 (8)
| -0.94$\rightarrow$0.79 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.94$\rightarrow$0.79 | -0.65$\rightarrow$0.75 | -0.88$\rightarrow$0.7 | -0.88$\rightarrow$0.7 | -0.88$\rightarrow$0.7
DIB(5074.5) | 0.87 (6) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.92 (5) | 0.21 (10) |  |  |
| -0.97$\rightarrow$0.95 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -1.$\rightarrow$1. | -0.65$\rightarrow$0.75 |  |  |
DIB(5418.9) | 0.50 (7) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.55 (7) | 0.21 (10) | 0.69 (5) |  |
| -0.73$\rightarrow$0.95 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.73$\rightarrow$0.95 | -0.65$\rightarrow$0.75 | -1.$\rightarrow$1. |  |
DIB(5705.1) | 0.91 (10) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.90 (8) | 0.21 (10) | 0.84 (9) | 0.84 (5) | 0.87 (6)
| -0.15$\rightarrow$0.92 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.12$\rightarrow$0.97 | -0.65$\rightarrow$0.75 | -0.21$\rightarrow$0.94 | -1.$\rightarrow$1. | -0.7$\rightarrow$1.
DIB(5711.6) | 0.72 (7) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.66 (6) | 0.21 (10) | 0.35 (9) | 0.35 (9) | 0.35 (9)
| -1.$\rightarrow$-1. | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -1.$\rightarrow$-1. | -0.65$\rightarrow$0.75 | -0.77$\rightarrow$0.74 | -0.77$\rightarrow$0.74 | -0.77$\rightarrow$0.74
DIB(5780.5) | 0.98 (12) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.97 (9) | 0.21 (10) | 0.90 (8) |  | 0.86 (6)
| 0.45$\rightarrow$0.96 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | 0.54$\rightarrow$0.99 | -0.65$\rightarrow$0.75 | -0.08$\rightarrow$0.97 |  | -0.99$\rightarrow$0.86
DIB(5797.1) | 0.97 (12) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.96 (9) | 0.21 (10) | 0.39 (11) | 0.39 (11) | 0.39 (11)
| 0.01$\rightarrow$0.9 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.39$\rightarrow$0.91 | -0.65$\rightarrow$0.75 | -0.78$\rightarrow$0.51 | -0.78$\rightarrow$0.51 | -0.78$\rightarrow$0.51
DIB(5849.8) | 0.91 (10) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.96 (9) | 0.21 (10) | 0.44 (5) | 0.44 (5) | 0.44 (5)
| -0.23$\rightarrow$0.91 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | 0.15$\rightarrow$0.97 | -0.65$\rightarrow$0.75 | -1.$\rightarrow$1. | -1.$\rightarrow$1. | -1.$\rightarrow$1.
DIB(6089.9) | 0.92 (9) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.88 (7) | 0.21 (10) | 0.41 (12) | 0.41 (12) | 0.41 (12)
| 0.66$\rightarrow$0.99 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | 0.37$\rightarrow$1. | -0.65$\rightarrow$0.75 | -0.08$\rightarrow$0.89 | -0.08$\rightarrow$0.89 | -0.08$\rightarrow$0.89
DIB(6196.0) | 0.21 (10) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.99 (12) | 0.21 (10) | 0.73 (10) | 0.83 (5) | 0.82 (7)
| -0.92$\rightarrow$0.15 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | 0.44$\rightarrow$0.96 | -0.65$\rightarrow$0.75 | -0.53$\rightarrow$0.82 | -1.$\rightarrow$1. | -0.93$\rightarrow$0.79
DIB(6203.1) | 0.28 (13) | 0.21 (10) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.94 (11) | 0.21 (10) | 0.28 (13) | 0.28 (13) | 0.28 (13)
| -0.61$\rightarrow$0.58 | -0.92$\rightarrow$0.15 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | 0.56$\rightarrow$0.98 | -0.65$\rightarrow$0.75 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58 | -0.61$\rightarrow$0.58
DIB(6269.9) | 0.30 (7) | 0.30 (7) | 0.21 (10) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.94 (11) | 0.21 (10) | 0.30 (7) | 0.30 (7) | 0.30 (7)
| -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92 | -0.92$\rightarrow$0.15 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | 0.38$\rightarrow$0.96 | -0.65$\rightarrow$0.75 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92 | -0.83$\rightarrow$0.92

