## Abstract

BALLET (BALloon Locomotion for Extreme Terrain) is a new concept vehicle for robotic surface mobility on planetary bodies with an atmosphere. The vehicle is composed of a buoyant balloon with six evenly distributed suspended payload modules each serving as a foot for locomotion over inaccessible rugged terrain. While the physics of BALLET will apply on Venus and Mars, the environmental conditions and available component technology limit our consideration to Titan. We describe the concept in detail, its applications for science missions on Titan, mission deployment scenarios, analyses of the concept under varying environmental conditions, and simulations of its locomotion. The concept is shown to be feasible and provides a new approach for exploration of rugged lakes, dunes, shorelines, and cryovolcanic regions on Titan.

## 1 Introduction

Safe and stable robotic in situ access to steep and rugged terrain on extraterrestrial bodies in our solar system has the potential for enormous science value in understanding geology, surface and subsurface chemistry, hydrology, and potentially prebiotic processes. BALLET (BALloon Locomotion for Extreme Terrain), a new concept proposed for mobility on Titan, is a limbed robot that uses a balloon for its structure and buoyancy and has its payload in its feet. Figure 1 shows a visualization of BALLET. Science and engineering subsystems on BALLET including instruments, electronics, power and control systems, and energy storage are evenly distributed into six modular feet. The combined mass of the feet is adequate to keep the balloon tethered to the ground, while the mass of each foot is low enough that the balloon buoyancy allows one or two feet to be lifted off the ground at a time. Each foot is connected to the balloon by three cables controlled with winches within the foot. Three cables are the minimum needed to control the foot position in 3D. Coordinated control of cable lengths places each foot at desired locations on the ground.

Fig. 1
Fig. 1
Close modal

To locomote, BALLET lifts one foot at a time, places it at a new location on the ground, and then re-positions the balloon with respect to the new feet positions by re-adjusting all cable lengths. This procedure is repeated in a sequence for the other feet. The balloon is small relative to the total payload mass because the buoyancy required is only needed to lift one foot, i.e., one-sixth of the total payload. BALLET is stable because it is effectively anchored to the ground with its center-of-mass close to ground level. An additional advantage BALLET offers is the potential to add a secondary mission by jettisoning five of its payloads and performing atmospheric exploration as a conventional balloon. While the physics of BALLET will also apply on Venus and Mars, the environmental conditions (extreme surface temperatures on Venus and very low atmospheric density and high surface winds on Mars) have limited our consideration to Titan. As an added bonus, BALLET can operate on Earth, where it would be developed and tested.

A thorough review of the previous published research on surface mobility systems and on balloons for Earth and planetary exploration applications was performed to confirm that BALLET is a novel concept. Survey papers, for example, on mobility [1] and balloons [24] have not considered this new hybrid concept. A range of mobility options have been considered [1,57] for access to rugged terrain on planetary surfaces. Some unusual surface mobility concepts with lightweight or buoyant components have been reported, for example, rovers with inflatable wheels and wind-driven tumbleweed rovers [8]. An underwater walking robot [9] has been proposed and developed that uses similar buoyancy principals although it does not place its payload in its feet. The use of multiple robotic platforms attached to a payload with cables for manipulation and transportation [10,11] has been reported. In the BALLET configuration, the problem is inverted and simplified with a single aerial platform and multiple payloads that are independently controlled.

Wheeled vehicles are used for surface exploration missions because they are relatively simple and highly efficient in traversing over benign terrain. Operational constraints for Mars (and likely for other planetary surfaces) limit their traverse over obstacles to less than the wheel height and slopes less than 20 deg. As a consequence, sites chosen for Mars’ missions trade-off science against mobility. Conventional legged vehicles handle more difficult terrain but with greater mass and complexity and reduced stability and safety.

This article is based on the report [12] submitted to the sponsor, and the NASA Innovative Advanced Concepts program extends the analysis reported in an earlier paper [13] on our investigation of the BALLET concept. We focused on four areas in this effort. They were (1) identifying the science targets and objectives with the corresponding requisite instrumentation and operational capabilities that could be achieved with a BALLET mission, (2) developing an architecture for the deployment and operation of this concept for a future mission to a planetary body, (3) analyzing a parametric physical model of BALLET under the environmental conditions of Titan and Earth to determine its feasibility, and (4) developing and demonstrating coordinated control and path planning of the BALLET mobility system to enable locomotion over rugged terrain. The results of our investigations in these areas are documented in the following sections.

## 2 Robot Vehicle Concept Description

BALLET achieves its benefits through several innovations: (1) use of a balloon for buoyancy and as a structural platform for locomotion, (2) limbs composed of cables in tension with significantly less mass than legs composed of links in compression, (3) partitioning the payload into six modular elements and lifting only one or two at a time to significantly reduce the needed balloon buoyancy and size, and (4) placement of the payload in the feet keeping the center of gravity very low and the platform highly stable.

