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IAC-17-D3.3.2 
 
NETWORK OF NANO-LANDERS FOR                                                                                     
IN-SITU CHARACTERIZATION OF ASTEROID IMPACT STUDIES 
 
Himangshu Kalitaa, Erik Asphaugb, Stephen Schwartzb, Jekan Thangavelauthama* 
 
a Space and Terrestrial Robotic Exploration Laboratory, Department of Aerospace and Mechanical Engineering, 
University of Arizona, Tucson, Arizona 85721, United States, jekan@arizona.edu 
b Space and Terrestrial Robotic Exploration Laboratory, Department of Planetary Science and Lunar and Planetary 
Laboratory, University of Arizona, Tucson, Arizona 85721, United States  
 
* Corresponding Author  
 
Abstract 
Exploration of asteroids and comets can give insight into the origins of the solar system and can be instrumental 
in planetary defence and in-situ resource utilization (ISRU). Asteroids, due to their low gravity are a challenging 
target for surface exploration. Current missions envision performing touch-and-go operations over an asteroid 
surface. In this work, we analyse the feasibility of sending scores of nano-landers, each 1 kg in mass and volume of 
1U, or 1000 cm3. These landers would hop, roll and fly over the asteroid surface. The landers would include science 
instruments such as stereo cameras, hand-lens imagers and spectrometers to characterize rock composition. A 
network of nano-landers situated on the surface of an asteroid can provide unique and very detailed measurements of 
a spacecraft impacting onto an asteroid surface. A full-scale, artificial impact experiment onto an asteroid can help 
characterize its composition and geology and help in the development of asteroid deflection techniques intended for 
planetary defence. Scores of nano-landers could provide multiple complementary views of the impact, resultant 
seismic activity and trajectory of the ejecta. The nano-landers can analyse the pristine, unearthed regolith shielded 
from effects of UV and cosmic rays and that may be millions of years old. Our approach to formulating this mission 
concepts utilizes automated machine learning techniques in the planning and design of space systems. We use a form 
of Darwinian selection to select and identify suitable number of nano-landers, the on-board instruments and control 
system to explore and navigate the asteroid environment. Scenarios are generated in simulation and evaluated against 
quantifiable mission goals such as area explored on the asteroid and amount of data recorded from the impact event. 
Our earlier work in this field applied to excavation robotics has shown that a machine-learning approach can 
discover creative solutions that exceed the capability of human devised solutions. In this work, we once again intend 
to compare a human-devised system to these machine evolved-systems. The results from these mission formulation 
and preliminary design studies will be used to identify a pathway towards a future asteroid CubeSat mission. 
 