Table 3: continued. | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB | DIB
---|---|---|---|---|---|---|---|---|---|---|---
| (6196.0) | (6203.1) | (6269.9) | (6283.8) | (6376.1) | (6439.5) | (6614.0) | (6993.1) | (13180) | (15650) | (1567)
DIB(6283.8) | 0.65 (11) | 0.65 (11) | 0.65 (11) | 0.21 (10) | 0.52 (10) | 0.37 (10) | 0.92 (10) | 0.21 (10) | 0.65 (11) | 0.65 (11) | 0.65 (11)
| -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.92$\rightarrow$0.15 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | 0.69$\rightarrow$0.99 | -0.65$\rightarrow$0.75 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86 | -0.31$\rightarrow$0.86
DIB(6376.1) | 0.52 (10) | 0.52 (10) | 0.52 (10) | 0.52 (10) | 0.21 (10) | 0.37 (10) | 0.98 (7) | 0.21 (10) | 0.52 (10) | 0.52 (10) | 0.52 (10)
| -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.92$\rightarrow$0.15 | -0.56$\rightarrow$0.81 | -0.27$\rightarrow$0.99 | -0.65$\rightarrow$0.75 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88 | -0.36$\rightarrow$0.88
DIB(6439.5) | 0.37 (10) | 0.37 (10) | 0.37 (10) | 0.37 (10) | 0.37 (10) | 0.21 (10) |  | 0.21 (10) | 0.37 (10) | 0.37 (10) | 0.37 (10)
| -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.92$\rightarrow$0.15 |  | -0.65$\rightarrow$0.75 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81 | -0.56$\rightarrow$0.81
DIB(6614.0) | 0.99 (12) | 0.94 (11) | 0.94 (11) | 0.92 (10) | 0.98 (7) |  | 0.21 (10) | 0.21 (10) | 0.71 (8) | 0.80 (5) | 0.82 (6)
| 0.44$\rightarrow$0.96 | 0.56$\rightarrow$0.98 | 0.38$\rightarrow$0.96 | 0.69$\rightarrow$0.99 | -0.27$\rightarrow$0.99 |  | -0.92$\rightarrow$0.15 | -0.65$\rightarrow$0.75 | -0.69$\rightarrow$0.89 | -1.$\rightarrow$1. | -0.7$\rightarrow$1.
DIB(6993.1) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10) | 0.21 (10)
| -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.92$\rightarrow$0.15 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75 | -0.65$\rightarrow$0.75
KI(7698.9) | 0.91 (12) | 0.87 (13) | 0.88 (13) | 0.83 (13) | 0.91 (9) | 0.58 (6) | 0.94 (10) | 0.96 (9) | 0.65 (10) | 0.66 (5) | 0.61 (7)
| -0.6$\rightarrow$0.66 | -0.62$\rightarrow$0.58 | -0.7$\rightarrow$0.48 | -0.63$\rightarrow$0.57 | -0.62$\rightarrow$0.85 | -0.85$\rightarrow$0.99 | -0.59$\rightarrow$0.79 | -0.51$\rightarrow$0.88 | -0.78$\rightarrow$0.61 | -1.$\rightarrow$1. | -0.94$\rightarrow$0.77
DIB(13180) | 0.73 (10) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.71 (8) | 0.21 (10) | 0.21 (10) | 0.29 (5) | 0.26 (5)
| -0.53$\rightarrow$0.82 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.69$\rightarrow$0.89 | -0.65$\rightarrow$0.75 | -0.92$\rightarrow$0.15 | -1.$\rightarrow$1. | -1.$\rightarrow$1.
DIB(15650) | 0.83 (5) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.80 (5) | 0.21 (10) | 0.29 (5) | 0.21 (10) | 0.26 (5)
| -1.$\rightarrow$1. | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -1.$\rightarrow$1. | -0.65$\rightarrow$0.75 | -1.$\rightarrow$1. | -0.92$\rightarrow$0.15 | -1.$\rightarrow$1.
DIB(15670) | 0.82 (7) | 0.28 (13) | 0.30 (7) | 0.65 (11) | 0.52 (10) | 0.37 (10) | 0.82 (6) | 0.21 (10) | 0.26 (5) | 0.26 (5) | 0.21 (10)
| -0.93$\rightarrow$0.79 | -0.61$\rightarrow$0.58 | -0.83$\rightarrow$0.92 | -0.31$\rightarrow$0.86 | -0.36$\rightarrow$0.88 | -0.56$\rightarrow$0.81 | -0.7$\rightarrow$1. | -0.65$\rightarrow$0.75 | -1.$\rightarrow$1. | -1.$\rightarrow$1. | -0.92$\rightarrow$0.15


