1
GUIDANCE, NAVIGATION AND CONTROL OF MULTIROBOT
SYSTEMS IN COOPERATIVE CLIFF CLIMBING
Himangshu Kalita,* Ravi Teja Nallapu,† Andrew Warren,‡ and
Jekan Thangavelautham §
The application of GNC devices on small robots is a game-changer that enables
these robots to be mobile on low-gravity planetary surfaces and small bodies.
Use of reaction wheels enables these robots to roll, hop, summersault and rest on
precarious/sloped surfaces that would otherwise not be possible with conven-
tional wheeled robots. We are extending this technology to enable robots to
climb off-world canyons, cliffs and caves. A single robot may slip and fall,
however, a multirobot system can work cooperatively by being interlinked using
spring-tethers and work much like a team of mountaineers to systematically
climb a slope. A multirobot system as we will show in this paper can climb sur-
faces not possible with a single robot alone. We consider a team of four robots
that are interlinked with tethers in an “x” configuration. Each robot secures itself
to a slope using spiny gripping actuators, and one by one each robot moves up-
wards by crawling, rolling or hopping up the slope. If any one of the robots loses
grip, slips or falls, the remaining robots will be holding it up as they are an-
chored. This distributed controls approach to cliff climbing enables the system
to reconfigure itself where possible and avoid getting stuck at one hard to reach
location. Instead, the risk is distributed and through close cooperation, the robots
can identify multiple trajectories to climb a cliff or rugged surface. The benefits
can also be realized on milligravity surfaces such as asteroids. Too fast a jump
can result in the robot flying off the surface into space. Having multiple robots
anchored to the surface keeps the entire system secure. Our work combines dy-
namics and control simulation to evaluate the feasibility of our approach. The
simulation results show a promising pathway towards advanced development of
this technology on a team of real robots.
INTRODUCTION
Wheeled and legged robots have been studied extensively in the recent years for exploration
of extreme environments. Some of the legged robots can even climb and maneuver on vertical

* PhD Student, Space and Terrestrial Robotic Exploration Laboratory, Arizona State University, 781 E. Terrace Mall,
Tempe, AZ.
† PhD Student, Space and Terrestrial Robotic Exploration Laboratory, Arizona State University, 781 E. Terrace Mall,
Tempe, AZ.
‡‡ Undergraduate Student, Space and Terrestrial Robotic Exploration Laboratory, Arizona State University, 781 E.
Terrace Mall, Tempe, AZ.
§ Assistant Professor, Space and Terrestrial Robotic Exploration Laboratory, Arizona State University, 781 E. Terrace
Mall, Tempe, AZ.
(Preprint)

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surfaces. However, they are still limited from exploring extreme environments such as caves, lava
tubes and skylights in off-world environments like the Moon or Mars due to inherent challenges
in motion planning and control on dusty surfaces. We follow a different approach to solving this
problem by utilizing teams of fully autonomous robots that hop, perform short flights and roll1.
These missions may require traversing low-gravity surfaces of asteroids, bypassing impassable
terrains or climbing extremely rugged terrains such as canyons, cliffs, craters walls and caves to
acquire critical science data (Figure 1). Exploring these off-world terrains is daunting and it re-
quires a holistic systems solution that utilizes the latest in robotic mobility combined with smart
planning to recover from missteps and slips. Guidance Navigation and Control devices such as
reaction-wheels, IMUs together with a propulsion system enables unprecedented mobility in pre-
carious surface conditions. We have proposed SphereX, a spherical robot, 3 kg in mass, and 30
cm in diameter that can hop, fly, roll and summersault on planetary surfaces and small-bodies.
Moreover, with the addition of a suitable gripping skin, these robots can grasp onto rough terrain
and rest on precarious/sloped surfaces. Hence, these robots can climb up a slope by hop-
ping/rolling a distance d and then gripping on the surface. However, a single robot may slip and
fall if the gripping mechanism fails to grasp. This can be avoided by developing a multirobot sys-
tem that can work cooperatively by being interlinked using spring-tethers and work much like a
team of alpine mountaineers to systematically climb a slope.
In this paper, we present dynamics and control simulation of an autonomous multirobot sys-
tem that cooperates to climb sloped surfaces by successively hopping, rolling and crawling. A
multirobot team exceeds the sum of its parts by tackling complex slopes that would otherwise be
too risky for a single robot to traverse. The multirobot system comprises of four spherical robots
that are interlinked with tethers in an “x” configuration. Each robot is secured to a slope using
spiny gripping actuators, and one by one each robot moves upwards by crawling, rolling or hop-
ping up the slope. If any one of the robots loses grip, slips or falls, the remaining robots will be
holding it up as they are anchored.