Keywords: robot swarms, asteroids, exploration, mobility, machine learning 
 
1. Introduction 
 
The exploration of small-bodies such as asteroids 
and comets can give us insight into the formation of the 
solar-system, planetary defence and future prospect for 
in-situ-resource utilization. Some asteroids are thought 
to be ancient ‘time capsules’ that have remained 
unaltered for billions of years.  Exploration of these 
asteroid can provide useful insight into the primordial 
solar system. Steady advancement in space systems 
technology enables us to send robotic spacecraft to 
asteroids and comets.  Recent examples include the 
Hayabusa I [2] and Rosetta missions.  More ambitious 
sample returns mission are on the way including 
OSIRIS-REx [1] and Hyabusa II [2]. The next 
technology milestone will be the ability to perform long 
duration surface missions on asteroids. 
With rapid advancement in lightweight structural 
materials, miniaturization of electronics, sensors, 
actuators and MEMS-based instruments it has become 
possible to develop small, low-mass and low-cost 
landers 
for 
exploration 
of 
asteroid 
surfaces. 
Furthermore, with the use of Guidance, Navigation and 
Control (GNC) devices such as reaction-wheels and 
inertial measurement units it is possible for these 
miniature landers to perform short flights, hops and rolls 
to multiple locations on an asteroid.  
In this paper, we study the feasibility of sending 
scores of nano-landers, each 1 kg in mass and volume of 
1U, or 1000 cm3 to an asteroid surface. These landers 
include science instruments such as stereo cameras, 
hand-lens imagers and spectrometers to characterize 
rock composition. Sending a network of nano-landers to 
an asteroid surface would give us the opportunity to 
perform unique and very detailed measurements of a 
larger spacecraft impacting an asteroid surface. The 
‘swarm’ of nano-landers would provide multiple 
complementary views of the impact, the resultant 
seismic 
activity 
and 
trajectory 
of 
the 
ejecta. 
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Furthermore, this swarm can analyse the pristine, 
unearthed regolith that may be millions of years old and 
is shielded from effects of UV and cosmic rays. In-situ 
measurements of the artificial impact will help 
characterize the asteroid composition and geology. 
Insight into asteroid composition and impact effects can 
further 
the 
development 
of 
asteroid 
deflection 
techniques intended for planetary defence. A swarm of 
nano-landers have many advantages including working 
cooperatively to climb precarious slopes or vertical 
walls of large craters and other extreme surfaces. 
Multiple landers can work cooperatively by being 
interlinked using spring-tethers and work much like a 
team of mountaineers to systematically climb a slope 
[3,4].  In addition, multiple landers can cooperatively 
simplify a complex task into its components through a 
process of task decomposition [17, 18].  Furthermore, 
with a swarm, the loss of one or a few landers does not 
end the mission.  A unique advantage to a swarm of 
landers is that it can operate in parallel performing 
many different tasks at once, hence reducing the total 
time required to complete time intensive tasks such as 
mapping or exploration. 
Unlike Earth, Mars or Moon, asteroid gravity is very 
low which brings news opportunities and challenges.  
The cost of hopping or flying over an asteroid is 
significantly low, however high-thrust can result in a 
lander attaining escape velocity and tumbling in space.  
A 
conventional 
multi-wheeled 
rover 
would 
be 
ineffective on an asteroid surface due to the low-traction 
and low escape velocity. Small asteroids typically have 
complex gravity fields because of their highly irregular 
shape.  This impacts surface operation, as the maximum 
operational speed is limited by the local gravitational 
field.  Having a swarm of landers minimizes the risks of 
overshooting the maximum speed and tumbling above 
an asteroid.  In addition, a swarm of landers can form 
redundant networks to effectively communicate images 
and videos from multiple points of view from many 
locations of an asteroid surface all at once.  In the 
following sections, we present background and related 
work 
followed 
by 
description 
of 
the 
asteroid 
environment, overview of the proposed nano-lander 
system, methods for surface mobility and strategies for 
swarming followed by discussions, conclusions and 
future work. 
 
2. Related Work 
 
Exploration of asteroids has been a major challenge 
in space exploration. Much work has been done in 
observing asteroids by ground based telescopes and 
space observatories but exploring asteroid surfaces with 
landers is a major challenge. Several asteroid sample 
return missions have been launched and several others 
are 
being 
studied 
worldwide. 
Japan 
Aerospace 
Exploration Agency (JAXA) developed an unmanned 
spacecraft named Hayabusa to return a sample of 
material from a small near-Earth asteroid named 25143 
Itokawa to Earth for further analysis. Hayabusa studied 
the 
asteroid’s 
shape, 
spin, 
topography, 
colour, 
composition, density and history and finally landed in 
November 2005 and collected tiny grains of asteroid 
material [2]. The spacecraft also carried a 591g small 
rover named MINREVA (Micro/Nano Experimental 
Robot Vehicle for Asteroid) which unfortunately 
hopped off the surface of the asteroid and tumbled into 
space [5]. 
The lessons learned from the successful Hayabusa I 
mission led to the development of Hayabusa II asteroid 
sample return mission. Hayabusa II was launched in 
December 2014 and is expected to reach its target 
asteroid, 162173 Ryugu (1999 JU3) in July 2018 [2]. 
The Institute of Space Systems of the German 
Aerospace Centre (DLR) in cooperation with French 
space agency (CNES) built a small lander called 
MASCOT 
(Mobile 
Asteroid 
Surface 
Scout) 
to 
complement the sample return mission. MASCOT 
carries an infrared spectrometer, a magnetometer, a 
radiometer and a camera, and can lift off the asteroid to 
reposition itself for further measurement [6]. 
Another asteroid sample return mission is NASA’s 
Origins, Spectral Interpretation, Resource Identification, 
Security, Regolith Explorer (OSIRIS-Rex) mission led 
by University of Arizona and was launched in 
September 2016.  It is expected to reach its target 
asteroid 101955 Bennu in August 2018. The spacecraft 
will measure Bennu’s physical, geological, and 
chemical properties and collect at least 60 g of regolith. 
Rosetta is another spacecraft built by the European 
Space Agency, launched in March 2004 and performed 
detailed study of comet 67P/Churyumov-Gerasimeko. 
Rosetta carried a ~98 kg lander named Philae which 
performed studies on elemental, isotopic, molecular and 
mineralogical composition of the comet, characterized 
the physical properties of the surface and subsurface 
material and the magnetic and plasma environment of 
the nucleus [1].  
NASA JPL also developed a planetary mobility 
platform called “spacecraft/rover hybrid” that relies on 
internal actuation. With the help of three mutually 
orthogonal flywheels and external spikes, the platform 
can perform both long excursions by hopping and short, 
precise traverses through controlled tumbles [7,8]. 
Another 
autonomous 
microscale 
surface 
lander 
developed is PANIC (Pico Autonomous Near-Earth 
Asteroid In-Situ Characterizer). PANIC has a shape of a 
regular tetrahedron with an edge length of 35 cm, mass 
of 12 kg and utilizes hopping as a locomotive 
mechanism in microgravity [9].   
In our work, we look towards the next milestone in 
asteroid exploration, namely to perform long-duration 
surface exploration and analysis.  Miniaturization of 
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space electronics makes it viable to build miniature 
landers.  However, to attain the full benefits of utilizing 
miniature landers require sending many of them that can 
operate independently and cooperate in teams.   
 
