Development of Tools and Strategies for Rover Vehicle Design

Development of Tools and Strategies for Rover Vehicle Design

Aravind Seeni

Department of Mechanical Engineering, PACE Institute of Technology and Sciences, Ongole, Andhra Pradesh

AbstractThe design process of a Mars rover is driven by multiple design constraints namely overall mass, power consumption and volume (dimensions). Various systems such as mobility, manipulation, power, thermal, communication, navigation, avionics and science instruments together make a complete rover vehicle and they should function cooperatively to perform a particular task. Each of the subsystems can be thought as modular blocks that are integrated together form a fully functioning rover vehicle. When approaching the designing of such a vehicle, the designer should take into account of cross design dependencies existent between different subsystems and technology limitations. For performing any particular task, this would lead to many design possibilities. Choosing the final design from many feasible solutions is arguably a daunting task. In order to make this process simple and convenient, as well as to understanding the design non-linearity existing in this solution space, the authors have employed a systems engineering approach to develop a tool comprising of subsystem models. The subsystem models comprise parametric, physics-based and FEM models. For designing to suitable user defined objectives, these models when integrated with Genetic Algorithm form an effective tool to support rapid design trade-offs during conceptual design process. This integrated modeling and optimization approach is thought to be efficient in identifying rover system concepts. For demonstrating the tools application, different design criteria based on user requirements are considered. This would be discussed subsequently.

Keywords Rover Design, Genetic Algorithm, Rover System Modelling, Computational Tool Development

Mmotor motor mass

Mbat battery mass

Mradiator thermal radiator mass

Tmot nominal motor torque

Tav.,persol average recharge time per sol

bwheel wheel width

Rcompaction compaction resistance

nwheels number of wheels

Ltrack length of vehicle track

L0.5base half-lengths of vehicle base

L0.5track half-lengths of vehicle track

D diameter of rock

D0 limiting rock diameter

(D) cumulative fractional number of rocks of diameter D

Cbat battery capacity

ebat specific energy of battery

NOMENCLATU RE

a desired acceleration

Asa

solar array area

k pressure-sinkage factor

xrms rms deviation

dwheel wheel diameter

o Stefan-Boltzmann constant

al albedo flux constant

mcell specific mass of solar cell

Prover,nom nominal power consumption of rover Prover,peak rover power consumption of rover Ps/s,exp.cycle power consumption per experimental cycle Pbat,charge power required for battery charge

g acceleration due to gravity

CI confidence interval

kc soil cohesion modulus

k soil friction modulus

n soil deformation component

day

P

nom, persol

P

night

nom, persol

nominal power consumption per sol during day

nominal power consumption per sol during

night

internal friction angle

Mpl payload mass

Mrover total rover mass

MACS attitude control subsystem mass

Mpow power subsystem mass

Mmob mobility subsystem mass

Mtelecom communications subsystem mass

MC&DH command and data handling subsystem mass

Mcabl cabling mass

Pday peak power consumption per sol during day

peak , persol

peak , persol

Pnight peak power consumption per sol during night

nom, persol

T day duration of nominal power consumption

during day

nom, persol

T night duration of nominal power consumption

during night

peak , persol

T day duration of peak power consumption during day

peak , persol

T night duration of peak power consumption during

The tool is built with integrated models that would have complete definition of the rover with mobility, power, thermal, communication, navigation and respective avionics subsystems. The subsystem models yield outputs of mass,

night

day efficiency of day-time operation

night efficiency of night-time operation

bat battery efficiency

cell solar cell efficiency

rad radiator efficiency

paint paint emissivity

rad radiator emissivity

DOD depth of discharge

rad material density of radiator material

Arad area of radiator

AWEB WEB area

AWEB,proj projected area of WEB exposed to sunlight

trad radiator thickness

Qalbedo heat due to albedo

Qpaint heat dissipated by paint

Qrad heat dissipated by passive radiator

Qdissp dissipated heat

QWEB heat dissipated from WEB

Qsun solar heat rate

mot angular velocity of motor

FwheelXY Wheel contact force with soil

science,sol science return ratio per sol Erover.egress energy required for rover egress ops Imean mean solar flux

FACdegrad degradation factor

FACtempeff temperature effect

FACpacking pack factor of solar array

-NA- Not applicable

1. INTRODUCTION

   In the year 2008, a scientific alliance project entitled Planetary Evolution and Life with members from different planetary and space research institutes of Germany and abroad was initiated. The objectives of the alliance are to engage in scientific activities in areas covering the broad spectrum of habitability possibilities in the bodies of the solar system. The study of subjects such as biology, geology, atmosphere, chemistry and relevant scientific areas give essential information to explore possibilities of presence of life or water and essential ingredients to begin life formation or evolution. The project consists of members from both planetary science and engineering community with collaborative involvements to realize new mission ideas and futuristic concepts. The Institute of Robotics and Mechatronics involved in this project within the auspices of work package Robotic Tools. As part of this involvement, a computational tool that would help in identifying design possibilities of a conceptual planetary rover applicable for a mars surface exploration mission was developed. The tool would help in performing a rapid analysis of the designspace for solutions, identify the best design and produce the output of the analyses to the user. The tool would also be a source of creativity and novelty to create new designs that are conceptual and are technologically feasible.

   power requirements and dimensions for assisting an optimization algorithm. The algorithm used is an evolutionary, metaheuristic, stochastic optimization algorithm called Gnetic Algorithm (GA). GA uses a numerical approach to perform maximization or minimization of a given function. The search process mimics the process of natural evolution of life as per Darwinian Theory. It is capable of handling discrete and continuous variables efficiently and has been used in numerous applications. Significant amount of research have so far been performed and reported on development of Genetic Algorithm. It has found applications in engineering, computational science and other fields. It has seen evolving over the years with significant performance improvements to results and computational cost. Considering its importance in engineering, GAs that will be used here as an optimization tool.

