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SAMPLING-BASED DESCENT TRAJECTORY PLANNING AND
AUTONOMOUS LANDING SITE SELECTION FOR ICY MOON
LANDER MISSIONS
Akash Arora1, P. Michael Furlong2, Uland Wong2, Terrence Fong2
1Australian Centre for Field Robotics, The University of Sydney, Australia, E-mail: aaro4138@uni.sydney.edu.au
2Intelligent Robotics Group, NASA Ames Research Centre, CA, USA, E-mail:
{padraig.m.furlong,uland.wong,terry.fong}@nasa.gov
ABSTRACT
Selecting suitable landing sites is fundamental
to achieving success in robotic lander missions.
However, due to sensing limitations, landing sites
that are both safe and scientifically suitably may
not be determined reliably from orbit prior to
descent, especially where orbital sensing data is
noisy or incomplete. In previous work we pro-
posed an algorithm which allows landers to au-
tonomously plan informative descent trajectories,
exploiting information gathered during descent to
land on high quality sites [1]. In this paper, we im-
prove the scalability of our approach through im-
portance sampling. Our method substantially re-
duces planning times without sacrificing the qual-
ity of the selected landing sites.
1 INTRODUCTION
The icy moons of Europa and Enceladus are
among the top priorities for NASAs exploration
objectives [2]. These bodies may be the best can-
didates for finding extra-terrestrial life in the solar
system, as interior liquid oceans may be present
and accessible from the frozen surface. Due to the
remote nature of these missions, however, human
intervention is limited and on-board autonomy is
necessary to execute complex tactical maneuvers
during entry, descent, and landing (EDL) and en-
sure the robot safely lands at the desired site.
In past lander missions, suitable landing sites were
selected a priori by domain experts from orbital
sensor measurements of geological features that
indicate the safety and scientific utility of sites.
Low level navigation, control, and hazard avoid-
ance were conducted on-board to ensure a safe
landing near the desired site without human in-
tervention. However, noisy, incomplete, or low
resolution orbital data can mask the true safety
and scientific value of landing sites. This is espe-
cially the case for icy moons, where key features
such as crevasses, jagged penitentes, liquids, and
ice thickness can either be either below the reso-
lution of orbital sensors or require non-traditional
sensors, like ground penetrating radar or thermal
imaging, to detect. These non-traditional sensors
have limited sensing range and cannot necessarily
resolve the required information from orbit.
In previous work [1], we presented a new ap-
proach to autonomous EDL which allows space-
craft to land in suitable sites under such sens-
ing constraints. We proposed a Bayesian net-
work (BN) architecture that conducts on-board
heterogeneous sensor data analysis and rapidly
updates estimates of safety and scientific suitabil-
ity of landing sites during descent. The estimated
values were fed into a sampling based planner
based on Monte Carlo Tree Search [3] to plan in-
formative descent trajectories such that the lander
can acquire high quality observations of promis-
ing landing sites during descent subject to fuel
constraints. The descent trajectories were up-
dated as new data were acquired and replanned
until landing. Our algorithm is anytime and re-
quires constant memory, making it particularly
well suited for missions with low computational
power and hard real-time constraints.
Previous work evaluated the approach in relatively
small landing site maps. This work aims to scale
up the approach to larger maps. We conduct a
complexity analysis of our approach which we use
to target areas where approximations would im-
pact performance. We then propose algorithmic
modifications based on importance sampling [4]
which significantly improves scalability of our ap-
proach to larger environments. Lastly, we present
an empirical evaluation of the approach in both
large simulated maps with realistic icy terrain and
thermal data based on physics models. We com-
plement these extensions with increased technical
detail, generalization to arbitrary EDL missions,
and additional discussion on the practical chal-
lenges of deploying our approach in practice.
2 RELATED WORK
In past lander missions, landing sites were chosen
by the science team based on orbital data and do-
main knowledge. Autonomous EDL research has
largely focused on hazard detection using com-
puter vision and navigation techniques to accu-
rately land in a desired location. On-board percep-
tion is used to match low-altitude terrain to maps
created from orbital data which helps determine if
a lander is accurately executing a predetermined
trajectory from relative motion [5, 6]. Last minute
diversions are allowed to avoid hazardous sites if
detected, but unlike our approach, the spacecraft
cannot tour multiple candidate landing sites and
learn more about the environment before commit-
ting to a site. We also consider the scientific utility
of sites, not just the safety.
