Coordinate Systems Specification

Transcription

1 Page: 1 of 22 ExoMars Rover DRD: ENG-32 CI CODE: E Prepared by: N Silva GNC Architect Date: Checked by: A R Davies GNC Architect R Slade Mechanical Architect Date: Approved by: J Clemmet Engineering Manager I Kilpin PA Manager Date: Authorised by: M Roe Project Manager Date: Export Control: This document has been rated for UK and EC export (no. 1183/2007 of 18Sep07). Rated at: 9E001 relating to 9A004 Rated by: N Silva This document may be exported from the UK to the EU without the need for an export licence. These technologies will require an export licence if exported out of the EU. Exporting to the US, Canada & Switzerland can be done under the CGEA No EU001. The current issue is the electronic copy available through EXOMARS CADM. All paper copies are for information only. Astrium Ltd 2010 Astrium Ltd owns the copyright of this document which is supplied in confidence and which shall not be used for any purpose other than that for which it is supplied and shall not in whole or in part be reproduced, copied, or communicated to any person without written permission from the owner. Astrium Limited, Registered in England and Wales No Registered Office: Gunnels Wood Road, Stevenage, Hertfordshire, SG1 2AS, England

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3 Page: 3 of 22 TABLE OF CONTENTS 1 INTRODUCTION Purpose Scope Summary of Defined Frames DOCUMENTS Applicable Documents Reference Documents Acronyms & Abbreviations COORDINATE FRAMES DEFINITION Mars Frames Mars Centred Mars Fixed (MCMF) Mars Local Geodetic (MLG) Rover and Unit Frames Rover Body (RB) Rover Local Geodetic (RLG) Pan & Tilt Unit (PTU) Pan & Tilt Rotating (PTR) Deployable Mast Assembly frame (DMA) Camera Measurement Reference Frames Sensor Frame (S) Optical Frame (O) Stereo Bench Reference Frame (SB) Generic Camera Frame (GC) Simulation and Analysis Frames Local Map Frame (LM) Local Map Indexing Dynamics Simulation Frame (DS) PANGU Simulation Frame (PS) PANGU Camera Frame (PC) Camera Image Frame (CI) LIST OF FIGURES Figure 1.2-1: Right-Handed Orthogonal Frame... 5 Figure 1.2-2: Right-Hand Grip Rule... 6 Figure 3.1-1: Mars Centred Mars Fixed Reference Frame... 8 Figure 3.1-2: Geocentric & Geodetic Latitude... 9 Figure 3.1-3: Mars Local Geodetic Reference Frame Figure 3.2-1: Rover Body Reference Frame Figure 3.2-2: Pan & Tilt Mechanism Coordinate System Figure 3.2-3: Pan & Tilt Rotating Reference Frame Figure 3.2-4: Pan & Tilt Rotating Reference Frame Angles Figure 3.2-5: DMA Frame Figure 3.2-6: Sensor and Optical frames Figure 3.2-7: Stereo Bench Reference Frame Figure 3.2-8: Stereo baseline Figure 3.2-9: Generic Camera Reference Frame Pinhole Model Figure 3.3-1: Local Map Frame Figure 3.3-2: Camera Image Frame LIST OF TABLES Table 1-1: Frame Summary... 6

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5 Page: 5 of 22 1 INTRODUCTION 1.1 PURPOSE This document provides the coordinate systems - or reference frames - for use within the design and development of the ExoMars Rover. 1.2 SCOPE This document provides the formulation and rationale of the reference frames or coordinate systems used in the design and development of the Exomars Rover, and anticipated in the operational interface of the Rover. It ensures the consistency of coordinate systems through a common reference source. The frames include those related to a reference on the surface of Mars, Rover Body and unit frames, plus frames associated with the simulation environment. Note that a number of the frames, especially the design, frames are currently simplified for the purposes of design cases for B2X and that a more rigorous definition of frames and their interfaces will occur as the EXM development continues. All frames are right-handed orthogonal (Figure 1.2-1) and rotations follow the right-hand grip rule (thumb follows the positive direction of the axis, fingers curl in the direction of positive rotation - Figure 1.2-2). Z O Y X Figure 1.2-1: Right-Handed Orthogonal Frame

6 Page: 6 of 22 +ve axis direction +ve rotation direction 1.3 SUMMARY OF DEFINED FRAMES Figure 1.2-2: Right-Hand Grip Rule Frame Abbreviation Mars Centred Mars Fixed MCMF Mars Local Geodetic MLG Rover Body RB Rover Local Geodetic RLG Pan & Tilt Unit PTU Pan & Tilt Rotating PTR Deployable Mast Assembly DMA Stereo Bench SB Generic Camera GC Local map LM Dynamics Simulation DS PANGU Simulation PS PANGU Camera PC Camera Image CI Table 1-1: Frame Summary

