68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 1 of 11 IAC-17-D3.3.2  NETWORK OF NANO-LANDERS FOR IN-SITU CHARACTERIZATION OF ASTEROID IMPACT STUDIES  Himangshu Kalita   a , Erik Asphaug   b , Stephen Schwartz   b , Jekan Thangavelautham a *  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 cm 3 . 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 cm 3   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.
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 2 of 11 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
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 3 of 11 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/s 2   in the x-z plane for the polyhedron model of asteroid shown in Fig. 1 with a density of 2.1 g/cm 3. 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.
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 4 of 11 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) 0   0   Azimuth beam-width. (b) 0   0   Elevation beam-width.  The   0   0   azimuth   beam-width   is   32   0   and   the   0   0 elevation beam-width is 36   0. 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:  𝜏𝜏 𝑟𝑟𝑟𝑟   =   −𝐾𝐾 𝑝𝑝 ( 𝑒𝑒 𝑑𝑑𝑑𝑑𝑑𝑑   − 𝑒𝑒 𝑎𝑎𝑎𝑎𝑎𝑎 )   − 𝐾𝐾 𝑑𝑑   ( 𝜔𝜔 𝑑𝑑𝑑𝑑𝑑𝑑   − 𝜔𝜔 𝑎𝑎𝑎𝑎𝑎𝑎 )   (1) Using RP-1 as the fuel, H   2 O   2   as the oxidizer, and with a throat diameter of 60   μ m, the propulsion unit can deliver a thrust of 0.0445 N with an I   sp   of 370 s. Fig. 7 shows a ballistic hop on an asteroid gravity of 0.001 m/s 2. 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-H   2O   2   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.
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 5 of 11 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:  𝜃𝜃 ̈   ( 𝑡𝑡 )   =   𝑚𝑚   𝑠𝑠   𝑔𝑔𝑔𝑔   sin   𝜃𝜃 ( 𝑡𝑡 ) −𝜏𝜏 ( 𝑡𝑡 )  𝐼𝐼 𝑠𝑠 + 𝑚𝑚   𝑠𝑠   𝑔𝑔 2   (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:  𝜏𝜏 𝑚𝑚𝑚𝑚𝑚𝑚   =   𝑚𝑚   𝑠𝑠   𝑔𝑔𝑔𝑔   sin( 𝛼𝛼   +   𝛽𝛽 )   (3) For hopping, the applied torque must be greater than that   for   tumbling   𝜏𝜏   ≫ 𝑚𝑚   𝑠𝑠   𝑔𝑔𝑔𝑔   sin( 𝜃𝜃 )   and   the corresponding reaction wheel velocity required to hop a distance   d   h   is given by:  𝜔𝜔 𝑟𝑟   =   � 2 𝑚𝑚   𝑠𝑠   𝑔𝑔𝑔𝑔 (1   −   cos( 𝛼𝛼   +   𝛽𝛽 ))/( 𝜂𝜂𝐼𝐼 𝑟𝑟 )   (4) Both the hopping angle and the lateral distance covered are a function of  τ   and  ω r   as shown by equation (5), (6) and (7):  𝜔𝜔 𝑟𝑟 ( 𝑑𝑑 ℎ )   =   �   𝑑𝑑   ℎ   𝑔𝑔 𝜂𝜂 2 𝑔𝑔 2   sin(2 ( 𝛼𝛼 + 𝛽𝛽 )   )   (5)  𝜃𝜃   ℎ   =   𝛼𝛼 −   𝜂𝜂𝐼𝐼   𝑟𝑟   𝜔𝜔 𝑟𝑟  2 2 𝜏𝜏   (6)  𝑑𝑑 ℎ   = sin(2 𝛼𝛼 − 𝜂𝜂𝐼𝐼 𝑟𝑟   𝜔𝜔 𝑟𝑟  2   / 𝜏𝜏 )   ( 𝜂𝜂𝑔𝑔𝜔𝜔 𝑟𝑟 )   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
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 6 of 11 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  ω r   and  τ   (  ω r   is in rpm,  τ   is in Nm,   g   = 0.001 m/s 2   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 ( R   c ); 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 ( R   s ) and equal communication   range   ( R   c ).   Each   lander   can communicate   its   location   and   orientation   to   its neighbours and has a laser rangefinder to locate and characterize obstacles.
