Robotic Tracking and Formation Movement using Ultrasonic Trilateration

Transcription

1 Robotic Tracking and Formation Movement using Ultrasonic Trilateration Chris Johnson, Mike Irvine, Saeid Azimi Moghadam, David Bauslaugh Abstract This document outlines the development and implementation of a robotic formation as a culminating, final year, design project. The research was primarily focused on robotic formations using trilateration: the location of an unknown point using three distances and three known points. The trilateration algorithm was implemented by combining radio communication and ultrasonic transmission, effectively exploiting the time delay between the signals, and accurately measuring distance and direction to a master robot. T I. INTRODUCTION his project will utilize analog, digital, and software systems to develop a swarm of inexpensive robots that interact with one another and behave as a single cohesive unit. A remotecontrolled master robot will serve as a human interface and ultimately as a leader for the swarm. Ideally, the slave robots will accompany the master by maintaining specific individual positions within a defined swarm formation. The robots will communicate over a 2.4 GHz wireless radio while detecting and calculating position using sensors at three distinct points on each robot, a process called trilateration. The main robot board will have two distinct functionalities: master mode and slave mode. While in master mode the Main Control Board will communicate This work was supported in part by McMaster University, the faculty of Electrical Engineering, and Dr. Steve Hranilovic. C. Johnson is a graduating student at McMaster University in Electrical Engineering and Management. M. Irvine is a graduating student at McMaster University in Electrical Engineering and Management. S.A. Moghadam is a graduating student at McMaster University in Electrical Engineering and Management. D. Bauslaugh is a graduating student at McMaster University in Electrical Engineering and Management. directly with a handheld receiver. In slave mode, the Main Control Board will communicate with the master robot and perform trilateration calculations. In both modes the Main Control Board will also communicate with the Motor Control Board. The Motor Control Board accepts a distance and direction value from the Main Control Board and computes the appropriate output for the left and right motor. The motor speed is controlled by pulse width modulation performed on the Motor Control Board. This combination of master/slave behavior allows a single node for human contact that can control a potentially limitless group of robots. II. LOCATION MECHANISM USING TRILATERATION With robots moving autonomously in a swarm, the ability to accurately locate other units is paramount. From preliminary research on existing robotic swarms, trilateration was selected as the ideal method for robot location. Trilateration is the process of locating a point using the coordinates of three known points, and their respective Euclidian distances from the unknown point. The method uses individual distances between the known and unknown points to construct a network of intersecting circles. The calculated intersection of the circles is the location of the uknown point. Figure 1 shows the process of trilateration in its graphical form. To simplify the calculations that would eventually be ported to relatively low-power, mobile devices, a constraint was placed on the location of the known trilateration points. The center of the robot was set, computationally, as the origin, with the three known sensor points arranged to form an orthogonal basis, with each sensor having only a single non-zero x or y component

2 Equations (1) and (2) show the simplified solutions for locating an unknown point, P(x,y), that is distance a, b, and c from three known points [1]. Figure 1: Solving the location of point P(x,y) using calculated distances a, b, and c, alongside a known, fixed distance, d. (1), (2) The trilateration calculations will undoubtedly come from noisy sensors, and as a result, extra care must be taken to minimize the sensitivity to error. The most easily controlled variable in the trilateration calculation is the fixed distance between trilateration sensors. Several trial simulations were run to chart the effect of increasing and decreasing fixed sensor distance. Figure 2 shows the simulation results, with errorprone calculated positions converging on the actual robot position as long as sensors are placed more than 0.2m apart. A. Ultrasonic Channel Model The chosen method for distance measurement was a combination of radio frequency (RF) communication and ultrasonic transceivers. Alongside an RF pulse that travels almost instantly, the time delay inherent to the speed of sound gives a predictable, easily-implemented method of measuring distance. Figure 2: Variance in calculated vs. actual position when sensor separation distance is changed