7 Page: 7 of 22 2 DOCUMENTS 2.1 APPLICABLE DOCUMENTS The following documents are applicable and are referred to as [AD xx] in the text: Document Number Issue Title / Author 2.2 REFERENCE DOCUMENTS The following documents are referenced for supporting information and are referred to as [RD xx] in the text: Document Number Issue Title / Author RD 01 EXM.MS.SSR.AI Mechanical and Thermal Design and Interface Requirements 2.3 ACRONYMS & ABBREVIATIONS The following acronyms and abbreviations are used within this document: AD ASU DMA ESA PTU RD RM RV TAS-I Applicable Document Astrium Ltd, UK Deployable Mast Assembly European Space Agency Pan & Tilt Unit Reference Document Rover Module Rover Thales Alenia Space - Italia

8 Page: 8 of 22 3 COORDINATE FRAMES DEFINITION 3.1 MARS FRAMES The main Mars frames are: Mars Centred Mars Fixed - a frame fixed with respect to Mars and thus rotates with Mars, and Mars Local Geodetic - a local Mars reference frame used by the RV GNC. It is not currently anticipated to fly an onboard ephemeris, due to accuracy, complexity and SW issues, and thus significantly cost, and so an inertial frame definition is not necessary. Ephemeris-based data required by the RV is intended to be supplied directly in the Mars Local Geodetic frame Mars Centred Mars Fixed (MCMF) The MCMF frame is related to the Martian reference ellipsoid. It is fixed with respect to Mars and thus rotates with the planet (See Figure 3.1-1). (The "prime meridian", or zero point of longitude, of Mars is defined as the longitude line that passes through the Airy-0 crater.) The origin O MCMF lies at the geometric centre of the Martian ellipsoid. The x-axis, X MCMF, lies along the intersection of the Martian reference meridian and the Martian reference ellipsoid equator. The z-axis, Z MCMF, lies parallel to the Martian rotation axis. The y-axis, Y MCMF, completes the orthogonal right-handed set. The MCMF frame will be used to define the latitude and longitude of the RV with respect to the Martian ellipsoid. Figure 3.1-1: Mars Centred Mars Fixed Reference Frame Geocentric coordinates are the familiar Cartesian x, y and z with respect to the geometric centre of the Martian reference ellipsoid. The geocentric latitude, φ', is also with respect to the geometric centre of the Martian reference ellipsoid and conversion between geocentric coordinates and longitude and latitude is easily calculated.

9 Page: 9 of 22 The geodetic latitude, φ, is the angle between the reference ellipsoid equator and the normal from a point on the reference ellipsoid. Because of flattening, the geocentric and geodetic latitudes are not the same (except at the equator and poles) (See Figure 3.1-2). The conversion between geocentric, geodetic, latitude and longitude are shown in TBD. b Semi-major axis a Semi-major axis Figure 3.1-2: Geocentric & Geodetic Latitude Mars Local Geodetic (MLG) The MLG frame is related to the local position of a point on, or close to, the Martian ellipsoid (See Figure 3.1-3). The origin O MLG is coincident with a defined point on the surface of Mars. The x-axis, of latitude). The z-axis, X MLG Z MLG The y-axis, Y MLG, lies tangential to the local geodetic horizontal in an eastern direction (i.e. parallel to lines, lies in the direction of the geodetic vertical, i.e. the negative gravity vector., completes the orthogonal right-handed set, and will lie northwards. For the purposes of the RV, the origin of the frame is initially defined to be coincident with the origin of the Rover Body frame, O RB, prior to the start of travel. During a travel sequence, this frame remains fixed with Mars, but becomes reset at the start of a new travel sequence. The rationale for this is that a travel sequence requires a stationary reference frame in which to measure position and coordinate navigation maps. The start of travel when the frame is reset may be at the start of each sol, or when new targets are generated (TBD).

