1. Navigation and Ancillary Information Facility NIF Using C-kernels to Capture Instrument Articulation June 28, 2002 Scott Turner (sturner@spice.jpl.nasa.gov)

2. Navigation and Ancillary Information Facility NIF Capturing Articulation... INS-82762_FOV_FRAME = ‘CASSINI_MIMI_LEMMS1’... FRAME_CASSINI_MIMI_LEMMS1 = -82762 FRAME_-82762_NAME = ‘CASSINI_MIMI_LEMMS1’ FRAME_-82762_CLASS = 3 FRAME_-82762_CLASS_ID = -82762 FRAME_082762_CENTER = -82 CK_-82762_SCLK = -82... SCLK_DATA_TYPE_82 = ( 1 )... Instrument-kernel Frame-kernel SCLK-kernel C-kernel SPK ID = -82762 ID = -82

3. Navigation and Ancillary Information Facility NIF The Cassini Frames Hierarchy J2000CASSINI_SC_COORD CASSINI_MIMI_LEMMS_BASE CASSINI_MIMI_LEMMS_ART CASSINI_MIMI_LEMMS1CASSINI_MIMI_LEMMS2 C-kernel Based Fixed Offset C-kernels communicate to the frame system what frame they are relative to, thus multiple paths through the frame tree can and do exist. While multiple paths may exist, at any epoch, the C-kernel priority system preserves the tree structure.

4. Navigation and Ancillary Information Facility NIF Multiple Paths, Segment Priority and Kernel Loading Use furnsh_c to load all SPICE kernels, including CK, SPK, IK, FK, and SCLK files. The standard SPICE paradigm regarding precedence is: “The last segment of the last kernel loaded has the highest priority”. Load nominal, background, or predict content first. –Background Orientation (Resting position of Articulating Instruments, etc.) –Any “fixed” offset C-kernels designed to support the articulation branch of the frame tree. Loading kernels in the wrong order can, and often will, result in retrieval of incorrect pointing or SPICE errors due to missing data.

5. Navigation and Ancillary Information Facility NIF Example: Properly Loaded CKs time File #1 “Fixed Offset” INS to ART File #2 “Resting Position” ART to BASE File #3 SEG#1: ART to BASE SEG#2: ART to BASE File #4 SEG#1: INS to SC SEG#2: INS to SC BA HIGHEST LOWEST

6. Navigation and Ancillary Information Facility NIF Example: Improperly Loaded CKs time File #1 “Fixed Offset” INS to ART File #2 “Resting Position” ART to BASE File #3 SEG#1: ART to BASE SEG#2: ART to BASE File #4 SEG#1: INS to SC SEG#2: INS to SC BA HIGHEST LOWEST

7. Navigation and Ancillary Information Facility NIF Creating C-kernels (1) The quaternions in a C-kernel encapsulate a C- matrix that rotates vectors from a base-reference frame to the “instrument” frame: V instrument = [C] V reference There are several types of C-kernel segments: –Type 1 - Discrete Pointing –Type 2 - Constant Angular Velocity –Type 3 - Linear Interpolation (*Commonly Used) –Type 4 - Chebyshev Polynomials There are several “styles” of quaternions that are in use in the space science community. SPICE style quaternions are what must be placed in a C- kernel.

8. Navigation and Ancillary Information Facility NIF Creating C-kernels (2) Including angular rates in C-kernel segments is usually better than omitting them. –spkezr_c ( “OBJECT”, et, “CASSINI_CDA”, “LT+S”, “CASSINI”, state, &lt ); –Any other computations involving state transformations require angular rates. –“Construction” of angular rates from quaternions or other rotational sources is not particularly difficult. Lastly, consider including a properly subsetted version of the relevant “fixed offset” CK segments in your predict C-kernels.

9. Navigation and Ancillary Information Facility NIF Creating a Type 3 C-kernel The following code fragment illustrates the creation of a type 3 C-kernel with a single segment. ckopn_c ( filename, “my-ckernel”, 0, &handle ); /* Insert code that properly constructs the sclkdp, quats, avvs, and starts arrays. */ ckw03_c ( handle, begtim, endtim, inst, “reference_frame”, avflag, “segment_id”, nrec, sclkdp, quats, avvs, nints, starts ); ckcls_c ( handle );

10. Navigation and Ancillary Information Facility NIF Anatomy of the ckw03_c Call (1) handle - file handle for the newly created C- kernel. begtim, endtim - start and stop time in SCLK ticks for the segment. inst - instrument ID code for the C-kernel. This can be obtained using: –namfrm_c ( “CASSINI_CDA”, &inst ); ref - name of the reference or base frame as known to SPICE. In the case of articulating instruments on Cassini: “CASSINI_ _BASE”. avflag - a SpiceBoolean indicating whether to include angular velocity in the segment. segid - a string identifying the segment. It should be less than 40 characters in length.

11. Navigation and Ancillary Information Facility NIF Anatomy of the ckw03_c Call (2) nrec - number of records in sclkdp, quats, and avvs sclkdp - monotonically increasing list of times in SCLK ticks that identify when quats and avvs were sampled. quats - a list of SPICE quaternions that rotate vectors from the ref to inst frames. –m2q_c ( C_matrix, quaterion ); avvs - angular rate vectors expanded in the ref frame. starts - a list of SCLK ticks indicating the start of interpolation intervals. They must correspond to entries in sclkdp. nints - number of entries in starts.

12. Navigation and Ancillary Information Facility NIF Converting an Angle Time-Series Suppose you have a time series of angles ( angles ) for a Cassini articulating instrument and with epochs ( epochs) in ephemeris time. Converting them to quaternions and ticks is as easy as: for(k=0; k<nrec; k++) { sce2c_c( scid, epochs[k], &sclkdp[k]); axisar_c( zaxis, -rpd_c()*angles[k], rotmat ); m2q_c ( rotmat, &quats[k][0] ); } where zaxis is ( 0, 0, 1 ) and scid is -82 for Cassini.

13. Navigation and Ancillary Information Facility NIF Approximating Angular Rates One of the easiest ways to accomplish this is to assume a constant rotation rate between subsequent quaternions: for(k=0; k<(nrec-1); k++ ) { q2m_c ( quats[k][0], init_rot ); q2m_c ( quats[k+1][0], final_rot ); mtxm_c ( final_rot, init_rot, rotmat ); raxisa_c ( rotmat, axis, &angle ); sct2e_c ( scid, sclkdp[k], &init_et ); sct2e_c ( scid, sclkdp[k+1], &final_et ); vscl_c ( angle/(final_et-init_et), axis, &avvs[k][0] ); } Lastly, simply copy the ( nrec-1 ) value of avvs into the last element of avvs.

14. Navigation and Ancillary Information Facility NIF A Few Words of Caution Constructing angular rates in this fashion assumes that between subsequent quaternions no more than a 180-degree rotation has occurred. In short raxisa_c chooses the smallest angle that performs the rotation encapsulated in the input matrix. Other techniques exist, including differentiating quaternions. Care must be exercised when taking that particular approach however. NAIF has a tool, msopck, that creates C-kernels from text input files listing quaternions, Euler angles, or rotation matrices tagged by UTC or SCLK times. It can be useful for validating C- kernel production code.