Designing a Robotic Hopping Cube for Lunar Exploration

Tim Hojnik∗, Robert Lee∗, Donald G. Dansereau, Jurgen LeitnerAustralian Centre for Robotic Vision (ACRV)

Queensland University of Technology, Brisbane, Australia

Abstract

This paper proposes a mechanically hopping 1UCubeSat-scale payload for lunar exploration.The high energy density of a mechanical com-pression spring-based locomotion system makesit very attractive for extra-terrestrial opera-tions, especially in lower gravity and thinneratmospheres. The main aim is to record im-ages and perform surface mapping from novelvantage points using on-board algorithms. Wedemonstrate prototypes of the locomotion andvision systems in terrestrial surrogate environ-ments. We envision similar systems playinga crucial role in supporting the operation ofground-based lunar explorers, such as, map-ping, (beyond-horizon) path planning and nav-igation.

1 Introduction

Space and its exploration have always driven science andscientific developments. Robotic systems allow us to ex-plore the remote corners of our solar system and havebeen used as precursors to human missions. Designingsystems for extraterrestrial operations is a complex task.Surviving a space mission requires a robot’s subsystems,from electronics to mechanics, sensing and planning towork flawlessly and in unison.

Spurred by international competitions such as theGoogle Lunar XPrize, Lunar exploration has seen a re-cent resurgence. Inspired by previous concepts for hop-ping robots [Kaplan and Seifert, 1969; Fiorini et al.,1999; Ball et al., 2013; Leitner et al., 2016] we propose aCubeSat-scale payload that can hop on the lunar surface.The higher vantage point this affords offers a greaterimage footprint for visual lunar surface reconstructionand planning, as well as beyond-horizon communicationsduring cooperative exploration missions [Leal Martinezet al., 2010].

1The authors contributed equally to this project.

Figure 1: Exploded view of the payload depicting thespring-based hopping mechanism and the two cameras.

Complications arise in both platform and launch pay-load limitations. On-board computation is restricted bythe energy stored or captured using photovoltaic cells.Weight and manufacturing constraints arise from limita-tions in lift and cost associated with current launch vehi-cles. Space vehicles such as satellites and rovers also havespecific geometric shapes, leaving empty cavities withinthe launch vehicle. These make the Cubesat form factorparticularly attractive, aiming to fill these otherwise un-used spaces and create opportunities for universities andprivate entities to fly payloads [Heidt et al., 2000].

This paper focuses on the design and the first exper-imental validation of mechanical and vision systems fora hopping lunar robot, as depicted in Figure 1 and pro-posed previously [Leitner et al., 2016]. We describe ahopping mechanism and explore the mechanical consid-erations appropriate to lunar surface mission require-ments. We explore methods for visual sensing and de-velop a prototype, built on a compact stereo camera,capable of 3D surface modelling using stereo Structurefrom Motion (SfM). Thermal management, radiationand dust are not discussed as these are well exploredelsewhere. Our focus is on exploring the design spacefor locomotion and visual sensing.

2 Background

2.1 Hopping and the Lunar Environment

Hopping is a very effective means of locomotion in roughterrain, cluttered environments, over substantial obsta-cles, and in low gravity. Evolution on Earth has allowedsmall animals to navigate obstacles by jumping throughthe air along pre-planned ballistic trajectories. We drawinspiration from this evolutionary adaptation to developa means of robotic propulsion that applies both on Earthand in lower-gravity environments.

The Lunar environment is vastly different to that onEarth, complicating robot design [Heiken et al., 1991;Berkelman et al., 1995]. Wheeled rovers face particu-lar challenges driving over rocky surfaces and navigatingaround large boulders. This is exacerbated by the lowsurface gravity of the Moon, about 1/6th that of theearth (gLuna = 1.622ms−2, gEarth = 9.807ms−2). Hop-ping robots, however, benefit from this lower gravity.Coupled with the lack of atmospheric drag, these sys-tems have a significant advantage in that they requiresubstantially less energy to achieve a desired height ordistance compared to similar systems on Earth.