10 Page: 10 of 22 Figure 3.1-3: Mars Local Geodetic Reference Frame The MLG frame is related to the longitude, λ, and geodetic latitude, φ. The conversion between geocentric, geodetic and MLG is shown in TBD. This frame is selected so that the Z axes of the MLG and Rover Body frame are parallel when the RV is on horizontal ground. Headings are then represented as rotations about the Z-axis of the MLG. When the RV is pointing East, both reference frames are co-aligned. 3.2 ROVER AND UNIT FRAMES Rover Body (RB) The Rover Body frame (coincident with the Rover Module Coordinate Frame) is fixed with the Rover and thus moves as the Rover moves (See Figure 3.2-1). It is defined in RD 01. The origin O RB is in the Lander baseplate upper surface and at the geometric centre of the Rover hold down points. The x-axis, The z-axis, terrain. X RB, lies towards the front of the Rover in the nominal direction of travel. Z RB, lies vertically upwards, antiparallel to the gravity vector when the RV is on flat, horizontal The y-axis, Y RB, completes the orthogonal right-handed set, and will lie to the left of the Rover.

11 Page: 11 of 22 +Z RB +Y RB +X RB Figure 3.2-1: Rover Body Reference Frame Rover Local Geodetic (RLG) The Rover Local Geodetic frame is a special case of a frame linking the local position on Mars with the Rover Body. It is used to enable commanding of targets in a frame with respect to the RV. The origin O RLG is coincident with O RB. The z-axis, Z RLG, lies in the direction of the geodetic vertical, i.e. the negative gravity vector. The x-axis, X RLG, is the projection of the RB frame X RB onto a horizontal plane passing though O RLG with Z as normal vector to the plane. RLG The y-axis, Y RLG, completes the orthogonal right-handed set, and will lie approximately along the projection of the RB frame Y RB onto the horizontal plane Pan & Tilt Unit (PTU 1 ) The Pan & Tilt Unit (PTU) coordinate frame is right-handed, orthogonal and has the origin at the top of the mast, just bellow the pan & tilt mechanism. The origin O PTM is defined as the intersection of the pan axis of rotation (along the horizontal about a vertical axis) and the tilt axis of rotation (along the vertical about a horizontal axis), where this intersection is assumed fixed with respect to the top of the mast (Figure 3.2-2). The origin O PTM is defined as the intersection of the tilt axis of rotation and a line which lies normal to both the tilt axis and pan axis. This intersection is assumed fixed with respect to the top of the mast (Figure 3.2-2) and allow for the eventually of the tilt axis and pan axis not intersecting. The z-axis, Z PTM, is parallel to the pan axis of rotation, and nominally lies vertically upwards. The y-axis, Y RB, is parallel to tilt axis of rotation, and nominally lies horizontally sideways. 1 Note: Formerly referred to as Pan & Tilt mechanism (PTM)

12 Page: 12 of 22 The x-axis, X PTM, completes the orthogonal right-handed set, and lies nominally horizontally. The origin is nominally a fixed translation from the RB frame, and the axes are nominally aligned to the RB frame with null pan & tilt; however the PTM frame can take into account possible deformations of the mast and knowledge alignment errors. Z PTM Y PTM X PTM Figure 3.2-2: Pan & Tilt Mechanism Coordinate System Pan & Tilt Rotating (PTR) The Pan & Tilt Rotating (PTR) coordinate system is right handed, orthogonal, with an origin coincident with PTM (i.e. a fixed translation in the Rover Body frame), but rotating with the direction of the Pan and Tilt (Figure 3.2-3). When the Pan and Tilt Mechanism has a zero pan and tilt, the PTR and the PTM frames are aligned. Pan and Tilt are then defined by the 321 Euler rotation, where pan is the first rotation (about the z-axis), tilt is the second rotation (about the y axis), and there is no possibility of rotation about the x-axis (Figure 3.2-4).

13 Page: 13 of 22 Figure 3.2-3: Pan & Tilt Rotating Reference Frame Tilt Z PTM ZPTR Pan Y PTR Y PTM X PTM X PTR Figure 3.2-4: Pan & Tilt Rotating Reference Frame Angles Deployable Mast Assembly frame (DMA) The DMA coordinate system is positioned at the base of the mast. The precise location shall be defined by the supplier with respect to the RB frame.

14 Page: 14 of 22 The origin is located at the base of the mast. The axes of the DMA frame are nominally aligned to the RB frame axes (within knowledge alignment errors). +Z PTU +X PTU +Y PTU +Z RB +Z DMA +Y DMA +X DMA +Y RB +X RB Figure 3.2-5: DMA Frame