   During the initial stages of the project, a questionnaire was designed to receive inputs from the planetary science community. The questionnaire was designed in an abstract manner for receiving inputs such as target body of interest (Mars, Titan etc.), location (atmosphere, surface, sub-surface), and scientific instrumentation needs for gathering data. Based on this information, it was determined that mobility of scientific payload is an essential required component for most missions proposed. Concepts of robotic vehicles or rovers were essential for such missions to realize envisioned futuristic scenarios. To address the needs the above mentioned computational tool was developed using GA as a systems engineering tool. Of most missions proposed, Mars was the target of interest for most scientists. The tool was thus designed to incorporate models concerning Mars especially to help develop new rover concepts.

   In the last 15 years, robotic missions from NASA have yielded valuable scientific data from Mars. The delivery of useful scientific data to us by traversing different sites is not an easily achievable feat. Mars surface presents a challenging environment for rover operations due to unforeseeable adverse environmental conditions as seen in the past. A mars rover mission is technically operationally risky. Associated with risks, comes costs. Therefore, while designing a system for such missions, it should be designed for a predetermined performance or objectives.

   So far, the vehicle design that has been traditionally and successfully used is a wheel-enabled mobile rover that can carry a suite of scientific payload on-board and capable of transferring it from one site to the other. Since the early Lunokhod missions to the Moon, low mass, high fault tolerant, power efficient components are being used to build individual systems. For instance, mobility components such as motors have so far reached high technological maturity levels. All the systems that support essential scientific tasks to be performed with on-board instruments and motion such as power, thermal control, avionics, navigation, communication subsystems are integrated to a mechanical structure called the suspension. The

   suspension should be designed to certain kinematics to efficiently climb slopes, rocks or other obstacles. The mobility system requires power for operation and is supported by the power subsystem. The power system is generally designed with a primary power source such as solar arrays and a secondary power source for storage such as batteries. Since the amount of electric power produced per sol is limited and to be efficiently used, the size of subsystems has to be optimized to avail the needed science returns without sacrificing mass and dimensional constraints. Thermal subsystems help in keeping the systems in allowable operational temperature conditions. Efficient operation of the vehicle dictates the expected total science return from the rover.

   Rovers that have been launched for exploring the surface of mars have yielded valuable science so far. The delivery of useful scientific data to us by traversing different sites is not an easily achievable feat. Mars presents a challenging environment for rover operations due to unforeseeable adverse environmental conditions. A mars rover mission is technically and operationally risky. Associated with risks comes costs. This forms the basis for perform design trade-offs and finding optimal designs that conform to mission specific objectives. A Genetic Algorithm (GA) based design methodology is implemented and a computational tool is developed to serve this purpose. In this tool, a rover model consisting of all essential subsystems is described suitably to perform a system- level design trade-off analysis using GA. GA serves the purpose of finding optimal designs by searching the trade space for feasible solutions, maximizing or minimizing user- defined objectives and satisfying design constraints. For designing vehicle systems such as rovers, the structural design parameters of one subsystem affects the design of one or other subsystems. All the systems that support essential scientific tasks such as power, thermal control, avionics, navigation, communication subsystems are integrated to a mechanical structure called the suspension. The suspension should be designed to certain kinematics to efficiently climb slopes and rocks. The mobility system requires electrical energy for operation and is supported by the power subsystem. The power system is modelled by assuming solar arrays as the primary power source and batteries as the secondary power source for storage. Since the amount of electric energy that can be produced per sol is limited and should be efficiently used, the size of subsystems has to be optimized. This is performed to avail predicted science returns and not sacrificing mass and dimensional constraints. Thermal subsystems keep systems in allowable operational temperature conditions. This inter- related system design dependency driving the rover design in terms of total mass, power consumption and volume can be utilized to suitable degrees to perform rapid trade analysis and choose a final design. Since the first missions to Mars, the rover vehicle configuration that has been successfully deployed is wheel powered. In this paper, a six-wheeled rover with kinematics based on rover developed for ExoMars mission will be assumed. For capturing all the rover systems within the model parametric models are required. Parametric system-level relationships are available for satellites as provided by Wertz and Larson [1] and hence so far have been widely used by designers. For rovers such relationships are not

   widely available. Empirical data mined from various sources is used to develop some of the parametric models. The tool essentially comprises of various modules that relate to each subsystem mobility, power and thermal control modules that are integrated to GA. A GUI interface to receive user inputs is provided. Two different case studies with different design objectives – 1) designing for minim al mass and 2) designing for maximal science return will be assumed to demonstrate the tools application. The results are analyzed and this work will be described in this paper.

2. TOOL ARCHITECTURE

   GUI

   The tool is designed to have a Graphical User Interface (GUI) that accepts essential mission level inputs from the user. The inputs, in general retrieves approximate information related to locational coordinates concerning rover operations, electronics box dimensions for heat accommodation and subsystem energy requirements. The GUI interface is shown in Figure 1.

   Figure 1 – GUI interface

   Environmental models

   Rover operations on Mars are generally influenced by local terrain topography and climatic conditions. The terrain topography with large boulders and rocks significantly reduces the traversal time between scientific points of interest. The rock density estimations on Mars surface presented by Golombek [2] allow a quantitative estimation of rock size in the rover operational vicinity for a certain geographical location. Based on these estimations, we plan to size the rover suspension system. Typically the landing site locational coordinates are decided during the late mission stages. Since the topogaphy on Mars is non-homogenous as on Earth, during conceptual design stages it is necessary to have the suspension dimensional design boundaries for chosen locations.