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 7 of 11 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:   F   cov ,   F   com   and   F   obs .   F   cov   causes the landers to repel each other to maximize the sensing range of the target area,   F   coms   constrains the degree of communication links for each lander by attracting landers (locally) when they are on the verge of losing connection.   F   obs   causes the landers to move away from neighboring obstacles [15]. Considering a network of   N   landers   1, 2, 3... N   with positions   r 1, r 2, r... r N   respectively and   || r   ij ||   representing the Euclidean distance between landers   i   and   j ,   F   cov   and  F   coms   are defined in (8) and (9) respectively:  𝐹𝐹   𝑐𝑐𝑐𝑐𝑐𝑐 ( 𝑚𝑚 ,   𝑗𝑗 )   =   �   𝐶𝐶   𝑐𝑐𝑐𝑐𝑐𝑐 �   𝑟𝑟   𝑚𝑚𝑗𝑗   � � �   𝑟𝑟   𝑚𝑚   −𝑟𝑟   𝑗𝑗 �   𝑟𝑟   𝑚𝑚𝑗𝑗   � �   (8)  𝐹𝐹 𝑎𝑎𝑐𝑐𝑐𝑐 ( 𝑚𝑚 ,   𝑗𝑗 ) =   ��−𝐶𝐶 𝑎𝑎𝑐𝑐𝑐𝑐   �𝑟𝑟 𝑖𝑖𝑖𝑖   �� � 𝑟𝑟 𝑖𝑖   −𝑟𝑟 𝑗𝑗 �𝑟𝑟 𝑖𝑖𝑗𝑗   �   �   𝑚𝑚𝑖𝑖   𝑑𝑑𝑒𝑒𝑔𝑔𝑟𝑟𝑒𝑒𝑒𝑒   <   𝐷𝐷  0   𝑐𝑐𝑡𝑡ℎ𝑒𝑒𝑟𝑟𝑒𝑒𝑚𝑚𝑠𝑠𝑒𝑒  (9) Similarly, for   L   obstacles   1, 2, 3... L   with positions  r 1, r 2, r 3... r L   respectively and   || r il ||   representing the Euclidean distance between lander   i   and obstacle   l ,   F   obs  is defined as follows.  𝐹𝐹   𝑐𝑐𝑜𝑜𝑠𝑠 ( 𝑚𝑚 ,   𝑔𝑔 )   =   �   𝐶𝐶   𝑐𝑐𝑜𝑜𝑠𝑠 ‖   𝑟𝑟   𝑚𝑚𝑔𝑔   ‖ � �𝑟𝑟   𝑚𝑚   −𝑟𝑟   𝑔𝑔 ‖   𝑟𝑟   𝑚𝑚𝑔𝑔   ‖ �   (10) Where,   C cov ,   C com   and   C obs   are the force constants and   the   net   force   experienced   by   lander   i   can   be expressed as follows:  𝐹𝐹 ( 𝑚𝑚 ) =   ∑   ( 𝐹𝐹 𝑎𝑎𝑐𝑐𝑐𝑐 ( 𝑚𝑚 ,   𝑗𝑗 ) +   𝐹𝐹 𝑎𝑎𝑐𝑐𝑐𝑐 ( 𝑚𝑚 ,   𝑗𝑗 )) 𝑁𝑁 𝑖𝑖=1 , 𝑖𝑖≠𝑖𝑖   +  ∑   𝐹𝐹 𝑐𝑐𝑜𝑜𝑑𝑑 ( 𝑚𝑚 ,   𝑘𝑘 ) 𝐿𝐿 𝑘𝑘=1   (11) The equation of motion for lander   i   can then be formulated as:  𝑚𝑚   𝑚𝑚 𝑑𝑑 2 𝑟𝑟   𝑚𝑚 𝑑𝑑𝑡𝑡 2   +   𝜇𝜇   𝑚𝑚 𝑑𝑑𝑟𝑟   𝑚𝑚 𝑑𝑑𝑡𝑡   =   𝐹𝐹 ( 𝑚𝑚 )   (12) Where,   m   i   is the mass and  μ i   is the damping factor of lander   i . When the distance between two landers tends to zero,   || F   cov ||   →   ∞   to avoid collisions. When the degrees of connection between a lander and neighbor is less than   D ,   || F   com ||   > 0   to prevent loss of connection. Similarly,   || F   obs ||   →   ∞   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,   R   c   = 5 units and sensor range,   R   s  = 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
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 8 of 11 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   C cov ,   C com   and   C obs  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   C cov   and the final five bits representing the   force   constant   C com   as   shown   in   Table   2. Furthermore, we assume   C cov   =   C obs . Table 2: Genotype of the nano-lander swarm.  N   D   C cov   C com  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 ( x   1 ,   y   1 ) ... ( x   N ,   y   N ) as the vertices. The area can then be calculated as:  𝐴𝐴   =   �   1 2   ��𝑥𝑥 1   𝑥𝑥 2 𝑦𝑦 1   𝑦𝑦 2   �   +   �𝑥𝑥 2   𝑥𝑥 3 𝑦𝑦 2   𝑦𝑦 3   �   +   ⋯   +   �𝑥𝑥 𝑁𝑁   𝑥𝑥 1 𝑦𝑦 𝑁𝑁   𝑦𝑦 1   ���   (13) The normalized fitness of the area function can then be calculated as  𝐴𝐴 𝑛𝑛   =   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  𝐷𝐷 𝑛𝑛   =   𝐷𝐷 𝑎𝑎𝑎𝑎 ℎ  𝐷𝐷 𝑟𝑟𝑑𝑑𝑟𝑟 (15) where,   D   ach   is the average degree achieved and   D req   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