15 Page: 15 of Camera Measurement Reference Frames Sensor Frame (S) The origin, O S, is located in the left top corner of the sensor (non-exposed pixels included) as shown in Figure The x-axis, X S, is parallel with the top edge of the sensor, pointing to the right. The y-axis, Y S, is parallel with the left edge of the sensor, pointing to the bottom. The z-axis, Z S, completes the orthogonal, right-handed set. z S o S optical centre o o lens z O optical axis x S Sensor plan (x,y) x O y O y S Figure 3.2-6: Sensor and Optical frames Optical Frame (O) The origin, O O, is located in the optical centre (principal point). The z-axis, Z O, is the optical axis. The x-axis, X O, is the axis orthogonal to Z O which projection on the sensor plan (X S OY S ) is parallel to the sensor rows (X S ). The y-axis, Y O, completes the orthogonal, right-handed set Stereo Bench Reference Frame (SB) The stereo bench reference frame (SB), where the terrain stereo reconstruction occurs, is attached to the cameras stereo bench and is defined as follows: The origin, cameras. O SB, is located at the middle of the segment linking the optical centres of the left and right The x-axis, The y-axis, The z-axis, X SB, is the projection of the left optical axis (Z O left ) on the plane perpendicular to Y SB.. Y SB, is in the direction from the right camera optical centre to the left camera optical centre. Z SB, completes the orthogonal, right-handed set. The SB frame is nominally a linear translation from the PTM frame, and the axes are like the PTM frame - also defined to be similar to the RB frame, when pan and tilt are null. (Note that alignments will not be exact due to misalignment errors etc.) The SB coordinate system is illustrated in Figure

16 Page: 16 of 22 Figure 3.2-7: Stereo Bench Reference Frame Left x S x S y S Right y S Stereo baseline Figure 3.2-8: Stereo baseline The Stereo baseline is defined as: For each camera, consider: The projection of the optical centre on the sensor plane (X S O Y S ) red spots in Figure The X S coordinate of each of the projections on the left camera sensor frame. The stereo baseline is the difference between the right and left coordinates as defined above. Figure does not shows relative rotations of the cameras, but the definition remains the same Generic Camera Frame (GC) The generic camera frame can be used for any camera on the RV. It is based on a pin-hole camera model (Figure 3.2-9). Each camera has an optical centre, an optical axis, and an associated image plane. The distance between the optical centre and the image plane is called focal distance, or focal length. The coordinate system is orthogonal right-handed and defined by: The origin is located at the optical centre ( c on Figure 3.2-9), corresponding to the pinhole in the model. The z-axis, Z GC, is parallel with the optical axis. The x-axis, X GC, is parallel with the top edge of the sensor, pointing to the right.

17 Page: 17 of 22 The y-axis, Y GC, is parallel with the left edge of the sensor, pointing to the bottom. The transformation between the image frame and the GC frame is simple. The position of the optical centre on the real cameras is located at a distance f ahead (i.e. towards the objects being viewed) from the sensor plane. Figure 3.2-9: Generic Camera Reference Frame Pinhole Model The nomenclature for the application of the Generic Camera frame on specific cameras on the RV is: Left NavCam frame (LNC) Right NavCam frame (RNC) Left LocCam frame (LLC) Right LocCam frame (RLC) This Generic Camera frame is compatible with the PANGU Camera frame. 3.3 SIMULATION AND ANALYSIS FRAMES Local Map Frame (LM) As shown in Figure the Local Map frame: is dependent on the x-y position and orientation of the MLG frame, the x, y and z origin of the RB frame and the nodesize parameter of the map; is coaligned with the MLG frame; has its x-y origin (but not z) in the MLG frame as an integer number of nodes, i.e., the x and y origin of the LM frame with respect to the MLG frame is defined as, L MLG,x = mw and L MLG,y = nw where w is the nodesize of the map such that m Z and n Z where Z is the set of integer numbers; has the z component of its origin in the MLG frame equal to the z component of the RB origin in the MLG frame i.e.: R MLG,z = L MLG,z, where R MLG,z is the origin of the RB frame, and L is the origin of the LM frame; and has its origin only half a nodesize away from the RB origin in x and y, i.e.:

18 Page: 18 of 22 L w w RMLG <,, MLG. j=row Y (MLG) axis Y (LM axis) Y (RB) Axis X (RB) Axis Figure 3.3-1: Local Map Frame Local Map Indexing The indexing of all maps is performed in the same manner such that for a given node at position [ x LM, y LM ] in the Local Map frame, where the map has I columns and J rows, the column and row of the node are found from, xlm 1 I i = floor( + ) + floor( ) w 2 2 Eq.1 j = ylm 1 J floor( + ) + floor( ) w 2 2 Eq.2 Where w is the size of a node and floor is the mathematical function that can be described fully as a function that returns the largest integral value less than or equal to x. Mathematically, it can be described by the following formula, where n is an integer, and Ζ is the set of integers (positive, negative and zero). floor( x) = max{ n Ζ n x} Eq.3 The inverse relation to move from a column and row index to a position of the centre of the node in the LM frame is, x LM = ( i I / 2) w Eq.4 y LM = ( j J / 2) w Eq.5 For these relations to be correct, a map must always have an odd number of columns and rows. Each map also has a parameter L MLG which is the position of its origin in the MLG frame so that the map can always be located in the MLG frame.