# Digital Twin-Driven Reinforcement Learning for Obstacle Avoidance in Robot
Manipulators: A Self-Improving Online Training Framework

Yuzhu Sun, Mien Van, Stephen McIlvanna, Nguyen Minh Nhat, Kabirat Olayemi,
Jack Close and Seán McLoone Yuzhu Sun, Mien Van (corresponding author),
Stephen McIlvanna, Nguyen Minh Nhat, Kabirat Olayemi, Jack Close and Seán
McLoone are with the Centre for Intelligent Autonomous Manufacturing Systems,
School of Electronics, Electrical Engineering and Computer Science, Queen’s
University Belfast, Northern Ireland, UK. ysun32, m.van, smcilvanna0, nnhat01,
kolayemi01, jclose06<EMAIL_ADDRESS>
###### Abstract

The evolution and growing automation of collaborative robots introduce more
complexity and unpredictability to systems, highlighting the crucial need for
robot’s adaptability and flexibility to address the increasing complexities of
their environment. In typical industrial production scenarios, robots are
often required to be re-programmed when facing a more demanding task or even a
few changes in workspace conditions. To increase productivity, efficiency and
reduce human effort in the design process, this paper explores the potential
of using digital twin combined with Reinforcement Learning (RL) to enable
robots to generate self-improving collision-free trajectories in real time.
The digital twin, acting as a virtual counterpart of the physical system,
serves as a ’forward run’ for monitoring, controlling, and optimizing the
physical system in a safe and cost-effective manner. The physical system sends
data to synchronize the digital system through the video feeds from cameras,
which allows the virtual robot to update its observation and policy based on
real scenarios. The bidirectional communication between digital and physical
systems provides a promising platform for hardware-in-the-loop RL training
through trial and error until the robot successfully adapts to its new
environment. The proposed online training framework is demonstrated on the
Unfactory Xarm5 collaborative robot, where the robot end-effector aims to
reach the target position while avoiding obstacles. The experiment suggest
that proposed framework is capable of performing policy online training, and
that there remains significant room for improvement.

_Keywords_ —digital twin, reinforcement learning, robot manipulator, hardware-
in-the-loop training, collision avoidance

