Monthly Archives: March 2015

Using the Arduino to read sensor data

Force Sensing Resistors and Inertial Measurement Unit

The first hardware parts to be tested were the inertial measurement unit (IMU) and the force sensing resistors (FSRs). The Arduino IDE was used for programming. The FSRs are straightforward analogue inputs, so I will concentrate on the IMU.

In order to be in line with the ROS coordinate frame conventions, the robot’s base frame will be in this orientation (right-hand rule):

  • x axis: forward
  • y axis: left
  • z axis: up

For now I am assuming the IMU is in the same orientation, but as it is not yet mounted to the robot, it might change later on. Again, in keeping with the ROS conventions on relationships beteen coordinate frames, the following transforms and their relationships have to be defined:

\text{map} \rightarrow \text{odom} \rightarrow \text{base\_link}

All these frames and their relationships can be easily managed using the ROS tf package.
I have added the imu_link to this chain, which represents the IMU’s orientation with respect to the odom frame. An additional link is also added to transform the standard base_link to the robot’s torso orientation. So the transform chain actually looks like this:
\text{map} \rightarrow \text{odom} \rightarrow \text{imu\_link} \rightarrow \text{base\_link} \rightarrow \text{torso\_link}

Calculating roll/pitch/yaw

I initially decided to let the A-Star (Arduino-compatible) board perform the IMU calculations and pass roll/pitch/yaw (RPY) values, and pass them as a ROS message to the PC. A ROS node will read these values and broadcast the transform from odom to imu_link using tf.

The IMU I am using, the MinIMU-9 v3 from Pololu, consists of an LSM303D accelometer-magnetometer chip and an L3GD20H gyro chip in one single package. The accelerometer, magnetometer and gyro are all three-axis types, providing 9 degrees of freedom and allow for a full representation of orientation in space. The data can be easily read using the provided Arduino libraries.

Rotations in Cartesian space will be represented in terms of intrinsic Euler angles, around the three orthogonal axes x, y and z of the IMU. As the order in which rotations are applied is important, I decided to use the standard “aerospace rotation sequence”, which has an easy mnemonic: An aeroplane yaws along the runway, then pitches during takeoff, and finally rolls to make a turn once it is airborne. The rotation sequence is thus:

  • Rotation about z: yaw (±180°)
  • Rotation about y: pitch (±90°)
  • Rotation about x: roll (±180°)

Pitch has to be restricted to ±90° in order to represent any rotation with a single set of RPY values. The accelerometer alone can extract roll and pitch estimates, but not yaw, as the gravity vector doesn’t change when the IMU is rotated about the y axis. This is where the magnetometer (compass) comes in use.

Hence, using these accelerometer and magnetometer values, the IMU’s orientation can be fully described in space. However these measurements are very noisy, and should only be used as long-term estimates of orientation. Also, any accelerations due to movement and not just gravity add disturbances to the estimate. To compensate for this, the gyro readings can be used as a short term and more accurate representation orientation, as the gyro readings are more precise and not affected by external forces.

The complementary filter

Gyro measurements alone suffer from drift, so they have to be combined with the accelerometer/magnetometer readings to get a clean signal. A fairly simple way to do this is using what is known as a complementary filter, where the gyro readings are trusted. It can be implemented in code fairly simply, in the following way:

Roll_{curr} = C_f \times (Roll_{prev} + X_{gyro} \times dt) + (1 - C_f) \times Roll_{accel}
Pitch_{curr} = C_f \times (Pitch_{prev} + Y_{gyro} \times dt) + (1 - C_f) \times Pitch_{accel}
Yaw_{curr} = C_f \times (Yaw_{prev} + Z_{gyro} \times dt) + (1 - C_f) \times Yaw_{magnet}

On every loop, the previous RPY values are updated with the new IMU readings. The complementary filter is essentially a high-pass filter on the gyro readings, and a low-pass filter on the accelerometer/magnetometer readings. C_f is a filtering coefficient, which determines the time boundary between trusting the gyroscope vs trusting the accelerometer/magnetometer, defined as:
C_f = \frac{ t_{const} }{ (t_{const} + dt) }
dt is the loop time, and t_{const} is a time constant, which determines the length of recent history for which the gyro data takes precedence over the accelerometer/magnetometer data, in calculating the new values. I have set this to 1 second, so the accelerometer data from over a second ago will take precedence and correct any gyro drift. A good source of information on the complementary filter can be found here.