We envision a hopping robot gathering spatial infor-mation about the lunar surface during its hop, buildingup a map of its surroundings. The robot can use thismap to drive obstacle avoidance and navigation over oraround large boulders or ravines, where a conventionalwheeled rover may be unable to proceed due to bothperceptual and locomotive limitations [Berkelman et al.,1995; Bandyopadhyay et al., 2016].

2.2 Mission Requirements and Limitations

A major goal for this project is to capture images ofthe lunar surface whilst in flight, and to process theseimages to create a 3D map of the surface. The 3D mapsgenerated by the platform can yield useful informationfor navigation, beyond-horizon path planning, and canbenefit cooperative ground-based exploration.

The major limitation of this platform however is size,being restricted to 100mm3 as it is required to fit intoits designated space in the launch vehicle. Furthermore,on-board power consumption is limited to what a photo-voltaic system can generate, for continuous use, or storein on-board batteries, for intermittent use.

It is unfavourable for the jumping system to use ex-plosive substances or liquid/solid fuel for propulsion assuch systems offer a limited number of hops before ex-pending their fuel. Furthermore, safety factors while intransit limit their appeal.

2.3 Existing Vision Systems

Multiple-view geometry has been paired with stereo vi-sion successfully in the past for the purposes of mo-bile robot navigation [Kitayama et al., 2015]. Stereo

correspondence is used to calculate the distance to fea-tures, and used in conjunction with Structure from Mo-tion (SfM) to create a map and position the camerawithin. These techniques form an effective method forscene mapping.

Novel lenses such as fish-eye lenses have also found usein such applications, allowing wide field of view capturein a single frame [Rameau et al., 2015]. This benefitsmotion estimation and scene reconstruction, using non-overlapping Structure from Motion techniques. Thoughsuch techniques could find application on the lunar sur-face, we will focus in this work on a compact stereo pair,as this gives instantaneous depth information and strikesa favourable balance between resolution and computa-tional requirements.

3 System Design

We propose a cube-shaped robot that conforms to the1U CubeSat standard. The robot’s mechanical system iscritical to this project, allowing the cube to move aroundthe lunar surface, capturing digital images as it explores.This mechanical system comprises of the cube frame, theself-righting mechanism, the photovoltaic system and thejumping system.

Capturing imagery of the lunar surface is also one ofthe major requirements for the project, as these images,while rare and novel on their own, would also prove avaluable resource for moon exploration when used in pro-ducing a reconstruction of the lunar scenery. To achievethis, we propose a setup with multiple cameras in con-junction with an on-board computer used to capturestereo image pairs whilst the cube is jumping.

3.1 Hopping Mechanism

Compressive Springs

We propose a propulsion system employing compressivesprings. It consists of a number of springs that instan-taneously release their stored potential energy, and con-verting it into linear action [Barse, 2015].

Springs are very reliable and yield a high energy den-sity when used appropriately. When maintained atan optimal temperature1 their characteristics are stableover time, and they can store energy with minimal ma-terial plastic deformation for a prolonged period of time.The springs are reliable due to their simplicity, and canwithstand hard impacts and high forces, as well as a vac-uum, providing the temperature is controlled. Materialproperties change with temperature: If the temperatureof the spring gets too low the metal becomes brittle andmay break; If the temperature becomes too high, the

1The interior of the cube needs to be kept at a constanttemperature, this would be done through a thermal controlsystem (TCS). However, the TCS considerations are not partof this paper, for more info see [Elkins and Leitner, 2016].

spring becomes flexible and may plastically deform. Bycontrolling payload temperature, a spring jumping sys-tem can be a very efficient option. Springs can be manu-factured to a specific spring coefficient, selected followingthe energy conservation law

k =2mgh

δ2, (1)

where k is the spring constant (Nm−1), m is the mass ofthe cube (kg), δ is the spring deflection (m), g is gravity(ms−2) and h is the desired maximum jump height ofthe robot in metres.

Spring Assemblies

We propose two alternative spring assemblies. One iscapable of multiple jumps, while the other can only jumponce without intervention and is primarily for testing.

