# ROS interconnections

In this post I will cover the current state of my ROS setup for controlling the Bioloid’s motors and custom hardware.

The rqt_graph package provides a way of visualising the interconnections between all running ROS nodes. The following graphs show the current setup:

Here is a breakdown of the running nodes:

• bioloid_sensors (MCU Arduino code): The MCU is running an Arduino program using the rosserial_arduino library, and publishes the IMU’s data as ROS messages over serial-to-USB. The rosserial package was useful as an easy way of sending ROS messages from the MCU to the controlling PC.
• serial_node: This is a node included in the rosserial_python package, which reads serial data from the MCU.
• imu_tf_broadcaster: This is a custom node which uses the IMU’s data to calculate the robot’s orientation, as detailed in this previous post.
• dummy_odom_frame_broadcaster: This is a static_transform_publisher node from tf, which transforms from the map to the odom frame without any actual change in orientation or position. This is simply to keep in line with the ROS conventions, as explained in this previous post.
• ax_joint_controller: This is another custom node for communicating with the AX-12 servos. This is a work-in-progress, but currently acts as a ROS wrapper around the USB2Dynamixel/USB2AX library. It publishes the servo positions (in radians) as a ROS sensor_msgs JointState message, on the ax_joint_states topic. It also runs a number of ROS services for controlling the servos from other ROS nodes. These are either higher level commands (such as for setting all motors to home position), or low level commands for directly reading from or writing to the AX-12 Control Table’s addresses.
• joint_state_publisher: The joint_state_publisher is a tool for setting and publishing joint state values for a given URDF file. The node here reads the values from the ax_joint_states topic (by setting the source_list parameter) and publishes on the joint_states topic. I suppose this node could currently be bypassed entirely, however it does provide a nice GUI window for visualising the joint positions as sliders, and is also useful for moving the robot’s joints in RViz when ax_joint_controller is offline.
• robot_state_publisher: The robot_state_publisher works in tandem with the joint_state_publisher and publishes the state of the robot to tf. The robot_state_publisher reads the configuration of the kinematic chain from the URDF file (set by the robot_description parameter). The set up of the URDF file has been covered in a previous post. The virtual model of the robot is then displayed in RViz, with joint positions reflecting those of the physical robot.

That is about it for the current setup. I have some work-in-progress nodes which interface with the above framework and test some of the robot’s motions, so in a following post I will discuss these and show some new videos of the physical robot in action!

# Wiring up the electronics

It’s been a while since the last update! I have mostly been working on the commununication between ROS and the servos, and now have a working read-write ROS servo interface, but will post about this later.

In the meanwhile, I added a bar display made up of 10 green LEDs for information feedback, as well as 4 blue decorative LEDs. I then moved the breadboarded electronics to a more permanent prototype board. I was initially hoping to make a box-shaped board which could fit nicely inside the Bioloid’s hollow “groin”, and would have the LED bar display in the front. However the USB cable connector protruded too much, so the LED bar will have to sit one side of the board. I also managed to squeeze the IMU on the underside of the board. There is still some room above the board, so I may be able to squeeze even more of the wiring/electronics in there.

Once the board was ready, I temporarily put all the hardware parts in roughly the right locations to gauge how much space will be taken up and how long the wiring should be. I have removed the AX-S1 sensor, as I probably won’t have much use for it. I think the Raspberry will sit much better on top of the torso rather than on the back, where the old CM-5 used to be. It’s very tempting to turn the screen into a VR face! As you can see, it will be a struggle to mount the massive 5500 mAh battery on the back, so I am planning on downsizing.

Here are some work-in-progress pictures plus a video:

# Pi power!

## Battery

Most of the parts for the Bioloid’s power supply have now arrived. Here are some pictures of the Pi 2 being powered by the 11.1 V, 5500 mAh battery. The battery also powers the SMPS2Dynamixel adaptor for the Dynamixel servos. The step-down to 5 V for the Raspberry Pi is performed by a 3A UBEC (Universal Battery Elimination Circuit), which has a handy MicroUSB output. This seems to be the ideal way of powering the Pi, rather than e.g. via the powered hub or GPIO pins, which bypass the voltage protection, especially when considering that the Pi has to power the peripherals. The USB2AX for the servo control is powered via the Raspberry’s USB port, as will the A-Star MCU.

## Raspberry Pi 2

The Pi is currently running Raspbian and now also has this great 480×320 touchscreen from Adafruit! I installed ROS Indigo from source using this guide. I have also added Conky on the desktop, a lightweight and fully customisable system monitor, as a way of directly visualising the Pi’s current status. The touchscreen feature of the screen will be of use in the future, if some simple GUI is made for the robot.

