IEEE Robotics & Automation Magazine - June 2020 - 109
ra = 0.4 m
1
y (m)
y (m)
1
0
0
-1
-1
-2
0
x (m)
2
-2
(a)
ra = 0.5 m
y (m)
y (m)
0
2
0
x (m)
2
0
-1
-1
-2
0
x (m)
2
-2
(g)
(b)
ra = 0.6 m
ra = 0.6 m
1
y (m)
1
y (m)
0
x (m)
(f)
ra = 0.5 m
1
1
0
0
-1
-1
-2
0
x (m)
(c)
ra = 0.7 m
2
-2
0
x (m)
(h)
ra = 0.7 m
2
-2
0
x (m)
2
1
y (m)
1
y (m)
0
0
-1
-1
-2
0
x (m)
(d)
ra = 0.8 m
2
(i)
ra = 0.8 m
1
1
y (m)
Verification Results
Verification was performed with
the methods in the "Verification" section. Here, we present the results for
the second drop-off task shown
i n F i g u re 4, namely, the case in
which the UAV starts in the set
x 0 ! [0, 1], y 0 ! [- 0.5, 0.5] and aims
to reach the goal at [4, 0] m, with
ra = 0.45 m and disturbances d x,
d y ! " - 0.1, 0.1 , m/s.
The verification results are presented in Figure 5. We divided the initial
set into smaller subsets and verified
each one separately to keep the approximation error in Flow* small enough.
The size of these subsets [i.e., the 5-cm
boxes in Figure 5(b)] was chosen after
some preliminary testing; these subsets
were large enough to verify the majority of the initial set with a small approximation error. Some subsets were
further refined when an instance
resulted in an error that was too large.
Refinements were necessary at the
NN's decision boundary as well as for
sets that triggered multiple if-cases in
the planner (e.g., when planning
around multiple obstacles). The verification was performed using Amazon
ra = 0.4 m
y (m)
distance marked on top of the figure.
Due to space constraints, we show
examples of data for only three avoidance distance values: ra = 0.3 m,
ra = 0.45 m, and ra = 0.7 m. Arrows
inside the workspace indicate the
direction of motion of the vehicle.
Inside each subfigure, the green (red)
dots represent initial positions from
which the trajectories to the goal are
labeled safe (unsafe) using reachability analysis. The green (red) circles
around the dots denote the decisions of the NN on the same training
points. As can be noticed and as
expected, when the avoidance distance increases, the number of safe
initial positions also increases in
both missions because the distance
between the desired trajectories and
the obstacles becomes larger. Therefore, increasing the avoidance distance improves safety; however, the
routes become longer, which generally
is not desirable due to energy concerns.
0
-1
0
-1
-2
0
x (m)
(e)
2
-2
Safe Labels
Unsafe Labels
NN Safe Labels
NN Unsafe Labels
Obstacles
Drop-Off Position
0
x (m)
(j)
2
Figure 6. The safe and unsafe training and NN results for the pickup and drop-off tasks
in the area where experiments were performed. An FP (red dot inside a green circle)
corresponds to an unsafe label (red dot) with a safe NN decision (green circle), while
an FN (green dot inside a red circle) is a safe label (green dot) marked as unsafe (red
circle). The number of FPs is zero for both NNs, and there are two and zero FNs for the
first and second NN, respectively. The drop-off tasks where (a) ra = 0.4 m, (b) ra = 0.5
m, (c) ra = 0.6 m, (d) ra = 0.7 m, and (e) ra = 0.8 m. The pickup tasks where (f) ra =
0.4 m, (g) ra = 0.5 m, (h) ra = 0.6 m, (i) ra = 0.7 m, and (j) ra = 0.8 m.