Figure 1. (Left) Cliff faces on Mars. (Right) Asteroid 2009 ES.
This multirobot approach for climbing sloped cliff surfaces holds great potential for exploring
cliff and extremely rugged surface environment on Mars, Moon and asteroids. Recent research
suggests that water flowed down the faces of several Martian cliffs as seen in high-resolution im-
ages acquired by the Mars Global Surveyor Orbiter Camera2. Getting up-close, traversing down
these slopes enables going back in time to better under the geological history of Mars. These ex-
treme environments cannot be accessed using conventional wheeled, legged or rolling robots.
Hence, there is an important need to develop next-generation robotic systems that can reach these
sites by flying or climbing steep slopes.
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Moreover, the benefits of the SphereX system can be realized on milligravity surfaces such as
asteroids. There are 150,000+ asteroids, with a large number located in the asteroid belt between
Mars and Jupiter23. They range in size with diameters ranging from a few meters to several hun-
dred kilometers. On milligravity surfaces, hopping and flying is simple and uses negligible pro-
pellant. However, the gravity varies throughout the surface and too much thrust can result in a
spacecraft achieving escape velocity. Using the proposed multirobot approach with robots an-
chored to the surface keeps the entire system secure. In the following sections, we present back-
ground and related work followed by system overview, dynamic simulations, discussions, conclu-
sions and future work.
RELATED WORK
Climbing remains a major challenge in robotics. Much work has focused on developing teth-
ered legged and wheeled robots. Dante II is an eight-legged walking rover that was used to ex-
plore the craters of volcanoes using a tethered rappelling mobility system3. However, it was not a
fully autonomous system and required teleoperation. Another example is the All-Terrain Hex-
Limbed Extra-Terrestrial Explorer (ATHLETE) rover developed by NASA JPL4. ATHLETE has
six 6-DOF limbs, each attached with a 1-DOF wheel. The wheels can be used for efficiently driv-
ing over smooth terrains and it can be locked and used as feet to overcome steep obstacles or rug-
ged terrains. Another example is the Teamed Robots for Exploration and Science on Steep Areas
(TRESSA) that was used for climbing steep cliff faces with slopes varying from 50 to 90 de-
grees5. It is a dual-tethered system that allows lateral motion on steep slopes and successfully
demonstrated semi-autonomous science investigations of cliffs. Another example is Axel devel-
oped by NASA JPL which is a two-wheeled rover tethered to its host platform for enhancing mo-
bility on challenging terrains like steep slopes and overhangs6. It is capable of in-situ measure-
ments and sampling on challenging terrains and successfully demonstrated accessing 90 degree
vertical cliffs and collecting samples.
The Legged Excursion Mechanical Utility Rover (LEMUR IIb) developed by NASA JPL is a
four-limbed robot that can free-climb vertical rock surfaces7. In addition to vertical rock surfaces,
it can traverse a variety of other terrains like urban rubble piles, sandy terrain and roads using
only friction at contact points. Several climbing robots employing suction cups, magnets and
sticky adhesives. One such example is the Stickybot developed at Stanford that employs several
design principles adapted from the gecko lizard like hierarchical compliance, directional adhesion
and force control to climb smooth surfaces at very low speeds8. Another robot developed is
Spinybot II that can climb a wide variety of hard, outdoor surfaces including concrete, stucco,
brick and sandstone by employing arrays of microspines that catch on surface irregularities9. The
Robots in Scansorial Environments (RiSE) is a new class of vertical climbing robots that can
climb a variety of human-made and natural surfaces employing a combination of biologically in-
spired attachments, dynamic adhesion and microspines10. Another application of micro spines
developed by NASA JPL has been an anchoring foot mechanism for sampling on the surface of
near Earth asteroids11. The mechanism can withstand forces greater than 100 N on natural rock
and has been proposed for use on the Asteroid Retrieval Mission (ARM).
Another technique developed at Stanford and NASA JPL uses 3-axis reaction wheels to creep
over rugged surfaces no matter how steep or uneven27. The technique works well in low-gravity
and small but steep slopes. It is unclear how a gyroscopic system will handle large steep surfac-
es; as they are bound to slip and fall after extend use/missteps. Multirobot systems have been
tested for space applications including exploration; base-preparation and resource-mining18. The
motivation for our multirobot system is taken from proven methods used by alpinists to climb
mountains. These mountaineers use ice axes and crampons to grip on the surface and climb steep
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mountain slops as shown in Figure 2. The use of legs and hands provide four contact points to
the sloped surface. Even when each attempt to grip onto a higher location fails, the climber is
still secure with his feet and one hand gripping tightly onto the slope.