Issues with filtering roll/pitch/yaw values

However, when using RPY calculations, applying this filter is not so straightforward. Firstly, when the roll/yaw values cross over the ±180° point, the jump has to be taken into account otherwise it causes large erroneous jumps in the averaged value. This can be corrected fairly simply, however another problem is gimbal lock, which in this case is caused then the pitch crosses the +-pi/2 points (looking directly. This causes the roll/yaw values to jump abruptly, and as a result the IMU estimation “jumps” around the problem points. My attempt at solving this issue by resetting the estimated values whenever IMU was near the gimbal lock position was not very effective.

After a lot of frustration, I decided that learning how to reliably estimate position using quaternions was the way to go, although they may at first seem daunting. So at this point I abandoned any further experimentation using RPY calculations, however the work was a good introduction to the basics of the A-Star board and representing orientations using an IMU. The Arduino code is posted here for reference. Links to tutorials on using accelerometer and gyro measurements can be found in the comments.

Code (click to expand):

// Hardware:
// Pololu A-Star 32U4 Mini SV
// Pololu MinIMU-9 v3 (L3GD20H and LSM303D)
// Interlink FSR 400 Short (x6)

// Important! Define this before #include <ros.h>
#define USE_USBCON

#include <Wire.h>
#include <ros.h>
#include <std_msgs/Int16MultiArray.h>
#include <geometry_msgs/Vector3.h>
#include <AStar32U4Prime.h>
#include <LSM303.h>
#include <L3G.h>
#include <math.h>

// Set up the ros node and publishers
ros::NodeHandle nh;
std_msgs::Int16MultiArray msg_fsrs;
std_msgs::MultiArrayDimension fsrsDim;
ros::Publisher pub_fsrs("fsrs", &msg_fsrs);
geometry_msgs::Vector3 msg_rpy;
ros::Publisher pub_rpy("rpy", &msg_rpy);
unsigned long pubTimer = 0;

const int numOfFSRs = 6;
const int FSRPins[] = {A0, A1, A2, A3, A4, A5};
int FSRValue = 0;
LSM303 compass;
L3G gyro;
const int yellowLEDPin = IO_C7;  // 13
int LEDBright = 0;
int LEDDim = 5;
unsigned long LEDTimer = 0;

float aX = 0.0;
float aY = 0.0;
float aZ = 0.0;
float gX = 0.0;
float gY = 0.0;
float gZ = 0.0;
float accelRoll = 0.0;
float accelPitch = 0.0;
float magnetYaw = 0.0;
float roll = 0.0;
float pitch = 0.0;
float yaw = 0.0;
float accelNorm = 0.0;
int signOfz = 1;
int prevSignOfz = 1;
float dt = 0.0;
float prevt = 0.0;
float filterCoeff = 1.0;
float mu = 0.01;
float timeConst = 1.0;

void setup()
    // Array for FSRs
    msg_fsrs.layout.dim = &fsrsDim;
    msg_fsrs.layout.dim[0].label = "fsrs";
    msg_fsrs.layout.dim[0].size = numOfFSRs;
    msg_fsrs.layout.dim[0].stride = 1*numOfFSRs;
    msg_fsrs.layout.dim_length = 1;
    msg_fsrs.layout.data_offset = 0;
    msg_fsrs.data_length = numOfFSRs; = (int16_t *)malloc(sizeof(int16_t)*numOfFSRs);


    // Wait until connected
    while (!nh.connected())
    nh.loginfo("ROS startup complete");


    // Enable pullup resistors
    for (int i=0; i<numOfFSRs; ++i)
        pinMode(FSRPins[i], INPUT_PULLUP);

    if (!compass.init())
        nh.logerror("Failed to autodetect compass type!");

    // Compass calibration values
    compass.m_min = (LSM303::vector<int16_t>){-3441, -3292, -2594};
    compass.m_max = (LSM303::vector<int16_t>){+2371, +2361, +2328};

    if (!gyro.init())
        nh.logerror("Failed to autodetect gyro type!");

    pubTimer = millis();
    prevt = millis();

void loop()
    if (millis() > pubTimer)
        for (int i=0; i<numOfFSRs; ++i)
            FSRValue = analogRead(FSRPins[i]);
  [i] = FSRValue;
            delay(2);  // Delay to allow ADC VRef to settle

        if (compass.a.z < 0)
            signOfz = -1;
            signOfz = 1;