19 Page: 19 of Dynamics Simulation Frame (DS) The ExoMars Rover Dynamics Model (RDM) utilises reference frames defined in this document, including a simulation-specific frame. In addition it defines a Dynamics Simulation (DS) reference frame which is specified below. The DS frame is related to the simulation world. It is fixed with respect to the simulated gravity field and the simulated terrain. O The origin DS ODS lies at the centre of the input terrain (Note: In future releases this will probably be moved to a corner of the input terrain). The z-axis, Z DS, lies vertically upwards, antiparallel to the gravity vector. The x-axis, X DS, lies parallel to the terrain x axis. The y-axis, Y DS, lies parallel to the terrain y axis and completes the orthogonal right-handed set. Therefore, if the rover position is [ X DS = 0, Y DS = 0, Z DS = 0] and orientation is [roll = 0, pitch = 0, yaw = 0] then the Dynamics Simulation frame (DS) coincides with the Rover Body frame (RB) PANGU Simulation Frame (PS) The PANGU Simulation frame is related to the generation of simulated images in the PANGU tool. The PANGU Simulation frame is attached to the PANGU terrain. The origin and the axis defined in this frame are used by PANGU to set the positions of rocks, rover, or camera position. The coordinate system is orthogonal right-handed and defined by: The origin The z-axis, The x-axis, OPS Z PS X PS is placed in the centre of the Digital Elevation Map (DEM)., lies vertically upwards, antiparallel to the gravity vector., lies tangential to the local geodetic horizontal in an eastern direction. The y-axis, Y PS, completes the right-handed set and tangential to the local geodetic horizontal in an northern direction. The base DEM used to model the surface is a kind of bitmap image where the value of each pixel is the elevation of the pixel. This bitmap is placed so that the y-axis points the top of the image, and the x-axis points the right. As a consequence, if the dynamics terrain and the PANGU terrain are set correctly, DS frame and PS frame are coincident PANGU Camera Frame (PC) The PANGU Camera frame is attached to the camera. The model of camera used in PANGU is a classic pinhole model. The origin O PC is placed at the projection centre of the camera (as defined in the pin-hole model). The coordinate system is orthogonal right-handed: The z-axis, Z PC, is parallel to the optic axis of the camera, pointing towards the field of view. The x-axis, X PC, is parallel to the rows in the image, pointing towards the right edge. The y-axis, Y PC, is parallel to the columns in the image, pointing towards the bottom edge.

20 Page: 20 of 22 The default orientation of the PC frame compared to the PS frame is when the x y and z-axis match each other between the two frames. The camera position is defined by the position of O in the PS frame Camera Image Frame (CI) There is maybe a need for a common frame for all the images processed by the GNC algorithms. Regarding the existing photosensitive frame (PHS_F defined in GNC Design Hypotheses ), the camera image frame should be defined in a similar way: The origin The x-axis, OCI X CI The y-axis, Y CI is placed at the top-left corner of the image., follows the top edge of the image, pointing at the top-right corner., follows the left edge of the image, pointing at the bottom-left corner. The words top, left, bottom and right refers to the standard orientation used to display images (some confusion could appear with the PHS frame were the image plane is behind the optical centre, thus making the image up side down on the CCD). The units used for these axes will follow the pixels of the image. Let M be a point in the image, with the coordinates x M and y M. This point is located inside the pixel at column P and row n (row and column numbers starting from the same origin). Then: p 1 x n 1 y M M p n The figure below shows an example. O 1 CI X CI PC 1 Row : 2 Column : 3 Y CI Figure 3.3-2: Camera Image Frame

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22 Page: 22 of 22 DOCUMENT CHANGE DETAILS ISSUE CHANGE AUTHORITY CLASS RELEVANT INFORMATION/INSTRUCTIONS A - - Initial Issue. B - - Sensor frame definition added ( ) Optical frame definition added ( ) Updated Stereo bench reference frame ( ) Added definition of stereo baseline ( ) DISTRIBUTION LIST INTERNAL EXTERNAL ASU ESA CADM M Roe P Baglioni J Clemmet L Joudrier I Renouf B Boyes A Davies N Silva R Lancaster TAS-I CADM D Lachat A Allasio L Stenqvist F Ravera E Bean A Merlo R Slade M Bonnar Configuration Management