##  I INTRODUCTION

In recent decades, collaborative robots have become increasingly important in
Industry 5.0 since the growing automation of modern manufacturing tends to re-
introduce human workers back into the loop. Unlike traditional fully pre-
programmed robots that operate independently behind safety cages, the latest
generation of collaborative robots are equipped with a suite of sensors that
enable them to operate alongside human workers in more complex environments.
Therefore, the need for being adaptive, flexible and cost-effective is growing
[1]. In this context, the recent advancements in artificial intelligence (AI),
such as machine learning, have demonstrated significant potential to enhance
the smart automation and problem-solving capabilities of robots. In
particular, similar to the natural learning process of humans, reinforcement
learning enables a robot to learn the optimal behaviour through trial-and-
error based on feedback from the environment [2]. While reinforcement learning
is a powerful tool, it still faces several limitations when applying it to
solve real-world problems. Training an RL agent for the robot in the real
world is costly, hazardous and even impossible the most of time. To tackle
this challenge, digital twin technology is introduced to provide a virtual
representation of the robot’s working environment, allowing the robot to
receive feedback through this simulated context of the physical world.
Therefore, the combination of RL and digital twins has gained significant
interest in robotics applications. Existing research mainly focuses on
applying digital twins to generate synthetic data for training the deep
learning model [3, 4, 5, 6]. However, this often leads to another research
area: sim-to-real transfer [7][8]. As a result, the performance of the trained
model directly depends on the accuracy of the virtual representation and the
extent to which sim-to-real techniques can compensate [9]. Moreover, when
robots are assigned more challenging tasks or the workspace environment
changes, the digital twin must perform re-modelling and re-training to adapt
to the new environment. This causes interruption during the tasks and
potentially reduces efficiency and productivity.

Figure 1: The structure of proposed system.

In summary, while reinforcement learning combined with digital twin technology
has been explored and applied to robots for specific tasks, its adaptation to
collaborative robots, which requires better flexibility and problem-solving
skills in uncertain environments, is still in its early stages. This paper
aims to answer the question: What can a digital twin contribute to improve a
robot’s adaptability to an uncertain environment? Through a collision-free
path planning case study, this paper develops a digital twin for a
collaborative robot (i.e., the Ufactory Xarm5 robot) based on Pybullet [10]
and Robot Operating System (ROS), and then explores its possibilities for
conducting a self-improving RL online training. In this framework, the digital
twin is continuously updated in real-time using video feeds from cameras,
while the RL agent constantly updates its policy when collisions or
unsuccessful task attempts are detected by the digital twin’s monitoring
system. The structure of proposed framework is shown in Fig.1. The main
contributions of this work are as follows:

  1. 1.

Instead of using digital twin solely for generating synthetic data to pre-
train the RL agent before task execution [3, 4, 5, 6], we propose a self-
improving online training framework conducted during the task. In this
approach, the RL agent continuously updates its policy based on real-time
observations through trial and error until it is able to absorb new
information from the environment and successfully complete tasks that were
previously deemed unachievable.

  2. 2.

According to [11], compared to existing robotic simulation software, Pybullet
is the most suitable software for machine learning research in terms of
resource usage and idle time. The framework proposed in this paper represents
the first instance of a digital twin developed based on Pybullet and the Robot
Operating System (ROS) combined with a 3D ZED Depth Camera, which is expected
to benefit the collaborative robotics research community.

##  II Related Work

###  II-A Reinforcement Learning for Robotic Manipulation

In recent years, RL algorithms have been extensively developed and applied to
robot manipulators. Different from the core concepts of supervised and
unsupervised learning, RL aims to maximize cumulative rewards, optimizing
robots’ behaviours through trial-and-error based on real-world feedback. [12].
The existing research inculding path/motion planning [13, 14, 15, 16], task
allocation [17], human-robot interaction/collaboration [18, 19], learning-by-
demonstration [20], and so on. With the development of collaborative robots,
there is an increasing focus on enhancing robots’ adaptability to dynamic
environments. In [21], RL was employed to balance human avoidance and task
efficiency during human-robot collaboration, utilizing a human avatar spawned
and animated by skeleton data collected from a camera. Similarly, in [2],
real-time collision avoidance and contact-rich tasks were achieved
simultaneously through goal-conditioned RL, with the co-worker’s hand position
animated by random trajectory. It is worth noting that these approaches are
offline training, as the RL agent is pre-trained before task execution.
Therefore, this paper investigates a self-improving RL online training
combined with digital twin technology to enhance robots’ adaptability and
reduce the need for human efforts in robot re-programming.