## Hardware layout

The next picture shows the current hardware layout of the whole robot. As there is a lot to power, I went for the beefy 5500 mAh battery, but as it weighs 417 grams, I might have to eventually get something lighter for the robot to be able to carry, at the expense of a shorter run time.

Hardware diagram

# Representing the robot in ROS

## Building a virtual robot

In this post, I’ll be describing the first stage in getting a working representation of the, as of yet unnamed robot, into the ROS world. I will also be briefly exploring the MoveIt! library, as this might be a useful tool for the future.

The virtual representation of the Bioloid will be built using CAD models of all the individual servos and support brackets. The robot will be loaded up in RViz, where its links an joints will be manipulated. Inverse kinematics will hopefully be calculated by the MoveIt! package later on. But first, a definition is needed of how the joints and links are all connected, and how to move between their frames of reference. The individual CAD components will be oriented correctly onto these frames.

On a side note, I had the chance to photograph the Bioloid in its current state, and also had a Raspberry Pi 2 delivered!

After some background reading, I found out that the best way to create this representation in ROS is by using a standardised XML format file called the Unified Robot Description Format (URDF).

In the past I had made a start on drawing a CAD model of the Robotis servo, but since then Robotis has released CAD drawings of all their robot kits online here (old link).

I tidied up the .stp files using FreeCAD, by removing some placeholder parts or sub-parts which would be of no use (e.g. screws, gears and electronics on the inside of the servos and CM-5). I then converted the files into .dae (Collada) format, and imported them into Blender to add some colour textures. For some reason, saving again as .dae in Blender shrunk the model dimensions by 100. I haven’t worried too much about the actual component size at the moment, as only their relative scales have to be correct for now. There is also a bug in RViz which replaces the ambient color of Collada materials by light grey if at least one component of the specified ambient color is 0. To fix this, I manually edited the file and replaced all 0’s with 0.1 in the “ambient” tags. Below are some of the main components, as rendered in Blender.

## The Unified Robot Description Format

The URDF file itself is written in a plain markup language. As the definition of various links is written more conveniently with some basic maths, and because many bits of code will inevitably be repeated or recycled (e.g. the mirroring of the left-hand side based on the right-hand side), ROS has a macro language called xacro, which makes it much easier to create and maintain URDF files. A URDF is generated from a xacro file using:

rosrun xacro xacro.py model.xacro > model.urdf

Creating the file for the Bioloid took a fair while, as I created all the translations by eye without knowing the actual distance measurements between the various links, but rather by relying on the CAD components as each one was placed in the chain. I started with the right side of the model, first with the easier arms, then with the legs.

The validity of the URDF file can be checked with teh check_urdf tool. Another great tool for visualising the final result is urdf_to_graphiz, which generates a diagram of the joint and link tree. The tree of my model is shown below. Each joint (blue circles) is positioned with respect to its parent link (black rectangles), and the following/child link is positioned has the same origin as the joint, as shown here. The xyz and rpy labels next to the arrows show the translation and rotation required to get from parent frame to child frame, or in other words, it is the representation of the child’s frame with respect to the parent’s frame. You will also notice the addition of the IMU link, as well as an additional camera link, although this is just a placeholder for a possible camera in the future, and at the moment won’t be used.

Graphviz diagram of URDF file

## The robot in RViz

The current state of the robot is shown in the screenshots below. The robot is displayed in RViz with the help of the ROS joint_state_publisher and robot_state_publisher. It is fully articulated and the individual joints can be moved with the help of the GUI which joint_state_publisher provides. The joint states will later be published from the joint values read by the real Bioloid servos. In addition to the kinematic model, I created bounding boxes around the components for the collision boundaries, which are shown in red. This was after the fact I realised that without them, the MoveIt! plugin would use the full CAD geometry in its collision detection routines, which made it almost grind to a halt!

## Integration with MoveIt!

I have only played around with MoveIt! briefly so far, but the results seem very promising. The library has a useful graphical setup assistant, which essentially enhances the URDF with a Semantic Robot Description Format (SRDF) file. The URDF only contains information about how the joints and links are arranged, as well as some other information such as joint limits, and the visual and collision data. The SRDF doesn’t replace the URDF, but exists separately and contains other information, such as further self-collision checking, auxiliary joints, groups of joints, links and kinematic chains, end effectors and poses. So far I haven’t found any need to edit the SRDF directly, as it can be generated and edited by the setup assistant.

The assistant generates a new ROS package with various templates for path planning and visualisation, which is done via an RViz plugin. So far I have managed to interact with the virtual Bioloid’s arms and legs, in a similar way shown in this PR2 robot tutorial. The aim will be to later on create some poses and walking gaits which I can try out on the real robot, but that is all for now!