3 The distance measurement is a function of the time delay associated with the ultrasonic pulse traveling through air. Figure 3 shows the time delay mechanism that makes distance measurement possible with ultrasonic waves. A parabolic cone allows all incoming planar sound waves to be collected to a single point, the focal point of the parabola. The converse is true for transmission, where the single ultrasonic source is dispersed into a planar direction. Figure 4 shows the dispersion characteristics of a parabolic cone on incoming and outgoing sound waves. Figure 4: Parabolic cone used for ultrasonic dispersion and collection [1]. Figure 3: Demonstration of distance measurement. RF pulse signals timers to start at the green line and transmission (red wave) begins. As the wave travels through air, it reaches each receiver at different times (blue waves). The delays obtained from each ultrasonic receiver are multiplied by the speed of sound (taken as m/s) to yield the distance from ultrasonic transmitter to receiver. In order to calculate the distance and direction to a robot, regardless of their orientation or location, the traditional ultrasonic transceiver had to be modified. In many cases, sensors labeled omnidirectional had a teardrop dispersion pattern of no more than 45 off the centre axis. A key requirement to the successful implementation of ultrasonic distance sensing, and ultimately trilateration, was the dispersion of an ultrasonic signal into a plane. This dispersion was accomplished with a parabolic cone defined in (3) [1]. 500, (3) , After fabricating the cones from two part epoxy, a single ultrasonic receiver/transmitter pair was tested for accuracy and channel characteristics. % of values 12% 10% 8% 6% 4% 2% 0% 2% Error in Distance Measurement (cm) Figure 5: Frequency of errors in ultrasonic distance measurement. The sensors exhibited an error in linear distance measurement of about +/- 6 cm centered around 2 cm. Theoretically, an overshoot in distance measurement would occur in the scenario where a timing delay was artificially lengthened. This timing delay that caused a 2 cm offset in distance measurement was attributed to the delay associated with overcoming the inertia associated with the ultrasonic transmitter/receiver cone. The - 3 -

4 delay associated with the sensor inertia was accounted for and mitigated in software. B. Swarm Simulation Environment In order to better understand swarm dynamics, a MATLAB environment (Figure 6) capable of realtime behavioural analysis was developed. The environment implemented the following features: variable swarm size variable formation shape variable robot speed (linear and rotational) simulated measurement errors based on measured error data real-time robot movement display real-time robot tracking (historical path tracing of user-defined length) The environment was implemented to be as complete and flexible as possible for use as a development and decision tool. All major algorithm decisions from formation configuration, to motor control, to trilateration were executed first in the simulation environment and adapted for implementation on the robot hardware. links. Without communication between all three major components, the robot is unable to function in a normal manner. A. Communication 1) Serial Peripheral Interface (SPI) Bus Communication between the radio and the Main Control Board was accomplished with the Serial Peripheral Interface (SPI) Bus. SPI is a master slave protocol where the master can talk to multiple peripherals, but the slaves do not normally communicate with each other. SPI uses three control signal pins, plus one extra pin per device that acts as an enable. The control signals that are used in the SPI protocol include Clock (SCK), Serial Data Out (SDO) or Master Out Slave In (MOSI), Serial Data In (SDI) or Master In Slave Out (MISO). To see the direction of communication refer to Figure 7. Master CSN SCK SDO SDI Slave Figure 7: SPI communication connection diagram. Figure 6: MATLAB simulation environment screenshot. III. HARDWARE IMPLEMENTATION The robot hardware implementation consists of three major components: the Remote Control Board, the Main Control Board, and the Motor Control Board. The remote is responsible for sending wireless radio commands from a human operator to a master robot. The Main Control Board handles trilateration calculations and the Motor Control board hanles the conversion from distance and direction of travel to outputs to the motor. The most important part of the hardware implementation comes from the communication The Clock signal is controlled only by the master. During a transmission, the desired device enable, controlled by the master is set active (usually low), and the master starts the clock. The device and master exchange data one character at a time until the transmission is complete, when the device enable is disabled (usually set high). A diagram of SPI communication with a Nordic semiconductor radio peripheral is shown in Figure 8. In this diagram the master is sending a single character to the slave and the slave is responding with multiple characters back to the master. The CSN signal (enable) is set active(low) for the entire duration of the communication Note that the clock is still controlled by the master even after it has finished sending data