Radial Wheel – Dual Spring

Figure 2 shows a proposed radial spring system in itscompressed state on the left and its uncompressed stateon the right. This system uses a radial rotating wheel tocompress and release the spring, translating rotationalenergy into a linear jump. The motor used to rotate theradial wheel required high levels of torque, in proportionto the spring value k and the wheel radius. The radius ofthe wheel is also proportional to the maximum deflectionof the springs, δ. This system is capable of multiplejumps. Note that in the figure the motor is concealedunderneath the wheel.

Linear Compression – Single Spring

A simpler system was also designed, comprised of a sin-gle spring and having a single-jump capability as thereis no means of re-compressing the spring. The systemis however smaller and lighter than the radial system.The mechanism makes use of four small clamps to holdthe spring compressed, and occupies a smaller volume of33, 722mm3 where the radial system in Figure 2 has avolume of 89, 952mm3 excluding motors. This system isdepicted in Figure 3.

Electromagnetic Solenoid

Preliminary testing and calculations showed that an elec-tromagnetic solenoid system would require a power stor-age device with a very high energy density and discharge

Figure 2: Radial spring jumping system capable of per-forming multiple jumps (inspired by [Barse, 2015]).

rate. This would require extra on-board batteries orcapacitors that exceed the volume and/or mass of thespring assemblies described above. We therefore con-clude solenoid-based systems to be inappropriate for thisproject.

Summary

We proposed two significantly different spring-based as-semblies. The linear compression system is lighter,smaller and more efficient, therefore appropriate for test-ing various spring types and values. The radial wheel hasa reload capability which is essential for multiple jumps,but it is heavier and larger.

3.2 Mechanical Design

Here we describe the non-propulsive mechanical elementsof the robot, including supporting frame, pusher plate,photovoltaic system and a self-righting mechanism.

Cube Frame

When conducting the initial tests, a 100x100x100mmframe was manufactured using 3D printing technology.This allowed fast development of a frame to be usedfor testing, while also providing the strength requiredto mount the cameras. This frame was used for proof-of-concept testing with initial jumps.

A second frame was constructed from 80x10x10mmaluminium beams, with 10x10x10mm corner pieces,holding the structure together. This frame was stur-dier and could sustain an impact with a solid surfaceat 7.92ms−1, while the printed frame could only with-stand an impact of 5.95ms−1. The frame has a weightof 390 g. Because it is sturdier, this frame was used forjump testing.

Pusher Plate

The pusher plate was designed for to operate on a softsurface, requiring a large surface contact area. We de-signed a plate consisting of a flat base 94x94mm in size,with protruding groves that minimise slip and maximise

Figure 3: Single jump linear spring system capable ofperforming a single jump.

Figure 4: Pusher plate design for soft sandy surfaces(left). Preliminary pusher plate imprint on sand (right).

traction. Our institution logo was found to provide greattraction when printed onto the pusher plate (Figure 4).

Self-righting Mechanism

Once the payload has completed its jump and has cometo a rest on the lunar surface, it needs to be repositionedin the correct orientation to be ready for its next jump.Systems such as reaction wheels were considered, butthese were found to require too much space and power.

We propose a system comprising of four 100×100mmsquare solar panels, mounted to four sides of the cube soas to allow each to pivot through a 90◦ arc. All four sidesare operated simultaneously by a single motor, though asecondary motor can be added for redundancy. Figure 5shows the solar panels mounted to the side of the cube.

Photovoltaic System

Five solar panels measuring 100x100mm each providesufficient power to operate the robot’s on-board systems.A single panel was fixed on the top-side of the cube, andone panel on each of the four sides as described above.

After the cube has been righted to its correct orien-tation, the four side panels open up to receive sunlight.At this point the top panel is also parallel to the lu-nar surface, and all five panels convert electromagneticradiation into electricity.

The energy gathered by the photovoltaic cells is gov-erned by the relationship

E = ArHc, (2)

where E is the energy (kWh/an), A is the total solarpanel area (m2), r is the solar panel efficiency, H is solarradiation and c is a further coefficient of losses (between0.5 - 0.9, typically around 0.75)

Photovoltaic cells capable of providing 2.4 W each arereadily available. These panels are 16.4% efficient whileproducing 4.8 A at 0.5 V at an irradiance of 1000 Wm−2,temperature 25◦C and an absolute air mass coefficent of1.5. According to these results coupled with the on-board battery, we expect that a photovoltaic systemcomposed of five solar cells will be capable of meetingthe on-board power requirements.

