How I Got Real Time + Big Workstation Mathematical Performance in a Single System

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2 Open-Source Electromagnetic Trackers and the Unusual Requirements for the Embedded System How I Got Real Time + Big Workstation Mathematical Performance in a Single System

3 6DOF Electromagnetic trackers Receiver is three concentric orthogonal coils. Transmitter is three concentric orthogonal coils. Electronics measures couplings between transmitter and receiver coils. Embedded processor calculates receiver position and orientation. 6DOF: six degrees of freedom, three position and three orientation. Distance out to one meter in usual designs.

4 5DOF Electromagnetic trackers Receiver is single coil. Transmitter is spread-out array of coils. 5DOF: five degrees of freedom, three position and two orientation. Orientation roll about receiver coil axis can't be measured. 5DOF trackers are not discussed further here.

5 Commercially-made coil trio The next slide shows a commercially-made coil trio. The three concentric orthogonal coils are wound one atop another, on a plastic cube about 1 cm on a side. These trios are also made by winding three coils of different sizes on mandrels, slipping the coils off the mandrels, and then nesting the coils together to form a trio.

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7 Homemade receiver coil trio The next slide shows my homemade receiver coil trio using three telecoils. Each telecoil is a ferromagnetic-core solenoid about 1 cm long and 2 mm diameter. Telecoils are normally used in hearing aids to pick up audio magnetic-field signals from telephone receivers or from loops in some concert halls.

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9 Homemade transmitter coil trio The next slide shows my homemade transmitter coil trio, built from six RF chokes forming three series pairs. Using pairs improves the concentricity of the three coils. Each of the six yellow chokes is about 1 cm in diameter. The plastic housing is 8 cm wide. Brown series-tuning capacitors are behind the coils.

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11 Homemade electronics block diagram The next slide shows a block diagram of my homemade electronics. Breadboard has enough functionality for algorithm development. Breadboard lacks features needed in a complete tracker system. USB is a USB-2.0 bulk-transfer interface. COMPUTER is the embedded processor. OPENIGTLINK or OpenIGTLink is an open-standard data format for sending position and orientation data over Ethernet.

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13 Homemade transmitter driver board The next slide shows my homemade dead-bug-style transmitter-driver board. A crystal oscillator drives a chain of counters. The counters drive the addresses of a RAM. The RAM contains waveform lookup tables. RAM data outputs drive audio DACs. DAC outputs are amplified to drive the series-tuned coils. One-ohm series resistors convert coil currents to ADC voltages.

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15 First breadboard tracker electronics The next slide shows my first tracker electronics. The driver board is hidden under the power supply on the left. The large blue PCB is a commercial evaluation board for an 8-channel 24-bit audio ADC. The input amplifiers are along the top edge. Most of the circuitry along the bottom and right edges, is for unused interfaces. The small green PCB in front of the large blue PCB, is the interface to the embedded processor. The colorful flat cable connects to the driver board, so the USB host can initialize the RAM table.

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17 Interface to the embedded processor The next slide shows the interface to the embedded processor. The large square chip is a 128Kx8 FIFO memory. The chip between the FIFO and the USB cable connector, is a USB2.0 device-interface chip. The chips to the left of the FIFO form the ADC clock synchronizer.

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19 FIFO buffers ADC data for non-realtime USB bulk transfers The serial outputs of the ADCs drive data inputs of the FIFO. The buffer comprises 128 Kibytes in the FIFO plus 2 Kibytes in the USB interface, for a total of 130 Kibytes. The ADCs output serial/parallel data, so one sample from all eight ADCs fills 64 bytes. The FIFO buffers up an entire dataset of 2048 ADC samples in real time. The USB chip then reads out the FIFO data at the USB host's pleasure. The USB host is the embedded processor for the tracker. The embedded processor needs to be fast, but does not need to be realtime.

20 Race problem in FIFO chip Watch out for races when using a FIFO chip. The chip has separate write and read clocks. However, the empty and full flags are affected by both clocks. To avoid race conditions, the write and read clocks' rising edges must never come within 5 ns of each other. I made the write clock the inverse of the read clock, and then synchronized the ADC serial data and clocks to the write clock. A race condition can lead to dropping a power of two data bytes. I drive one data bit input to the FIFO from a modulo-seven counter, so I can verify that this problem is not happening.

21 Choice of embedded processor For this presentation, I am using a Linux laptop computer for the embedded processor. However, I could just as well use anything that has a USB-2.0 host port, a C compiler, libusb(), enough double-precision floating-point speed, and an Ethernet port to output position and orientation data.

22 Tasks of the embedded processor Running the USB port. Checking for modulo-seven errors. Extracting Fourier components from the ADC data. Calculating coupling from each transmitter coil to each receiver coil. Calculating receiver position and orientation from coil couplings. Outputting position and orientation over Ethernet.

23 Fourier transform window with first sidelobe at -61 db and 42 db/octave rolloff of sidelobes w(t) = 0 for t > L/2 w(t) = (1/L) (a[0] +a[1]cos(2pi t/l) +a[2]cos(4pi t/l) +a[3]cos(6pi t/l)) a[0] = 10/32; a[1] = 15/32; a[2] = 6/32; a[3] = 1/32 Albert H. Nuttall, "Some Windows with Very Good Sidelobe Behavior", IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-29, No.1, February 1981, pages 84-91, Figure 10.

24 Position-and-orientation algorithm and accuracy-testing references Frederick H. Raab, "Quasi-Static MagneticField Technique for Determining Position and Orientation", IEEE Transactions on Geoscience and Remote Sensing, Vol. GE19, No. 4, October 1981, pages Direct-calculation algorithm. Frederick H. Raab, Ernest B. Blood, Terry O. Steiner, Hebert R. Jones, "Magnetic Position and Orientation Tracking System", IEEE Transactions on Aerospace and Electronic systems, Vol. AES-15, No. 5, September 1979, pages Iterative algorithm. Herbert R. Jones, Jr, "Non-Concentricity Compensation in Position and Orientation Measurement Systems, expired U.S.Patent 05,307,072. Figure 3 shows nonconcentricity compensation by subtracting correction from sensor data matrix. Christopher Nafis, Vern Jensen, Lee Beauregard, Peter Anderson, "Method for estimating dynamic EM tracking accuracy of Surgical Navigation tools", SPIE Medical Imaging Proceedings, Low-cost methods of testing tracker accuracy using known-flat surface.