Typical EDL sensor packages include lidar, radar,
and cameras to characterize terrain geometry. In-
teractions of these sensors with icy moon surfaces
however could lead to increased sensor noise.
Non-traditional sensors like bore-sight imagers,
thermal cameras, and sounding radar may need to
be used which have varying sensing ranges and
noise models. Our approach is sensor agnostic
and can incorporate an arbitrary number of sen-
sors with arbitrary noise models.
Serrano et al. proposed a Bayesian network (BN)
for planetary landing site selection which fuses
data from multiple sensor sources, and other crite-
ria such as reachability and scientific utility to de-
termine probabilistic estimates of quality of land-
ing sites [7]. We also use BNs to fuse multi-modal
data but unlike Serrano’s work, we account for al-
titude dependent sensor noise and use the prob-
abilistic estimates to actively explore and gather
information about the environment.
Desaraju, et al., explores terrestrial rooftop envi-
ronments with a UAV to select the best landing
site [8]. They use a Gaussian process to model the
environment and combine it with information gain
functions to explore the environment. The work is
similar in principal to ours, but is application spe-
cific and does not incorporate multi-modal sens-
ing and the decision of when to use which sensor.
Descent trajectory planning is traditionally
viewed from an optimal control perspective
where the target location is provided a-priori [9].
In contrast, we plan trajectories using Monte
Carlo Tree Search (MCTS) which is a sampling
based, approximate tree search algorithm [3].
MCTS is anytime, giving it a unique advantage
over both gradient descent and other sampling
based approaches like Rapidly Exploring Random
Trees. Our adaptation of MCTS allows principled
reasoning over long horizons, and accounts for
partially observability [10] which is particularly
advantageous in an EDL situation where there are
hard real time constraints and observations from
sensors are noisy or incomplete. Furthermore our
approach allows spacecrafts to simultaneously
plan movements and schedule when to make
sensor measurements to gain further information-
a capability beyond the scope of existing research
in descent trajectory planning. Sampling based
methods, however, inherently discretize the plan-
ning space but can be fused with continuous space
optimization techniques to ensure smoothness
and dynamic feasibility.
3 PROBLEM FORMULATION
The spacecraft must generate descent trajectories
and sensor schedules which gather information
on promising landing sites and terminate on a
site that is both safe and scientifically valuable.
This section describes the environment model, the
properties of our simulated lander, and formally
defines the planning problem being solved.
Environment Representation: This work uses
a grid world representation of the environment
where each grid cell is a potential landing site.
Cells are described by feature vectors, F. On icy
moons, these features could include ice thickness,
terrain jaggedness, slope, and thermal properties.
The lander can take noisy measurements of these
features through its on-board sensors.
We assume that there are functions that map fea-
ture vectors to safety, VT:F→ {U nsa f e,S a f e},
and the scientific value, VS:F→[0,...,∞),
of the candidate landing sites. There exists prior
work which aims to estimate landing site safety
from sensor data, using techniques such as plane
fitting, edge detection, and neural network classi-
fication [6, 11]. We can use these functions in our
approach to supply VT.
VSindicates which geological features are high
priority for the mission’s science goals. This func-
tion must be elicited from the mission science
team. The overall site utility Uis a function of
the scientific value and the safety of the site.
Lander Properties: At any given time, the lander
Sensor noise model
Science preferences
Terrain safety model
BN utility model
Other criteria
Orbital data
Probabilistic belief
over landing site
features, safety
and science utility
Select leaf node to
expand
Forward simulation
Sample observations
Estimate reward
Update tree
Planner
GNC system
Planetary Surface
Science Team
Sensing
action
Take
observations
Sensor data
Waypoints
Figure 1: The systems architecture of our approach
can choose a maneuvering action which changes
the vehicle’s direction of motion and select which
of its P-many sensors to use. An example sensor
payload for an icy moon lander could include a
high resolution camera, ground penetrating radar,
thermal sensor, and a reflectance spectrometer.