5 Figure 8: SPI timing diagram [2]. 2) Inter-Integrated Circuit (I 2 C) Bus Communication between the Main Control Board and the motor control board was done using the Inter Integrated Circuit (I 2 C) communication protocol. I 2 C is also a master slave protocol but uses a bidirectional data channel. It also does not have an enable pin for each of its slaves, reducing the number of required communication wires to two. The signals are Serial Clock (SCL), and Serial Data (SDA). These signals are shared to create a bus between multiple devices. With the I 2 C protocol, multiple masters may be established giving each device the ability to communicate with any other device on the I 2 C bus. To differentiate between devices, each slave has a distinct address that is accessed by the current master. The structure of an I 2 C command is a seven 1 bit address followed by the data to be sent to the device. The address is left shifted by one, and a control is shifted into the least significant bit. The control bit is a zero if the master is writing to the slave or one if the master is going to read from the slave. Like SPI, I 2 C transmits one character (eight bits) at a time. Master SCL SDA SDA SCL Device 0 SDA SCL Device 1 Figure 9: I 2 C connection diagram. 1 A 14 bit I 2 C address can also be used. SDA SCL Device 2 SDA SCL Device 3 I 2 C Bus 3) Wireless Protocol For inter-robot communication and Remote Control Board commands to the robots, a wireless protocol was developed. A simple command structure was implemented to determine the action each robot had to take after their radio interrupt service routine was activated. The structure is a single character followed by a variable-length argument list of data. A table of instructions is shown in Table 1. For identification control, each robot was dynamically assigned a different ID when it became active and joined a formation. To ensure that the robots could always talk to at least the master a standard master radio ID was used. The wireless protocol uses the following bit pattern: ID command param[25]...param[0] 5 Bytes 1 Byte 26 Bytes Table 1: Wireless Radio Command Table Cmd. Param. Bytes Description p 2 This sends a desired percentage of left and right motor power. t 0 This command has the robot perform trilateration (receiver side) c 0 This command is used to configure the trilateration delay from the radio, a fixed point is used to set delay values. m 32 This commands comes from the master device to the slave device, the data bits contain - 5 -

6 more information. s 32 This command comes from the slave to the master device the data bits contain more information. f 1 This command changes the formation a 0 This command announces that a robot has just become active and is answered by the master e 1 This command either establishes or relinquishes control as the master. B. Remote Control Board Figure 10: Remote Control Board render. The Remote Control Board was the first circuit designed; it was created as a launch point for all of the other circuit boards that would be created. As a result, locations for many expansion devices were incorporated into the design but were not implemented (see Appendix A: Schematic diagrams). The Remote Control Board is driven by the a 28-pin Microchip PIC 18F Microcontroller. This devices was chosen because it has a built in SPI bus, as well as a separate UART, with sufficient pins for other basic input output devices. The devices that were implemented included the Nordic Semiconductor Radio (nrf24l01+), four input pushbuttons, the on-chip UART, and output debugging LEDs. The choice of these devices allowed for the initial coding and debugging of the Wireless Radio (nrf24l01+) over the SPI protocol using a second controller board. By doing this, the radio communication protocol was established and a custom radio library was written for future use with the Microchip family of microcontrollers. The Remote Control Board operates in a standby mode, it continuously checks both the input peripherals (selection buttons), and the radio Interrupt Flag Pin, which is asserted when data has arrived and is ready to be read. If any of the buttons are pressed then the radio sends to the master a left and right percentage for the left and right motor respectively. This left and right percent directly control the master robot, creating a radio-controlled device that the other slave robots will follow. The Remote Control Board is the sole source of human input to the robotic swarm. C. Ultrasonic Trilateration Modules After choosing an appropriate method for distance detection, and constraining the final size of the robot based on error sensitivity, the main distance sensor designs were developed. The platform required three individual receiver (Rx) sensors, and a single centralized transmitter (Tx). To eliminate the need for four ultrasonic sensors, the sensor at the origin was designed as both a transmitter and receiver whose operation mode was controlled via an output pin on the Main Control Board. To transmission functionality of the Tx/Rx board (Figure 11) uses a 555 timer as an astable multivibrator operating at 40 KHz and provides a low voltage signal for a MAX232 driver chip. The MAX232 uses charge capacitors to turn a single +5V supply into +9V and -9V signals that are used to drive the ultrasonic sensor. The MAX232 chip is normally used in communication and is not designed to drive loads so the actual output in testing was ±6V. In order to get the most out of the MAX232, the 555 timer signal was inverted and supplied to the second input of the MAX232 and used to drive the negative pin of the ultrasonic sensor