   The distance a rover can traverse in a straight path along a particular heading angle on a terrain until it encounters an obstacle to cause turning can be defined as the mean free path. The mean free path if desired to be large would increase the size of suspension and wheels in order to aid motion over obstacles such as rocks. This is called vehicle trafficability. In our tool, the mean free path requirement is a constraint that is a function of the suspension and wheel sizes. Mean free path can be further explained through the following equation [3]:

   L 1

   1 track D(D) dD D2 (D) dD

   D

   x 2 D0 2 0

   bwheel

   Ltrack (D) dD D(D)dD

   D0 D0

   (1)

   L0.5track

   Apart from rocks and boulders on the surface, rover traversal can be affected by soil. Soft soil causes high resistive losses to motion. The weight of the rover contributes to wheel sinkage in to the soft soil. The resistance due to wheel sinkage can be termed as the soils compaction resistance. The amount of wheel sinkage depends on the soil properties and wheel dimensions. The capacity to move with low compaction resistance can be termed as terrainability of the rover. This can be further explained as follows:

   L0.5track

   L0.5base

   base

   L0.5

   b k zn1

   Rcompaction

   wheel

   n 1 (2)

   dwheel

   The soil sinkage, z is given by,

   2

   3 M g

   2n 1

   z rover

   (3)

   n

   wheels

   (3 n)k d

   wheel

   Figure 2 – Characterization of mobility system parameters

   k is a factor first coined by Bernstein when he established the following pressure-sinkage relationship:

   Mobility module

   A rovers mobility subsystem consists of the following elements – suspension bogies, wheels, actuators and interfaces.

   p kz n

   (4)

   The bogies are the axles that carry the load and provide a platform for carrying all on-board systems. Actuators consist

   Bekker further improved the relationship using soil parameter values of kc, k, and n as follows:

   k

   of motor and gear that is connected to the wheel. The motor and gear mass relationships are derived simply as follows. The mass of motor and gear is thought to be proportional to motor torque and gear ratio respectively. Data that accounts for 92

   k c k zn

   (5)

   motor and 26 gear models are retrieved from motor designs

   bwheel

   The climate on Mars is seasonal. Mars experiences both summer and winter and this influences rover operations. A rover designed with solar arrays depends on the amount of solar insolation available or reaching Mars surface from the Sun. Solar insolation availability also would depend on the locational coordinates. The solar insolation modelled here is

   manufactured by Maxon motors AG [8]. Motors from Maxon have been used in the past on the following missions – Mars Exploration Rovers, Spirit and Opportunity and ExoMars rover breadboard design and development. Scalar factors that relate motor mass (Mmotor) to torque and gear mass (Mgear) to gear ratio are determined by least squares determination (Figure 3 and Figure 4). The relationships are stated as follows:

   based on [9]. The solar insolation availability also depends on dust storms prevalent regionally and originates occasionally. This model serves the purpose of designing the solar arrays of the rover for experimental and subsystem power requirements.

   M motor

   M gear

   3.52 103 T

   mot

   gear

   0.0025.103.i

   (kg)

   (kg)

   (6)

   (7)

   where Tmot and igear are minimal required motor torque and gear ratio respectively. The mass of wheels and axles are calculated based on physical dimensions and assumed material properties. The material chosen here is a Titanium alloy with material density of 4506 kg/m3.

   1400

   Motor mass, kg (x 10-3)

   1200

   of the overall array mass. The relationships for determining power subsystem mass is given as follows:

   1000

   800

   M arrayblank et 6mcell Asa

   (8)

   600

   400

   Marraystruct

   0.82M

   arrayblanket (9)

   200

   0

   0 50 100 150 200 250 300 350 400

   Nominal torque, mNm

   Cbat

   e

   M

   bat

   bat

   (10)

   Figure 3 – Curve fitting plot of motor mass variation with nominal torque

   12

   Gear mass, kg (x 10-3)

   10

   8

   6

   4

   2

   0

   0 1000 2000 3000 4000 5000

   Gear ratio (no unit)

   Figure 4 – Curve fitting plot of gear mass variation with gear ratio

   A quasi-static system with kinematics based on RCL-E [7] is the suspension model considered here (Figure 2). The RCL-E design comprises two longitudinal bogies attached on the sides of the Warm Electronics Box (WEB) and one traverse bogie at the back. The contact forces between wheel and ground is necessary to be calculated in order to understand stability conditions of the vehicle on uneven terrain and slope climbing. The suspension should be tested for contact forces variation

   The mass of the array blanket (Marrayblanket) is dependent on the specific mass of solar cell and the area of solar array required. This mass is scaled by a factor 6 to account for supporting components. The area of the solar array needed is calculated based on energy requirements per experimental cycle of operation and the battery charge requirements of the rover. An experimental cycle means the duration in which a pre-defined set of science and operational activities are completed. The duration can vary anywhere between one or any number of sols.

   The area of solar array is defined based on the power requirements per experimental cycle as well as battery charge requirements. The solar arrays are designed to support nominal power requirements and the batteries are designed to suffice peak power requirements during operations. Additionally, batteries are the power source during egress from lander in case the solar arrays cannot be deployed immediately after landing.

   The area of solar array can be calculated as per Error! Reference source not found. and is given by,

   A Prover,nom

   during up, down and cross-slope motion. The interaction between wheel and ground is modelled as a point contact. The

   sa I

   mean

   cell

   • (1 FAC

   deg rad

   ) cos (1 FACtempeff

   ) FAC

   packing (11)

   wheels are assumed to be rigid with no elastic properties. The contact force at all six wheels can be statically determined by solving a set of force and moment equilibrium equations.

   Power module

   The area of solar array, as mentioned above is defined based on the power requirements per experimental cycle as well as battery charge requirements. The, the power requirements, Prover,nom is given by,

   The power system modelled here is a photovoltaic system or solar arrays that act as the primary power source. The solar arrays must generate sufficient amount of power to satisfy

   Prover,nom

   Ps/s,exp.cycle

   • Pbat ,ch arg e (12)

     subsystem load and battery recharge demands. Batteries supply energy during peak operations and during non-sunlight

     night night day day

     P T P T

     nom, persol nom, persol nom, persol nom, persol

     availability. Batteries should also maintain the temperature of

     rover systems during cold nights. Solar arrays consist of solar

     Ps/s,exp.cycle

     night

     T

     day

     (13)

     cells that are available in different technologies. They are responsible for converting solar energy to electrical energy by photovoltaic effect. Here GanP/GaAs/Ge triple junction cell

     Pbat,ch arg e T

     Cbat

     day

     technology with a conversion efficiency of 26.8% is assumed. The solar arrays are assumed inclinable or tiltable to suitable angles by means of actuators. This method enables the capability of tracking the sun to maintain maximum solar radiation reaching the cells during the entire sol. Likewise, the battery is assumed to be of Li-ion technology with an operational efficiency of 95%. Although solar cells suggest a primary element of the solar array, it may not contribute significantly to overall mass. The structure (Marraystruct), cover glass, interconnects and substrate forms the significant portion

     av., persol (14)

     Whereas the solar arrays are designed for nominal power requirements, the batteries are designed to suffice peak power as and when needed by the rover. Peak power requirements of each subsystem vary dependent on the operation and is also pre-defined. The batteries are the only source of power for rover egress from lander if the solar arrays cannot be deployed immediately after landing. If the solar arrays can be deployed, energy requirements for rover egress need not be accounted.