Each sensor observes different subsets of the fea-
ture vector Fand has its own noise model and
field of view which varies with the spacecraft al-
titude. We discretize the maneuvering space m
into Kactions. This produces an action space,
A={m1,...,mK}×{s0,s1,...,sP}.
Problem Statement: The lander must plan a se-
quence of maneuvering and sensing actions a1...L
which maximize some reward function Rmeasur-
ing the likelihood of landing at a site with high
overall utility. Each maneuvering or sensing ac-
tion aiincurs some predefined cost given by the
cost(ai) function and the overall sequence is sub-
ject to a budget B. This budget could be the delta-
V or time. The optimization problem is stated be-
low:
a∗
1..L=arg max
a1...L∈A
R(a1...L)
s.t.
L
X
i=1
cost(ai)≤B
(1)
Lastly, when the lander budget expires, it must be
within some radius Lof the selected landing site.
|xf−xend| ≤ R(2)
where xend is the lander’s terminal position and
xfis the desired landing site. It is expected that
at this point in a real mission the lander will be
very close to the surface, and the powered descent
stage will begin and the divert capabilities will be
limited to hazard avoidance.
4 OVERVIEW OF APPROACH
Our approach consists of two main components:
estimating candidate site utilities, and planning in-
formative descent trajectories. A systems archi-
tecture of the approach is illustrated in Fig. 1. This
section provides an overview of these components
and how they can be applied in real missions.
4.1 Site Utility Estimation
As mentioned in Sec. 3, the environment is dis-
cretized into cells where each cell is a potential
landing site. To maximize the reward function in
Eq. 1 and land on high quality sites, the spacecraft
needs a way to infer the safety and science utili-
ties of sites from on-board heteregeneous sensor
measurements taken during descent. Since sensor
observations are inherently noisy, we probabilis-
tically model the inference of safety and science
utility using the Bayes’ Net in Fig. 2.
Orbital data is used to initialize Bayesian prior
distributions over the geological features Fin
each cell. These distributions are updated us-
ing data collected during descent from the on-
board sensors through observations Zp, where p∈
{1,...,P}is the sensor used. There is an indepen-
dent BN associated with each landing site.
Each sensor measures different subsets of these
geological features from which the safety T, sci-
ence utility Sand overall utility Uof a landing site
can be estimated. In this problem setting we set
the Zand Fnodes to be discrete categorical vari-
ables as it simplifies inference, Sas a continuous,
non-negative, variable and Tas a variable ranging
from 0 to 1 indicating the probability whether a
site if safe or not.
FT
S
ZpU
P
Figure 2: Bayesian network to calculate sci-
ence utilities based on observations. Observa-
tions from the different senors, Z1,...,Zpinform
the feature vector Fwhich provides information
on science value, S , and landing site safety T .
Given an observation, the overall utility of a
site can be recursively estimated by conducting
Bayesian updates:
P(U|Z)=X
T,S
P(U|T,S,Z).P(T,S|Z)
=X
T,S
P(U|T,S)X
F
P(T|F)P(S|F)P(F|Z)
(3)
The conditional probability terms in Eq. 3 quan-
tify the probabilistic relationships between vari-
ables. It can be deduced that P(F|Zp) defines a
feature classification model, while the P(T|F) and
P(S|F) terms classify the safety and scientific util-
ity of the site based on the geological features. We
now define each of these terms in more detail.
Quantifying Science Utility: Prior to the mis-
sion, scientists’ preference for desired attributes
in landing sites can be formulated as a value func-
tion that maps features of a region to some score.
In icy moon missions, the features of interest may
include presence of bio-markers, proximity to liq-
uids, or desirable thermal properties of ice. We as-
sume that the scientists’ utility function is known.
We use a weighted linear function of geological
features but any arbitrary function can be used.
Quantifying Site Safety: Landing sites need to
be classified as either “Safe” or “Unsafe”, based
on geological features at the site and the design
of the lander. We assume this term is provided
a priori based on domain knowledge or existing
learning and classification techniques [11, 7].
Feature Classification: Discriminative classifiers
have been extensively used to classify geologic
features in remote sensing data [12]. We use a
Figure 3: Our sensors have circular fields of view.
The viewing cone is characterized by angle θand
spacecraft altitude A.
generative classifier, P(F|Zp), because our planner
requires the ability to predict future observations.