JUNE 2020
*
IEEE ROBOTICS & AUTOMATION MAGAZINE
*
109
IEEE Robotics & Automation Magazine - June 2020
Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - June 2020
Contents
IEEE Robotics & Automation Magazine - June 2020 - Cover1
IEEE Robotics & Automation Magazine - June 2020 - Cover2
IEEE Robotics & Automation Magazine - June 2020 - Contents
IEEE Robotics & Automation Magazine - June 2020 - 2
IEEE Robotics & Automation Magazine - June 2020 - 3
IEEE Robotics & Automation Magazine - June 2020 - 4
IEEE Robotics & Automation Magazine - June 2020 - 5
IEEE Robotics & Automation Magazine - June 2020 - 6
IEEE Robotics & Automation Magazine - June 2020 - 7
IEEE Robotics & Automation Magazine - June 2020 - 8
IEEE Robotics & Automation Magazine - June 2020 - 9
IEEE Robotics & Automation Magazine - June 2020 - 10
IEEE Robotics & Automation Magazine - June 2020 - 11
IEEE Robotics & Automation Magazine - June 2020 - 12
IEEE Robotics & Automation Magazine - June 2020 - 13
IEEE Robotics & Automation Magazine - June 2020 - 14
IEEE Robotics & Automation Magazine - June 2020 - 15
IEEE Robotics & Automation Magazine - June 2020 - 16
IEEE Robotics & Automation Magazine - June 2020 - 17
IEEE Robotics & Automation Magazine - June 2020 - 18
IEEE Robotics & Automation Magazine - June 2020 - 19
IEEE Robotics & Automation Magazine - June 2020 - 20
IEEE Robotics & Automation Magazine - June 2020 - 21
IEEE Robotics & Automation Magazine - June 2020 - 22
IEEE Robotics & Automation Magazine - June 2020 - 23
IEEE Robotics & Automation Magazine - June 2020 - 24
IEEE Robotics & Automation Magazine - June 2020 - 25
IEEE Robotics & Automation Magazine - June 2020 - 26
IEEE Robotics & Automation Magazine - June 2020 - 27
IEEE Robotics & Automation Magazine - June 2020 - 28
IEEE Robotics & Automation Magazine - June 2020 - 29
IEEE Robotics & Automation Magazine - June 2020 - 30
IEEE Robotics & Automation Magazine - June 2020 - 31
IEEE Robotics & Automation Magazine - June 2020 - 32
IEEE Robotics & Automation Magazine - June 2020 - 33
IEEE Robotics & Automation Magazine - June 2020 - 34
IEEE Robotics & Automation Magazine - June 2020 - 35
IEEE Robotics & Automation Magazine - June 2020 - 36
IEEE Robotics & Automation Magazine - June 2020 - 37
IEEE Robotics & Automation Magazine - June 2020 - 38
IEEE Robotics & Automation Magazine - June 2020 - 39
IEEE Robotics & Automation Magazine - June 2020 - 40
IEEE Robotics & Automation Magazine - June 2020 - 41
IEEE Robotics & Automation Magazine - June 2020 - 42
IEEE Robotics & Automation Magazine - June 2020 - 43
IEEE Robotics & Automation Magazine - June 2020 - 44
IEEE Robotics & Automation Magazine - June 2020 - 45
IEEE Robotics & Automation Magazine - June 2020 - 46
IEEE Robotics & Automation Magazine - June 2020 - 47
IEEE Robotics & Automation Magazine - June 2020 - 48
IEEE Robotics & Automation Magazine - June 2020 - 49
IEEE Robotics & Automation Magazine - June 2020 - 50
IEEE Robotics & Automation Magazine - June 2020 - 51
IEEE Robotics & Automation Magazine - June 2020 - 52
IEEE Robotics & Automation Magazine - June 2020 - 53
IEEE Robotics & Automation Magazine - June 2020 - 54
IEEE Robotics & Automation Magazine - June 2020 - 55
IEEE Robotics & Automation Magazine - June 2020 - 56
IEEE Robotics & Automation Magazine - June 2020 - 57
IEEE Robotics & Automation Magazine - June 2020 - 58
IEEE Robotics & Automation Magazine - June 2020 - 59
IEEE Robotics & Automation Magazine - June 2020 - 60
IEEE Robotics & Automation Magazine - June 2020 - 61
IEEE Robotics & Automation Magazine - June 2020 - 62
IEEE Robotics & Automation Magazine - June 2020 - 63
IEEE Robotics & Automation Magazine - June 2020 - 64
IEEE Robotics & Automation Magazine - June 2020 - 65
IEEE Robotics & Automation Magazine - June 2020 - 66