Figure 5: Solar panel positions during a self-righting pro-cedure. (Cube insulation is omitted in this rendering toallow for internal components to be seen).

On-board Power Storage

The payload requires a steady supply of electricalpower, for the on-board computers to perform their pro-grammed tasks. However, solar cells cannot be relied onto supply constant, uninterrupted power. As such, anuninterrupt-able power supply (UPS) is required.

A back-up battery is kept on board, capable of sup-plying power to the flight computers, when the cube isnot exposed to sunlight or whilst undertaking a jump.Though appropriate batteries are readily available. Im-portant factors in battery selection [NASA, 2002] are:

• Battery amp hour capacity

• Discharge and charging rates

• Extreme temperature and mechanical conditions atlaunch and transit

• On-board air pressure/ vacuum

• Risk of explosion during transit

Mechanical Systems Summary

A well designed cube frame is essential as it houses thescientific payload and all flight computers. Coupled withan effective self-righting mechanism, the hardware de-sign needs to be robust and have multiple redundancies[Brown, 2002]. In the event of a major failure of the self-righting system malfunctioning and depriving the solarcells of sunlight, the on-board battery allows the cube tocontinue functioning for a set period of time to transmitcollected data to the primary payload (e.g. a rover).

3.3 Vision Systems

For a successful exploratory mission to the moon, the vi-sion system must be able to capture images that containvaluable information about the landscape and terrain.To collect the data and perform the image processingtasks a computation system is required that can fit intothe cube. Multiple camera views, from multiple cameras,from different viewpoints during the hop are integratedto create a range of views, particularly useful for taskssuch as navigation, planning and surface reconstruction.

On-board Cameras

Two identical cameras, in a stereo configuration, aremounted inside the frame facing downwards to collectimages. The most interesting images to capture are dur-ing the hop, but due to that motion, requirements on theperception system are stringent. In particular the cam-eras must be able to perform well under fast accelerationwithout excessive motion blur. For initial testing, globalshutter PointGrey FireFly cameras provide grayscale im-ages (owing to the fact that the lunar scenery is largelymonochromatic). To reproduce lunar-like images and tominimise blur the exposure was set to the lowest valuepossible while still retaining adequate lighting to achievefeature matches.

On-board Computation

The prototype contains a Raspberry Pi 2B capture andsaving of a continuous stream of images. It allows inter-facing with multiple USB cameras, and due to the nativeLinux kernel, supports OpenCV and the PointGrey Fly-Capture SDK. The image processing is then performedoff-line on a standard desktop PC using MATLAB.

Multi View Integration

Inspired by the Panono [Pfeil, 2014], a throw-ablepanoramic camera ball, the cube was proposed to cap-ture images with each camera during its hop. The im-ages will then be integrated together to create a morecomplete (visual) representation of the lunar surface.

Image stitching is achieved by finding and matchingfeatures that are shared by the two camera views. Aprojective transform is then applied each image so thatthe matched points align. Feature matching algorithmssuch as SURF [Bay et al., 2006] are popular methodsfor finding these features, and RANSAC [Fischler andBolles, 1981] in conjunction with homography transfor-mations are used to align the images together. RANSACis an iterative method, which randomly samples pointsfrom the list of matches. Assuming there are relativelyfew mismatches, there is a high likelihood of the samplehaving a good indication of the model, which simultane-ously computes the fundamental matrix and eliminateserroneous matches.