###  II-B Digital Twin

Digital twins, often described as a virtual counterpart or digital
representation of a physical entity, have garnered increasing interest over
the past five years in both academia and industry [22]. The concept of the
digital twin was initially introduced by Professor Grieves of the University
of Michigan [23], and its significance has continued growing with the
development of the Internet of Things (IoT), big data analytics, sensors,
robotics, simulation techniques, cloud computing and AI [24]. Digital twins
are not only valuable for designing, monitoring, and controlling physical
entities but also for predicting and optimizing them in real time. These
capabilities make it an ideal tool for robotics research combined with machine
learning, as it offers a safe and cost-effective way for training. In
robotics, the focus of digital twin applications spans various tasks such as
grasping [25][26], navigation [27], obstacle avoidance [28], task allocation
[29][30], and so on. It’s worth mentioning that in [31], the path of a bridge
inspection robot is online planned using a digital twin that is updated with
video feeds from real robots. This hardware-in-the-loop approach enables the
digital twin to be aware of real-time situations and update its strategy
accordingly. Indeed, the accuracy of the digital twin may play a crucial role,
as it could vary over time after the model has been trained. Inspired by the
aforementioned work, this paper aims to develop a digital twin-based RL online
training framework to enhance robots’ adaptability to uncertain environments.

##  III Digital Twin Online Training Framework

This section provides details on the proposed online training framework,
including the training algorithm, sensor perception, simulator development,
and bidirectional data transmission.

###  III-A RL based Obstacle Avoidance

####  III-A1 Markov Decision Process

Reinforcement learning relies on an agent learning how to perform a specific
goal by directly interacting with its environment through trial and error. It
uses the framework of Markov decision processes (MDPs) which mathematical
structures the essential features of the artificial intelligence problem [32].
The learner to be trained is called the agent and the surroundings outside of
the agent are called the environment. During the interaction, the agent
receives the environment’s state $S_{t}\in S$ and selects an action $A_{t}\in
A$ based on the transition probability $P\left(s_{t+1}|s_{t},a_{t}\right)$ at
the time step $t$, where $S$ and $A$ is the space of states and actions. As
the consequence of $A_{t}$, the agent receives a feedback reward $R_{t+1}\in
R\subset\mathbb{R}$ and finds itself a new state $S_{t+1}$ from the
environment. An MDP is thereby usually represented as the following tuple:

$\left[S,A,P\left(s_{t+1}|s_{t},a_{t}\right),R\left(s_{t},s_{t+1},a_{t}\right),\gamma\right]$
(1)

The overarching objective of the agent is to maximize the cumulative rewards
received from environment
$G_{t}=\sum\nolimits_{k=0}^{\infty}{\gamma^{k}r_{t+k+1}}$, where
$0\leqslant\gamma\leqslant 1$ is a discount factor. A higher $\gamma$ emphasis
on long-term rewards and a lower $\gamma$ tends to encourage agents to pursue
immediate rewards.

####  III-A2 State

In this paper, the objective of robot is to reach the goal (a cube) and
avoidance the obstacles (boxes with different sizes). Therefore, the relevant
observation for the training process including the current time step $t$,
position of cube in the $x-y$ plane $pos_{goal}$, the size of obstacles
$\left[h,w\right]$, the position $pos_{tcp}$ and velocity $vel_{tcp}$ of the
robot end-effector and the closest points between robot $pos_{A}$ and
obstacles $pos_{B}$. Thus, the state space $S$ is defined as:

$S=\left[t,pos_{goal},pos_{tcp},vel_{tcp},h,w,pos_{A},pos_{B}\right]$ (2)

####  III-A3 Action

Choosing the appropriate action greatly influences learning performance.
Typically, there are two options for defining a robot’s action space. One
approach is to define the action space in the joint space of the robot, which
requires calculating inverse kinematics (IK) at each time step since the
positions of goals and obstacles are defined in Cartesian space. However,
considering that many robots on the market today come with internally built-in
inverse kinematics, training a policy in Cartesian space-based policy makes it
easier to transfer to other robots. Therefore, we defined the action space $A$
as:

$A=\left[\varDelta x,\varDelta y,\varDelta z\right]$ (3)

where $\varDelta x$, $\varDelta y$ and $\varDelta x$ represent the relative
motion along the $x$, $y$ and $z$ axes in Pybullet world coordinates.

