Port-based Modeling and Simulation of Planetary Rover Locomotion on Rough Terrain

P. Poulakis(1), L. Joudrier(1), S. Stramigioli(2)

(1)European Space Agency, ESTEC/TEC-MMA

Keplerlaan 1 NL-2201 Noordwijk, The Netherlands

Email: Pantelis.Poulakis@esa.int, Luc.Joudrier@esa.int

(2)University of Twente EL/CE, P.O. Box 217

7500AE Enschede, The Netherlands Email: S.Stramigioli@utwente.nl

ABSTRACT This paper presents the implementation of a planetary rover simulation environment focused on locomotion aspects. A multibody, port-based modeling approach was taken combined with screw theory for the description of the kinematics and dynamics. Bond graphs are used as the modeling language. The contact model considers the interacting surfaces to be smooth and utilizes their differential geometry parameters. For the tracking of the wheel-terrain contact points, we utilize contact kinematic equations previously published in literature. The proposed wheel-terrain interaction model combines a Kelvin-Voigt viscoelastic system with Bekker terramechanics equations. The first simulation results of the developed system are presented, with main focus on a static stability case study for the Type-E candidate concept chassis for the ExoMars mission. 1. INTRODUCTION ESA’s ExoMars mission is the first flagship mission of the Aurora Exploration programme. Its aim is to characterize the biological environment of Mars for future robotic missions and successively human exploration. The scientific work of the mission will be carried out by a Mars rover comprised of several complex subsystems, the main ones being the payload, the locomotion subsystem and the avionics. Part of the work of ESTEC’s Automation & Robotics section is to provide support for the ExoMars mission. In this context rover concept chassis are built, avionics architectures are defined and implemented and various navigation and control algorithms are tested. The work presented here was carried out in collaboration with the Control Engineering group of the University of Twente. It describes the approach on the development of a simulation environment, based on the commercial tool 20-sim [1], for modeling and simulating planetary rover concept chassis on rough terrain. Since rovers are a key element to planetary exploration missions, with NASA’s Mars Exploration Rovers (MER) being very successful and with ESA’s ExoMars and NASA’s Mars Science Laboratory (MSL) planned in the near future, substantial work has been conducted by the scientific community on the development of rover simulation tools. Bauer et.al. [2] have developed a dynamic simulation tool specifically for the Type-E ExoMars concept chassis, called RCAST. In RCAST Matlab’s SimMechanics rigid-body dynamics engine is used together with AESCO’s AS2TM terramechanics module. Jain et.al. [3] and Sohn et.al. [4] describe the recent developments on the ROAMS simulation environment and the implemented wheel-terrain contact model respectively. ROAMS, developed at the Jet Propulsion Laboratory (JPL), is an overall mission simulators used successfully in the MER mission. It is being used as stand-alone simulator, as a closed-loop simulator with onboard software and as an operator-in-the-loop simulator with the main requirement to being to have real-time performance. Gibesch et.al. in [5] present different modeling methods of tyre-soil interaction, and use SIMPACK as the simulation tool for their models. Finally, Patel et.al. [6] describe the development of RMPET, a rover chassis evaluation tool, which utilizes Bekker theory to calculate several mobility performance parameters and a 3D simulator for Solidworks designs based on COSMOS/Motion. As this project is an ongoing work, the current status of the rover simulation environment is going to be described. The structure of the paper is the following. Section 2 describes the methodological modeling approach including an overview of the main tool, 20-sim. Section 3 begins with a description of the simulation system architecture and in respective subsections the modeled rover chassis, the contact detection model and the implemented wheel-terrain