The design for a BALLET mission to Titan includes a 45 kg radioisotope thermoelectric power generator (RTG) power system and a science instrument suite with a total mass up to 15 kg (about 2.5 kg per foot) on a 11.5 m3 sized helium-filled balloon. On benign terrain, BALLET walks at up to 1 cm/s, where feet do not have to lift significantly above the terrain. On rugged and steep slopes vehicle, speed will necessarily be reduced. Extraterrestrial robotic surface mobility is very slow. Speeds are limited by available power, environmental conditions including temperature and lighting conditions, limited computing power to process perception and navigation sensor data, and precautionary operating procedures. For comparison, the top speed on the MSL rover on Mars is 4 cm/s, but its average speed is significantly slower. If driven continuously, MSL would cover more than 3 km per day. It has, however, driven less than 22 km since its landing in 2012. BALLET will be slow but its ground speed is not a significant factor for operations and science return compared to other fielded planetary surface mobility missions

The balloon material would be fabricated with 2 mil thick polyester, the balloon would have a mass of 2.5 kg and in stowage would be rolled into a cylinder that is approximately 53 cm long by 14 cm diameter. The six instrument modules are baselined to each be approximately 15 kg and 2U in size (20 cm by 10 cm by 10 cm).

The limits to the duration of a BALLET mission is the loss of lift gas from the balloon. Two mechanisms contribute to gas loss: diffusion and pinhole leaks. A 5-day test [14] found that the diffusion leakage rate was undetectable. Super-pressure balloon test flights conducted more than 50 years ago had durations exceeding 6 months, and one flew for more than 1 year [15]. Improvements in materials technology since then would extend these results. Long duration operation of a balloon of 1 year or more is expected to be easily accomplished [16] because the Titan atmosphere is cold and thus reduces diffusion loss, does not contain ozone and high energy particles, and has low intensities of ultraviolet light that weaken polymer film materials [15,17]. With careful handling, inspection, packing, and deployment, the risk of creating pinhole leaks will be minimized.

Both helium and hydrogen are feasible lift gasses for Titan. Hydrogen is 8% more efficient but diffuses at significantly faster rates [18]. Helium is the conservative choice made in our analysis because it is inert, safe, has the potential for a longer life mission, and represents the worse-case larger balloon size. There are several mitigation strategies to compensate for loss of lift gas. The simplest method would be to use a slightly larger balloon than necessary and carry ballast on the balloon, which would be released as the balloon lift decreases over time. Another method could take advantage of the methane component of the atmosphere and extract hydrogen gas to add to the balloon. A feasibility study for a Titan blimp concluded that this is a viable technique for achieving long lifetime [19]. Third, it is conceivable that BALLET could return to the landing vessel and reconnect to the lift gas supply for a refill

Each payload would be enclosed in a 2000 cm3 2U volume enclosure as illustrated in Fig. 2 with an estimated mass of 2.5 kg. The three winches (arranged in a symmetric 120 deg offset pattern), computing, control and power components, will occupy about half of this mass and volume (10 cm by 10 cm by 10 cm). The cable would have a 0.5 mm diameter of braided stainless steel with a rated strength of 10 kg. With a 2 cm diameter and 0.5 cm width spool, a 1 m length of wire will take no more than two layers of windings on the spool. Each foot will have three cable-winch components. Each cable-winch component will include a spool, a spring-based cable tension sensor, spool rotation sensor, a brushless DC motor, and a motor controller. For cable length control, an initial calibration process will allow the use of spool rotational position to determine the cable length. Power will be supplied by two lithium-polymer battery packs with a total mass of 0.5 kg and 75 W h of energy with cooling fans that fit in a 10 cm by 10 cm by 3 cm volume.

Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal

Each foot payload will house a self-contained computing system with the software and power necessary to utilize its assigned instruments and winches. A single board computer will run the control and sensing software. Power will be provided by two battery packs housed in each payload as shown in Fig. 2. The computer in each foot will also be used to interface to the instrument or instruments within the foot. In the eventual mission application, coordination of instrument operation and services for command and data handling, mobility, resource monitoring, fault management, and communication will be distributed among the computers in the feet.

For mobility, one of the six computers will act as the coordinator, synchronizing the movement between the payloads for various gaits. This unit will receive commands from a wireless controller and broadcast commands wirelessly to the other five computers. To facilitate this model, each payload module is required to have Wi-Fi or Bluetooth communication.

## 3 Science Objectives

BALLET is particularly suited for exploration at extreme terrain locations on Titan. Titan, the largest moon of Saturn, has many challenging regions. Titan is the only other body aside from Earth with standing liquid on its surface. However, due to its low surface temperature (94 K), this liquid is not water but hydrocarbons—primarily methane and ethane, which pool in lakes at the poles [20]. Due to the absorption and scattering of methane and haze particles in Titan’s atmosphere, respectively, determination of surface composition by remote sensing is extremely challenging. Observations through the methane windows in the near infrared spectrum only allows rough slopes to be estimated; no spectral assignments can be made to identify species. In situ sampling, or spectroscopy at the surface, avoids these issues. Further, in situ missions have much greater spatial resolution and are able to discern trends invisible to orbit or flyby missions.

### 3.1 Titan Shorelines.

Recent work provides fairly rigorous constraints on the composition of the lake liquid [21]; however, the composition of the evaporite region around existing lakes and of dry lakebeds (Ref. [22] and references therein) is still a mystery. Although many lake landers and submersibles have been proposed [23,24], it is questionable whether such a platform could navigate to safely sample the edge of the lake where the evaporite resides, especially considering that most of these depressions either have steep walls [25,26] or are surrounded by topographically high areas on the order of 1 km over distances of 50–100 km [27] (see Fig. 3). Any platform would certainly benefit from being able to move along the evaporite, as the composition likely changes with radial distance (less-soluble species will precipitate first and should reside in an outer ring around the lake, while more soluble species will precipitate last and be concentrated closer to the center). Several instruments would help with the identification of key molecules and their chemical environments (co-crystal, clathrate, etc.).