7 Figure 11: Transmitter Board layout. A number of components were implemented to provide the dual-mode operation of the Tx/Rx board. The first step in dual mode operation involved disabling the transmitter. A PNP transistor was added to control the power to the MAX232. The PNP was used to cut off the power supply to the MAX232 and pull the signal to ground through a pull down resistor. Although the MAX232 supply had been tied to ground, the charge capacitors still had enough charge to emit almost two volts to the ultrasonic sensors. To remove the voltage a decoupling capacitor was added. The second element of dual-mode operation is an enable signal. An enable signal was used to start and stop the 40 KHz output from the 555 timer. Finally, an NPN transistor was used to ground the negative pin of the ultrasonic sensor when trying to receive and during transmission the signal was cut-off from ground to allow it to travel between 6 volts and 0 volts. The resultant output wave in transmit mode can be seen in Figure 12. The receiving portion of the Tx/Rx board and the Rx board itself were identical and were implemented using a gain stage, a gain and filter stage, and finally a comparator stage. The first gain stage inverts the signal and amplifies it by a factor of 66 using an LF412 operational amplifier. As it is running a 40 khz signal and the gain bandwidth of the op-amp is 4 GHz, the maximum gain possible is 75. The second gain stage, shown in Figure 13, uses the second op-amp in the LF412 IC. It implements an inverting gain of 30 and a low pass filter with cut-off frequency of 75 KHz. The frequency response is shown in Figure 14. Figure 13: Second gain-stage circuit. Figure 14: Frequency response of second stage (gain is green). Figure 12: Transmitter output signal. The third and final stage of the receiving circuit is a simple LM311 voltage comparator. Using a voltage divider of 40 KΩ and 100 KΩ the reference voltage going to the negative input of the LM311 is 1.4 volts. With the previous two gain stages of 66 and 30 the total amplification is 1980 and therefore any error of 0.7 mv will cause a false output signal. To eliminate this possibility a capacitor was added in series with the output to the voltage comparator to remove any low - 7 -

8 frequency noise that might have been amplified. Testing was also done on the ultrasonic receivers to ensure no noise was created from the motors or the environment. D. Main Control Board Figure 15: Main Control Board render. The Main Control Board was created as the workhorse of the robotic design. The PIC32 microcontroller was chosen for a number of reasons. The PIC32 provides the ability to perform floating point operations which are crucial for trilateration calculation [1], [3]. The PIC32 also has multiple UARTs allowing more flexible I/O configurations as devices are attached and pin configurations are changed. The PIC32 has multiple I 2 C and SPI ports, these were used to route the connections to the nrf24l01+ wireless radio, and to the Motor Controller Board [3]. The traces for the radio were run as short as possible to help eliminate interference in the communication lines. The I 2 C connector was routed as close as possible to the location where the motor board would be mounted. This minimized the length of wire needed for the connector, and increased the robustness of the device. Because the I 2 C, SPI, and UART were configured with separate pins debugging was possible while the robot was fully assembled and connected without having to resort to bit banging, or basic status information LEDs. The PIC32 was set to operate at 80MHz or 12.5ns per clock cycle. The peripheral clock divider was set so that the external and internal peripheral devices were configured to run at the same high frequency. Running the microcontroller at 80Mhz allowed for an increase in the resolution of the timers used for counting ultrasonic delays. For future expansion, it was imperative that as many pins as possible were broken out from the board. Using a 64 pin device allowed for a 26 pin expansion port that was named the I/O Expander. The I/O expander can be used to implement any number of devices. It allows access to several entire ports on the PIC32 including analog to digital pins, another I 2 C bus, another UART, and general purpose I/O. Currently the only device that exist for the I/O Expander is the debug board (see Appendix A: Schematic diagrams). The PIC32 was also chosen for the free ANSI C-compatible compiler [4]. The C programming language allowed for faster development on Microchips PIC Microcontroller devices, and it also allowed for the creation and sharing of a common library for the nrf24l01+ wireless radio link. SPI was used because the nrf24l01+ wireless radio communicates via an SPI connection. I 2 C was chosen for inter-board communication because of the low pin count and simple interface and support as an industry standard. It also allows for hardware abstraction, if another propulsion device was implemented the Main Control Board would not have to be changed. The I 2 C bus was clocked at 400KHz, which was sufficient for data transfer of motor commands to the Motor Controller board occurring at most four times per second 2. The trilateration interface on the Main Controller board consisted of three interrupts from each of the trilateration boards, the power connections needed for each trilateration board (- 5V, 5V, GND), and an active high enable for the transmitter board. Like the Remote Control board, the Main Control Board does very little while running. Most of the control is done through the use of interrupts. Current radio interrupts include a trilateration start that triggers a timer and enables the interrupts for each trilateration sensor. When the ultrasonic 2 Based on the maximum number of updates available through the radio (4Hz)