     Cbat

     Prover, peak

     DOD bat (15)

     Parametric modelling

     Owing to limited number of flight missions completed, the dataset primarily comprises information from studies during

     P Pnight T night

     Pday T day

     E

     early mission design phases of past missions. Therefore, it is

     rover,peak

     peak,persol

     peak,persol

     peak,persol

     peak,persol

     rover,egress(16)

     possible that the mass estimates in these missions are very optimistic. The data taken from missions from on-going rover

     Thermal Control module

     The thermal subsystem of a rover is modelled to use radioisotope heating units or RHUs for heating components in the Martian cold. In order to avoid excess heating and also if there is no need for transferring excess heat from hot to cold regions, heat has to be dissipated safely to the surroundings. A passive radiator that can be fixed to any safe location on the WEB enables this task. The WEB is the box component that houses the avionics, batteries and thermal systems. The thermal subsystem has to maintain a safe temperature inside the WEB to prevent overheating of sensitive systems. Other systems such as locomotion actuators are assumed to have built-in thermal control. The mass of the radiator depends on the volume of the radiator from which heat is liberated and the material density. This can be shown as,

     M A t

     studies may not reflect the final space-flying configuration. Some estimates did not include margins in their budgets. The data are hard to be corrected individually, and there exists a certain uncertainty in the model. With some level of uncertainty, it is attempted to analyse data heuristically to derive some relationships. Some data comes from completed space flown missions. Additionally, data are collected from JPLs Team X trade studies and the ExoMars mission studies. G.E.P.Box and K.B.Wilson introduced the method of Response Surface Methodology (RSM) in 1951[4]. Springmann and de Weck used the methodology to model system-level parameters as functions of design variables for deriving relationships for communication satellites [5] [6]. The idea of RSM is to use a sequence of designed experiments to obtain an optimal response. A mathematical model is derived that best fits the data collected. Let us assume the following model:

     rad

     rad

     rad rad (17)

     y f (x,) (23)

     where trad is the thickness. Additionally, a WEB thermal coating made of Kapton with emissivity of 0.49 is assumed.

     The heat dissipating capacity of the radiator is determined by the emissivity property of the material used for manufacture. Radiators are passive in nature and do not require active components for functioning. In addition, paints with emissive properties are also normally used surrounding the WEB to prevent entry of direct heat due to sunlight. To choose the type of paints and the radiator size, it is necessary to determine the amount of heat the rover would be exposed to as well as the temperature at which the WEB should be maintained. The amount of heat collected inside the WEB is the heat expelled by the RHUs, batteries and avionics, in addition to external heat collected from sunlight. The solar heat rate, Qsun depends on the projected WEB area in contact with sunlight at any given time. al is the albedo flux constant.

     where,

     x = [x1, x2, . . . , xk]T are independent, explanatory variables,

     = [1, 2, . . . , k ]T are unknown parameters, and

     is an (unknown) error term.

     The aim is to determine the least-squares estimate of . This can be obtained by minimizing the function,

     S( ) [ f (x, ) yu]2 (24) where,

     y u is the uth observed value of the response at the point xu1, xu2, . . . , xuk,

     u = 1, 2,,N.

     Qsun

     I max

     AWEB, proj

     (18)

     A measure to model uncertainty is the rms deviation that is the square root of the sum of residual squares divided by the

     Qalbedo AWEB al (19)

     number of observations. The rms deviation is given by,

     The amount of heat dissipated into the surroundings by the rover, is the summation of heat that can be dissipated by paint

     xrms

     S() / N

     (25)

     and the passive radiator.

     Qdissp Qpa int Qrad (20)

     Q A T 4

     Just like any other process of spacecraft design, it is thought

     that the overall rover mass is an important parameter to be estimated for establishing mission feasibility. It is thought that the rovers final mass depends on the total payload mass it carries. A relationship between rover mass and payload mass

     pa int

     Q

     pa int WEB

     A

     WEB

     T 4

     (21)

     is described here based on a power law model. It is defined as follows:

     rad

     rad rad

     rad

     rad

     (22)

     o is the Stephan Boltzmann constant.

     M rover 19.6M pl

     0.76

     (26)

     Wheel diameter is another variable that influences overall rover mass and design. The variation of the diameter of wheel with rover mass is quite linear. It is already known that desired improvement in rovers mean free path in rocky terrain can be achieved by increasing the wheel diameter. So far, rovers that have been designed for missions in the past, present and future, have proportionately improved in volume (size) and wheel diameter. A slightly better correlation between the data can be obtained if this variable is also introduced into the model as follows:

     1100

     1000

     900

     800

     Rover Mass [kg]

     700

     600

     500

     400

     300

     200

     Mrover

     5.4(5.3M pl

   • dwheel

     )0.76

     (27)

     100

     0

     0 20 40 60 80 100 120 140 160

     Payload Mass [kg]

     The diameter of wheel can range from very small size (~10 cm) to as much as 50 cm depending on the rover size and mass. Mass estimates from above relationship are shown with data points and 95% confidence levels in the Figure 5. It also represents minor modelling improvements over relating with one single variable, payload mass. The two mass models as described by Eqns. (4) and (5) are compared in Table 1.

     Table 1. Comparison of rover mass models before and after inclusion of

     wheel diameter

     Model	Variables	xrms, kg	95% CI, kg
     Eqn. (4)	MPL	138,98	±119,94
     Eqn. (5)	MPL, dwheel	138,94	±117,39

     Individual subsystem masses are best estimated as percentages of total rover mass. Data from rover studies are too sparse to provide a reasonable basis for using parametric relationships other thanpayload. The percentages of subsystem masses using existing data are compiled in Table 2.