3. The Asteroid Environment 
Most asteroids are irregular in shape and are pock-
marked by impact craters. An asteroid’s shape can be 
described using a polyhedron, whose surface consists of 
a series of triangles. In this paper, we use an irregular 
polyhedron model of asteroid Castalia (Fig. 1) [10].  
 
Fig. 1. Polyhedron model of asteroid Castalia. 
 
Using the polyhedron model, the gravitational 
surface potential of an asteroid can be determined [11, 
12].  Fig. 2 shows the distribution of acceleration due to 
gravity in m/s2 in the x-z plane for the polyhedron 
model of asteroid shown in Fig. 1 with a density of 2.1 
g/cm3. 
 
Fig. 2. Acceleration due to gravity for the polyhedron 
model of asteroid Castalia in the x-z plane. 
 
We use this representative gravitational model of 
asteroid Castalia to perform our design and control 
studies described in the paper.  
 
4. Nano-Lander System Overview 
  
Each nano-lander has a mass of 1 kg and a volume 
of 1U or 1000 cc. Fig. 3 shows the internal and external 
views of the lander. Three mutually orthogonal reaction 
wheels are mounted on adjacent faces of the lander to 
maximize its moment of inertia and allow more space 
for scientific payload and avionics. The system consists 
of one spike on each corner to facilitate hopping and 
tumbling. 
 
 
Fig. 3. CAD Design of a 1U Nano-lander Concept. 
 
The top half of the proposed nano-lander consists of 
a scientific payload including a miniature x-ray 
spectrometer, hand-lens imager and stereo cameras. 
Below the instruments are the avionics which consists 
of an on-board computer, IMU, radio transceivers, 
power board and batteries. The lower-half consists of 
the propulsion system, with storage tanks for the fuel 
and the oxidizer connected to a min-thruster. Solar cells 
with an anti-dust cohesion coating are placed on the 
external surfaces of the lander and slot antennas are 
located around the cells. 
 
4.1 Communication 
Each nano-lander is required to communicate with 
its neighbours and to the mothership in orbit around the 
asteroid. Since each lander hops and rolls around the 
asteroid surface, use of a deployable antenna is not 
feasible. A feasible alternative is to place multiple patch 
antennas on each face of the lander. For our design, we 
consider use of slot antennas that are complementary 
dipole antennad and have roughly omnidirectional 
radiation patterns. Its undesirable to radiate into the 
electronics and hence the antennas have a reflector 
backing to radiate outwards from the spacecraft.  
Fig. 4 and 5 show the radiation pattern of the 
reflector backed slot antenna. The slot has a dimension 
of 75 × 2 mm fed with a 50 Ω lumped port at the centre. 
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The reflector has a dimension of 10 × 10 cm with 0.7 
cm spacing. The antenna has a forward gain of 10.2 dBi 
at 3.8GHz. 
 
 
Fig. 4. Radiation pattern of the reflector backed slot 
antenna.  
 
 
Fig. 5. (a) 00 Azimuth beam-width. (b) 00 Elevation 
beam-width. 
 
The 00 azimuth beam-width is 320 and the 00 
elevation beam-width is 360. Fig. 6 shows the return 
loss of the antenna. 
 
 
Fig. 6. Return loss of the reflector backed slot antenna. 
 