We can invert our classifier to produce P(Zp|F) for
planning purposes, using Bayes theorem.
Sensor Model: We model onboard sensors with a
circular field of view, as in Fig. 3. Decreasing al-
titude increases the resolution of the sensor, and
decreases the effects of sensor noise. The sen-
sor noise model for sensor pat altitude Ais given
by Eq. 4. RMax is the maximum sensing range,
P(Z|F)best(p)is the best case sensor noise model
and Gpis the distribution of the sensor’s intrinsic
noise model. For example, a thermal camera Gp
may model pink noise, while a laser altimeter Gp
may be a uniform distribution. Non-linear noise
functions can also be used here.
P(Z|F)p,a=αP(Z|F)best(p)+(1 −α)Gp
α=
0,if A≥RMax(p)
1−A
RMa x(p),0≤A<RMax(p)
1,A<0
(4)
We assume RMax,P(Z|F)best (p),Gp, and the type
of features seen depend on the sensor type and
are known a priori. Sensor measurements taken
throughout the mission are fed into the BNs to
recursively update features estimates in each ob-
served landing site. Updated feature descriptors
are then used to predict safety and science utilities
along with the uncertainty using Eq. 3. We use
particle filters and message passing to propagate
the belief updates through the network.
4.2 Planning Descent Trajectories
According to decision making theory, the optimal
sensing action sequence is one which in expecta-
tion terminates at the highest utility (U) landing
site. We define the reward function to optimize
R(·) as:
R(a1...L)=X
Z1...L
E(U(xf|Z1...L))P(Z1...L|a1... L)(5)
Z1...Lare the observations made by taking actions
a1...L,P(Z1...L|a1...L) is the probability distribution
of observations that can be made given a sensing
sequence, and U(xf|Z1...L) is a mapping of the ob-
servations made by the robot to the expected or
average overall utility of the landing site. Both the
observation distribution and expected utility terms
are derived from the BN framework in Sec. 4.1.
Optimal decision making in partially observable
environments is in general intractable [13]. Previ-
ously, we used an approximate sampling solution
based on Monte Carlo Tree Search, described in
detail in [1]. In our tree search, tree nodes are
valid spacecraft states, defined by x-y position,
orientation, remaining budget, and altitude. Node
edges are the actions the spacecraft can take.
The key idea is to conduct forward simulations in
the decision space, sample observations resulting
from future movement and sensing actions, and
simulate belief updates to estimate rewards. The
proposed approach allows principled long horizon
planning in an anytime manner while avoiding lo-
cal minima. Another major advantage of our ap-
proach is that it is sensor agnostic and can be ap-
plied to arbitrary dynamic models, and number of
sensors without algorithmic modifications.
5 COMPLEXITY ANALYSIS
Evaluating the reward of forward simulated can-
didate trajectories is the most computationally in-
tensive operation in planning. As mentioned in
Section 4.2, reward is calculated by sampling ob-
servations along candidate trajectories and prop-
agating belief updates to deduce the best land-
ing site. The most expensive term to compute
in this process is determining the posterior utility
of landing sites given observations, P(U|Z), com-
puted with Eq. 3. We define TLas the time to
compute P(U|Z) for one landing site.
Since we have to evaluate P(U|Z) for each landing
site observed during the forward simulation, the
complexity of evaluating the reward for a single
forward simulation is O(Nsites TLH) where Nsites is
the number of sites updated for observations taken
at a single timestep, and His the number of ac-
tions in the planning horizon. The total time taken
for the MCTS is therefore O(NSNsites TLH) where
NSis the number of forward simulations.
This complexity analysis shows there are two
ways to reduce computation time: reduce the in-
ference time, TL, or reduce the number of times
inference has to be done. The second can be
achieved by reducing one of the planning horizon,
the number of sites updated during the forward
simulation, or the number of forward simulations,
NS, needed to find good trajectories. We limit the
discussion to reducing inference times and reduc-
ing number of sites updated.