In Proceedings of the 9th ESA Workshop on Advanced Space Technologies for Robotics and Automation'ASTRA 2006' ESTEC, Noordwijk, The Netherlands, November 28-30, 2006

interaction model are explained. The results obtained so far are presented in Section 4 consisting of a static stability case study of the Type-E concept chassis. A discussion of the design choices and the results follows in Section 5 and the paper concludes with the future work planned out for the project in Section 6. 2. METHOD The modeling approach taken for the rover locomotion system and its subsystems is that of port-based modeling. With physical systems, signal modeling is not suitable because there is always a bidirectional interconnection between subsystems, comprised of generalized forces and generalized velocities. When using signals only one of the variables is used in the interconnection, and this has to be taken into account in the derivation of the overall model. Using ports this restriction doesn’t exist and systems interact with each other through bidirectional ports that are simultaneously carrying the effort and flow variables, which define power. This approach offers a systematic way of modeling, giving a unified way to represent and interconnect systems from different physical domains, such as mechanical, electrical, hydraulic, thermal, etc. The most natural way to formalize this approach is through the modeling language of bond graphs introduced by Paynter [7] in 1961. Subsystems are defined using power-ports and interact with each other by exchange of energy through links called bonds. Therefore the model of a complete system is called a bond graph. The analysis of a model in this framework is obtained through causal analysis, which is employed to derive a simulation model, to verify the correctness of it and to get an insight to its dynamic behavior. Briefly, a bond has two collocated power variables, one effort (generalized force) and one flow (generalized velocity). The half arrow at one side indicates the reference direction of positive power flow. A stroke on either side of the bond defines the direction of computation, or, the causality: the effort signal travels in the direction of the stroke and hence the flow signal travels in the opposite direction. Making the bond graph causal is placing the causal stroke in a sensible way, so the explicit dynamic equations of the system can be derived correctly. Of the elements that comprise the bond graph notation we are going to refer here only to junctions. These are power continuous elements where they apply the constraint of one power variable being equal on all connected bonds to the junction. A 1-junction is constrained to have the flows on all bonds equal, and a 0-junction is constrained to have the efforts on all the bonds equal. Actually, the junctions are generalized Kirchoff laws. The above can be seen in Fig.1 (left) followed by a simple example of a spring-damper system and its bond graph representation (right). For more information on bond-graph theory see [7], [8]. A second element of our approach is the representation of complex dynamical systems, such as the rover chassis, in the port-Hamiltonian framework [9], where the state variables are positions and momenta. A more commonly used framework for the analysis of mechanical systems is the Lagrangian framework, where the state variables are positions and velocities. Although these frameworks are almost equivalent for mechanical systems, the port-Hamiltonian separates mechanical systems in energy exchanging subsystems, and variables are considered in pairs of collocated power variables. Especially when energy efficiency or passivity is important, which is the case with planetary rovers, the port-Hamiltonian representation can be very useful and can give a good intuition of the energetic structure of the system. It is clear that for the representation of port-Hamiltonian systems and their interconnection with other subsystems bond graphs are very well suited.

Fig.1. Bond graph junctions (left), example of a simple mechanical system and its bond graph (right)

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Screw Theory is the final tool we use in our approach in the modeling and simulation of planetary rover locomotion. Fundamental elements in Screw Theory are Twists, which represent in mechanics the velocity of a rigid body motion geometrically (i.e., coordinate-free).

(1) ⎥⎦

⎤⎢⎣

⎡= cb

a

cbacb

a vT ,

,, ω

The twist of Eq.(1) represents the motion of the body connected to frame aΨ with respect to expressed in framecΨ bΨ . Note that v is not the relative velocity of the origins of the coordinate frames, but the velocity of an imaginary point connected to frame a ,which at each instant coincides with the origin of frame b. The big advantage of twists over velocities is that every point on a rigid body can be described with the same twist but not the same velocity. Generalized forces acting on a body i and expressed in frame k, are defined through a Wrench as in Eq.(2), where F denotes the linear force and τ the momentum.