     The mobility, power and radiator masses are estimated based on physics-based relationships. Each subsystem model is represented as a module that transfers data to other subsystem modules.

     Table 2. Typical subsystem masses as percentages of total rover mass

     Subsystem % Mrover (std. dev.)

     ACS	2 (2)
     Thermal Control	6 (3)
     Communications	5 (2)
     Command & Data Handling	6 (4)

     Cabling 7 (2)

     Figure 5 – Payload vs. total rover mass data plotted with 15% uncertainty. Rover mass expressed as a function of Mpl and dwheel and drawn as a least- square function

3. INTEGRATED MODELING AND OPTIMIZATION APPROACH

   An integrated modelling and optimization approach by searching rover design options in the feasible designspace, simultaneously optimize rover subsystems and selecting the best design is proposed. The model of the proposed approach to rover design is illustrated in Figure 6. Technology options and architecture options available for subsystem design should be initially chosen. This consists of choosing the type of solar cells (single, double, triple junction silicon cells etc.) or the type of batteries (Lithium ion, Nickel Cadmium, Nickel-metal hydride, etc.) to be sized. Also architecture options such as fixed or inclinable solar array should be chosen. In the next steps, a Genetic Algorithm uses models defined for capturing the rover vehicle and the searches for the best design solution by minimizing or maximizing specific objective. The models used are parametric or physics-based. While GA explores the designspace, several feasible design options are searched. The designspace is vast and not well defined and there are may be multiple feasible solutions. This is because of the parametric interdependency existing between various subsystems.

   Figure 6 – Design process model

   The primary factors that drive the design process such as mass, power and heat dissipation need form a closed loop of data interaction and interdependency between the subsystems. This can be illustrated picturesquely in Figure 7. This forms the basis of optimizing systems simultaneously.

   To derive system mass estimates, two possibilities exist. The first method involves finding masses of individual components from the bottom up for each system and summing up. This process is tedious and almost impossible. The other method involves using empirical data of systems from past rover missions and studies to derive mass estimation relationships. The drawback of this method is that dataset should be vast to reduce errors related to uncertainty in the parametric models.

   Science payload

   Warm Electronics Box

   Communication

   Pcomm

   Mpl

   information covering mass, power budgeting relationships for satellites [1]. However, models for rovers are not widely available in literature. Here empirical models are developed using data mined by a comprehensive literature survey.

4. VEHICLE SYSTEM OPTIMIZATION

   A case to design a rover concept that should carry scientific payloads of 50 kg in mass is considered to demonstrate the feasibility of the approach. Genetic Algorithm is chosen as the optimization technique because of the large number of design variables and serving the purpose of efficiently handling global optimization problems. GA works on the principle of life evolution process based on the Darwinian principle. Goldberg first introduced it as a meta-heuristic, numerical optimization technique [10]. In GA, a set of operations is performed on a population of encoded solutions known as individuals or chromosomes. Each possible solution is encoded as a set of genes. During each iteration (or

   Navigation

   Mweb

   Avionics

   Cabling

   Pavcs

   Pnav Qweb

   Mtherm

   Mobility

   Mpow

   Power

   Qpow

   Thermal Control

   generation), the individuals in the population undergo selection, crossover, mutation and fitness evaluation operations. The global search of design solutions followed in GA prevents convergence of solutions or trapped in the local optima. Unlike other optimization methods, GA does not require gradients or derivatives of the function to be minimized. Also it does not require initial guess values of the design variables. Only the boundary values to the designspace are needed. GA varies the values of design variables over a

   number of generations until satisfying a set of criteria. In GA,

   Figure 7 – Block diagram with dataflow between subsystems illustrating design interdependency

   The modelling process is composed of different modules each representing different subsystems. Each of the modules interact feeding in and back data. For conceiving this approach, parametric and physics based models of rover systems are essential. Mobility, Power and Thermal Control subsystems are modelled based on conventional physics. Other subsystems such as mass relationships are necessary to be developed for some of the other subsystems. Robotic spacecraft designers rely a lot on mass estimating relationships. This is because, detailed knowledge of mass down to all component of all assembles of various systems is needed and obtaining such a bottom-up estimate is nearly impossible. Such relationships exist in literature for orbiting satellites. Larson and Wertz have provided a suit of

   the fitness function represents the objective functions and constraints. A higher fitness indicates better solution. In the fitness function, the constraints are handled such that unfeasible solutions are penalized by a penalty factor. With each GA generation, the fitness of the population is improved. The best solution selected is the individual with the best fitness at the end of the last generation.

   Mission requirements definition

   The model requires mission level inputs from the user that informs the environment and vehicle operational conditions on Mars. They help in understanding the soil type that is described by Bekkers friction and cohesion properties [11]. Also the terrain conditions are specified to understand whether the rover should operate on slopes. Operational requirements define the nominal and peak power consumption of systems.

   Battery recharge duration available per sol is also specified. Temperature conditions to be maintained inside WEB should be also provided.

   vehicle base (x4), half-lengths of vehicle track (x5) and gear ratio (x6) and wheel width (x7).

   The optimization statement can be formulated as follows:

   minimize Mrover

   Environmental conditions

   The mission specifications are as follows: The rover is expected to operate in the 20° latitude. Areocentric longitude of Mars about Sun during landing is assumed to be 180°. The rover should be capable of climbing and descending slopes up to 35° and also safely traverse obstacles. The reference soil properties are assumed based on estimated soft soil properties by [12] Cohesive deformation modulus as 6800 N/mn+1, frictional deformation modulus as 210000 N/mn+2 and soil

   deformation component as 1. The assumed operational rock

   s.t.,

   0.01 Arad 2

   0.01 dwheel 1

   0.01 bwheel 1

   0.01 Tmot 500

   0.01 L0.5base 2

   M .V (a gsin )

   0.01 L0.5track 2 1 igear 1000

   g1: rover rover (T

   ) 0

   coverage for the terrain is assumed to be 15%.