### 3.2 Titan Dunes.

The dunes in the equatorial region of Titan (Fig. 4) are another primary target of exploration. These are found mainly within ± 30 deg of the equator in dark regions (in the visible, NIR and radar) and cover approximately 20% of Titan's surface [28,29]. Although the fact that they are dark in most wavelengths suggests that they are composed of a significant proportion of organics, we still do not know the composition of these dunes or how they formed or may be changing. The dunes appear to be approximately 100 m in height, with slopes ranging from steep (20:1 to 50:1) to shallow (200:1), although higher slopes could be present below the resolution of Cassini radar. We note that the steepest slope attempted by any rover on Mars to date is 32 deg, and slippage was so great in this case that the course was abandoned [30]. Slopes greater than 20 deg are considered steep for rover traversal; this becomes significantly more challenging on terrains with loose material, as unconsolidated dune inclines most likely would have.

Fig. 4
Fig. 4
Close modal

### 3.3 Titan Cryovolcanic Regions.

Several areas of Titan’s surface, such as Sotra Patera and Hotei Regio (Fig. 5), have features that have been identified as putative cryovolcanoes [31]. Cryovolcanism may be an important resurfacing process on Titan and may also be a major contributor to atmospheric methane [32]. Importantly, these regions may be the only places on Titan where material from the global, subsurface water ocean is being expressed on the surface. Any mission seeking to understand the habitability of this subsurface ocean would find areas of cryovolcanism very attractive sampling sites. As these regions exhibit some of the greatest elevation change on Titan’s surface, only a mission architecture capable of traversing/sampling steep slopes can reach these areas to confirm their composition and origin.

Fig. 5
Fig. 5
Close modal

## 4 Mission Formulation

On Titan, the density of the atmosphere is relatively high and gravity is low, so BALLET could carry a 45 kg RTG for power. The Titan balloon envelope would be made from a laminate of polyester fabric and film and would have a volume of approximately 12 m3. Laminated film materials are less susceptible to pin hole leaks than single-layer films. The science payload and supporting systems for telecom, command, and data handling would be divided among the feet that anchor the balloon to the surface.

The BALLET vehicle would be packaged inside a nested flight system for delivery to Titan. The major flight system components include a carrier vehicle, atmospheric entry system, lander platform, and the BALLET vehicle. The carrier vehicle would be powered with its own RTG system for Titan and would also serve as an orbiting communication relay. As an orbiter, it could have its own science mission that could compliment the BALLET mission.

After launch, the cruise vehicle would separate from the launch vehicle and provide for all thermal, power, and communication needs for BALLET. Health checks and software uploads would be typical interaction with the vehicle during cruise to Titan. The cruise vehicle would have propulsion needed to provide trajectory correction maneuvers and spin capabilities for inertial guidance. The Titan cruise vehicle would also need to reject RTG waste heat from both the cruise and the BALLET vehicles.

As the spacecraft approaches Titan, the atmospheric entry vehicle, as illustrated in Fig. 6, would separate from the cruise vehicle. The cruise vehicle would then be diverted to a separate trajectory into the atmosphere to avoid collision with the entry vehicle. The cruise vehicle would enter into an orbit around Titan and become an orbiter. The entry vehicle would be kicked off the orbiter, which would track the progress of the entry into the atmosphere. The orbiter continues to circle Titan and perform relay functions for the BALLET vehicle during entry, deployment, and mission operations.

Fig. 6
Fig. 6
Close modal

The sequence of events between atmospheric entry and landing the BALLET vehicle is shown in Fig. 6. On atmospheric entry, shown in Fig. 6(a), the heat shield removes a significant amount of energy from vehicle slowing it down until a parachute can be deployed. The shape of the aeroshell and the location of the center of gravity could be designed, such that it could be used as a lifting body and provide guided entry (Fig. 6(b)) to reduce landing ellipse error for the target destination. Backshell thrusters would be used to provide navigational guidance during entry. Deployment of the parachute uses a drogue chute first to pull out the main parachute (Fig. 6(c)). Once the parachute deployment has stabilized, the heat shield would be jettisoned (Fig. 6(d)) and fall to the ground and out of the way of the vehicle. As the BALLET lander approaches the surface (panel E), the lander legs would be deployed and it would be dropped from the backshell. Then descent thrusters and guidance navigation would slow the lander until touchdown on the surface. Lander rocket thrusters would also perform a lateral maneuver to avoid collision between the falling backshell/parachute and the lander vehicle during descent.

After the lander pallet has reached the surface, the BALLET balloon would be inflated. The balloon sits on the top of the lander pallet and is released from a constraint envelop that holds the folded balloon in place until ready for inflation. Compressed helium gas would be stored on board the lander for balloon inflation. The science payload would be packaged on the top surface of the lander but underneath the balloon. An inflation hose connected to the balloon would be cut after the inflation is completed, and a valve on the balloon would be closed to seal the balloon. After the inflation hose is cut, the balloon would be raised up from the lander by extending the instrument tethers. Once the balloon is stable, the BALLET vehicle would move the feet using the tethers to walk off the lander and move to a target destination and begin its science mission.