9 pulse is received at the sensor the interrupt line is brought high and the interrupt service routine samples the timer, storing the value. When all three interrupt routines have been run then the board processes the three times and computes the location of the sending robot. This is then used to find the desired direction and distance based on further processing from the formation control routine. The new direction and distance data is finally passed to the Motor Control Board via the I 2 C bus. Another radio interrupt sets the left and right motors duty cycle percent. This command forwards the information to the Motor Controller Board again through the I 2 C bus. Configuration of trilateration timing based on radio delay is also initialized through a radio interrupt. The Main Control Board uses a specified distance and direction (0 o at 50cm) and configures the timing offset so that the trilateration result is the same location, this allows for accurate trilateration timing information to be acquired. A specialized configuration routine was created for each robot to auto-configure the individual delays, this was based off a two robot procedure including a configuring robot (configurer) and robot that was being configured (configuree). The configuree would be started and would then wait for a configuration radio command. When the configurer robot was started it would send out a configuration pulse and start transmitting an ultrasonic pulse. The configuree then calculates the offset and sends back a done command, and the configurer repeats the process. This allows for many configuration values to be averaged together, ideally these values would then be stored onboard using the built in SD card reader. The main board layout can be seen in Figure 16. A start up algorithm was developed so that the bots would be able to dynamically assign identification numbers and positions in the swarm. The first step involves sending out a command looking for the master using the I m active command. If no master is found, the current robot becomes the master. If a master receives the I m active command then it responds with the current robot s new identification number. Currently it assigns robots in sequential order stating at one. Zero is reserved for the master. Once the individual robot knows its identification number, it changes its radio address and can join the swarm. Further implementation would include having the new robot receive, in addition to its identification number, the current formation. Figure 16: Board layout for Main Control Board. E. Motor Control Board Figure 17: Motor Control Board render. The Motor Control Board pictured above used the dspic33 microcontroller. This microcontroller - 9 -

10 has the 2-pin I 2 C module which was set up as the slave and received commands from the Main Control Board. This was routed at the top right of the board (see Figure 18) to reduce the noise inherent with the rotating magnetic field of the motors. This also allowed for a shorter wiring harness to be run from the Main Control Board to the Motor Control Board. Figure 19: Motor driver truth table [3]. For position feedback, the dspic33 included two Quadrature Encoder Interfaces, these were used for velocity feedback control. The dspic33 received on off pulses from the IR sensors on the Quadrature Encoder Board shown in Figure 20. The board was designed to fit directly onto the robot chassis surrounding the axle. Figure 18: Board Layout of Motor Control Board. The dspic33 was chosen because it incorporated two Pulse Width Modulation (PWM) channels. Each PWM channel was implemented to control the duty cycle of a motor. By varying the duty cycle, the amount of power that is delivered to the motor is increased or decreased. However, the relationship between the duty cycle and the amount of power delivered to the motor are nonlinear, since power is related to the square of the voltage. The PWM channels were connected to the enables of the motor driver chip. This allowed the motor to coast during the off portion of the PWM wave as the output terminals were set in high impedance mode see Figure 19. Figure 20: Quadrature Encoder Board render. 1) Movement algorithm Each robot has the ability to become the slave and follow the master, or become the master and follow commands from the Remote Control Board. The master robot, by default, is configured to run at 75 percent of its maximum speed, to allow slave robots to catch up and assemble into formations. Under slave mode, the desired angle and distance are communicated to the Motor Control Board from the Main Control Board via I 2 C