 
 
5. System Mobility 
 
5.1 Mobility Utilizing Propulsion 
Propulsion enables each lander to perform ballistic 
hops on the asteroid surface. This section describes the 
control approach of each lander to perform ballistic 
hops using the propulsion unit or on-board 3-axis 
reaction wheel system [13]. During each ballistic hop, 
the thrust generated by the propulsion unit acts along +z 
axis with gravity acting along –z axis. The 3-axis 
reaction wheel system applies torque about the lander’s 
three principle axes to change its Euler angles and 
angular velocities according to a PD control law shown 
as below: 
 
 𝜏𝜏𝑟𝑟𝑟𝑟= −𝐾𝐾𝑝𝑝(𝑒𝑒𝑑𝑑𝑑𝑑𝑑𝑑−𝑒𝑒𝑎𝑎𝑎𝑎𝑎𝑎) −𝐾𝐾𝑑𝑑(𝜔𝜔𝑑𝑑𝑑𝑑𝑑𝑑−𝜔𝜔𝑎𝑎𝑎𝑎𝑎𝑎)     (1)  
 
Using RP-1 as the fuel, H2O2 as the oxidizer, and 
with a throat diameter of 60 µm, the propulsion unit can 
deliver a thrust of 0.0445 N with an Isp of 370 s. Fig. 7 
shows a ballistic hop on an asteroid gravity of 0.001 
m/s2.  
  
Fig. 7. Trajectory of a nano-lander performing a rocket-
propelled ballistic hop on an asteroid. 
 
The lander can hop 3.8 m by burning only 20 mg of 
RP1-H2O2 propellant. Fig. 8 shows the velocity of the 
lander during its flight. The maximum velocity achieved 
is 0.07 m/s which is lower than the escape velocity of 
the asteroid considered. 
 
Fig. 8. Velocity of a lander during the ballistic hop. 
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Each reaction wheel has a mass of 100 g, radius of 
4.3 cm and can produce a maximum torque of 10 mN. 
Each reaction wheel operates according to the PD law 
and provides a torque to change the orientation of the 
lander. Fig. 9 and 10 shows the Euler angles and angular 
velocity respectively of a lander during each ballistic 
hop.  The reaction wheel simplifies the control 
architecture by maintaining a steady, commanded 
direction while hopping. 
  
Fig. 9. Euler angles of the lander.  
 
Fig. 10. Angular velocity of the lander during ballistic 
hop. 
 
5.2 Mobility Utilizing Reaction Wheels 
 
With the reaction wheels, the nano-lander system is 
capable of two-modes of mobility: tumbling and 
hopping. The lander can produce momentarily large 
reaction forces at the surface by exerting internal 
torques with the help of the 3-reaction wheels. The 
contact forces between the spikes and the surface can be 
modelled as a spring-damper force normal to the 
surface, and a Coulomb friction force tangential to the 
surface [14]. The spikes act as a pin-joint and the model 
can be described by the angle, 𝜃𝜃, and torque, τ, as can be 
seen in Fig. 11 along with the other parameters [7,8].  
 
 
Fig. 11. 2D model of the lander with all physical 
parameters. 
 
In the tumbling mode, the system pivots to the right 
and lands on the next consecutive spike. The hopping 
mode consists of a stride phase, when the system is 
supported by a single spike, and a flight phase when the 
spike leaves the ground (negative normal force). The 
equations of motion for the stride phase can be written 
as: 
 
             𝜃𝜃̈(𝑡𝑡) =
𝑚𝑚𝑠𝑠𝑔𝑔𝑔𝑔sin 𝜃𝜃(𝑡𝑡)−𝜏𝜏(𝑡𝑡)
𝐼𝐼𝑠𝑠+𝑚𝑚𝑠𝑠𝑙𝑙2
                       (2) 
 
For tumbling, the minimum torque required to 
initiate angular acceleration (−𝜃𝜃̈) from rest is given by 
(9). The corresponding minimum reaction wheel 
angular velocity required is given as follows: 
          𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚= 𝑚𝑚𝑠𝑠𝑔𝑔𝑔𝑔sin(𝛼𝛼+ 𝛽𝛽)                       (3)  
 
For hopping, the applied torque must be greater than 
that 
for 
tumbling 𝜏𝜏≫𝑚𝑚𝑠𝑠𝑔𝑔𝑔𝑔sin(𝜃𝜃) 
 
and 
the 
corresponding reaction wheel velocity required to hop a 
distance dh is given by: 
 
    𝜔𝜔𝑟𝑟= ඥ2𝑚𝑚𝑠𝑠𝑔𝑔𝑔𝑔(1 −cos(𝛼𝛼+ 𝛽𝛽))/(𝜂𝜂𝐼𝐼𝑟𝑟)        (4) 
 
 Both the hopping angle and the lateral distance 
covered are a function of τ and ωr as shown by equation 
(5), (6) and (7): 
           𝜔𝜔𝑟𝑟(𝑑𝑑ℎ) = ට
𝑑𝑑ℎ𝑔𝑔
𝜂𝜂2𝑙𝑙2 sin(2(𝛼𝛼+𝛽𝛽))                  (5)  
 