URDF:

MoveIt!:

RViz scaling and ambient colour issues:

# Using quaternions to create a better IMU complementary filter

## A better alternative to the RPY approach

After realising in my previous post that solving the gimbal lock problem for the complementary filter requires fiddly and inelegant fixes, I decided to dive into the world of quaternions. Luckily, the theory behind quaternions doesn’t need to be fully understood, in order to use them to represent 3D rotations. Particularly useful are the conversions between quaternion and rotation matrix, and axis-angle representation.

I initially tried to make the Arduino MCU (A-Star) perform the filtering process and pass the IMU frame transform to the PC, however this presented a couple of issues, the first being that there is no standard vector and matrix library in Arduino. Second, although I could write a very simple library for vector cross and dot products etc., the MCU’s 32 KB of flash memory was already almost full with all the rosserial and IMU libraries, leaving little space for anything else.
Hence I opted for letting the MCU simply pass a number of ROS message streams over to the PC, which could then do the required transformations using the ROS tf library. The Arduino code is listed at the end of this post (bioloid_sensors.ino).

The MCU reads the MinIMU-9 v3 IMU data and publishes it as ROS messages on the following topics:

• LSM303 accelerometer x, y, z values (“accel”)
• LSM303 magnetometer x, y, z values (“magnet”)
• L3G gyroscope x, y, z values (“gyro”)
• LSM303 magnetometer heading value (“heading”), derived from the LSM303’s library, as the angular difference in the horizontal plane between the x axis and magnetic North

ROS has a very handy plotting tool for topics, called rqt_plot. Below is an example dump of all the IMU data.

IMU messages plotted in rqt_plot

## Quaternion-based filter

Having spent too much time on the RPY approach already, I wanted to find a simple way to achieve a relatively stable orientation from the IMU readings. I ended up implementing the method from this AHRS maths tutorial from the Firetail UAV system. The method is explained very well in that link, so there is no need to go into the details. The only change I have made is in the calculation of the filter coefficient, based on a set time constant as was done previously. My version using a ROS subscriber on the PC side is again listed at the end of this post (imu_tf_broadcaster.cpp and .h files).

## Videos

Here are two videos comparing the original RPY approach against the improved quaternion approach. The resulting IMU transform is published by tf, which is used by the robot model you see in RViz, the ROS visualisation tool. The model is generated using a URDF file; I will explain this in detail in a following post.

Although in both cases the rotation is fairly smooth, you can see the problems that the RPY filtering encounters when it nears the gimbal lock position (when the robot lies horizontally). For my purposes of orientating the robot, I think the current quaternion approach is perfectly suited. I doubt I will be needing to play around with Kalman filters and the likes, as I currently don’t need the precision that UAVs etc. may need!

So that’s it for IMUs and orientation for the time being. In my next post I will start detailing the current progress with the virtual bioloid in ROS, which was seen in the above videos.

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 <std_msgs/Float32.h>
#include <AStar32U4Prime.h>
#include <LSM303.h>
#include <L3G.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_accel;
ros::Publisher pub_accel("accel", &msg_accel);
geometry_msgs::Vector3 msg_magnet;
ros::Publisher pub_magnet("magnet", &msg_magnet);
geometry_msgs::Vector3 msg_gyro;
ros::Publisher pub_gyro("gyro", &msg_gyro);
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;

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;
msg_fsrs.data = (int16_t *)malloc(sizeof(int16_t)*numOfFSRs);

nh.initNode();

// Wait until connected
while (!nh.connected())
nh.spinOnce();

Wire.begin();

// 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.enableDefault();

// 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!");
}
gyro.enableDefault();

pubTimer = millis();
}

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

// 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
// Gravity is measured as an upward acceleration:
// Stationary accel. shows +1 g value on axis facing directly "upwards"
// Convert values to g
msg_accel.x = (float)(compass.a.x)*0.061/1000.0;
msg_accel.y = (float)(compass.a.y)*0.061/1000.0;
msg_accel.z = (float)(compass.a.z)*0.061/1000.0;

// Compass - magnetometer:
// 16-bit, default range +-2 gauss, sensitivity 0.080 mgauss/digit
msg_magnet.x = (float)(compass.m.x);
msg_magnet.y = (float)(compass.m.y);
msg_magnet.z = (float)(compass.m.z);
// 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

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

pub_fsrs.publish(&msg_fsrs);
pub_accel.publish(&msg_accel);
pub_magnet.publish(&msg_magnet);
pub_gyro.publish(&msg_gyro);