Figure 2. Mountain climbers use an ice axe and crampons to climb steep icy slopes. They use their
two hands and two feet to grip onto the icy slope.

Inspired by mountaineers, our approach utilizes a multirobot climbing and flying system that
has inherent redundancies to recover from individual missteps and slips. Our proposed approach
is a total systems solution to address the challenge of off-world climbing. The system utilizes
multiple SphereX robots that are interlinked with spring-tethers. The multirobot system works
cooperatively to fly over impassable terrain and climb off-world cliffs, canyons and caves. The
system uses an array of microspines to grip on the rough surface while climbing.
SYSTEM OVERVIEW
Our proposed design consists of four spherical robots interlinked together with spring tethers
in an “x” configuration. Figure 3 shows the internal and external views of each spherical robot,
without the micro-spine skin. The lower half of the sphere contains the power and propulsion sys-
tem, with storage tanks for fuel and oxidizer connected to the main thruster. The attitude control
system is at the center and contains a 3-axis reaction wheel system for maintaining roll, pitch and
yaw. The main thruster enables translation along the +z axis and in combination with the attitude
control system it enables the robot to move along 3-axes. Next is the Lithium Thionyl Chloride
batteries with specific energy of 500 Wh/kg arranged in a circle as shown.

Figure 3. Internal and external views of each SphereX robot.
An alternative to batteries are PEM fuel cells. PEM fuel cells are especially compelling as
techniques have been developed to achieve high specific energy, solid-state fuel storage systems
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that promise 2,000 Wh/kg15,16,17. However, PEM fuel cells require further development for a field
system in contrast to lithium thionyl chloride that has already been demonstrated on Mars.
A pair of stereo cameras and a laser range finder rolls on a turret. This enables the robot to
take panoramic pictures and scan the environment without having to move using the propulsion
system. Moreover, the stereo camera and laser range finder would aid in navigation and percep-
tion. Above the turret are two computer boards, IMU and IO-expansion boards, in addition to a
power board. The volume above the electronics is reserved for climbing mechanism and equip-
ment of up to 1 kg1.
Apart from the proposed propulsion subsystem, all other hardware components can be readily
assembled using Commercial Off-the-Shelf (COTS) CubeSat components. The proposed propul-
sion system uses RP-1 as the fuel and H2O2 as the oxidizer. The mass budget for a single SphereX
robot is shown in Table 1.
Table 1. SphereX robot mass budget
Major Subsystem
Mass (kg)
Computer, Comms, Electronics
0.2
Power
0.3
Stereo Camera, Laser Rangefinder
0.3
Propulsion
0.8
ADCS
0.4
Climbing Payload
1
Total
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DYNAMIC SIMULATION
We are using four SphereX robots, each of mass 3 kg. Each robot has a propulsion unit to
provide the thrust required for hopping and a 3-axis reaction wheel system to change the orienta-
tion of the robot. The combination of propulsion unit and the reaction wheels will help us achieve
ballistic hopping capabilities. The surface area of each robot consists of a microspine that enables
the robot to grip onto rough surfaces while climbing sloped cliffs.
Ballistic Hops using Rocket Propulsion
For ballistic hops, a liquid propellant rocket motor is used to provide thrust along the +z axis.
Analysis has been done for different types of solid and liquid propellants based on their Isp, flight
time and feasibility14. The thrust generated by a rocket motor depends on the mass flow rate, noz-
zle exhaust velocity and combustion chamber pressure as shown below12:

(1)
where, F is the thrust generated, p is the combustion chamber pressure, Ath is the nozzle throat
area, pe is the nozzle exit pressure and k is the ratio of specific heats. With the thrust provided by
the rocket motor along +z axis, a set of reaction wheel is used to control the orientation of the ro-
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bot which enables the robot to move along 3-axes. The reaction wheel system applies torque to
the spherical robot about its principal axes according to the control command resulting in change
in orientation and angular velocity. This is done by applying conservation of angular momentum
to the robot and reaction wheel system, and can be expressed by setting the time derivative of the
total angular momentum to zero shown below13:

(2)
where, L is the angular momentum of the system, JB and JRW are the moment of inertia of the ro-
bot and the reaction wheels, B and RW are the angular velocity of the robot and reaction wheels
respectively. The system has three inputs that are torques exerted by the reaction wheels. The
three outputs are the desired Euler angles of the robot. The required torques can be calculated by
a PD control algorithm as shown below:

(3)
where, rw is the torque generated by the reaction wheels, Kp and Kd are the proportional and de-
rivative controller gains, edes and eact are the desired and actual Euler angles,
and
are the
desired and actual angular velocity of the spherical robot respectively. Figure 4 shows the trajec-
tory of a spherical robot for a PD control algorithm in a Martian environment with acceleration
due to gravity of 3.71 m/s2. The desired Euler angles were 0.27, 0.25 and 0.07 radians and the
desired angular velocities were 0 rad/s. Moreover, we have simulated the system with RP-1 as a
fuel and hydrogen peroxide (H2O2) oxidizer and it consumes 5 grams of propellant for every hop.
It is clear from the figure that for every hop, the robot can travel a distance of 0.37 m along x-
axis, 0.41 m along y-axis and can attain a height of 0.28 m along z-axis (Figure 4).

Figure 4. Trajectory of SphereX robot performing a rocket-propelled ballistic hop.

Ballistic Hops using only Reaction-Wheels
The ballistic hopping mechanism discussed above, uses a liquid propellant rocket motor and a
system of 3-axis reaction wheel. Although this mechanism can achieve controlled hopping, the
system does expend significant amounts of fuel. An alternative approach to hopping utilizes or-
thogonal reaction wheels surrounded by external spikes19,20,21 as shown in Figure 5.
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Figure 5. Externa layout of robot using reaction wheels to perform ballistic hops.

Using a linear combination of internal torques with the help of the three reaction wheels, the
system can produce momentarily large reaction forces at the surface. The contact forces between
the spikes and the surface comprises of spring-damper forces normal to the surface, and a Cou-
lomb friction component tangential to the surface21,22. With sufficient torque applied, the system
can produce momentary large reaction forces, causing the platform to leave the surface, hopping
forward in a ballistic trajectory. The approach consists of a hybrid control algorithm, where the
reaction wheels are slowly accelerated to a desired angular velocity, and the impulsively braked
to generate the torque needed to produce hopping20. With this control strategy, the desired angular
velocity  and braking torque  can be regarded as the two control variables and they are a func-
tion of lateral distance to be covered d and acceleration due to gravity g.
Figure 6 shows the desired angular velocity and braking torque required to hop a lateral dis-
tance of 1 m as a function of g. For our analysis, we have considered the mass of each reaction
wheel as 0.35 kg, radius of each reaction as 3.5 cm, length of each spike from the center of the
robot as 25 cm. For surfaces like Phobos with acceleration due to gravity 0.006 m/s2, the desired
angular velocity of the reaction wheel is 314 rad/s (~3,000 rpm) and the desired braking torque is
0.063 Nm. However, for Mars, it is 7,952 rad/s (~75,940 rpm) and 38.8 Nm respectively which is
extremely high and not practical.

Figure 6. Angular Velocity (left) and braking torque (right) to hop a lateral distance of 1 m as a
function of g.
Figure 7 shows the lateral hopping distance, d as a function of input torque, t and reaction
wheel speed w on a surface with acceleration due to gravity 0.006 m/s2. It shows that a SphereX
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robot can hop up to a distance of 4 m with an input torque of 0.33 Nm and reaction wheel speed
of 6,000 rpm. This makes reaction-wheel based ballistic hops practical for milligravity environ-
ments.