        // Compass - accelerometer:
        // 16-bit, default range +-2 g, sensitivity 0.061 mg/digit
        // 1 g = 9.80665 m/s/s
        // e.g. value for z axis in m/s/s will be: compass.a.z * 0.061 / 1000.0 * 9.80665
        //      value for z axis in g will be: compass.a.z * 0.061 / 1000.0
        //accelRoll = atan2( compass.a.y, sqrt(compass.a.x*compass.a.x + compass.a.z*compass.a.z) ) ;
        //accelPitch = atan2( compass.a.x, sqrt(compass.a.y*compass.a.y + compass.a.z*compass.a.z) );
        // Angle between gravity vector and z axis:
        //float accelFi = atan2( sqrt(compass.a.x*compass.a.x + compass.a.y*compass.a.y), compass.a.z );
        // Alternative way:
        // Angles - Intrinsic rotations (rotating coordinate system)
        // fi: roll about x
        // theta: pitch about y
        // psi: yaw about z
        // "Aerospace rotation sequence"
        // yaw, then pitch, then roll (matrices multiplied from right-to-left)
        // R_xyz = R_x(fi) * R_y(theta) * R_z(psi)
        // Convert values to g
        aX = (float)(compass.a.x)*0.061/1000.0;
        aY = (float)(compass.a.y)*0.061/1000.0;
        aZ = (float)(compass.a.z)*0.061/1000.0;
        //accelRoll = atan2( aY, aZ );
        // Singularity workaround for roll:
        accelRoll  = atan2( aY, signOfz*sqrt(aZ*aZ + mu*aX*aX) );  // +-pi
        accelPitch = atan2( -aX, sqrt(aY*aY + aZ*aZ) );            // +-pi/2

        // Compass - magnetometer:
        // 16-bit, default range +-2 gauss, sensitivity 0.080 mgauss/digit
        // Heading from the LSM303D library is the angular difference in
        // the horizontal plane between the x axis and North, in degrees.
        // Convert value to rads, and change range to +-pi
        magnetYaw = - ( (float)(compass.heading())*M_PI/180.0 - M_PI );

        // Gyro:
        // 16-bit, default range +-245 dps (deg/sec), sensitivity 8.75 mdps/digit
        // Convert values to rads/sec
        gX = (float)(gyro.g.x)*0.00875*M_PI/180.0;
        gY = (float)(gyro.g.y)*0.00875*M_PI/180.0 * signOfz;
        gZ = (float)(gyro.g.z)*0.00875*M_PI/180.0;

        dt = (millis() - prevt)/1000.0;

        filterCoeff = 1.0;
        // If accel. vector magnitude seems correct, e.g. between 0.5 and 2 g, use the complementary filter
        // Else, only use gyro readings
        accelNorm = sqrt(aX*aX + aY*aY + aZ*aZ);
        if ( (0.5 < accelNorm) || (accelNorm > 2) )
            filterCoeff = timeConst / (timeConst + dt);

        // Gimbal lock: If pitch crosses +-pi/2 points (z axis crosses the horizontal plane), reset filter
        // Doesn't seem to work reliably!
        if ( (fabs(pitch - M_PI/2.0) < 0.1) && (signOfz != prevSignOfz) )
            roll += signOfz*M_PI;
            yaw += signOfz*M_PI;
            // Update roll/yaw values to deal with +-pi crossover point:
            if ( (roll - accelRoll) > M_PI )
                roll -= 2*M_PI;
            else if ( (roll - accelRoll) < - M_PI )
                roll += 2*M_PI;
            if ( (yaw - magnetYaw) > M_PI )
                yaw -= 2*M_PI;
            else if ( (yaw - magnetYaw) < - M_PI )
                yaw += 2*M_PI;

            // Complementary filter
            roll  = filterCoeff*(roll  + gX*dt) + (1 - filterCoeff)*accelRoll;
            pitch = filterCoeff*(pitch + gY*dt) + (1 - filterCoeff)*accelPitch;
            yaw   = filterCoeff*(yaw   + gZ*dt) + (1 - filterCoeff)*magnetYaw;

        roll  = fmod(roll,  2*M_PI);
        pitch = fmod(pitch,   M_PI);
        yaw   = fmod(yaw,   2*M_PI);

        msg_rpy.x = roll;
        msg_rpy.y = pitch;
        msg_rpy.z = yaw;


        prevSignOfz = signOfz;

        prevt = millis();

        pubTimer = millis() + 10;  // wait at least 10 msecs between publishing

    // Pulse the LED
    if (millis() > LEDTimer)
        LEDBright += LEDDim;
        analogWrite(yellowLEDPin, LEDBright);
        if (LEDBright == 0 || LEDBright == 255)
            LEDDim = -LEDDim;