Utilising the cube’s movement the cameras are captur-ing multiple images during the hop, further informationabout the lunar surface is collected. In combination withSfM, three-dimensional structure is estimated from a se-quence of images. A high quality, three-dimensional mapof the surface provides additional information for navi-gation and planning of further jumps or for other assetson the ground. Both perception pipelines, the one forimage stitching and the one for surface reconstruction,rely on the same feature matching process and the as-sumption that the camera parameters are the same foreach image. A transformation can then be found that

holds information about how the camera moved. Thiscan be represented simply by

x′1Fx2 = 0, (3)

where x1 and x2 are corresponding points in the im-age pair, and F is the fundamental matrix that relatesthe two and can be found using RANSAC.Once the fun-damental matrix has been estimated, the transform be-tween images can be solved. We can assume the camerasto be calibrated, and thus compute results for featuresmatches found between the pair, as well as, found be-tween the same camera after some movement.

An implementation of the Structure from Motionpipeline, specifically for grayscale images and stereo datawas implemented based on SFMedu [Xiao, 2013], a freelyavailable SfM pipeline. Particularly the feature match-ing and point plotting functionality had to be adjusted.Our proposed pipeline is fed the images from one cam-era sequentially and only later merged with the calcu-lated points from the second camera using bundle ad-justment [Richards, 1985; Triggs et al., 1999] to createthe final surface reconstruction.

4 Experimental Validation

Terrestrial prototypes were built to test both the me-chanical and perception systems proposed.

The mechanisms were designed with the aid of CADsoftware and prototyped using 3D printing technologies.This allowed for quick iterations of prototype systems,yet had limited structural integrity requiring a strengthreduction of the spring used and leading to tests for therelease mechanism with a weaker spring.

4.1 Compressed-Spring Jumping System

The use of compressive springs for a jumping system ofthe cube proved very effective. Testing validated thecompressive spring high energy density and a very lowpercentage of losses in the spring system, as theoreti-cally expected. The spring, once compressed to a desiredlength, is able to discharge at a high rate, transferringits energy into the jump in a single, smooth action overa very short period of time.

At first the single hop spring mechanism was tested toindependently vary the effectiveness of the reload mech-anism for the multi-hop setup. For the single hop springswere manually compressed for each independent jump,making use of a servo motor to act as the automatic re-lease mechanism. Figure 6 shows the theoretical jumpheight versus the average tested jump height.

Using Eq. 1 the projected maximum height for a num-ber of spring coefficients, under Earth’s gravity, was de-termined. The single and multi-hop mechanism weretested separately. In addition both of these were tested

Spring constant Theoretical Hop height Hop height Efficiency Efficiency(Nm−1) height (m) Hard surface (m) Soft surface (m) Hard surface (%) Soft surface (%)

250 0.816 0.55 0.43 67.41 52.691500 2.315 1.50 1.21 64.75 52.263450 2.534 1.75 1.42 69.06 56.04

Table 1: Single hop mechanism: nominal jump height vs. actual tested height (weight: 0.12kg).

Spring constant Theoretical Hop height Hop height Efficiency Efficiency(Nm−1) height (m) Hard surface (m) Soft surface (m) Hard surface (%) Soft surface (%)

2 × 250 0.816 0.06 0.04 7.35 4.902 × 1500 2.315 0.18 0.14 7.78 6.01

Table 2: Multiple hop mechanism: system nominal jump height vs. actual tested height (weight: 0.22kg).

on a hard surface (tiled floor) and a soft surface (ki-netic sand). Table 1 shows the data gathered duringthe single hop system experiments, while Table 2 repre-sents the multiple hop system results. All four setupswere conducted four times, average experimental data ispresented.

It can be seen that the system is more efficient on ahard surface. This is due to less energy being dissipatedinto compressing the soft surface. The surface of themoon is however a sandy surface, therefore the systemwill require further optimisation for such environments.

One can also see that the current multi-hop systemis less efficient than the single hop mechanism. Lossesare most likely stemming from a non-ideal placement ofthe springs, as well as the lack of a guide. Addition-ally testing composed of an ABS plastic release mecha-nism, a spring and a digital metal geared servo for springreloading and subsequent release, which introduced fur-

Figure 6: The projected vs. actual height using the singlehop mechanism on a hard surface.

ther losses.