## 5 Concept Evaluation

Analyses were performed with the goal of characterizing the stability of the BALLET balloon in the environments of Earth and Titan. Evaluation for Earth was performed because prototype development would be performed on Earth. A representative balloon size was chosen for these analyses as defined in Eq. (1).
$a=2b=4c$
(1)
where a, b, and c are the lengths of the semimajor axes in the x, y, and z directions, respectively.
Due to symmetry, the buoyant force of the balloon is assumed to act at the center of the ellipsoid. From Archimedes’ principle, the buoyant force is equal to the weight of the air displaced by the balloon. In this analysis, the buoyant force is considered to be the total upward force after subtracting the weight of mass added to the balloon. Added mass includes the mass of the balloon material, as well as the RTG proposed for a mission to Titan. The buoyant force Fb and balloon volume V are given by
$Fb=(ρatm−ρHe)V−maddg$
(2)
$V=43πabc$
(3)
ρatm is the atmospheric density, ρHe is the density of helium at the planet’s surface, g is the gravitational acceleration, madd is the mass added to the balloon, and a, b, and c are the semimajor axis given in Eq. (1). Note that the density of the atmosphere and helium can vary cyclically with days and seasons on Earth and Titan causing the buoyant force to fluctuate according to Eq. (2). Initial estimates of the required balloon volume for testing on Earth and proposed missions to Titan and Mars are presented in Table 1 with added mass and buoyant force. Table 1 also presents the semimajor axis lengths resulting from the defined balloon volumes, following the relationship defined in Eq. (1).
Table 1

Balloon sizes and shapes on Earth, Titan, and Mars

PlanetBalloon volume (m3)Semimajor axis lengths (a, b, c) (m)Added mass (kg)Buoyant force (N)
Earth1.925(1.54, 0.77, 0.39)0.514.72
Titan11.534(2.80, 1.40, 0.70)4510.14
Mars88.134(5.52, 2.76, 1.38)0.15.51
PlanetBalloon volume (m3)Semimajor axis lengths (a, b, c) (m)Added mass (kg)Buoyant force (N)
Earth1.925(1.54, 0.77, 0.39)0.514.72
Titan11.534(2.80, 1.40, 0.70)4510.14
Mars88.134(5.52, 2.76, 1.38)0.15.51

Note: This table considers the three proposed locations (rows) and four parameters of interest (columns) and provides information for each of the parameters specific to the location that the balloon would be deployed.

Each limb of BALLET is made up of three cables connecting the balloon and a payload. To simplify the analysis, each limb is modeled as a single cable connecting the payload center to the average position of the three connection points on the balloon.

### 5.1 Balloon Static Equilibrium Analysis.

An analysis of static equilibrium of the balloon is used to determine the upper and lower bounds of the mass of the feet for a given balloon volume. If the foot mass is too low, the balloon is at risk of sliding on the surface or lifting off the ground. With a foot mass that is too great, the balloon may tilt unstably and have some limb cables become slack when lifting a leg. Determining the acceptable range of the mass of the foot is necessary for feasibility of the concept, balloon equilibrium, and quantifying requirements for the scientific instruments to be placed within the feet.

Figure 7 depicts the static force and the moment balance analysis that is performed in this article. The simplification of the limbs as single, vertical cables reduces the number of static balance equations to three:
$∑Mx=0$
(4)
$∑MY=0$
(5)
$∑FZ=0$
(6)
where Mx are moments about the x-axis, My are moments about the y-axis, and Fz are forces along the z axis.
Fig. 7
Fig. 7
Close modal

#### 5.1.1 Minimum Foot Mass.

The minimum mass of the feet is found in Eq. (6). The buoyant force must be completely counteracted by the weight of the feet. For the balloon to remain tethered to ground, the sum of the weight of all feet must be equal to or greater than the buoyant force. Assuming all feet will have the same mass, Eq. (7) defines the minimum mass of a single foot mmin as follows:
$mmin=Fb6g$
(7)
where Fb is the buoyant force and g is the acceleration due to gravity. Equation (7) remains true for both the single and dual limb locomotion techniques.

#### 5.1.2 Maximum Foot Mass.

The maximum mass of an individual foot is limited by the moment imparted on the balloon when lifting feet. When lifting one or two feet at a time, the analysis of tension in the remaining cables yields an underdetermined system with an infinite number of solutions. In each case, this system is still governed by the three static balance equations. When lifting one foot, the remaining five cable tensions are indeterminate. Similarly, when lifting two feet, the remaining four cable tensions are indeterminate. To find a solution to this system, a least squares optimization method was used. This method finds the case where the magnitude of the solution vector with respect to a cost function is a minimum, while still satisfying the system of equations. For our optimization, we have chosen to find the solution that maximizes the foot mass. At the maximum mass, one or more cables will have zero tension. If any additional mass were to be added, that cable would go slack due to its inability to resist compressive loads, and the balloon would tilt. To solve for the maximum mass, SciPy’s Sequential Least SQuares Programming (SLSQP) minimization capability [33] was used in python. This algorithm minimizes a scalar objective function where the objective function or constraints is nonlinear. The tension in the cables is affected nonlinearly by the tilt of the balloon, prompting the need for SLSQP. The minimization problem is defined by Eqs. (8) and (9):
$minimize(−x)$
(8)
$xg≥T(x,n)≥0;n={1,2,3,4,5,6}$
(9)
where x is the mass of a foot, g is the acceleration due to gravity, and T(x,n) is the tension in the nth cable when the foot mass is x. Equation (8) represents minimizing the negative mass, or equivalently, maximizing the mass. Equation (9) enforces two constraints: (1) the cable tension should be greater than zero and (2) the cable tension is less than the weight of the foot. This analysis was conducted for each leg-lift condition.

