IEEE Robotics & Automation Magazine - September 2020 - 114

uniform predefined path. The experiments used an acetone vapor source with a release/emission rate of
approximately 1.5 g/s and the UAS described in the section "The System."
The field used during the experiments was located near to
Loughborough University, Leicestershire, United Kingdom.
A large square within the field (approximately 40 × 40 m), containing the release, was intended to represent the domain Ω
that forms a part of the input to the algorithm. The remaining inputs are initial probability distributions that are
required as prior information to the inference algorithm.
They are as follows:
●● 
The prior distributions for the location of the source
[p 0 (x s), p 0 (y s), p 0 (z s)] are set to uniform within the
search area Ω.
●● A gamma distribution is used as the prior for the emission
rate p 0 (q s) = G (1, 5) . This is a long-tailed distribution to
account for a large amount of uncertainty in the emission
rate of the source. This prior was fixed during all of the
experimental trials.
●● 
The meteorological variables [p 0 (z s), p 0 (u s)] are assigned
with normal distributions N (n, v) upon initialization of
the algorithm. In the future, the meteorological variables
should be measured in situ, onboard the UAV (as seen
in [27]).
●● 
The dispersion parameters [g s1, g s2] were given uniform
distributions with an appropriate range.
●● 
The probabilities for nondetection events are set as
Pb = 0.1, Pm = 0.2, and Ps = 0.7.
At each time step, the UAV would hover to take an
averaged measurement from the onboard atmospheric
sensor. The sample duration was set to 5 s. This was a
short amount of time compared to STE methods incorporating static sensors, where it is more common to
sample for a few minutes. The 5-s sampling time was
chosen as a tradeoff between the measurement accuracy
and search time. After the sample is collected and the
source parameter estimates are updated, the UAV would
Algorithm 3: Select optimal control action a*k
(i )

  1:  for all a k ! W do
  2:  p k + 1 = p k + a k
(l )
N
  3:  draw samples {zt k + 1} l =z 1 using Algorithm 2
  4:  for l = 1, 2, f, N z do
t (i, l ) } Ni = 1 using Algorithm 1, with
t (ki+, l )1, H
  5:   
generate {w
k+1
(i )
(i )
(l )
arguments {H k , ~ k } Ni = 1, zt k + 1 and p k + 1
t (i , l )
t (ki+, l)1 ln w k(+i )1
  6:   calculate utility Y (l ) = / Ni = 1 w
wk
  7:  end for
  8:   E [ Y (zt k + 1 (a k))] = 1 / Nl =z 1 Y (l )
Nz
  9:  end for
10:  a )k = arg max E [Y (zt k + 1 (a k))]
ak ! W

Ensure: a )k

*

IEEE ROBOTICS & AUTOMATION MAGAZINE

Illustrative Run
An illustrative run of an experiment, trial 1, using the information-theoretic planning algorithm is described in Figure 3, and a video of trial 9 is available in the multimedia
material available in IEEE Xplore. Overlaid on a map of the
experimental field, the figure shows the flight path of the
UAV executing the information-theoretic search at various
snapshots in time, the measurements at each sampling
location where the measured value is represented by the
size of the white circles along the path, and the true position of the source. To begin the search, the system is initialized at discrete time step k = 0 with the relevant prior
information. The starting position of the UAV is indicated
by the white square. The large number of red dots represents the random sample approximation used in the
sequential Monte Carlo algorithm at the current time step
(i.e., the current posterior distribution). At initialization, in
Figure 3(a), this is a uniform distribution within the search
area. Each red dot represents a weighted source term realization {H (ki), w (ki)}, where only the marginalized position
estimates are visualized in the figure.
Figure 3(a)-(d) shows the path of the UAV and the measurement positions at various time steps. The figure demonstrates how the information-theoretic planner begins the
search by moving in a crosswind direction, because this is the
direction of maximum information gain. In response to positive detections from the PID detector, the estimation algorithm is able to narrow down the location of the source in
the crosswind direction, as shown in Figure 3(b). At this
point it begins to travel upwind toward the source. By timestep k = 29, shown in Figure 3(d), the red dots have converged onto the location of the acetone vapor source, given
by the blue circle. In this example, the estimate of the location of the source was within 1.42 m of the true value. The
emission rate estimate was reasonably accurate but overpredicted by 1.26 g/s.

( i)

Require: weighted samples: {H k , ~ k } Ni = 1;

114

proceed to the next measurement location defined by
the information-theoretic planning algorithm. The
incremental step size between each measurement location was set to 4 m.

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SEPTEMBER 2020

Results
The illustrative run and two other experiments are summarized in a condensed form in Figure 4. Figure 4(a)-(c)
shows the resulting flight path (white line), wind direction (red arrow), and marginalized posterior estimate of
the source location (heat map). The starting and ending
positions of the UAV are given by the white square and
diamond, respectively. The true position of the source is
indicated by the black circle filled with a white cross, and
the algorithm's mean estimate is given by the hollow
black circle. In a similar manner to the illustrative run,
the information-theoretic search algorithm guides the
UAV crosswind until it begins to pick up positive measurements from the PID sensor. The final estimate,
IEEE Robotics & Automation Magazine - September 2020

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