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 9 of 11 time and energy taken by the 40-lander system as shown below:  𝑇𝑇 𝑛𝑛   =   𝑡𝑡 40   −   ∆ 𝑎𝑎  𝑡𝑡 40 (16)  𝐸𝐸 𝑛𝑛   =   𝑒𝑒 40   −   ∆ 𝑑𝑑  𝑒𝑒 40 (17) where,   t 40   and   e   40   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 . 5 𝐴𝐴 𝑛𝑛   +   0 . 25 𝐷𝐷 𝑛𝑛   +   0 . 125 𝑇𝑇 𝑛𝑛   +   0 . 125 𝐸𝐸 𝑛𝑛   (18) An elitist non-dominated sorting algorithm (NSGA-II) is used in this paper [16]. The initial parent population,  P   t , 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  O t   of size   M . Both the parents and children are then combined   to   produce   C t   =   P   t ∪ O   t   of size 2 M . The population   C t   is then sorted via non-dominance and assigned a rank. The first   M   individuals of the set   C t  based on the non-dominant level is then selected for the next generation. The next population   P   t+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,   R   c , 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
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 10 of 11 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 cm 3   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  K p ,   K d   = Proportional and derivative controller gains  e   des ,   e   act   = Desired and actual Euler angles  ω des   and  ω act   = Desired and actual angular velocity  m   s   = Mass of the lander  g   = Acceleration due to gravity  l   = Length of spike  τ   = Applied torque by reaction wheel  I   s ,   I   r   = Moment of inertia of lander and reaction wheel  η   = Energy transfer efficiency  References  [1] D. S. Lauretta, et al., “OSIRIS-Rex: Sample Return from Asteroid,”   Space Science Reviews , 2017. [2] J. Kawaguchi, A. Fujiwara, T. Uesugi, “ Hayabusa – Its   technology   and   science   accomplishment summary and Hayabusa 2,”   Acta Astronautica   62 (2008) 639-647. [3]   H.   Kalita,   R.   T.   Nallapu,   A.   Warren,   J. Thangavelautham,   “Guidance,   Navigation   and Control of Multirobot Systems in Cooperative Cliff Climbing,”   Advances in the Astronautical Science , February 2017. [4] H. Kalita, J. Thangavelautham, “Multirobot Cliff Climbing   on   Low-Gravity   Environments,”   11   th NASA/ESA Conference on Adaptive Hardware and Systems , Pasadena, USA, 2017, 24-27 July. [5] T. Yoshimitsu, T. Kubota, I. Nakatani, “MINREVA rover which became a small artificial solar satellite,”  20   th   Annual   AIAA/USU   Conference   on   Small Satellites , 2006. [6] C. Dietze, F. Herrmann, S. Ku β , C. Lange, M. Scharringhausen, L. Witte, T. van Zoest, H. Yano, “Landing   and   Mobility   Concept   for   the   Small Asteroid Lander MASCOT on Asteroid 1999 JU3,” 61   st   International Astronautical Congress,   Prague, 2010. [7] R. Allen, M. Pavone, C. McQuinn, I. A. D. Nesnas, J. C. Castillo-Rogez, Tam-Nquyen, J. A. Hoffman, “Internally-Actuated Rovers for All-Access Surface Mobility:   Theory   and   Experimentation,”   IEEE Conference on Robotics and Automation (ICRA) , St. Paul, Minnesota, 2012. [8] B. Hockman, A. Frick, I. A. D. Nesnas, M. Pavone, “Design, Control, and Experimentation of Internally- Actuated Rovers for the Exploration of Low-Gravity Planetary Bodies,”   Conference on Field and Service Robotics , 2015. [9] K. Schindler, C. A. Thomas, V. Reddy, A. Weber, S. Gruska, S. Fasoulas, “PANIC - A surface science package for the in-situ characterization of a near- Earth asteroid,”   Acta Astronautica , 68 (2011) 1800- 1810. [10] C. Neese, Ed. “Small Body Radar Shape Models V2.0,” EAR-A-5-DDR-RADARSHAPE-MODELS- V2.0,   NASA Planetary DATA System , 2004. [11]   R.   S.   Park,   R.   A.   Werner,   S.   Bhaskaran, “Estimating Small-Body Gravity Field from Shape Model and Navigation Data,”   Journal of Guidance, Control, and Dynamics , Vol. 33, No. 1, 2010. [12] Z. Zhenjiang, C. Hutao, C. Pingyuan, Y. Meng, “Modelling and Analysis of Gravity Field of 433 Eros   using   Polyhedron   Model   Method,”   2   nd
68 th   International Astronautical Congress (IAC), Adelaide, Australia, 25-29 September 2017. IAC-17-D3.3.2   Page 11 of 11  International   Conference   on   Information Engineering and Computer Science , 2010. [13]   H.   Kalita,   R.   T.   Nallapu,   A.   Warren,   J. Thangavelautham, “GNC of the SphereX robot for extreme   environment   exploration   on   Mars,”  Advances in the Astronautical Science , 2017. [14] G. Gilardi, I. Sharf, “Literature survey of contact dynamics modelling,”   Journal of Mechanism and Machine Theory , Vol. 37, No. 10, 2002. [15] S. Poduri, G. S. Sukhatme, “Constrained Coverage for Mobile Sensor Networks,”   IEEE International Conference   on   Robotics   &   Automation ,   New Orleans, LA, 2004. [16]   K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,”   IEEE   Transactions   on   Evolutionary Computation , Vol. 6, No. 2, April 2002. [17]   J.   Thangavelautham,   N.   Abu   El   Samid,   P. Grouchy,   E.   Earon,   T.   Fu,   N.   Nagrani,   G.M.T. D’Eleuterio,   “Evolving   Multirobot   Excavation Controllers and Choice of Platforms Using Artificial Neural   Tissue   Controllers,”   IEEE   Symposium   on Computational   Intelligence   for   Robotics   and Automation , 2009. [18]   J. Thangavelautham, K. Law, T. Fu, N. Abu El Samid, A. Smith, G.M.T. D’Eleuterio, “Autonomous Multirobot   Excavation   for   Lunar   Applications,”  Robotica , pp. 1-39, 2017.