(2) ⎥⎦

⎤⎢⎣

⎡= k

i

kik

i FW

τ

The dual product of a twist and a wrench (when expressed in the same coordinate frame) is equal to the power flow. Twists and wrenches can be used in bond graphs as flow and effort variables. The only difference is that each power variable on a bond will be a 6x1 vector instead of a scalar. These bond graphs are called Screw Bond Graphs. For an extensive overview of Screw Theory for robotics see [10]. 2.1 Overview of 20-sim The main tool used for the development of the rover simulator is the modeling and simulation package 20-sim, which is a spin-off product of the research work at the Control Engineering group of the University of Twente. It is a port-based modeling tool and thus inherently supports the methods described in the beginning of this section. Systems can be modeled using equations, state space descriptions, bond graphs, block diagrams or iconic diagrams, where these representations can be fully coupled to create mixed models. Additionally 20-sim offers the possibility to build hybrid models from different physical domains, such as mechanical, electrical, thermal, etc. 20-sim’s 3D Mechanics Editor provides the environment to build 3D rigid body dynamic models and to define the means of actuation or interaction with the environment through power ports. The equation models derived from the 3D Editor give a port-Hamiltonian representation of the dynamics combined with the geometric approach of Screw Theory. Model simulation and analysis is performed by the Simulator, offering several tunable numerical integration algorithms and high customization in the representation of the results. 3D animation of the simulated models is available through the Animation toolbox, which is linked to the Simulator and offers various features for arranging the 3D representation scenery. Finally, 20-sim has an open interface to Matlab and offers C-code generation of the developed models. 3. SYSTEM ARCHITECTURE We first describe the overall architecture of the simulator and successively we present in more detail its key elements: the rover chassis models, the contact kinematics and dynamics and the wheel-terrain interaction model.

Fig.2. Architecture of the rover simulator

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3.1 Overview The overall system architecture can be seen in Fig.2. Each rover chassis model was built in the 3D Mechanics toolbox and then exported to 20-sim’s editor as an equation model. There it is connected with the models of subsystems such as the motors and the controllers. The overall main model is complete with the addition of the contact block, comprised of the contact tracking algorithm and the wheel-interaction model. The initial contact conditions are calculated through a call to a developed Matlab routine. As it will be presented in sub-section 3.2, the contact model is based on parametrized smooth surfaces. The parametrization mathematics are implemented in a Maple worksheet and exported as a code block into to 20-sim’s contact submodel. The complete model is executed within the Simulator and, together with the defined plots, a link to the Animation toolbox provides 3D visualization during simulation. The visualization scenery of the rover chassis is imported from the 3D Mechanics Editor and the representations of the terrain surfaces are created using the freeware mathematical visualization software JavaView [11]. The direction of the arrows in Fig.2 represents loosely the flow of information between the blocks of the system. 3.2 Rover Chassis Models Possible ExoMars locomotion subsystems have been proposed by the Russian company RCL in the frame of an ESA contract: the Type-D and Type-E concept rover chassis [12]. They are both based on the principle of using passive suspensions with parallelograms to allow close vertical displacement and normal force distribution between the wheels. Type-D, which has been built as the ExoMaDeR prototype, is using an averaging mechanism between the left and right suspension and has 6 wheels, all of which are driven and 4 are steered (front and back ones). The Type-E chassis is a simpler design with three independent suspension modules and also has 6 wheels, where all are driven and 4 are steered. Models of both chassis were built in the 3D Editor of 20-sim (Fig.3). The geometrical and inertial information of the suspensions were taken from the CAD design drawings. For the visualization, each part was exported as an STL file from Solidworks and then imported in the 3D Editor. The terrain would interact with the wheel through a 6 degrees of freedom (DoF) power-port, placed in the center of each wheel. On the same point a sensor was placed to provide the position and orientation of each wheel to the Contact Tracking submodel during simulation. 1 DoF power-ports were used for the steering and the driving of the respective wheels.

Fig.3. RCL Type-D (left) and Type-E (right) concept chassis in 20-sim’s 3D Mechanics Editor

3.3 Contact Kinematics and Dynamics The uneven terrain in our simulator is represented using smooth surfaces, oriented such that the normal is pointing outwards. We choose an orthogonal parametrization g(u,v) of the terrain surface S1 around a point with local coordinates (u,v). On this point p we attach a coordinate frame, called the normalized Gauss frame G

1Sp∈1(u,v) with the

following properties: the X-axis of this frame is the unit vector in the direction of the coordinate u, the Y-axis is the unit vector in the direction of v and the Z-axis is their unit normal vector (Fig.4 – left). Using the above we can derive differential geometry properties of the surface, namely the metric M1, the curvature K1 and the torsion T1 as defined by

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Montana in [12]. Modeling each wheel as a sphere or a spheroid with a parametrization f(θ,φ) for its surface S2 we apply the same procedure, acquiring a Gauss frame G2 for the wheel and the parameters M2, K2 and T2.