                 𝜃𝜃ℎ= 𝛼𝛼−
𝜂𝜂𝐼𝐼𝑟𝑟𝜔𝜔𝑟𝑟2
2𝜏𝜏                            (6)    
 
       𝑑𝑑ℎ= sin(2𝛼𝛼−𝜂𝜂𝐼𝐼𝑟𝑟𝜔𝜔𝑟𝑟
2 /𝜏𝜏)(𝜂𝜂𝜂𝜂𝜔𝜔𝑟𝑟)2/𝑔𝑔          (7)  
 
For both hopping and tumbling, the torque required 
is produced using a hybrid control algorithm, where the 
reaction wheels are slowly accelerated to the desired 
angular velocity and then impulsively braked. This 
control approach also restricts the reaction wheel to 
reach its saturation speed. Fig. 12 shows the torque 
required for tumbling at various g and Fig. 13 shows the 
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torque required for hopping 1 m, 5 m and 10 m. The 
length of the spike is 0.1 m for the simulations. Fig. 14 
shows the hopping trajectories of each lander for 
different values of reaction wheel angular velocities and 
torque. 
 
 
 
Fig. 12. Torques for tumbling motion (spike = 0.1 m). 
 
 
 
Fig. 13. Torques for hopping motion (spike =  0.1m). 
 
 
 
Fig. 14. Hopping trajectories of the lander for different 
values of ωr and τ (ωr is in rpm, τ is in Nm, g = 0.001 
m/s2 and l = 0.1 m) 
 
6. Maximum Coverage Algorithm for Multiple 
Landers 
 
Utilizing the mobility strategies described earlier, we 
can enable a swarm of nano-landers to achieve mobility 
on the asteroid surface and perform exploration. The 
asteroid surface is scattered with fragments of rocks and 
large boulders. These objects maybe dangerous 
obstacles for the nano-landers.  A key requirement is to 
avoid them. So, the system of multiple nano-landers 
deployed on the asteroid surface are required to avoid 
obstacles, while maximizing area coverage.  A third 
requirement is that the nano-landers maintain multiple 
communication links so that acquired science data 
maybe communicated effectively to a mothership.  
In this section, we describe an algorithm developed 
to distribute a fleet of N nano-landers on an asteroid 
surface (Table 1).  We use the concept of virtual forces 
to repel each lander from the rest of the fleet. 
 
Table 1. Pseudo-code for area coverage maximization 
using a fleet of lander. 
 
Algorithm: Maximize coverage for multiple landers 
 
Require: Initial position, orientation for all landers i= 
1 to N; 
1. Compute the Euclidean distance between each 
lander; 
2. Compute the degree D for each lander based on 
the communication range (Rc); 
3. Compute the Euclidean distance between each 
lander and its neighboring obstacle; 
4. for k = 0 to K do 
5. 
    for i = 1 to N do 
6. 
       Compute the net force on lander i,       
       according to (8) - (11); 
7.     end for 
8.     for i = 1 to N do 
9.       for t = 0 to k+1 do  
        Move each lander i according to (12)  
       end for      
10.       At t = k+1, compute the new      
11.        Euclidean distances and degree D; 
     end for      
12. end for 
 
 
The nano-landers are all identical and operate in a 
distributed fashion without relying on a single surface 
asset.  They have equal sensing range (Rs) and equal 
communication 
range 
(Rc). 
Each 
lander 
can 
communicate its location and orientation to its 
neighbours and has a laser rangefinder to locate and 
characterize obstacles.  
 
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In our area coverage algorithm, the landers interact 
with each other through a combination of global 
repulsion combined with local, limited attraction.  The 
repulsion and attraction are achieved using a concept 
called virtual forces that we simulate to enable 
collective control over the nano-landers. The modelled 
virtual forces used to position the landers are of three 
kinds: Fcov, Fcom and Fobs. Fcov causes the landers to repel 
each other to maximize the sensing range of the target 
area, Fcoms constrains the degree of communication links 
for each lander by attracting landers (locally) when they 
are on the verge of losing connection. Fobs causes the 
landers to move away from neighboring obstacles [15]. 
Considering a network of N landers 1, 2, 3… N with 
positions r1, r2, r… rN respectively and ||rij|| representing 
the Euclidean distance between landers i and j, Fcov and 
Fcoms are defined in (8) and (9) respectively:  
 
          𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐(𝑖𝑖, 𝑗𝑗) = ൬
𝐶𝐶𝑐𝑐𝑐𝑐𝑐𝑐
ฮ𝑟𝑟𝑖𝑖𝑖𝑖ฮ൰൬
𝑟𝑟𝑖𝑖−𝑟𝑟𝑗𝑗
ฮ𝑟𝑟𝑖𝑖𝑖𝑖ฮ൰                   (8) 
 
𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐(𝑖𝑖, 𝑗𝑗) = ൝൫−𝐶𝐶𝑐𝑐𝑐𝑐𝑐𝑐ฮ𝑟𝑟𝑖𝑖𝑖𝑖ฮ൯൬
𝑟𝑟𝑖𝑖−𝑟𝑟𝑗𝑗
ฮ𝑟𝑟𝑖𝑖𝑖𝑖ฮ൰      𝑖𝑖𝑖𝑖 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑< 𝐷𝐷
0                                       𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
     (9) 
 
Similarly, for L obstacles 1, 2, 3… L with positions 
r1, r2, r3… rL respectively and ||ril|| representing the 
Euclidean distance between lander i and obstacle l, Fobs 
is defined as follows.  
 
           𝐹𝐹𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖, 𝑙𝑙) = ቀ
𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜
‖𝑟𝑟𝑖𝑖𝑖𝑖‖ቁቀ
𝑟𝑟𝑖𝑖−𝑟𝑟𝑙𝑙
‖𝑟𝑟𝑖𝑖𝑖𝑖‖ቁ                 (10) 
 
Where, Ccov, Ccom and Cobs are the force constants 
and the net force experienced by lander i can be 
expressed as follows: 
 
𝐹𝐹(𝑖𝑖) = ∑
(𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐(𝑖𝑖, 𝑗𝑗) + 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐(𝑖𝑖, 𝑗𝑗))
𝑁𝑁
𝑗𝑗=1,𝑗𝑗≠𝑖𝑖
+
                     ∑
𝐹𝐹𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖, 𝑘𝑘)
𝐿𝐿
𝑘𝑘=1
                                (11) 
 
The equation of motion for lander i can then be 
formulated as: 
 
                𝑚𝑚𝑖𝑖
𝑑𝑑2𝑟𝑟𝑖𝑖
𝑑𝑑𝑡𝑡2 + 𝜇𝜇𝑖𝑖
𝑑𝑑𝑟𝑟𝑖𝑖
𝑑𝑑𝑑𝑑= 𝐹𝐹(𝑖𝑖)                  (12)   
 
Where, mi is the mass and µi is the damping factor of 
lander i. When the distance between two landers tends 
to zero, ||Fcov|| → ∞ to avoid collisions. When the 
degrees of connection between a lander and neighbor is 
less than D, ||Fcom|| > 0 to prevent loss of connection. 
Similarly, ||Fobs|| → ∞ when the distance between a 
lander and an obstacle tends to zero to avoid collisions. 
For simulation of the stated algorithm, we 
considered 40 landers deployed at random positions 
inside a square test area. Each lander has a 
communication range, Rc = 5 units and sensor range, Rs 
= 2.5 units. The target area consists of obstacles of 
random sizes at random positions. The 40 landers must 
move in the 2-D space in such a way that it maximizes 
the coverage area, avoiding collision with each other 
and the obstacles and maintaining a degree of 
communication links, D = 3. Fig. 15 shows the lander 
positions at different times.  The landers disperse to 
maximize distance while maintaining a communication 
link between two neighbours. The red dots are the 
obstacles, black dots the landers and the lines 
connecting them are the active communication links 
 
 
Fig. 15. Simulation of a system of 40 landers at timestep 
0, 15, 30, 60, 100 and 200. 
 
 
Fig. 16 shows the variation of the coverage area with 
time for different values of D = 2,3,4,5, and 6. The 
swarm of nano-landers can provide unique and very 
detailed measurements of a spacecraft impacting onto 
the asteroid surface. Fig. 17 shows a second simulation 
of a swarm of robots being simulated to repel a target 
area and form ‘donut’ around the area.  This will enable 
the swarm to track and record the impact event and 
collect data from multiple viewpoints. The red dots are 
the obstacles and the black dots are the landers. The 
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landers were placed randomly on the target area and the 
impact event is supposed to take place at coordinates (3, 
-1). Each lander positions itself to be at a safe distance 
from the target impact site, while avoiding obstacles. 
 
 
Fig. 16. Area coverage by a swarm of 40 robots with 
respect to settling timesteps. 
 