The function T(x,n) is obtained through the static force and the moment analysis of Eqs. (4)(6). A diagram of this analysis is shown in Fig. 7. When the balloon is pitched, the moment arms that determine the balloon stability are altered as shown in Fig. 8. In addition, the moment arms are not equally affected on opposite sides of the balloon due to the connection points lying outside of the x–y plane. This results in the cable tensions shifting toward the front or back of the balloon in both the single and two-legged gait patterns. To determine the effect of this on the maximum foot mass, the analysis was repeated for balloon pitch angles between 0 and 50 deg.

Fig. 8
Fig. 8
Close modal

### 5.2 Aerodynamic Force Analysis.

Aerodynamic forces from wind will affect BALLET on Earth and Titan. Drag will introduce transverse forces on the balloon, which can cause the feet to slide or otherwise effect the balloon’s stability. Lift can also be a concern if the balloon begins to tilt relative to the wind direction. Two methods were used to quantify the effects of wind on BALLET. The first method estimates drag force FD as follows:
$FD=12ρu2CDA$
(10)
where u is the flow velocity, CD is the drag coefficient, ρ is the air density, and A is the reference area. For these estimates, a CD of 0.5 is used.

The second method uses openfoam, an open-source software for computational fluid dynamics.1openfoam's pisofoam solver was used to characterize the transient behavior of incompressible turbulent flow around the balloon. To simplify this analysis, no turbulence models were considered. It is likely that this simplification also results in the worst-case aerodynamic effects due to pressure drag dominating skin friction drag for bluff body shapes like the BALLET balloon.

openfoam's blockmesh and snappyhexmesh tools were used with an standard triangle language (STL) model of the balloon to create a mesh for the simulation. For simulations measuring drag, symmetry was used on two planes to reduce the problem's complexity. Simulations measuring lift used symmetry on one plane, allowing for the balloon to tilt. All lift simulations were performed at an angle of attack of 10 deg. Simulation flow inlets were given freestream velocity and zero gradient pressure boundary conditions. Flow outlets were given zero gradient velocity and zero pressure boundary conditions. Note that for incompressible flow, the pressure differential drives flow, not the pressure value. These boundary conditions result in a steady flow at the desired velocity. Flow in both the positive x and positive y axes were simulated to understand how the angle of incoming wind effects BALLET’s stability. The boundary conditions of the balloon are no-slip velocity and zero gradient pressure, allowing for a boundary layer to form on the balloons surface. Images of typical drag and lift simulations are depicted in Fig. 9.

Fig. 9
Fig. 9
Close modal

### 5.3 Earth Proof-of-Concept Analysis.

The goal of this analysis is to find the range of stable balloon volumes for the proof-of-concept given the proposed balloon material and payload mass. Similar to the stable foot mass analysis, SciPy’s SLSQP minimizer was used to solve the following problem:
$minimize(V)$
(11)
$mpg≥T(V,n)≥0;n={1,2,3,4,5,6}$
(12)
where V is the balloon volume, mp is the payload mass, g is the acceleration due to gravity, and T(V,n) is the tension in cable n at volume V. The buoyant force required when calculating T(V,n) is obtained through Eq. (2), with the additional mass madd calculated as follows:
$madd=1110Sρb$
(13)
where ρb is the area density of the balloon material and S is the ellipsoid surface area. The coefficient of 11/10 is introduced to account for seams and attachment features represented by a 10% increase in balloon mass.

### 5.4 Results.

The parameters used in the analysis are presented in Table 1.

#### 5.4.1 Balloon Static Equilibrium Analysis.

Due to the symmetry of the balloon at 0 deg pitch angle, there are only four unique cases: (1) lifting a front-left or right foot, (2) lifting a middle-left or right foot, (3) lifting a front-left or right or back-left or right foot and the corresponding diagonally opposite foot on the balloon, and (4) lifting the middle-left and middle-right feet. Figures 10(a) and 10(b) depict the maximum stable foot mass on Titan on flat ground for the balloon size presented in Table 1. These results show the tension in each cable with the specified leg lifted off the ground.

Fig. 10
Fig. 10
Close modal

As shown in the aforementioned figures, at the maximum foot mass, one or more cable tensions go to zero in all cases. When a single leg is lifted, the moment imparted on the balloon limits the foot mass. The maximum stable mass in these cases is dependent on the balloon shape and the volume. When two opposing legs are lifted as shown in Figs. 10(c) and 10(d), they cancel out the moment imparted by a single lifted payload, resulting in no moment on the balloon. The weight of each payload at the maximum stable mass is equal to half of the buoyant force in this case. When lifting two opposing payloads simultaneously, only the balloon volume effects the maximum stable foot mass. This result shows that a two-legged gait provides the most stable configuration. If maneuvers can be limited to two-legged gaits exclusively, this would allow more scientific instruments to be stored in the payload or reduce the necessary size of the balloon when compared to single-legged gaits. For either case, the minimum stable foot mass is 1.25 kg according to Eq. (7).

It may be necessary to pitch the BALLET balloon when traversing a slope for multiple reasons. On a steep slope, it is possible that the front or back of the balloon could come into contact with the slope if a pitch is not applied. Also, if winds are flowing along a slope, a pitch can be applied to reduce the balloon’s angle of attack, preventing lift and drag from overwhelming the balloon. The stability analysis applied for nonzero balloon pitch angles showed that the maximum stable payload masses are reduced as pitch increases.