   Operational conditions

   The rover should be capable of performing necessary science

   actuator

   g2: mfp + 15 0

   g3: Rcompaction 125 0

   mot dwheel

   mot

   mot

   activities allocated for one experimental cycle as well as complete data transfer and communications. Each

   g4: igear

   0

   60Vrover

   experimental cycle lasts for 12 sols. The operational conditions are provided as in Table 3.

   Now, two different optimization procedures applicable for mars rover designing will be discussed. One procedure involves minimizing the rover mass. The other procedure involves maximizing science returns requirement from the rover.

   	Nominal Peak
   Day power consumption per exp. cycle	Communication (W) Drilling (W) Science (W) Thermal control (W)	30 45 21 8		255 80 21 8
   Night power consumption per exp. cycle	Thermal control (Whr)	96		540
   Operational hours per exp. Cycle	Communication (hrs) Drilling (hrs) Science (hrs) Thermal control (hrs)	1 1 1 1		1 1 1 1
   	Battery recharge plan: [day 1, day 2, ..,day 12] (hrs)	[2, 2, 2, 1, 2, 2, 3, 3]	2,	1,	1,	2,
   	Temperature inside WEB (K)	293

   Table 3. Assumed operational requirements for one experimental cycle

   g5-g10: [1 FwheelA, 1 FwheelB, 1 FwheelC, 1 FwheelD, 1

   FwheelE, 1 FwheelF] 0 (uphill)

   g11-g16: [1 FwheelA, 1 FwheelB, 1 FwheelC, 1 FwheelD, 1

   FwheelE, 1 FwheelF] 0 (crosshill)

   p: QWEB Qdissp = 0

   For GA, each design variable is provided with a boundary limit. The other equality and non-equality constraints can be explained as follows: g1 specifies the motor power requirements. g2 specifies the mean free path requirements of the rover for a terrain with specific rock coverage. This is then

   used for calculating the mean free path. g3 restricts the compaction resistance suffered by the wheel in soft [13]. g

   4

   addresses the gear ratio requirements. g5-g10, g-g11 defines the static stability requirements by maintaining a positive wheel contact force of the vehicle in up-hill and cross-hill respectively. p limits the temperature to be maintained inside WEB.

   Designing for minimal mass

   In designing for minimal mass, the GA searches for a feasible solution in the designspace with the minimal total mass. The total mass is the summation of masses of all subsystems.

   11000

   10000

   9000

   8000

   Best fitness

   7000

   6000

   5000

   4000

   3000

   2000

   1000

   Mrover

   Mmob

   • M pow

   • MTC

   • M ACS

   • Mtelecom

   • MC&DH

   • Mcabl (28)

   0 0 200 400 600 800 1000

   Generation

   Figure 8 – Convergence history of best fitness

   where, Mrover, Mmob, Mpow, MTC, MACS, Mtelecom, MC&DH and Mcabl are the total rover, mobility (structures), power, thermal control, attitude control, telecommunication, command and data handling and cabling masses respectively. All 1,2,N solutions in the population are evaluated for their fitness and constraint values and assigned a relative merit to each solution.

   The design variables are namely, radiator area (x1), wheel diameter (x2), nominal motor torque (x3), half-lengths of

   1

   0.9

   1

   0.9

   Thermal radiator area, Arad

   0.8

   0.7

   0.6

   0.5

   0.4

   0 200 400 600 800 1000

   Generation

   (a)

   0.8

   Wheel diameter, d

   wheel

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0

   200 400 600 800 1000

   Generation

   (b)

   120

   100

   Motor torque, T

   mot

   80

   60

   40

   20

   0

   0 200 400 600 800 1000

   Generation

   (c)

   1.4

   Half lengths of vehicle base, L

   0.5base

   1.2

   1

   0.8

   0.6

   0.4

   0.2

   0

   0 200 400 600 800 1000

   Generation

   (d)

   2

   Half lengths of vehicle track, L

   0.5track

   1.8

   1.6

   1.4

   1.2

   1

   0.8

   0.6

   0.4

   0.2

   0 200 400 600 800 1000

   Generation

   (e)

   1

   0.9

   0.8

   Gear ratio, i

   gear

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0 200 400 600 800 1000

   Generation

   (f)

   1

   0.9

   0.8

   Wheel width, b

   wheel

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0.1

   0 200 400 600 800 1000

   Generation

   (g)

   Figure 9 – Convergence histories of: (a) radiator size, (b) wheel diameter size, (c) minimal required motor torque, (d) half-lengths of vehicle base, (e) half-lengths of vehicle track, (f) gear ratio, (g) wheel width size

   Table 4. Constraint values for final design solution

   g1	g2	g3	g4	g5	g6	g7	g8
   0.03	-1.46	-7.67	0	-30.93	-30.93	-30.93	-30.93

   g9	g10	g11	g12	g13	g14	g15	g16	p
   -281.17	-281.17	-217.02	-11.67	-217.02	-11.67	-114.35	-114.35	0.02

   The number of GA individuals or population size is set at 21. The crossover and mutation probability rates are set to 0.6 and

   0.01 respectively. The GA optimization is run for 1000 generations. The fitness function appears to converge on a final design after satisfying given constraints. The best fitness trend over each generation is illustrated in Figure 8 and the design variables in Figure 9. As seen, the design solution

   2

   1

   0.8

   Normalized value

   x1

   0.6 x2

   x3 x4

   0.4 x5

   x6

   selects a power configuration fitted with a 2.02 m solar array

   0.2 x7

   and a 246.85 Whr capacity battery. The wheel diameter and wheel width are 0.35 m and 0.55 m respectively. The wheel compaction resistance for this design solution is 117.32 N. The overall mass of the rover at the end of the optimization procedure is found to be 185.55 kg. The results of the design variables are listed in Table 5 and the constraints in Table 4.

   Table 6 lists the individual subsystem masses of the design solution. The full lengths of the vehicle base and track are 0.26 m and 0.31 m respectively. In a 15% rock covered terrain, a

   37.05 m mean free path performance is expected.