Fig.4. Gauss frame of a surface (left), shortest distance between wheel and terrain (right)

The relative pose of each wheel and the terrain, before or while they are in contact, is uniquely defined by six contact coordinates: the two local parameters (u,v) and (θ,φ), the relative angle a and the relative distance d, as shown in the right side of Fig.4., while the Z-axis of the Gauss frames of the surfaces is pointing towards each other. In order be able to apply a dynamic model for the wheel-terrain interaction we need to track the contact points while the rover is traversing the terrain. For that we use contact kinematics equations derived by Visser et.al. in [14], as a generalization of Montana’s equations in [13]. Once the initial conditions have been set properly, the model uses the differential geometry parameters of the terrain and the wheels (parametrization, metric, curvature and torsion) to track a set of contact points per wheel: one on the wheel itself and the respective one on the terrain. The advantage of the generalized kinematics equations is that they track the (candidate) contact points even when the wheel has detached from the surface. The only restriction this algorithm poses is that the relative curvature of the objects in contact has to be positive, so that only a single set of contact points exists always per wheel. The initial conditions of the contact model are derived by solving the minimization problem of calculating which contact coordinates give the shortest relative distance between the wheel and the terrain. The problem is visualized in Fig.4 (right) and can be formulated as follows: { } { }),(),(minmin 2,,,,,,

vugfPdvuvu

−+= φθφθφθ

(3)

In order to induce forces between the contact points in our simulations, we implemented the contact dynamics model architecture proposed by Visser et.al. [14], Stramigioli et.al. [15], Duindam [16] and which can be seen in Fig.5. We remind that in a screw bond graph the power conjugate variables are not forces and velocities, but wrenches and twists. The functionality of the model will be presented briefly for one wheel, since the same model runs for every wheel individually during simulation.

Fig.5. Screw bond graph form of contact dynamics model proposed by Visser et.al.

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One power port is assigned to the wheel and one to the terrain (of size 6x1). With the 0-junction the model subtracts the world twists of the objects giving their relative twist, expressed in the World frame. The MTF element performs a reference frame change for the twist which is now expressed in the wheel’s contact (Gauss) frame. The Wheel-Terrain interaction model is connected to the rest of the bond graph only if the objects are in contact and the switch is on. The goal of the structure of the system is that the interaction model is applied directly on the contact point of the wheel. 3.4 Wheel - Terrain Interaction Model The wheel-terrain interaction model is responsible for injecting forces between the interacting objects, in the normal direction and the tangential plane defined by the contact points. The forces acting on a driven wheel while it traverses soft soil can be seen on the left of Fig.6. The wheel carries a load W and is driven by a torque T. The wheel sinks into the soil by z and while it shears the soil, due to the applied torque, the soil applies a shear reaction force Fs, which provides the traction. Finally a normal reaction force Fn is applied in the center of pressure of the contact area, and a compaction resistance appears on the wheel axle because of the soil compression in front of the wheel Many methods have been proposed in literature for the calculation of the normal forces in a simulation environment. The reason for this is that since the vehicle is in contact with the ground on multiple points (six in our case), the problem is statically indeterminate. Actually, it is statically indeterminate if we accept that the system’s structure has infinite stiffness. This is never the case in reality, and nature “solves” the problem of static indeterminacy because physical objects have finite stiffness. The calculation of the normal force in simulation systems is required for two reasons: first to make the rover balance on the virtual terrain and second because it is the essential magnitude for any contact mechanics model. In our implementation we consider the center of pressure to be the wheel-terrain contact point. For the calculation of the normal forces we use a 1 DoF Kelvin-Voigt compliant system between each set of contact points in the direction of their Z-Gauss axes: GnGnn zdzkF &+= (4) where Fn is the normal force, kn is the spring’s stiffness, dn is the damping constant and zG is the displacement in the direction of the Gauss frames. Using compliance based methods introduces extra states to the system but they allow a unique solution to be found. Additionally since compliance methods rely on the system’s state, they require very short computational times in a multibody dynamic simulator. It is important to note that this is a technique to compute the normal force and not to model the physical effect of wheel sinkage into the soil. Thus we want to avoid large spring deflections that would affect the pose of the rover. In order to minimize this effect we make the virtual spring kn rather stiff, up to a point that it won’t introduce instabilities to the simulation or require large computation times to calculate its deflection. The forces acting on the tangential contact plane, which is the plane perpendicular to the normal direction, are the ones that provide traction to the vehicle. Our tangential contact model is also a compliant model combined with the terramechanics theory by Bekker [17] and Wong [18]. As shown in Fig.6 (right) the model is decomposed to a longitudinal and a lateral model.