IEEE Robotics & Automation Magazine - June 2020 - 67
IEEE Robotics & Automation Magazine - June 2020 - 68
IEEE Robotics & Automation Magazine - June 2020 - 69
IEEE Robotics & Automation Magazine - June 2020 - 70
IEEE Robotics & Automation Magazine - June 2020 - 71
IEEE Robotics & Automation Magazine - June 2020 - 72
IEEE Robotics & Automation Magazine - June 2020 - 73
IEEE Robotics & Automation Magazine - June 2020 - 74
IEEE Robotics & Automation Magazine - June 2020 - 75
IEEE Robotics & Automation Magazine - June 2020 - 76
IEEE Robotics & Automation Magazine - June 2020 - 77
IEEE Robotics & Automation Magazine - June 2020 - 78
IEEE Robotics & Automation Magazine - June 2020 - 79
IEEE Robotics & Automation Magazine - June 2020 - 80
IEEE Robotics & Automation Magazine - June 2020 - 81
IEEE Robotics & Automation Magazine - June 2020 - 82
IEEE Robotics & Automation Magazine - June 2020 - 83
IEEE Robotics & Automation Magazine - June 2020 - 84
IEEE Robotics & Automation Magazine - June 2020 - 85
IEEE Robotics & Automation Magazine - June 2020 - 86
IEEE Robotics & Automation Magazine - June 2020 - 87
IEEE Robotics & Automation Magazine - June 2020 - 88
IEEE Robotics & Automation Magazine - June 2020 - 89
IEEE Robotics & Automation Magazine - June 2020 - 90
IEEE Robotics & Automation Magazine - June 2020 - 91
IEEE Robotics & Automation Magazine - June 2020 - 92
IEEE Robotics & Automation Magazine - June 2020 - 93
IEEE Robotics & Automation Magazine - June 2020 - 94
IEEE Robotics & Automation Magazine - June 2020 - 95
IEEE Robotics & Automation Magazine - June 2020 - 96
IEEE Robotics & Automation Magazine - June 2020 - 97
IEEE Robotics & Automation Magazine - June 2020 - 98
IEEE Robotics & Automation Magazine - June 2020 - 99
IEEE Robotics & Automation Magazine - June 2020 - 100
IEEE Robotics & Automation Magazine - June 2020 - 101
IEEE Robotics & Automation Magazine - June 2020 - 102
IEEE Robotics & Automation Magazine - June 2020 - 103
IEEE Robotics & Automation Magazine - June 2020 - 104
IEEE Robotics & Automation Magazine - June 2020 - 105
IEEE Robotics & Automation Magazine - June 2020 - 106
IEEE Robotics & Automation Magazine - June 2020 - 107
IEEE Robotics & Automation Magazine - June 2020 - 108
IEEE Robotics & Automation Magazine - June 2020 - 109
IEEE Robotics & Automation Magazine - June 2020 - 110
IEEE Robotics & Automation Magazine - June 2020 - 111
IEEE Robotics & Automation Magazine - June 2020 - 112
IEEE Robotics & Automation Magazine - June 2020 - 113
IEEE Robotics & Automation Magazine - June 2020 - 114
IEEE Robotics & Automation Magazine - June 2020 - 115
IEEE Robotics & Automation Magazine - June 2020 - 116
IEEE Robotics & Automation Magazine - June 2020 - 117
IEEE Robotics & Automation Magazine - June 2020 - 118
IEEE Robotics & Automation Magazine - June 2020 - 119
IEEE Robotics & Automation Magazine - June 2020 - 120
IEEE Robotics & Automation Magazine - June 2020 - 121
IEEE Robotics & Automation Magazine - June 2020 - 122
IEEE Robotics & Automation Magazine - June 2020 - 123
IEEE Robotics & Automation Magazine - June 2020 - 124
IEEE Robotics & Automation Magazine - June 2020 - 125
IEEE Robotics & Automation Magazine - June 2020 - 126
IEEE Robotics & Automation Magazine - June 2020 - 127
IEEE Robotics & Automation Magazine - June 2020 - 128
IEEE Robotics & Automation Magazine - June 2020 - 129
IEEE Robotics & Automation Magazine - June 2020 - 130
IEEE Robotics & Automation Magazine - June 2020 - 131
IEEE Robotics & Automation Magazine - June 2020 - 132
IEEE Robotics & Automation Magazine - June 2020 - 133
IEEE Robotics & Automation Magazine - June 2020 - 134
IEEE Robotics & Automation Magazine - June 2020 - 135
IEEE Robotics & Automation Magazine - June 2020 - 136