   From Figure 8, it can be seen that the fitness function trend is smooth. The GA performance can be additionally described by the population distribution at the 1000th generation. Figure 10 shows the normalized values of the design variables for the final generation. As seen, the individual values for each variable remain fairly equal. The population statistics of the 1000th generation is given in

   Table 7.

   Table 5. Best design solution after 1000 iterations Design variables Value

   Radiator area (m2) 0.34

   Wheel diameter (m) 0.35

   Drive motor nominal torque (mNm) 2.92

   Half wheel base length (m) 0.26

   0

   0 5 10 15 20

   Design/Individual

   Figure 10 – Population distribution at 1000th GA generation

   Table 7. GA final population properties

   GA property Value Best fitness 185.5

   Mean fitness 2744

   Median fitness 187.8

   Designing for maximal science returns

   The scientific return rae from a surface mission depends on rovers capabilities to move from one site to other, place on- board instruments on soil or rock samples, measure data and transmit back to Earth. In order to achieve higher science return rate from a mission, the mobility performance and capacity to remain mobile for most period of the time is essential. The only constraining factor is the electrical energy required to cover large distances and perform experiments. If the rover travelling at 1 m/s and the cumulative time of travel per sol is equivalent to duration of one sol, then the science rate is unity. The science returns ratio per sol, science,sol may be expressed as:

   V t

   Half wheel track length (m) 0.31

   Gear ratio 8067

   Wheel width (m) 0.55

   science,sol

   actual motion

   tsol ,day

   (29)

   Table 6. Mass breakdown of systems Subsystem Value

   Payload (kg) 50.0

   Mobility (kg) 14.26

   Power (kg) 24.96

   Thermal Control (kg) 19.68

   Other subsystems (kg) 76.65

   Total mass (kg) 185.55

   where tmotion is the total motion time by rover. This parameter indirectly relates to the rover time for conducting science activities in different sites.

   The design variables are namely, radiator area (x1), wheel diameter (x2), nominal motor torque (x3), half-lengths of vehicle base (x4), half-lengths of vehicle track (x5) and gear ratio (x6), wheel width (x7) and motion duration per sol (x8). Motion duration per sol is used as a design variable in order to maximize the amount of science returns from the mission.

   1

   0.9

   Thermal radiator area, Arad

   0.8

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0 100 200 300 400 500 600 700 800 900 1000

   Generation

   (a)

   1.3

   1.2

   Wheel diameter, d

   wheel

   1.1

   1

   0.9

   0.8

   0.7

   0.6

   0.5

   0.4

   0 100 200 300 400 500 600 700 800 900 1000

   Generation

   (b)

   1

   0.9

   0.8

   Motor torque, T

   mot

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0.1

   0

   0 200 400 600 800 1000

   Generation

   (c)

   1

   Half lengths of vehicle base, L

   0.5base

   0.8

   0.6

   0.4

   0.2

   0

   0 200 400 600 800 1000

   Generation

   (d)

   Half lengths of vehicle track, L

   0.5track

   1.6

   1.4

   1.2

   1

   0.8

   0.6

   0.4

   0.2

   0

   0 200 400 600 800 1000

   Generation

   (e)

   1

   0.9

   0.8

   Gear ratio, i

   gear

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0.1

   0

   0 200 400 600 800 1000

   Generation

   (f)

   1

   0.9

   Wheel width, b

   wheel

   0.8

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0 200 400 600 800 1000

   Generation

   (g)

   1.1

   1

   Mobility time per day, t

   motion

   0.9

   0.8

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0 200 400 600 800 1000

   Generation

   (h)

   Figure 11 – Convergence histories of: (a) radiator size, (b) wheel diameter size, (c) minimal required motor torque, (d) half-lengths of vehicle base, (e) half-lengths of vehicle track, (f) gear ratio, (g) wheel width size, (h) mobility duration per day

   Table 8. Constraint values for final design solution

   g1	g2	g3	g4	g5	g6	g7	g8
   0.09	0.86	-25.19	0	-0.22	-39.05	-39.05	-39.05

   g9	g10	g11	g12	g13	g14	g15	g16	g17	p
   -39.05	-378.9	-378.9	-296.8	-7.86	-296.8	-7.86	-152.33	-152.33	-0.17

   0.2

   0.18

   0.16

   0.14

   Best fitness

   0.12

   0.1

   0.08

   0.06

   0.04

   0.02

   0

   0 200 400 600 800 1000

   Generation

   Figure 12 – Convergence history of best fitness

   Population distribution after 1000 gen.

   1

   p: Qweb Qdissp = 0

   The constraints used here are similar to as used in the mass minimization problem (Section 3.2) except for total mass constraints. This assumption is prudent because larger structural components deliver better science returns and vice-versa.

   The GA crossover and mutation operators are set similar to as described in Section 3.2. The population size is set to be

   16. The GA is run for 1000 generations. It seems that the convergence for best design solution is reached as seen in the trend of the fitness function in Figure 12. The convergence histories of all design variables are shown in Figure 11.

   Table 9. Best design solution after 1000 GA iterations Design variables Value

   0.8

   0.6

   0.4

   x1

   2

   x2 Radiator area (m )

   x3

   x4 Wheel diameter (m)

   x5

   x6 Drive motor nominal torque (mNm)

   x7

   x8 Half wheel base length (m)

   0.44

   0.80

   75.71

   0.26

   0.2

   0

   0 2 4 6 8 10 12 14 16

   Design/Individual

   Figure 13 – Population distribution at 1000th GA generation

   maximize science,sol Payload (kg)		50.0
   Mobility (kg)		15.29
   0.01 Arad 2 Power (kg)		84.89
   0.01 dwheel 1	Thermal Control (kg)	19.82
   0.01 bwheel 1	Other subsystems (kg)	76.65
   0.01 Tmot 500 0.01 L0.5base 2	Total mass (kg)	246.65