4.2 Vision System

At first the camera setup was tuned to create lunar-surrogate pictures to be fed into the processing pipeline(Figure 7a). The camera setup was then tested dur-ing several jump simulations. For these the cube wassuspended with a cable from a bar and lowered down to-wards the surface. The cameras faced downwards, look-ing at a cloth to represent the lunar surface. Imageswere collected on-board and streamed to a mobile phonefor monitoring. Images collected were then used in thecomputer vision pipelines proposed.

Selectively stereo camera images were fed into theStructure from Motion reconstruction pipeline. A pointcloud was produced and also further processed into amesh surface (Figure 7c). Two different simulations werecarried out. First, the cube was gently swung from sideto side during image capturing, and then the cube wasraised via the cable to imitate a jump.

The comparison of the source and reconstructed sur-face shows that the structure from motion techniques areindeed able to recreate even low texture surfaces compa-rable to the lunar environment (Figure 7a and 7b). Thecombination of a stereo camera pair with a Structurefrom Motion pipeline creates an advantageous way tocapture the surfaces, especially for navigation and plan-ning (as proposed by [Kovac et al., 2010]).

5 Conclusion and Future Work

We propose a mechanically hopping system for lunar ex-ploration to be used as a secondary payload. A sensorsuite based on two cameras is proposed to provide ad-ditional information for beyond-horizon navigation andplanning. The hopping mechanism propels the platformabove the lunar surface to collect the required images.

(a) (b) (c)

Figure 7: (a) Example of a photo taken from the camera during a simulated hop. (b) Reconstructed 3D point cloud.(c) Reconstructed 3D mesh from the two monochrome cameras.

A single and multi-hop system was developed, proto-typed and tested. The single hop mechanism demon-strated up to 56% efficiency on a lunar-like surface. Itis noted that the multi hop system requires further workto match the efficiency of the single hop system.

Mechanical spring systems have significant advantagesover an electrical solenoid, such as weight and power re-quirements. Additionally, with the aim is to eventuallydevelop a platform that is able to perform multiple jumps(compare [Kovac et al., 2010]), an automatic releasemechanism is proposed. These two sub systems weretested individually to prove the concept, then mergedtogether into a functioning hopping system.

The vision system proposed incorporates a camerapair to generate multi-view data of the lunar surface.Panoramic stitching was proposed as a method to gain awide view of the lunar surface, stitching together imagesfrom multiple cameras, however such images do not con-tain information about the surface elevation itself andtherefore have only limited applicability to navigationalpurposes. A Structure from Motion pipeline was pre-sented to create a three dimensional map of the surface.When using the camera pair together, the view angle en-hancing benefits greatly enhance the perception of the(simulated) lunar surface in our experiments.

The success of the vision system on-board indicatesthat utilising multiple cameras and employing multiple-view computer vision techniques provides valuable todata for (robotic) exploration. This is particularly use-ful for other ground based assets, for example, (beyond-horizon) rover navigation, path planning in difficult ter-rain, as well as, human lunar exploration.

5.1 Future Work

This is a first prototype for a hopping, seeing lunar pay-load. Future work on the hopping system will need tofocus on improving the system’s efficiency and reliabil-ity. The forces in the multiple jump system can become

unbalanced at full compression, requiring better forcealignment of the system to increase it’s efficiency. Othermaterials, such as Aluminium or Titanium, to improvethe systems’ strength and coupled with this, springs withhigher constant (k) value, need to be investigated andtested to achieve better performance.

Flexible FramesPreliminary studies into flexible frames have been con-ducted and should be explored further, as a means ofshock absorption upon touch down. The corners wouldbe very robust, in order to maintain the structure’sshape, while the sides would have between 6-12% flexi-bility factor to allow for deformation. This would allowfor the cube frame itself, to absorb energy on impact,dampening the forces exerted on the payload.

VisionThe addition of more cameras to the cube is a con-cept that will be explored in greater depth, in order tomaximise the value of vision and surface reconstruction.There is a trade-off between the extra weight and theincreased storage but this approach might yield a returnby being more fault tolerant and providing additionaldata.

Acknowledgment

The authors would like to thank the Australian Centrefor Robotic Vision (ACRV) and the Queensland Univer-sity of Technology (QUT) for providing the resources toperform this research. T.H. and R.L. contributed equallyto the work presented in this paper.

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