IEEE Robotics & Automation Magazine - June 2020 - 137
IEEE Robotics & Automation Magazine - June 2020 - 138
IEEE Robotics & Automation Magazine - June 2020 - 139
IEEE Robotics & Automation Magazine - June 2020 - 140
IEEE Robotics & Automation Magazine - June 2020 - 141
IEEE Robotics & Automation Magazine - June 2020 - 142
IEEE Robotics & Automation Magazine - June 2020 - 143
IEEE Robotics & Automation Magazine - June 2020 - 144
IEEE Robotics & Automation Magazine - June 2020 - 145
IEEE Robotics & Automation Magazine - June 2020 - 146
IEEE Robotics & Automation Magazine - June 2020 - 147
IEEE Robotics & Automation Magazine - June 2020 - 148
IEEE Robotics & Automation Magazine - June 2020 - 149
IEEE Robotics & Automation Magazine - June 2020 - 150
IEEE Robotics & Automation Magazine - June 2020 - 151
IEEE Robotics & Automation Magazine - June 2020 - 152
IEEE Robotics & Automation Magazine - June 2020 - 153
IEEE Robotics & Automation Magazine - June 2020 - 154
IEEE Robotics & Automation Magazine - June 2020 - 155
IEEE Robotics & Automation Magazine - June 2020 - 156
IEEE Robotics & Automation Magazine - June 2020 - 157
IEEE Robotics & Automation Magazine - June 2020 - 158
IEEE Robotics & Automation Magazine - June 2020 - 159
IEEE Robotics & Automation Magazine - June 2020 - 160
IEEE Robotics & Automation Magazine - June 2020 - 161
IEEE Robotics & Automation Magazine - June 2020 - 162
IEEE Robotics & Automation Magazine - June 2020 - 163
IEEE Robotics & Automation Magazine - June 2020 - 164
IEEE Robotics & Automation Magazine - June 2020 - 165
IEEE Robotics & Automation Magazine - June 2020 - 166
IEEE Robotics & Automation Magazine - June 2020 - 167
IEEE Robotics & Automation Magazine - June 2020 - 168
IEEE Robotics & Automation Magazine - June 2020 - 169
IEEE Robotics & Automation Magazine - June 2020 - 170
IEEE Robotics & Automation Magazine - June 2020 - 171
IEEE Robotics & Automation Magazine - June 2020 - 172
IEEE Robotics & Automation Magazine - June 2020 - 173
IEEE Robotics & Automation Magazine - June 2020 - 174
IEEE Robotics & Automation Magazine - June 2020 - 175
IEEE Robotics & Automation Magazine - June 2020 - 176
IEEE Robotics & Automation Magazine - June 2020 - 177
IEEE Robotics & Automation Magazine - June 2020 - 178
IEEE Robotics & Automation Magazine - June 2020 - 179
IEEE Robotics & Automation Magazine - June 2020 - 180
IEEE Robotics & Automation Magazine - June 2020 - 181
IEEE Robotics & Automation Magazine - June 2020 - 182
IEEE Robotics & Automation Magazine - June 2020 - 183
IEEE Robotics & Automation Magazine - June 2020 - 184
IEEE Robotics & Automation Magazine - June 2020 - Cover3
IEEE Robotics & Automation Magazine - June 2020 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2023
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2023
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2023
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2023
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2022
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2022
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2022
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2022
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2021
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2021
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2021
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2021
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2020
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2020
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2020
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2020
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2010
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2010
https://www.nxtbookmedia.com