Figure 7. Later hopping distance as a function of reaction wheel input torque and reaction wheel
speed surface with acceleration due to gravity 0.006 m/s2 (Phobos).

Gripping Mechanism
The gripping mechanism consists of microspines. Each microspine toe consists of a steel
hook embedded in front of a rigid frame with elastic flexures acting as a suspension system (Fig-
ure 8)11. For a spine of tip radius rs, it will engage to asperities of average radius ra such that ra 
rs.

Figure 8: Microspine toe securely gripping and hanging from a rocky surface11.
Engagement of the spine to asperities depend on the angle  of the normal vector to the traced
surface and is possible only if it is larger than some critical angle min. The angle min depends on
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the angle at which the spines are loaded, load, and coefficient of friction, , between the steel
hook and the rocky surface as shown below9:

(4)
Hence, smaller spines with smaller tip radius rs are more effective at engaging to asperities on
smooth surfaces. However, smaller spines also carry smaller loads. Moreover, the maximum load
of the spine/asperity contact increases as rs
2, while the expected number of asperities per unit area
decreases as 1/rs
2. Thus, as we decrease the tip radius of the hook, it can engage to smoother as-
perities but the load carrying capacity decreases9. The elastic flexures act as a suspension system
and allow each hook to move relative to its neighbors. When the array of microspines are dragged
along a surface each toe is stretched and dragged to find a suitable asperity to grasp and share the
overall load uniformly. This system of microspines can attach to both convex and concave asperi-
ties as shown in climbing robots like RiSE10 and Spinybot9. The maximum load that a spine can
sustain is a function of the tensile stress of the hook and square of the radii of curvature of the
spine tip and asperity as shown is below9.

(5)

where,

(6)
where, max is the tensile stress and E is the modulus of elasticity of the material.

Cliff Climbing Multirobot System
For climbing sloped surfaces, each spherical robot is equipped with an array of microspines.
The robot hops using the propulsion system and reaction wheels and then grips on the rough sur-
face using the array of microspines. However, climbing sloped or vertical cliffs for a single robot
is a risky matter. A single robot may slip and fall if the gripping mechanism fails to grasp into the
rough surface. However, a multirobot system can work cooperatively by being interlinked using
spring-tethers and work much like a mountaineer to systematically climb a slope. We have con-
sidered a system of four spherical robots that are interlinked with four spring-tethers in an “x”
configuration which work cooperatively to climb a slopped rough surface as shown in Figure 9.

Figure 9. Cliff climbing multirobot system.
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The connections between the robots and tether are made with ball and socket joints. The
spring tether introduces one translational degree of freedom in the system which allows each ro-
bot to translate with respect to the other robots. The ball-socket joint introduces three rotational
degrees of freedom in the robot-tether connection and the tether-tether connection, which allows
each robot to hop with respect to the other robots resulting in 3-dimensional movement of the
whole system. Figure 10 shows a Matlab 3D VRML dynamics simulation of a team of 4 robots
climbing a slopped surface. In Figure 10.1 all robots are gripping onto the slope surface. Robot 1
disengages its grip and hops a distance d forward and then grips again on the surface. When robot
1 hops, the other three robots are still gripped to the surface, hence if robot 1 loses grip, slips or
falls, the remaining robots will be holding it up as they are anchored. Robot 1 continues to hop
until it is able grip onto the surface at a distance d from its initial position. Similarly, in Figure
10.3-10.5 robot 2, 3 and 4 hops and grips on the surface as shown until each robot is displaced by
a distance d. Figure 10.5 shows the final configuration of the robot system after it had climbed a
distance d up the slope.
The surface of each SphereX robot consists of hundreds of microspines. For the robot to climb
a wide variety of rough surfaces, it has a combination of large spines as well as smaller spines
spread uniformly. Each spine has a shaft diameter of 200-300 m and a tip radius of 12-25 m.
The maximum load that each spine can sustain per asperity is 1-2 N. Each robot has a mass of 3
kg and each tether has a mass of 0.15 kg, making the mass of the whole system approximately
12.6 kg. On Mars, with a g of 3.7 m/s2, the spines need to sustain a load of 47 N. With each
spine/asperity contact capable of sustaining 1-2 N load, a minimum of 28 spines should be en-
gaged. With each robot rolling or hopping at a time, the other three robots must share the total
load, hence a minimum of 10 spines need be engaged for each robot.