As a torque is applied on the axle of the wheel, a shearing action is initiated on the soil at its circumference, in the longitudinal direction, making the contact points drift apart. The reaction force from the soil in this direction is computed using a 1 DoF Kelvin-Voigt compliant model shown in Eq.(5). In this equation FS is the shearing reaction force applied on the wheel, kS and dS are the spring-damper coefficients, and y is the longitudinal position of the wheel contact point with respect to the terrain contact point.

Fig.6. Driven wheel on soft soil (left), tangential contact model (right)

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ydykF SSY &+= (5) There is a limit to the shear stress that the soil can bear from the wheel and thus to the reaction force it can apply. This is when the soil has reached its maximum shear capacity and “soil failure” occurs, introducing slippage to the wheel. The magnitude of the shear capacity depends on the properties of the soil and is calculated in terramechanics theory by Eq(6). φtanmax nS FcAF += (6) with FSmax the maximum shear force, c and φ being soil properties (cohesion and internal friction angle respectively), A is the contact area of the wheel with the soil and Fn the normal force at the wheel contact point. In order not to go too deep introducing terramechanics equations here, we are going to describe briefly the algorithm of deriving the maximum shearing capacity in each simulation cycle. Initially the wheel sinkage is computed from Bekker’s theory which, apart from soil parameters, it depends on the normal force. Based on the wheel model of Fig.6 (left) we calculate the contact angle θ1 and successively the contact area A considering the wheel to be cylindrical. Finally the computed magnitudes are used in Eq.(6) to derive the shearing capacity of the soil. During each simulation cycle, if the force of the compliant model doesn’t exceed the maximum shearing capacity (computed in the same cycle), then the wheel is rolling without slipping and the longitudinal force between the wheel-terrain contact points is given by Eq.(5). If FY>FSmax then there is slippage and the longitudinal force between the contact points is FSmax. The terramechanics effects on the lateral direction of the wheel are much more complex and are subject of the ongoing work on the simulator. The current implementation makes use of the longitudinal FSmax in the lateral direction as well, together with a compliant model similar to the one described by Eq.(4). 4. RESULTS On the left side of Fig.7. the complete 20-sim model for the Type-D chassis and its locomotion subsystems can be seen. The submodels are connected via their power ports, where the double-lined power bonds in the model are carrying twists and wrenches as the power conjugate variables. Each wheel interacts with the terrain model and the obstacle models via the 6 DoF power port in its center. The forces applied on the wheel by the terrain and the obstacles are added via a 1-junction in the bond graph model.