   The optimization statement can be formulated as follows: s.t.,

   Half wheel track length (m) 0.30

   Gear ratio 1112

   Wheel width (m) 0.53

   Motion time per sol (hrs) 11.98

   Table 10. Mass breakdown of rover subsystems Subsystem Mass value

   0.01 L0.5track 2 1 igear 10000

   0.01 tmotion 12

   g1: M rover .Vrover (a g sin ) (T

   ) 0

   Some observations can be made of the design solution obtained after the optimization procedure. For producing sufficient power to sustain the rover motion, a trade-off case exists between solar array dimensions and the duration of

   actuator

   g2: mfp + 15 0

   g3: Rcompaction 125 0

   mot

   mot

   motion in the presence of mass constraints. In order to gain high science returns, this the rover should move at high speeds. It can be seen from Figure 12(c) that the GA selects duration of nearly 12 hours of motion per sol for the rover.

   g4: igear

   • (motor dwheel ) 0

   60Vrover

   To sustain this capability, the rover will have a 7.16 m2 solar array and a 777.44 Whr capacity battery. This means a

   g5-g10: [1 FwheelA, 1 FwheelB, 1 FwheelC, 1 FwheelD,

   1 FwheelE, 1 FwheelF] 0 (uphill)

   g11-g16: [1 FwheelA, 1 FwheelB, 1 FwheelC, 1 FwheelD,

   1 FwheelE, 1 FwheelF] 0 (crosshill)

   g17: Mrover 250 0

   maximal science returns of up to 0.18 can be derived from

   this rover. This corresponds to a rover velocity of 0.18 m/s. Furthermore, the wheel has a size of 0.8 m diameter and

   0.53 m width. This causes a compaction resistance of 99.81 N during motion on soft soil. The optimized suspension full

   lengths and widths are 0.52 m and 0.6 m respectively. The mean free path performance for tis suspension is estimated to be 108.27 m. The overall mass of the rover is 246.65 kg. The best design solution is summarised in Table 9. The constraints are listed in Table 8. The subsystem mass breakdown is given in Table 10.

   Table 11. GA final population properties

   GA property Value Best fitness 0.18

   Mean fitness 0.11

   Median fitness 0.14

   Figure 13 shows the normalized values of the design variables in the final generation. The individuals are evenly distributed which means after satisfying given constraints, a design convergence has been attained. The population statistics of the 1000th generation is given in Table 11.

5. SUMMARY

   Rover design trade-off studies during conceptual design phases should take into account of subsystem dependencies and performance expectations. In traditional practice, engineers tend to test available components and decide the final design solely based on trial and error. The concept of optimizing systems for users objectives and taking into account of subsystem interrelationships are generally not considered. Furthermore, conventional optimization techniques are limited in scope because of the large number of design variables and difficulty in finding global optima. In this paper, the author has described a GA-based methodology for optimizing mars rover designs. In particular two optimization approaches are highlighted with different objectives (1) mass minimization and (2) science returns maximization. For the same payload of 50 kg, the mass minimization procedure produced a design solution of

   185.55 kg mass. The science returns maximization procedure produced a rover with a science returns ratio of

   0.18. In both cases, GA optimization technique is used. The GA utilizes newly developed parametric mass models in combination with physics-based models for rover subsystem sizing. The proposed method has been found to demonstrate efficiency and satisfactory results. Integrated Genetic algorithms helped in identifying candidate designs and determine the best design trade-off. This approach has been found to be a sensible with reasonable results. This reported work lies within the framework of a computational tool development that helps in efficient design process of rover systems. The tool can be useful for identifying design concepts for future rover missions.

6. ACKNOWLEDGEMENTS

   The work reported in this paper was performed within the framework of work package Robotic Tools of Helmholtz Alliance project entitled Planetary Evolution and Life. The partial support provided by the Alliance is highly acknowledged. The authors would like to thank Dr. Bernd Schäfer for his advice provided during the course of this work.

7. REFERENCES

1. J.R.Wertz, W.J.Larson, Space Mission Analysis and Design (3rd edition), Springer Limited, London, 1999.

2. M.P.Golombek, A.F.C.Haldemann, N.K.Forsberg-Taylor, E.N.DiMaggio, R.D.Schroeder, B.M.Kakosky, M.T.Mellon, J.R.Matijevic, Rock size-frequency distributions on Mars and implications for Mars Exploration Rover landing safety and operations, Journal of Geophysical Research 108 (12), 2003.

3. B.Wilcox, A.Nasif, R.Welch, Implications of Martian Rock Distributions on Rover Scaling, Planetary Society International Conference on Mobile Planetary Robots and Rover Roundup, Santa Monica CA, 1997.

4. G. E. P. Box, K.B.Wilson, On the Experimental Attainment of Optimum Conditions (with discussion), Journal of the Royal Statistical Society, Series B 13(1), pp. 145, 1951.

5. O.L.de Weck, P.N.Springmann, D.D.Chang, A Parameteric Communications Spacecraft Model for Conceptual Design Trade Studies, 21st International Communications Satellite Systems Conference and Exhibit, 2003.

6. P.N.Springmann, O.L. de Weck, Parametric Scaling Model for Nongeosynchronous Communications Satellites, Journal of Spacecraft and Rockets, Vol. 41, No. 3, 2004.

7. V.Kucherenko, V.Gromov, I.Kazhukalo, A.Bogatchev, S.Vladkin, A.Manykjan, Engineering Support on Rover Locomotion for ExoMars Rover Phase A ESROL-A, Science & Technology Rover Company Limited (RCL), Report No. FR-1011/2004/RCL, 2004.

8. Maxon Motor AG, Maxon Motor Catalog, Program 09/10.

9. J.Appelbaum, G.A.Landis, Solar Radiation on Mars Update 1991, NASA Technical Memorandum 105216, 1991.

10. D.E.Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1989.

11. M.G.Bekker, Theory of Land Locomotion: The Mechanics of Vehicle Mobility, University of Michigan Press, 1956.

12. A.Ellery, N.Patel, L.Richter, R.Bertrand, J.Dalcomo, Exomars Rover Chassis Analysis & Design, Proceedings of the 8th International Symposium on Artifical Intelligence, Robotics and Automation in Space, Munich, Germany, 2005.

13. J.Y.Wong, Theory of Ground Vehicles, 4th edition, John Wiley & Sons, New Jersey, 2008.