Reducing Inference Time: An analytic compu-
tation of P(U|Z) requires summing over all pos-
sible instances of the feature space vector, F, as
in Eq. (3), which grows rapidly with the size of
F. We can construct simpler, faster Bayes nets
by mapping sensor data to a smaller, discretized,
semantic feature space instead of using raw fea-
tures. However, semantic features can be expen-
sive to compute. Trade-offs between feature ex-
pressiveness, dimensionality, and simplicity is ap-
plication dependent. For larger and more com-
plex BN’s, we can use approximate Bayesian in-
ference techniques [14], but in this problem in-
stance, our combination of particle filter updates
and message passing already yields near optimal
inference times.
Reducing Number of Sites Updated: Currently,
the MCTS samples observations and updates be-
liefs for every site seen during a forward simula-
tion. The maximum number of sites seen during a
single sense for a robot with a circular sensor FoV
(Fig. 3) is given by Eq. 6:
Nsites =FoVArea ×GridResolution
=πAtan θ
22
GridRe solution
(6)
where Ais the lander altitude and θis the sensor
viewing cone angle. Nsites is upper bounded by the
number of sites on the map. Aand θare system
parameters and outside the control of the planning
algorithm. We could adapt the grid resolution dur-
ing the mission. Early in the mission, when the
robot is at high altitude, little information is lost
by using a coarse grid. As the robot approaches a
landing site, we can increase the resolution, sim-
ilar to the approach of Popovic et al. [15]. The
challenge remains in preserving and transforming
information through different resolutions.
Alternatively, instead of updating beliefs on all the
sites seen during a forward simulation, we can
Figure 4: The generated feature maps along with
the corresponding safety and science utility
track the beliefs of a subset of sites which are
more promising landing sites, a concept known as
importance sampling [4]. This will cut the plan-
ning time by a ratio equal to Ntracked
Nsites - a significant
speedup for large environments. The problem re-
mains of deciding how many sites to track and
how to track these sites.
At the beginning of forward simulations, we sam-
ple the top N% of landing sites based on their cur-
rent expected utility. During forward simulations,
we only sample observations and update beliefs of
sites in this set. Importance sampling ensures that
information gain on only the promising sights is
considered and the lander does not waste planning
time tracking sites that are likely low quality.
6 EXPERIMENTAL SETUP
Map Generation: Previously [1], our experi-
ments used randomly generated 10×10 and 20×20
feature maps. In this paper, we generate geo-
logically realistic maps. Feature maps are cre-
ated by procedural generation of rocks, craters,
and striae on icy terrain. Rock and crater size
and placement are governed by power-law distri-
butions commonly found on airless bodies, while
the striae are mostly qualitative. Slope and ter-
rain roughness of local regions, the first two fea-
tures, were calculated from the terrain map. We
used the Stefan-Boltzmann law to estimate sur-
face temperature for a Europa-like body, while
the visual appearance of the surface was rendered
with the Hapke and Phong reflectance functions
and mixed with pre-generated icy textures. Sur-
face temperature and intensity formed the last two
features. All features were discretized into three
categories– low, medium and high.
We sub-sampled a map of size 100 ×100 which
had a large diversity of features. This equates to a
total of 10000 sites the robot can potentially land
on, and replicates the large scale nature of real
world missions. Ground truth safety of the sites
was set to be a function of the slope and terrain
roughness of the site given by Table 1.
Table 1: Landing site safety score as a function of
discretized terrain geometry features.
Slope
L M H
Terrain Roughness
L 1 0.8 0.4
M 0.8 0.6 0.2
H 0.4 0.2 0
The science utility of a landing site xwas defined
as a weighted function of all four site features,
Slope, Terrain Roughness, Surface Intensity, and
Surface Temperature:
S(x)=0.1FS+0.2FT R +0.3FS I +0.5FS T (7)
Applying Table 1 and Eq. (7) to the feature maps
yields the maps shown in Fig. 4. The overall util-
ity is defined as the product of safety and science
utility. The weights as well as which features af-
fect safety and science utility are arbitrarily set
and can be varied as per mission requirements.
Lander Parameters: The simulated lander is
equipped with two sensors: a visual sensor that
takes noisy observations of slope and roughness,
and a spectrometer that can take noisy measure-
ments of temperature and intensity. Both sensors
have noise models discussed earlier in Eq. 4 with
a circular field of view with a viewing cone angle
of 8 degrees and RMax of 100 units. The visual
sensor has a maximum accuracy of 80% while the
spectrometer has a maximum accuracy of 95%.