####  III-A4 Reward Function

To achieve the goal of reaching the target while avoiding obstacles, the agent
has two separate objectives: (i) minimizing the distance between the end-
effector and the goal position, and (ii) maximizing the distance between the
end-effector and obstacles. Therefore, the reward function can be designed as
follows:

$r=c_{1}r_{g}+c_{2}r_{a}+c_{3}r_{o}$ (4)

where $r_{g}$ represents the reward provided by the change in distance between
the end-effector and the goal position:

$r_{g_{t}}=d_{t-1}\left(pos_{goal_{t-1}},pos_{tcp_{t-1}}\right)-d_{t}\left(pos_{goal_{t}},pos_{tcp_{t}}\right)$
(5)

where $d_{t}\left(pos_{goal_{t}},pos_{tcp_{t}}\right)$ is the distance between
end-effector and obstacles at step $t$. $r_{a}$ denotes the penalty for the
amount of effort exerted by the robot to achieve the goal, designed to assist
the robot in finding an optimal path and speeding up the process:

$r_{a_{t}}=-\left\|\varDelta a_{t}\right\|$ (6)

$r_{o}$ represents the penalty when the robot gets too close to obstacles:

$r_{o_{t}}\begin{cases}-1\ \ \
if\,\,d\left(pos_{A_{t}},pos_{B_{t}}\right)<d_{thre}\\\ 0\ \ \ \ \
if\,\,d\left(pos_{A_{t}},pos_{B_{t}}\right)\geqslant d_{thre}\\\ \end{cases}$
(7)

where $d_{thre}$ is the distance threshold between robot and obstacles.
$c_{1}$, $c_{2}$ and $c_{3}$ are weights that balance the influence of
different rewards. These weights can significantly impact training, as
inappropriate values may cause the learning agent to converge to a suboptimal
solution rather than a globally optimal one. In this study, we utilized
Proximal Policy Optimization (PPO) [33] from Stable-Baselines3 [34]. For
brevity, detailed formulations of PPO are omitted here.

###  III-B Object Detection and Localization

Figure 2: Object detection results.

Transforming video feeds from cameras to 3D information involves two main
steps: (i) object detection and classification of goals and obstacles, and
(ii) mapping the positions of objects from real-world coordinates to Pybullet
world coordinates. For object detection and classification, we utilized YOLOv8
[35], one of the most popular object detection algorithms known for its high
accuracy and fast speed. Our object detection model was trained on a dataset
of 400 images collected from cameras, achieving an mAP (mean Average
Precision) of $99.4\%$. The dataset can be accessed at [36]. The information
obtained from YOLOv8 detection includes the pixel values $x$ and $y$, as well
as width $w$ and height $h$ of a 2D bounding box. By combining this
information with the depth information from the ZED Stereo Camera, we are able
to derive a 3D bounding box that represents the object’s class, position (in
pixels), and height in the real world. This integration allows for more
comprehensive understanding and analysis of the objects detected in the scene.
For calibrating the coordinates from pixel values to the $x$, $y$, $z$ in
Pybullet world coordinate, we first collected the pixel values of four corners
of the workspace (the rectangular area marked with black tape), and then apply
the Perspective Transformation in OpenCV to get a transformed video so that we
can get better insights into the required information that we need (as can be
seen in Fig.2). Finally, we calculating the ratio between the goal pixels
value $x$ and the total pixels in transformed camera view $a$, and then apply
exactly same ratio into the digital word according to the word coordinates in
Pybullet. The mapping equation is given as follows:

$\begin{cases}x=-0.482\left(\frac{x_{p}}{660}\right)+\varDelta x\\\
y=0.587\left(\frac{y_{p}}{540}\right)+\varDelta y\\\ z=0.025\\\ \end{cases}$
(8)

where $x_{p}$ and $y_{p}$ are pixel values of YOLOv8 output in the transformed
camera view, and 0.482 and 0.587 are the ratios mentioned previously, 660 and
540 represent the total number of pixels in the camera’s horizontal and
vertical dimensions, respectively, and $\varDelta x$, $\varDelta y$ denote the
linear offset measured in the real world.

###  III-C Integrated Digital Twin

The proposed digital twin is built upon Pybullet, a Python-based simulation
environment utilizing the Bullet physics engine. To translate the
aforementioned mathematical concepts such as agent, environment, state, and
action within the simulation, we use OpenAI Gym in conjunction with Pybullet.
OpenAI Gym offers a pre-defined modular framework for constructing
reinforcement learning (RL) environments, which means we can easily plug in
any RL algorithm to test on our custom environment as long as it get
registered with OpenAI Gym. This approach facilitates the development and
experimentation of RL algorithms in our simulated environment, enhancing
flexibility and ease of implementation.

Figure 3: The flowchart of proposed framework.

Before initiating the proposed online training framework, the agent will be
pre-trained within the digital twin environment. It will be initially trained
with simpler and general objectives, such as navigating around a small
obstacle. Throughout the task, bidirectional data transmission facilitated by
ROS ensures synchronization between the digital and physical systems. Each
component of system is programmed as a ROS node, including, ZED camera object
detection node, physical robot control node, OpenAI gym environment node and
resume training node. The flow chat of proposed frame is depicted in Fig. 3.

Notably, the virtual robot operates one episode ahead of the real robot to
predict and monitor the environment’s dynamics in advance (usually taking 1-2
seconds, depending on the PC’s performance). If the digital robot completes
the task safely and successfully, the joint commands are transmitted from
Pybullet to the physical robot. Conversely, if the digital robot encounters
difficulties (can not reach the goal or have collision with obstacles), it
updates its observations based on the new environment captured by the camera
and resumes training based on the pre-trained model until convergence of
reward is achieved again. Subsequently, the improved RL model is employed to
simulate scenarios within the digital twin environment, and if deemed safe and
successful, the joint poses commands are sent to the physical robot once more.
The pseudocode of proposed self-improving training framework is depicted in
Algorithm 1, which offers a substantial enhancement in robot adaptability,
eliminating the need for repetitive reprogramming in case the environment is
changed.

Input : $t,pos_{goal},pos_{tcp},vel_{tcp},h,w,pos_{A},pos_{B}$

Output : $flag_{task}$, $flag_{safe}$

Operate virtual robot at $k$ episode

if  _$flag_{task}=0$ or $flag_{safe}=0$_ then

ROS publish joint configurations from Pybullet to physical robtot

$k=k+1$

else

repeat

Resume training

until  _Reward converged, $flag_{task}=flag_{safe}=1$_;

Publish retained joint configurations to physical robot

$k=k+1$

end if

Algorithm 1 Self-Improving RL online training framework.