 
Fig. 17. Simulation of a system of 40 landers 
commanded to avoid a target impact site at 0, 50, 100 
and 150 timesteps. 
 
7. System Optimization  
 
In the previous section, we have shown that a swarm 
of nano-landers have the potential to solve the intended 
task.  However, what is apparent is that there are several 
system parameters that a critical for enabling area 
coverage maximization.  Selection of swarm parameters 
such as the number of landers, N and Ccov, Ccom and Cobs 
are non-intuitive.  This is a scenario where Evolutionary 
Algorithms have potential, as they can generate good 
enough solutions through a directed, trial and error 
search.   
Here we use Evolutionary Algorithms to find the 
minimum number of landers required for maximum 
coverage of a target area with redundant communication 
links. The genotype of the EA population (see Table 2) 
are represented by binary numbers so that they can be 
easily manipulated by standard genetic operators such 
as crossover and mutation. Each individual is 
represented by 19 bits with the first seven bits 
representing the number of landers, next three bits 
representing the degree, next four bits representing the 
force constant Ccov and the final five bits representing 
the force constant Ccom as shown in Table 2. 
Furthermore, we assume Ccov = Cobs.  
 
Table 2:  Genotype of the nano-lander swarm. 
 
N 
D 
Ccov 
Ccom 
a b c d e f g h i j k l m n o p q r s 
Binary [1,0] 
 
7.1 Fitness Function  
 
The total coverage area is estimated by considering the 
formation of the swarm as a non-self-intersecting 
polygon with the coordinates of the landers (x1, y1) … 
(xN, yN) as the vertices. The area can then be calculated 
as: 
 
𝐴𝐴= ቛ
1
2 ቀቚ𝑥𝑥1
𝑥𝑥2
𝑦𝑦1
𝑦𝑦2ቚ+ ቚ𝑥𝑥2
𝑥𝑥3
𝑦𝑦2
𝑦𝑦3ቚ+ ⋯+ ቚ𝑥𝑥𝑁𝑁
𝑥𝑥1
𝑦𝑦𝑁𝑁
𝑦𝑦1ቚቁቛ (13) 
 
The normalized fitness of the area function can then be 
calculated as 
𝐴𝐴𝑛𝑛= 𝐴𝐴
900 
(14) 
 
The degree of communication links for each lander is 
calculated by calculating the number of landers within a 
distance of 5 units and then averaged for all the landers. 
The normalized fitness is then calculated as 
 
𝐷𝐷𝑛𝑛= 𝐷𝐷𝑎𝑎𝑎𝑎ℎ
𝐷𝐷𝑟𝑟𝑟𝑟𝑟𝑟
 
(15) 
 
where, Dach is the average degree achieved and Dreq is 
the average degree required. The settling time objective 
function is then calculated by determining the time step 
at which the swarm settles down and doesn’t move 
further (16). Similarly, the energy objective function is 
calculated by determining the number of hops each 
lander takes to until the formation is settled (17). To 
calculate the normalized fitness of the settling time 
objective function and energy objective function, first 
we take the time required and energy dissipated by a 40-
lander swarm to cover a target area of 30×30 units.  
Then we specify the normalized fitness relative to the 
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IAC-17-D3.3.2                    
 
 
 
 
 
 
 
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time and energy taken by the 40-lander system as shown 
below:  
 
𝑇𝑇𝑛𝑛= 𝑡𝑡40 −∆𝑡𝑡
𝑡𝑡40
 
(16) 
 
𝐸𝐸𝑛𝑛= 𝑒𝑒40 −∆𝑒𝑒
𝑒𝑒40
 
 
(17) 
where, t40 and e40 are reference values for time and 
energy corresponding to the 40-lander system, ∆t and ∆e 
are the differences in the actual values and reference 
values. The overall fitness of the system is then 
determined by taking the weighted average as: 
 
𝐹𝐹= 0.5𝐴𝐴𝑛𝑛+ 0.25𝐷𝐷𝑛𝑛+ 0.125𝑇𝑇𝑛𝑛+ 0.125𝐸𝐸𝑛𝑛 
(18) 
 