11 protocol. The motor control algorithm compares the values of the desired angle and distance against preset values and executes one of the following actions: Stop: If the desired distance is below the minimum distance threshold, the enable pin on the H-Bridge for both motors are disabled. Go straight: If the desired angle is within the threshold value ( θ <5) the motor will enter a forward drive mode where drive pins on the H- Bridge are forward enabled and the PWM value across the enable pins is set to maximum speed. Gradual turn: If the desired angle is less than 45 off the robot s centre line, the PWM ratio between the two motors is set as 25%:50% according to the direction of the turn. In this mode, each robot will turn and move forward simultaneously, turning gradually to the right or left depending on the sign of the desired angle. Stop and turn: If the desired angle is greater than 45 off the robot s centre line, the PWM ratio between the two motors is set as -37%:37% according to the direction of the turn. In this mode, each robot will turn on the spot. The point of reference for calculating the desired angle is in front of the robot (on the bisector of the trilateration arms). A positive angle translates to a turn left command where a negative angle requires a turn right. The direction update frequency is configured so that there will be multiple updates within the time needed for the motor to complete an individual directives thus providing a smooth transition on tracking and movement of each robot. 2) Quadrature Encoder Interface Velocity feedback is implemented with the use of the built-in Quadrature Encode Interface (QEI) on the dspic33. The QEI inputs are driven from an optical encoder circuit with two reflective object sensors positioned 90 out of phase, and looking at the encoder disc on the inner face of the wheels. Each tick of the QEI will trigger a timer on the dspic33 which is used to calculate the length of n discrete encoder pulses [4]. The accumulated length of the pulses is then divided by the number of the pulses to provide the velocity of each motor. The calculated velocity is fed back to the controller and checked against predetermined reference values for each PWM value. This enables all robots to maintain identical speed while preserving the formation. Since the encoder pulses are not necessarily synchronized with the polling period, each polling interval sees a loss of data that can approach the size of one full encoder tick. For this reason, the quadrature encoder was not enabled for final demo purposes. F. Mechanical Design The main robot mechanical design was modeled and constructed completely in a software CAD package before construction (Figure 21). Adjustments were made on the model, and the main chassis was exported for computer-aided milling. Figure 21: CAD model of main robot assembly. The robot chassis was made of 1/10 clear Plexiglas to provide a lightweight, sturdy design for the chassis that can be easily CNC milled. The power sources are connected to the boards through a double-pole double-throw switches which allow a single switch to operate two individual power supplies (digital and motor supply) simultaneously and without interference. All the wire connections were electrically isolated with heat-shrink tubing to help keep any failures in the software domain where they can be easily debugged and resolved. A two-wheel design was used to eliminate the need for any dedicated steering component. This reduced cost, complexity, and allowed for an independent height adjustment on the front of the robot. This design also allowed the use of a Tamiya Double Gearbox motor with left/right independent 4-speed functionality. Set with gear ratio 114.7:1, each motor provides maximum of

12 115 rpm with a maximum torque of 1618 N.cm across both motors. Different gear configuration provide flexibility in mechanical adjustments of speed and torque. This in return allows the use of a cheaper SN H-bridge or equivalent motor driver instead of more expensive L298 driver. It also eliminates the need for a heat sink on the Motor Control Board. IV. CONCLUSION In conclusion, each individual module of the project was able to perform as designed. The cause of most failures, however, came from the unknown effects associated with connecting working modules together (ie. connecting Main Control Board to trilateration modules). Repeated hardware issues plagued the project and ranged from faulty components, to broken wires, to conductive solder flux, to dead batteries. The other major stumbling block with the project came from the modularity of the design. While a modular design is a better practice in theory, the overhead and complexity associated with module communication can provide a substantial source of unnecessary error and uncertainty. At the time of project completion, the issues with module communication were resolved, and plans to move forward with expansion and improvement are in discussion. Expanding on the features currently built into the robot, improvements and advancements can be easily added with a minimal amount of effort. Figure 22: Three robots in a line formation

13 APPENDIX A: SCHEMATIC DIAGRAMS Figure 23: Quadrature encoder schematic

14 Figure 24: Debug shield schematic

15 - 15 -

16 Figure 25: Main Control Board schematic

17 Figure 26: Remote Control Board schematic

18 Figure 27: Motor Control Board schematic

19 Figure 28: Wireless Breakout Board schematic

20 ACKNOWLEDGMENT The authors would like to thank Dr. S. Hranilovic, M. Kadonoff, D. Vacar, the McMaster IEEE Student Branch, and Microchip Technical Support for their continued input and aid for the duration of this project. REFERENCES [1] Rodney Heil. (2004, August) A Trilaterative Localization System for Small Mobile Robots. PDF Document. [2] Nordic Semiconductor. (2007, July) nrf24l01 Single Chip 2.4GHz Transceiver Product Specification. PDF Document. [3] Microchip Technology Inc. (2008, July) PIC32MX3XX/4XX Family Datasheet. PDF Document. [4] Texas Instruments Incorporated. (1995, November) SN QUADRUPLE HALF- H DRIVER. PDF Document. [5] Microchip Technology Inc. (2007, February) dspic33f Family Reference Manual. PDF Document. [6] Microchip Technology Inc. (2008, March) dspic33fj32mc302/304, dspic33fj64mcx02/x04, and dspic33fj128mcx02/x04 Data Sheet. PDF Document. [7] Microchip Technology Inc. (2007, July) PIC32 Peripheral Libraries for MPLAB C32 Compiler. PDF Document