Fig.7. Type-D chassis: Complete 20-sim model (left), simulation snapshot while negotiating obstacle (right)

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Under the rover icon in Fig.7.(left) lie the dynamic equations of the rover chassis, described in the port-Hamiltonian framework. Each Terrain and Obstacles model contains submodels for the contact kinematics, the contact dynamics and the interaction models of each wheel with the terrain and the placed obstacles respectively. The context and the interconnection of the models is identical for each wheel. The Steer and Drive subsystems contain models of the actual motors and gear boxes of the rover. Within the Propulsion block we define the input signals for the driving motors and inside the Navigation block we program the trajectory for the rover to follow by setting the steering signals. As an indication of the size of the model, The Type-D chassis model is comprised of 36 rigid bodies and 44 rotational joints. The complete 20-sim model of Fig.7 consists of 2203 equations, 50 constraints and 211 independent states. On the right side of Fig.8., a snapshot from an obstacle negotiation simulation run using the described model, can be seen. 4.1 Case Study: Static Stability of Type-E Concept Chassis The requirements for the ExoMars mission [19], state that the static stability limit of the rover should not be below 40º in any heading direction (downslope, cross-slope, etc.). Within the RCET Aurora R&D activity, results of which are published in [20], it was reported that the stability limit of the current configuration of the Type-E concept chassis is much lower than the requirements. Using the developed simulation tool at the Automation & Robotics Section of ESTEC, we were able to verify the stated problem through simulation experiments. Naturally for any conclusion to be solid either an analytical or experimental verification has to be provided. Nevertheless, a well-defined modeling approach and correctly set simulation experiments provide valuable insight. The scope of our experiments was to define the lowest terrain slope angle that causes static instability for Type-E. The experiments were conducted for the rover heading downslope, which intuitively seems to be a direction prone to stability problems because of the configuration of the left and right wheel modules. The rover chassis model is in 1:1 scale with the geometrical and inertial data taken from the CAD drawings. For the static stability simulation experiments the Center of Mass (CoM) was placed at 0.55m above the ground plane. In order to define the minimum terrain slope that the chassis tips over, we locked the wheels to prevent them from rolling. The wheel-terrain friction was set high, by stiffening the compliant model and eliminating the soil’s maximum shearing force above which the wheels slide. The compliant system supporting the rover in the normal direction of the plane was tuned to be critically damped. Several simulation runs with the terrain slope angle as the varying magnitude resulted that the static stability limit, for the presented configuration of Type-E chassis, is at approximately 27º slope while heading downslope. On Fig.8. (left) experiment plots are displayed. The top one shows a plot of the terrain slope angle, which naturally is constant, together with the pitch angle of the rover as the tip-over effect evolves. The lower plot displays the normal force on the wheel contact points during the same experiment. The way that the magnitude of the normal force evolves for each set of wheels shows that the rover is tipping over while heading down the slope. First the two back wheels loose contact, and as they do the load on the middle and front wheels increases. Successively the middle wheels detach from the ground uniformly, resulting to a load increase on the front wheels from the weight of the chassis, also evident by the increase of the normal force. On the right side of the figure, a snapshot of the 3D visualization of the same experiment can be seen. The frames that are visible under the wheels in the snapshot are the Gauss frames placed on the contact points 5. DISCUSSION In this paper the current status of a rover simulation environment, developed at the Automation & Robotics section of ESTEC, was presented along with a case study regarding the static stability of Type-E rover chassis. The current implementation of the simulator aims at testing rover locomotion subsystems on uneven terrain. Several rather innovative approaches in the field of dynamic systems modeling were incorporated, like port-based modeling, the Screw theory geometrical approach and the use of bond graph networks. These methods proved to be very efficient and to give a very intuitive representation of the system with emphasis on its energy structure. Additionally the developed simulator provides high customization features limited only by the intuition and modeling capabilities of the engineer. To that aspect the use of 20-sim as the modeling and simulation tool played an important

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role. Its inherent support of the port-based modeling method and screw theory along with the built-in toolboxes provided the possibility to use it as the main platform for the simulator.