The static equilibrium analysis with varying pitch angles was also applied for a balloon on Earth. The combined results are summarized in Fig. 11. The results indicate that feet containing cable winches and associated electronics to control position and instrument suites for science operations are possible with the BALLET concept. We also found that, at low values of pitch, the dual leg locomotion technique shows far more stability than the single-legged technique. At high values of pitch, the advantage of the two-legged gait is greatly minimized, to the point at a slope of 50 deg, and single-legged gait is equally stable.

Fig. 11
Fig. 11
Close modal

#### 5.4.2 Buoyancy Changes With Atmospheric Conditions.

The surface temperature on Titan, measured remotely from the Cassini spacecraft, was found to vary between 91 K and 95 K diurnally, seasonally, and spatially between −60 deg and +60 deg latitudes [34]. This results in relatively small variation in BALLET’s buoyancy force over time. Effects of changes in atmospheric conditions were not considered on Titan due to its fairly stable climate.

While the atmospheric conditions on Earth vary greatly with latitude, time of day, and season, the Earth balloon would be built as a proof-of-concept for a future Titan mission. It would be tested under controlled conditions where atmospheric conditions like temperature and wind can be chosen to avoid large differences in buoyancy and stability. Therefore, this study assumed average conditions that would be found indoors and did not attempt to define the stability of BALLET for all climates expected on Earth.

#### 5.4.3 Aerodynamic Forces.

A first estimate of drag forces on the BALLET balloon using Eq. (10) is calculated. A worst-case drag coefficient estimate of 0.5 is used. The resulting drag forces are as follows: 4.073 N drag when flow is in the x direction and 8.147 N drag when flow in the y direction.

An open-source computational fluid dynamics package, openfoam, was used to simulate and analyze the aerodynamic forces on BALLET. The simulation parameters used for Titan are a freestream velocity of 1 m/s, air density of 5.280 kg/m3, and kinematic viscosity of 1.246 × 10−6 m2/s. Kinematic viscosity of Titan’s atmosphere was estimated as that of pure nitrogen gas at Titan’s average surface temperature due to the belief that Titan’s atmosphere is greater than 95% nitrogen. Results of these simulations are presented in Fig. 12.

Fig. 12
Fig. 12
Close modal

openfoam results show lower drag than Eq. (10) estimate, which is expected given the large drag coefficient used in that calculation. The simulations also show that it is preferable to face BALLET into the wind, such that the flow is perpendicular to the balloon’s smallest cross-sectional area. Facing this way will result in the lowest possible drag and lift forces. The drag forces found in the simulation are significant when compared to the buoyancy of the proposed Titan balloon of 10.14 N. In the case that BALLET sees flow from its y direction, the magnitude of the drag force will be about 40% of the buoyant force. The effect of these forces on stability will need to be analyzed further. In the event that the flow incidents the balloon at an angle of attack of 10 deg, the lift forces can be large enough to carry the balloon away or push it into the ground. Note that the proposed size of the Titan balloon is large enough to accommodate a 45 kg radioisotope thermoelectric generator for power. One way to minimize the expected lift and drag forces is to reconsider the size of this generator, allowing for a significantly smaller balloon. More analysis can be done to determine the relationship between lift and angle of attack for this balloon shape, allowing for a maximum acceptable tilt value to be defined.

The drag forces on the BALLET balloon using Eq. (10) is calculated. A worst-case drag coefficient estimate of 0.5 is used. The resulting drag forces are as follows: 13.946 N drag when the flow is in the x direction, and 27.891 N drag when the flow is in the y direction. openfoam simulations were performed as described previously. The simulation parameters used for Earth are a freestream velocity of 7 m/s, air density of 1.217 kg/m3, and kinematic viscosity of 1.5 × 10−5 m2/s. Results of these simulations are presented in Fig. 12. The results for Earth are similar to that of Titan.

While the magnitudes of aerodynamic forces on Earth and Titan vary greatly, the general trend remains the same. Lift and drag are significantly smaller when wind is flowing along the balloon’s x-axis due to the smaller cross-sectional area. In the event that the balloon tilts and/or wind flows along the balloon’s y-axis, there is a much greater chance of instability occurring. The forces found by this analysis show that winds on Earth would be an issue. As stated earlier, an Earth balloon would be largely used indoors, where the stability issues due to wind will be minimized. Given the similarity of these results to Titan, it would be feasible to test a physical proof-of-concept balloon on Earth under these simulated conditions. This could lend confidence to the simulations and allow for extrapolation to behavior on Titan.

#### 5.4.4 Earth Proof of Concept.

Finally, a proof-of-concept design is considered. The purpose of this analysis is to properly size the balloon for this proof-of-concept so that it will maintain the stability through a range of testing. Two balloon shapes were considered in this study. Shape 1 is defined by Eq. (1). Shape 2 is defined by Eq. (14):
$a=103,b=102$
(14)
where a, b, and c are the semimajor axis of the ellipsoid. Equation (13) is used to determine the balloon skin-material mass, where ρb is 0.127 kg/m2.