An elitist non-dominated sorting algorithm (NSGA-II) 
is used in this paper [16]. The initial parent population, 
Pt, is created randomly of size M which is then sorted 
based on the non-domination and then assigned a rank 
based on the fitness which is equal to its non-dominant 
level. The initial population then undergoes crossover 
and mutation to produce the set of offspring population 
Ot of size M. Both the parents and children are then 
combined to produce Ct = Pt∪Ot of size 2M. The 
population Ct is then sorted via non-dominance and 
assigned a rank. The first M individuals of the set Ct 
based on the non-dominant level is then selected for the 
next generation. The next population Pt+1 of size M then 
again undergo selection, crossover and mutation.  The 
process is repeated until the system achieves the desired 
fitness. 
For our analysis, we have considered an initial 
population of 50 with a crossover probability of 0.8 and 
a mutation probability of 0.2. For non-dominated 
sorting, we have considered four fitness objectives. The 
first fitness is the coverage area, second fitness is the 
average communication links (degree) of each robot, 
third fitness is the time step required for maximum 
coverage and the fourth fitness is the average energy 
consumed by each lander. Each of these fitness values 
are then normalized between 0 and 1, with 1 
representing the fittest value. The weighted average of 
the four fitness values are then multiplied with their 
corresponding weights 0.5, 0.25, 0.125 and 0.125 
respectively which represents the overall fitness of the 
system (18). Moreover, to test the redundancy of the 
communication links, 10% of the landers are killed off 
in every generation. Each lander has a communication 
range, Rc, of 5 units and the goal is to cover a target area 
of 30 × 30 units. 
Fig. 18 shows the fitness of each objective function 
over 40 generations. Fig. 19 shows the overall fitness of 
the swarm over 40 generations. 
 
 
 
Fig. 18. Component fitness of a swarm evolved over 40 
generations.  Results obtained from an average of 5 
Evolutionary Algorithm runs. 
 
 
 
 
Fig. 19. Overall fitness of a swarm evolved over 40 
generations.  Results obtained from an average of 5 
Evolutionary Algorithm runs. 
 
8. Discussion 
 
Our approach to designing and utilizing a swarm of 
nano-landers to perform asteroid exploration presents 
important challenges but also new opportunities.  We 
show the initial feasibility of a decentralized swarm of 
robots that can be used to attain maximum area 
coverage over an asteroid surface while avoiding 
obstacles and maintaining sufficient number of 
redundant communication links.  In addition, the swarm 
can be used to position themselves around a target event 
and obtain multiple views at once. 
This initial analysis shows the potential of a swarm, 
but the parameters required to obtain suitable 
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IAC-17-D3.3.2                    
 
 
 
 
 
 
 
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performance was not well understood.  Further, it was 
unclear if the system could be further optimized.  This is 
where 
machine 
learning 
approaches 
such 
as 
Evolutionary Algorithms shine.  Where there is limited 
domain knowledge of the task at hand, the algorithm 
can find desirable solutions through a process of 
directed trial and error search. 
The results show that a system of 65 landers with 
degree D = 5 as the best solution (found to date) for 
maximum coverage area of 30 × 30 units.  Using EAs 
we have effectively improved the overall system fitness, 
including maximum area covered and increased number 
of communication links, while maintaining a nearly 
constant energy consumption.  This shows the algorithm 
is effective in improving energy utilization of the 
swarm.  With a more dispersed system, the settling time 
inevitably increases.  Overall, our approach shows a 
promising pathway towards further refining of our 
system design parameters towards detailed design of the 
mission concept. 
 
8. Conclusions  
 
The next major phase of asteroid exploration will 
require sending landers to perform surface exploration.  
We have analysed the preliminary feasibility of 
operating scores of nano-landers, each 1 kg in mass and 
volume of 1U, or 1000 cm3 on an asteroid surface. 
These landers would hop, roll and fly over the asteroid 
surface. The landers would include science instruments 
such as stereo cameras, hand-lens imagers and 
spectrometers to characterize rock composition. A 
network of nano-landers situated on the surface of an 
asteroid can provide unique and detailed in-situ 
measurements of a spacecraft impacting onto an 
asteroid surface.   In this work, we demonstrate an 
algorithm that utilizes the concept of virtual forces to 
enable a decentralized swarm of nano-landers to 
effectively 
attain 
maximum 
area 
coverage 
for 
exploration and to position themselves to witness an 
impact event from multiple viewpoints.  Our approach 
model 
multibody 
dynamical 
systems 
and 
uses 
Evolutionary Algorithms to further optimize for area 
coverage and communication performance.  The results 
show a promising pathway towards field study in a 
more detailed, simulated asteroid surface environment. 
 
Nomenclature  
 
Kp, Kd = Proportional and derivative controller gains 
edes, eact = Desired and actual Euler angles 
ωdes and ωact = Desired and actual angular velocity 
ms = Mass of the lander 
g = Acceleration due to gravity 
l = Length of spike 
τ = Applied torque by reaction wheel 
Is, Ir = Moment of inertia of lander and reaction wheel 
η = Energy transfer efficiency 
 
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