Fig.8. Case study plots (left), Type-E chassis while tipping over at 27º slope (right)

The lack of a collision detection within 20-sim required us to implement such an algorithm for the wheel terrain contact. Two possible options were considered. The first was to apply a contact tracking model based on parametrized smooth surfaces and the kinematic equations developed by Montana and generalized by Visser et.al.. This method has been previously used in haptics applications. The second option was to include in the simulator a computational geometry algorithm specialized in the collision detection of polygonal objects moving in space. The former option was chosen for the current development phase of the simulator, as it could be implemented as a 20-sim model and would not require calls to external libraries. Although it proved to be an efficient and compact method, the implemented contact tracking model poses restrictions to the shapes of the terrain surfaces that can be used. Different smooth surface functions can be applied within the same model as contact patches but the relative curvature between the wheel and each surface has to be positive, in order for one set of contact points to exist always between the terrain and the wheel. Additionally if many contact patches are utilized the application becomes heavy since it has to track the global position of each wheel relatively to the contact patch in every iteration. 6. FUTURE WORK As the development of the simulator is ongoing the focus of future work lies mainly on the improvement and the validation of the wheel interaction model. The presented model in this paper incorporates the basic terramechanics effects combined with a Kelvin-Voigt compliant system for the tangent forces on the wheel-terrain contact plane. Our goal is to include more terramechanics effects in the wheel-terrain interaction and use experimental results to validate and tune our model. To this task a Single Wheel Testbed is going to be utilized which is developed by DLR under an ESA contract, and is expected to be delivered to the Automation & Robotics Lab very soon.

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In order to make the collision detection and contact tracking model more generic, a computational geometry algorithm is planned to be included in our simulation environment. The main reason lies in the fact that we need to be able to incorporate any arbitrary terrain shape to the simulator. This would allow us to make simulation experiments on exactly the same terrain profile that we perform the experiments with the rover prototypes. The terrain profile will be provided as a Digital Elevation Map (DEM) by special laser measuring equipment already acquired in the lab. In long term the work on the tool is aimed at extending it to be an overall rover systems simulator, and not solely for locomotion subsystems. The scope is to include and simulate several critical -to an exploration mission- subsystems and to simulate actual mission scenarios. 7. ACKNOWLEDGMENTS The authors would like to acknowledge the 20-sim development team and especially Frank Groen for his frequent support, and Martijn Visser for his valuable expertise on the field of contact modeling. Additionally the Head of the Automation & Robotics Section Gianfranco Visentin for the stimulating discussions and knowledge offer. Finally, the authors would like to thank Andre Schiele for the constant interaction and the valuable inputs throughout the work on the project. 8. REFERENCES [1] http://www.20sim.com [2] R. Bauer, W. Leung and T. Barfoot, “Development of a dynamic simulation tool for the ExoMars rover”, in 8th

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[5] A. Gibbesch, B. Schäfer, “Advanced modeling and simulation methods of planetary rover mobility on soft terrain”, in 8th ESA Workshop on Advanced Space Technologies for Robotics and Automation, Noordwijk, The Netherlands, Nov. 2-4, 2004

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Advanced Space Technologies for Robotics and Automation, Noordwijk, The Netherlands, Nov. 2-4, 2004 [7] H. Paynter, “Analysis and design of engineering systems”, M.I.T. Press, 1961 [8] G. Golo, “Interconnection of structures in port-based modeling: Tools for analysis and simulation”, PhD thesis,

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[13] D. Montana, “The kinematics of contact and grasp”, International Journal of Robotics Research, vol.7 no. 3, pp.17-32, Jun. 1998

[14] M. Visser, S. Stramigioli and C. Heemskerk, “Screw bondgraph contact dynamics”, in IEEE Int. Conference on Intelligent Robots and Systems (IROS), Lausanne, Switzerland, pp. 2239-2244, Sep. 30 – Oct. 4, 2002

[15] S. Stramigioli, V. Duindam, “Port based modeling of spatial visco-elastic contacts”, European Journal of Control, 2004

[16] V. Duindam, “Port-based modeling and control for efficient bipedal walking robots”, PhD thesis, University of Twente, 2005

[17] M. Bekker, “Introduction to terrain vehicle systems”, University of Michigan Press, Ann Arbor, USA, 1969 [18] J.Y. Wong, “Theory of ground vehicles”, 3rd ed., John Wiley & Sons, Inc., 2001 [19] ESA, “ExoMars Rover/Pasteur system requirements document”, Aurora/MW/KC/006.03 [20] S. Michaud et.al. “Rover chassis evaluation tools using the RCET”, in 9th ESA Workshop on Advanced Space

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