Figure 10. Sequence of robot movement to climb a steep slope. Each robots hops up the slope, indi-
vidually and in sequence and grips to the surface. The robots are all attached using spring tether.

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Figure 11 shows how the position of each robot and the “instantaneous center” of the whole
system changes with time. The initial position of robot 4 is at the origin (0,0,0) and that of robot
1, robot 2 and robot 3 are (1,1,0), (1,0,0) and (0,1,0) (m) respectively. It is clear that each robot
hops one at a time resulting in the change in position of the instantaneous center. Figure 12 shows
the change in x, y and z coordinates of the “instantaneous center” of the system as its climbing.
After four successive hops total, one by each robot, the instantaneous center moves a distance of
0.75 m along y-axis in 10 seconds.

Figure 11. Change in position of each robot and the instantaneous center during a climb.

Figure 12. Change in x, y and z coordinate of the instantaneous center during a climb.
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Figure 13 shows the y-coordinates of each robot and the “instantaneous center” when robot 1
fails to grip on the surface after hopping. All the robots successfully grip onto the surface after the
first hop. Then, robot 1 fails to grip after its second hop and slips down. However, the remaining
robots hold it up as they are anchored. Robot 1 then hops again to attain the desired height and
grips on the surface on its next attempt. Failure of any robot to grip on a surface leads to more
consumption of fuel and time to climb a certain height.

Figure 13. Y-coordinate of each robot and the instantaneous center when robot 1 fails to grip on the
surface.
DISCUSSION
The proposed cooperative cliff climbing technique using four spherical robots interlinked with
tethers in an “x” configuration is suitable for exploring cliff faces on Mars, the Moon, surfaces of
asteroids and other planetary bodies. With an array of microspines attached to each robot, the
multirobot system can grip to any rough surface and then climb or crawl without the risk of fall-
ing from a cliff or flying off an asteroid. Moreover, each robot has hopping/flying capability with
the help of the propulsion and the ADCS system. Climbing enables persistent access of the
sloped surface. This multirobot system has unique advantage over other wheeled or legged
climbing robot systems.
This multirobot system can have higher climbing speed compared to other wheeled or legged
systems due to the use of a propulsion system. Each robot can hop a distance of 0.75 m in 2 sec-
onds on Mars with an expenditure of 5 grams of RP1-H2O2 propellant. Alternative methods to
hop include use of a mechanical hopping mechanism and use of reaction-wheels applied with a
braking torque. With four robots interlinked the system must perform four successive hops to
climb a particular distance. Assuming each robot can grip onto the surface on its first attempt, the
whole system can climb a distance of 0.75 m in approximately 10 seconds. In milligravity surfac-
es like asteroids, the climbing/crawling speed will be even more efficient. The robots can use the
reaction wheels alone to hop on an asteroid. In addition, the robots could simply fly to a location
and land onto to the side of the cliff before performing climbing a few meters to reach a desired
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science target. The system of stereo cameras and laser rangefinder enables the robots to accurate-
ly navigate the surface and find the best possible path to climb avoiding obstacles.
CONCLUSION
In this paper we have introduced a multirobot system for cooperative cliff climbing and
steeped surface exploration. This multirobot system is suitable for climbing cliff faces on the
Moon, Mars and other low-gravity bodies. We have devised a system that can withstand individ-
ual missteps, slips or falls by a robot during the climbing process. A combination of flying, hop-
ping and climbing enables the proposed system to access hard to reach sites. However, the sys-
tem does expend significant quantities of fuel when using propulsion. Alternative approaches to
hopping include use of reaction wheels applied with braking-torque. This approach enables hop-
ping without use of propellant however it is only feasible for low-gravity environments such as
surface of asteroids and small-bodies. The dynamics and control simulations for a single hopping
robot with propulsion and ADCS system were presented. Finally, the cliff climbing mechanism
was simulated using four robots and four spring tethers. The paper presents insight on the feasi-
bility and the advantages/disadvantages of this multirobot system for exploring steeped planetary
surfaces, asteroids and small-bodies.
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