Figure 13 shows the range of stable balloon volumes that result from this analysis. For a given payload mass, the balloon volume must be between the upper and lower lines to maintain stability during testing. The two balloon shapes show very similar results, indicating that these results are not very sensitive to balloon ellipsoid size ratios. For a proposed payload mass of 2 kg, the balloon volume would need to be approximately 10 m3.

Fig. 13
Fig. 13
Close modal

## 6 Locomotion

Mobility algorithms for legged robotic systems have been investigated since the 1960s [35]. The approach we propose for controlling the mobility of BALLET is to leverage the algorithms developed in prior research for legged robots [36,37]. As a conservative, simple and low-energy approach, statically stable walking is chosen. There are several levels of software control needed to implement locomotion on BALLET. At the top level is the generation of a path to the desired destination while stepping around or over the obstacles and hazards. The output from this element is a set of waypoints that define the path to the destination. Curved paths between waypoints and corresponding foot trajectories are calculated to execute the locomotion along the segments. We developed a software package to model BALLET and demonstrate and visualize its locomotion in 3D.

### 6.1 Obstacle Avoidance Motion Planning.

The first step in motion planning is to construct a map of the environment and identify the destination and the obstacles in the field. For BALLET, the maximum step height determines the size of obstacle that can be stepped over. Larger obstacles are designated as hazards that have to be avoided. In addition, the slope of the terrain was also evaluated and regions with the slope greater than 40 deg were designated as hazardous. This process was used to identify unsafe regions in the field—if obstacles were smaller than the step size, they did not pose a problem for motion planning but needed to be considered in foot placement. The motion planning problem was decoupled into two parts. The first is vehicle motion planning with hazards designated as no-go regions. Sample-based path planning algorithms are widely used in the literature, and they can be used to determine a route to the desired destination to generate a motion plan for BALLET. For example, the review article by Ref. [38] describe the RRT and RRT* algorithms for optimal motion planning around obstacles. The implementation of the path planning for BALLET was adapted from the open-source RRT* motion planning software in Refs. [39,40] using the algorithm described in Ref. [38]. The output from this process is a set of waypoints defining the path to the desired destination.

### 6.2 Foot Placement.

Given an optimal route defined by a set of waypoints from the motion planner, a foot placement algorithm is then used to plan the steps to be taken to step over or around the obstacles within constraints of placement area available for each foot. Given the waypoints, destination position, and map of field designated safe-step regions, based on grade, roughness, terramechanics, etc., a path is constructed to allow stepping through the waypoints to the destination.

A path planning algorithm was developed to sequence the motion of each foot to traverse along paths generated by the motion planning algorithm. From the overall motion plan generated using the approach described in Sec. 6.1, path segments are generated. Each path segment to a local destination will consist of arc motions over the surface. For any local locomotion from an initial position to a destination, an arc of a circle can be constructed, as is illustrated in Fig. 14(a) with a corresponding radius and arc angle. The arc is subdivided into step-sized segments.

Fig. 14
Fig. 14
Close modal

To demonstrate locomotion with BALLET, a simple statically stable gait was identified and implemented on a geometric model. In this procedure, to locomote to a new desired position, a circular arc projected onto a horizontal plane from the current balloon centroid to the new position is constructed (see Fig. 14(a)). This arc defines the path the balloon must take. Similarly, arcs are constructed for each foot defining the path each foot takes while maintaining its relative position with respect to the balloon. For any locomotion destination, the foot that has the longest path determines the number of steps to be taken to complete the path using a predetermined maximum step length. The remaining feet paths are then discretized to have the same number of steps.

Following this initialization procedure, for single-step locomotion, the trajectory for the first foot is computed by lifting vertically a set height, moving horizontally to the same height position above its next step position then lowering down until the foot is on the surface. Foot motion to follow, the computed trajectory is accomplished by varying the three cable lengths that suspend the foot from the balloon as illustrated in Fig. 14(b).

The cable lengths corresponding to a desired foot position are computed by vector differences between the desired foot position (P4 or P4′) in 3D space and the respective cable tie point on the balloon (P1, P2, or P3). The available positioning volume is shown in yellow on Fig. 2. To take a step, for example, all three cables are shortened to raise the foot up. The cables attached to P1 and P3 are then shortened further while lengthening the cable attached to P2 to move the foot to P4’. The foot is then lowered vertically by lengthening all three cables appropriately. In practice, foot positioning control will be iterative and use updated estimates of P1, P2, P3, and P4 as the balloon pose shifts with changing cable loads. The foot also rotates during the step to match the motion of the balloon and the curvature of the path. The balloon is then moved one-sixth of its step and rotated appropriately by varying all the cables that attach it to the ground to follow the curvature of the path and to follow the slope of the ground beneath. The second foot is then moved, followed again by the balloon and so on until all six feet have taken a step and the balloon has moved a full step. For double-step locomotion, the front-left and the back-right feet simultaneously take a step, followed by the middle-left and middle-right feet and then the front-right and back-left feet. Between each pair of feet stepping, the balloon is moved one-third of its step along the balloon path.

This procedure is repeated until the balloon reaches the desired position and orientation. The algorithm accommodates undulating terrain by always positioning the foot a set height above the target step position before being lowered to the ground. A finite-state machine shown in Fig. 15 was implemented to control the locomotion algorithm. Simulations demonstrated single-step and double-step locomotion as recommended by the force and moment analysis in Sec. 5.