Gpis set to be a uniform distribution.
For illustration we simplified the planning prob-
lem to the x-y domain where the descent rate and
speed of the lander are fixed at 1.5 and 5 units
per time step. The lander motion primitives were
chosen to be Dubin’s curves which orientate the
lander in -45, -30, 0, 30 and 45 degrees relative to
the current orientation. Since there were two sen-
sors, and in each time step the lander can choose
a motion primitive and type of sensor to use, the
total action space is of size 10. The cost for us-
ing the visual sensor was 1 unit while the cost for
using the spectrometer was 5 units.
Algorithms: To study the effect of importance
sampling on planning time and landing site qual-
ity we compared with approximation factors of
40%, 20%, 10%, 5%. We compare against
the algorithm from [1], labeled ’original’, a ran-
dom planning baseline where random actions are
taken, observations are collected, and landing site
is the best site within the landing radius of the ter-
minal state, and a greedy baseline which selects
and lands at the best site in the orbital data.
20 trials were run with 5 trials starting from the
center of each of the four edges of the map with an
initial altitude of 50 units. The lander was given a
sensing budget of 50 units. Orbital data was gen-
erated by convolving a 9×9 median filter over the
ground truth feature maps to the create low reso-
lution data. The Bayesian priors on landing site
features were initialized with the orbital data.
7 RESULTS
The utility of the algorithms’ selected landing
sites is shown in Fig. 5. ‘Global’ gives the true
utility of all landing sites in the map. ‘Random’
yields higher utility landing sites than ‘global’,
showing the advantage of using collected obser-
vations. Our MCTS-based approaches and and
the greedy algorithm have the same median util-
ity. However, the sites selected by greedy have
greater variability, which often leads to sites with
low utility. This occurs when low quality orbital
data masks the true value of the sites. If the or-
bital data is poor enough, the performance of the
greedy approach could worsen arbitrarily.
The median utility of sites is unchanged as the
proportion of sites tracked, N, is decreased. Fur-
ther, as Nis reduced, the tracked sites had a ten-
dency to be close to each other, since nearby sites
tend to have similar features, as seen in Fig. 4. As
a result the spacecraft often flew towards the same
set of sites, which could lead to being stuck in lo-
cal minima. Importance sampling strategies that
incorporate spatial variability and site utility un-
certainty into the sampling process instead of only
expected utility remains for future investigation.
The planning times are given in Table 2. Min-
imum times occur near the end of the mission,
when the budget or altitude are near zero. Max-
imum planning times occur near the beginning of
missions when the robot forward simulates trajec-
tories for the entire horizon. The minimum time
remains constant, while maximum significantly
reduces as Nas decreased. At N=5%, the dif-
ference between minimum and maximum times is
4 seconds, while in the full MCTS the difference
is 40.6 seconds. Importance sampling mitigates
the effects of planning horizons on planning time
meaning we can search even longer horizons.
When horizons are near zero, constant time oper-
ations dominate planning time. Further analysis
showed that is was largely due to the copying of
the probability distributions of all landing sites be-
fore each forward simulation. More efficient data
structures that only copy the relevant parts of the
belief space should lead to significant reductions
in planning times.
Table 2: Minimum and maximum run time for 200
iterations of MCTS
Min time (s) Max time (s)
Original 27.6 68.2
40% 27.7 54.8
20% 27.7 41.5
10% 27.4 34.7
5% 27.3 31.3
8 CONCLUSIONS
This paper discussed a sampling based descent
trajectory planner that enables spacecraft to ex-
ploit information gained during descent to select
landing sites that are both safe and have high sci-
ence utility. Our approach reduces precursor data
quality requirements, potentially reducing costs of
both icy moon missions and robotic lander mis-
sions in general. We derived the complexity of
our approach and used importance sampling to
improve scalability.
Our modifications substantially reduced the plan-
ning time without affecting the quality of landing
sites. In future work, we would like to experiment
with reward functions that do not require sampling
observations and simulating belief updates (and
hence much faster to evaluate), and integrate our
approach with continuous space optimizing tech-
niques to achieve an end to end solution for EDL.
Acknowledgements
This work was supported by the ICICLES project
as part of NASA’s Coldtech grant.
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