        // 50 msec increments, 2 sec wait after each full cycle
        if (LEDBright != 0)
            LEDTimer = millis() + 50;
            LEDTimer = millis() + 2000;


Robot Revival

The Bioloid story

Many moons ago, I purchased my first humanoid robot, an 18-servo Bioloid Comprehensive Kit. At the time, humanoid robotics for hobbyists was at its early stages, and I chose the Bioloid after much deliberation and comparison with its then main competitors, the Hitec Robonova and Kondo KHR-2HV. I went for the Bioloid mainly because of the generous parts list, which doesn’t limit the design to just a humanoid robot, as well as the powerful AX-12+ Dynamixel servos. These have a number of advantages over the more traditional simple servos, such as multiple feedback options (position, temperature, load voltage, input voltage), powerful torque, upgradeable firmware, internal PID control, continuous rotation option, a comms bus that enables the servos to be daisy-chained … and the list goes on!

After building some of the standard variants trying out the demos, attempting a custom walker, and playing around with Embedded C on its CM-5 controller board, I never got around to actually doing the kit any real justice. I have finally decided to explore the potential of this impressive robot, and make all that money worthwhile!

This post begins one of hopefully many, in which I will detail my progress with the Bioloid robot.

Initial hardware ideas

The general plan for hardware is to extend the base platform with various components, avoiding the need for custom electronic boards as far as possible, as I want my main focus to be on software.
The Bioloid’s servos are powered and controlled by the CM-5 controller, which has an AVR ATMega128 at its core. I have played around with downloading custom Embedded C to the CM-5, but in terms of what I have in mind, it is much more convenient to be able to control the servos directly from a PC. The standard solution is the USB2Dynamixel, however much of this chunky adaptor is taken up by an unnecessary serial port, so I went for a functionally identical alternative, a USB2AX by a company called Xevelabs. The PC/laptop control will hopefully be replaced by a Raspberry Pi 2 Model B (on back order!) for a more mobile solution. I have not thought about mobile power yet!

Despite the impressive servos, the stock Bioloid offers little in terms of sensors. A provided AX-S1 sensor module has IR sensors/receiver, a microphone and a buzzer, all built in to a single package, which resembles on of the servos, and acts as the Bioloid’s head. Although updated controllers by Robotis have emerged over the years, the original CM-5 had no way of directly integrating sensors to it, and was limited to the AX-S1.

Since a bunch of servos without any real-world feedback does not really make a robot, I am going to add a number of sensors to the base robot. The current plan is to use a MinIMU-9 v3 for tilt/orientation sensing, and a number of Interlink FSR 400 Short force sensing resistors on the feet. Very conveniently, the undersides of the Bioloid’s feet have indents in their four corners which perfectly match the shape of the FSRs! A Pololu A-Star 32U4 Mini SV (essentially an Arduino board) will perform the data collection and pass it over to the PC via serial-to-USB.

That is as far as my current considerations go in terms of hardware. At some point I will look into vision, which may be as simple as a normal webcam. I originally thought that an Xbox Kinect would be ruled out because of size, but apparently it can be done!

Initial software ideas

I plan on using ROS (Robot Operating System) as the main development platform, with code in C++. As well as playing around with ROS in the past, its popularity in a large number of robotics projects and large number of libraries makes it a very development platform. Also, I recently discovered the MoveIt! package, which would be great to try out for the Bioloid’s walking gait.

For simplicity, the A-Star will be programmed using the Arduino IDE. I was pleasantly surprised that I wouldn’t have to write any serial comms code to get the sensor data into the ROS environment, as a serial library for the Arduino already exists. ROS is already looking like a good choice!

The A-Star will initially just serve ROS messages to the PC. It may potentially perform other functions if it has the processing power to spare, but for now there is no need. A ROS service running on the PC will be needed to interface with the Dynamixel servos, instructing the servos to move, reading their feedback and publishing the robot’s joint states to various other ROS nodes.

My next post will focus on the new sensor hardware. Until then, please let me know your thoughts and suggestions, all feedback is welcome!