Fig. 15
Fig. 15
Close modal

A more sophisticated stepping algorithm is possible to optimize the foot placement to step over local and small hazards, for example, using the algorithm demonstrated in Ref. [41]. The foot placement is chosen to maintain the stability, and the step size is adaptively chosen to approach close to then step over hazards that are smaller than the maximum step possible.

### 6.3 BALLET Model and 3D Visualization.

3D computer graphic model and visualization of BALLET and its locomotion was implemented to illustrate its mobility using the open-source Blender visualization engine. The object-oriented software implementation consisted of two parts.

The first part is a parametric kinematic model of BALLET consisting of a Balloon, six Limbs, each with three LimbCables and one Foot, and a model of the Terrain. The BALLET object also contains the finite state machine mobility algorithms for locomoting over the surface using the RRT* motion planning algorithm. The unified modeling language (UML) object diagram of this part of the software is illustrated in Fig. 16. The second part is the BALLET Visualization software to display BALLET and its environment in 3D and orchestrate locomotion, lighting, and camera motion to render images to create animations of the locomotion. The ModalTimerOperator object assists with triggering the refreshing of the 3D rendering of all the objects in the scene during the creation of animation sequences.

Fig. 16
Fig. 16
Close modal

Examples of the 3D visualization for locomotion are shown in Fig. 17. The sequence of feet taking steps is front-right, front-left, middle-right, middle-left, back-right, and finally back-left.

Fig. 17
Fig. 17
Close modal

## 7 Conclusion

In this article, we describe a new robotic concept for surface mobility and analyze its performance. This study determined that compelling science targets for a BALLET mission are lake-shores and cryo-volcanos on Titan. Instrument suites tailored for these respective science targets have been identified and are feasible for deployment on a BALLET-based mission. An entry, descent and landing architecture was developed for BALLET. The design of a deployment system for BALLET from the lander was also developed. Power and communications for operations have also been investigated showing a feasible mission architecture for these bodies. We have also developed locomotion algorithms using coordinated limb motions to enable traverse over a range of terrain types. A 3D visualization of the operation of BALLET was developed to illustrate its operation.

Titan has the most favorable conditions for BALLET. The combination of a dense atmosphere, low gravity, and low surface wind speeds allow use of a 45 kg RTG power system and a science instrument package with a mass up to 15 kg. Conditions on Mars were also studied and found to be less favorable so that they are not reported here. In the thin Martian atmosphere, a larger balloon is needed and, with nominal wind speeds of 5 to 10 m/s, drag forces on the balloon approach the weight of the payloads. However, special precautions to actively anchor BALLET could be taken under high-wind conditions where speed can reach 26 m/s.

A two-legged locomotion technique was found to be more stable than single-legged locomotion. When lifting one payload at a time, a moment is imparted on the balloon that becomes the limiting factor for stability. Lifting opposing legs results in zero moment applied to the balloon. In this case, stability is only limited by the balance of vertical forces due to buoyancy and payload weight. The range of stable payload mass is greater for two-legged locomotion because of this affect.

When traversing a slope, tilting the balloon with the slope will result in a narrower stable payload mass range. At very high slopes, two-legged locomotion loses its stability benefit over single-legged locomotion. The analysis also found that buoyancy does not change significantly with atmospheric conditions on Titan due to its stable climate.

Aerodynamic forces will be a major factor in balloon stability. Titan’s low wind speed and high atmospheric density make it the most favorable option in dealing with aerodynamic forces. In all cases, facing BALLET such that its smallest cross-sectional area is perpendicular to the flow will result in the smallest lift and drag forces possible for the proposed balloon shape.

A proof-of-concept BALLET system on Earth is possible with a moderately sized balloon. For payload masses of 2 kg in each foot, an approximate stable balloon volume of 10 m3 would be necessary. Algorithms for motion planning and navigation over rough terrain from the previous research of legged robotics systems can be leveraged for BALLET. Coordinated control of the cable system and feet placement for locomotion, a problem unique to BALLET, has been shown to be algorithmically feasible.

As with other cable-controlled manipulation systems, BALLET has a number of challenges that will have to be addressed in its deployment. Among these are oscillations and vibration in the cables [42], mitigating cable slack conditions [10], and controlling length and tension [43] of the cables. In addition, coordinated motion with 18 cables and 7 rigid bodies to be simultaneously monitored and controlled will be complex. Under the anticipated environmental conditions, BALLET will be statically stable and so locomotion can be slowed down to accommodate the sensing and computational burden as we gain familiarity with the platform.

Contact science on targets in rugged terrain with BALLET enables the direct measurement of water and salt content, enables local temporal and spatial coverage, provides options for multiple measurements with alternative instruments, and potentially enables shallow subsurface sampling. BALLET provides an alternative means to access these sites, increases the range of surface mobility, and favorably expands the trade between mobility and science. Our investigation showed that BALLET has compelling advantages for science exploration at lake-shore and cryo-volcano sites on Titan that remain inaccessible to other surface mobility approaches. BALLET could also be used on Earth for the transport of materials over rugged terrain and in undersea applications where the significantly higher density of water will allow moving much more heavy objects.

## Acknowledgment

This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, and was sponsored the National Aeronautics and Space Administration under the NASA NIAC program (Grant #80NM0018F0579). Manit Ginoya was supported by a grant from the University of Ottawa and a Mitacs Globalink Research Award. © 2019. California Institute of Technology. United States Government sponsorship acknowledged. The information presented about the BALLET mission concept is pre-decisional and is provided for planning and discussion purposes only.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

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