##  IV Experiments and Results

###  IV-A Task Description

In this section, obstacle avoidance is selected as a case study to demonstrate
the effectiveness of the proposed online training framework, as it is
fundamental to the safe and efficient operation of robots in diverse
environments. This experiment serves as a proof-of-concept to evaluate the
efficacy of our framework. The objective of the experiment is for the robot to
reach the goal (cubes) while simultaneously avoiding obstacles (boxes). In the
case of any unsafe or unsuccessful attempts within the digital twin, the robot
automatically resumes training until it achieves successful task completion.
The experiment was conducted on Ubuntu 20.04 with an Intel(R) Core(TM)
i9-9960X CPU, 32GB of memory, and an NVIDIA GeForce RTX 4070Ti GPU. The camera
used for capturing the environment is the ZED 2i Depth Camera of Stereolabs,
and the robot manipulator is the Ufactory Xarm5 robot. Prior to task
execution, we pre-trained an RL agent to reach the goal and avoid a small
obstacle (as can be seen in Fig. 4), with the goal and obstacle positions
randomly sampled within the observation space. The 3D model of the robot was
loaded into Pybullet from the Xarm5 URDF file, and the built-in inverse
kinematics (IK) function in Pybullet was utilized to translate the RL agent’s
actions into 5 degrees of freedom joint poses for animating the virtual robot.

Figure 4: Pre-training robot with small obstacle.

###  IV-B Agent Retain Training

After the robot is able to finish the task with small obstacles, we proceeded
to replace the obstacle with a larger one. As depicted in Fig. 5(a) and Fig.
5(b), the robot collides with boxes while attempting to reach the goal, as it
is assuming the obstacle was still small enough to navigate around. Detecting
such collisions in real-time poses significant safety concerns and can be too
late to prevent accidents, which shows the advantages of utilizing a digital
twin. Pybullet provides a built-in collision detection function so that we can
easily predict the collision in the digital twin. It is worth noting that we
use collision detection solely to generate a flag message indicating whether
the task is safe or not. For RL agent training, we employ the shortest
distance function provided by Pybullet as the observation, allowing the robot
to maintain a safe distance from obstacles.

(a) Digital twin

(b) Physical world

Figure 5: Robot failed to avoid higher obstacle.

The ROS launches the resume training node as soon as it receives the flag
message of task failure. Fig. 6(a) and Fig. 6(b) illustrate the training
reward of both the pre-trained and re-trained models. Initially, the reward of
the pre-trained model starts from 0. After approximately $9.7\times 10^{5}$
steps of training, it reaches the optimal reward. However, the reward sharply
drops when the re-trained model starts, due to numerous collisions
significantly reducing the reward. Subsequently, after around $1.2\times
10^{4}$ steps, the reward begins to rise and ultimately converges after
approximately $1\times 10^{5}$ steps. It is worth noting that although the
pre-training is scheduled for $1\times 10^{6}$ steps, the optimal reward
appears at $9.7\times 10^{5}$ steps instead of the final step, that’s why the
training was resumed from the model at $9.7\times 10^{5}$ steps. The
retraining process demonstrates significant efficiency, requiring only 10% of
the time to adapt to the new environment compared to the pre-training process.
Fig. 7 depicts the retraining process.

(a) The reward of pre-trained model

(b) The reward of re-trained model

Figure 6: Training reward. Figure 7: RL retaining

After the retraining process is completed, as demonstrated in Fig. 8(a) and
Fig. 8(b), the robot autonomously avoids a higher obstacle. The video
showcasing the experiment is available in [37].

(a) robot successfully avoid a higher obstacle in digital twin.

(b) robot successfully avoid a higher obstacle in physical world.

Figure 8: Retain results.

##  V Conclusions

This paper presents a self-improving hardware-in-the-loop training framework
that integrates digital twin with RL. Digital twin is a powerful tool for
conducting machine learning research in robotics. Unlike existing researches
that apply the digital twin to generate synthetic data, this paper trains RL
agents directly within the digital twin environment, which continuously
updates based on real-world interactions. A proof-of-concept experiment is
conducted to validate the effectiveness of the proposed framework. Although
the results show that the robot can adapt to a more challenging task than
before, certain limitations exist. First, the proposed framework only works
when the changes in the environment are registered inside the RL agent’s
observation space (in our case, the size of the obstacles). Therefore, the
robot may struggle to adapt to completely unpredictable scenarios. Moreover,
the camera also has its limitations in capturing the entire environmental
context. Integrating multiple sensors could potentially address this
limitation.

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