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;
else
LEDTimer = millis() + 2000;
}

nh.spinOnce();
}




int main(int argc, char **argv)
{
ros::NodeHandle n;
ros::Rate loop_rate(1000);  // Hz

ros::Subscriber accelSub   = n.subscribe("accel",   1000, &Broadcaster::accelCallback,   &broadcaster);
ros::Subscriber magnetSub  = n.subscribe("magnet",  1000, &Broadcaster::magnetCallback,  &broadcaster);
ros::Subscriber gyroSub    = n.subscribe("gyro",    1000, &Broadcaster::gyroCallback,    &broadcaster);

while(n.ok())
{
tf::StampedTransform(
tf::Transform(broadcaster.getQ(), tf::Vector3(0.0, 0.0, 0.0)),
loop_rate.sleep();
ros::spinOnce();

//        std::cout << "dt: " << broadcaster.getDt() << std::endl;
//        std::cout << "q.x: " << broadcaster.getQ().x() << std::endl;
//        std::cout << "q.y: " << broadcaster.getQ().y() << std::endl;
//        std::cout << "q.z: " << broadcaster.getQ().z() << std::endl;
//        std::cout << "q.w: " << broadcaster.getQ().w() << std::endl;
//        std::cout << "----" << std::endl;
}

return 0;
}

prevt(ros::Time::now().toSec()),
dt(0.0),
timeConst(1.0),
filterCoeff(0.0)
{
q.setRPY(0.0, 0.0, 0.0);
}

{

}

void Broadcaster::accelCallback(const geometry_msgs::Vector3::ConstPtr& msg)
{
accel.setX(msg->x);
accel.setY(msg->y);
accel.setZ(msg->z);
}

void Broadcaster::magnetCallback(const geometry_msgs::Vector3::ConstPtr& msg)
{
magnet.setX(msg->x);
magnet.setY(msg->y);
magnet.setZ(msg->z);
}

{
}

void Broadcaster::gyroCallback(const geometry_msgs::Vector3::ConstPtr& msg)
{
dt = ros::Time::now().toSec() - prevt;

gyro.setX(msg->x);
gyro.setY(msg->y);
gyro.setZ(msg->z);

angularVel.setX(gyro.x());
angularVel.setY(gyro.y());
angularVel.setZ(gyro.z());

filterCoeff = timeConst / (timeConst + dt);

// Use accelerometer and magnetometer data to correct gyro drift
correctOrientation();

updateRotation();

prevt = ros::Time::now().toSec();

//    std::cout << "angularVel x: " << angularVel.x() << std::endl;
//    std::cout << "angularVel y: " << angularVel.y() << std::endl;
//    std::cout << "angularVel z: " << angularVel.z() << std::endl;
//    std::cout << "----" << std::endl;
}

{
// New quaternion, from axis-angle notation for gyro
tf::Quaternion qNew(angularVel.normalized(), angularVel.length()*dt);

// Update previous value
q *= qNew;
q.normalize();
}

{
// Use acceleration data only if vector is close to 1 g
if ( fabs(accel.length() - 1) <= 0.1 )
{
// These vectors have to be perpendicular.
// As there is no guarantee that North is perpendicular to Down,
// set North to the cross product of East and Down.
// Gravity is measured as an upward acceleration.
tf::Vector3 Down(accel);  // Should be -accel, but not sure why this produces inverted axes!?
tf::Vector3 E = Down.cross(magnet);
tf::Vector3 N = E.cross(Down);

Down.normalize();
E.normalize();
N.normalize();

// The rows of the rotation matrix represent the coordinates in the original
// space of unit vectors along the coordinate axes of the rotated space
tf::Matrix3x3 gyroRotMat = tf::Matrix3x3(q);

// Correction vector
tf::Vector3 cv = ( N.cross(gyroRotMat.getRow(0)) +
E.cross(gyroRotMat.getRow(1)) +
Down.cross(gyroRotMat.getRow(2)) ) * filterCoeff;

angularVel += cv;
}
}




#include "ros/ros.h"
#include "geometry_msgs/Vector3.h"
#include "std_msgs/Float32.h"

{
public:
void accelCallback(const geometry_msgs::Vector3::ConstPtr& msg);
void magnetCallback(const geometry_msgs::Vector3::ConstPtr& msg);
void headingCallback(const std_msgs::Float32::ConstPtr& msg);
void gyroCallback(const geometry_msgs::Vector3::ConstPtr& msg);
//void updateTimers();
void updateRotation();
void correctOrientation();
tf::Quaternion getQ() const {return q;}
double getPrevt() const {return prevt;}
double getDt() const {return dt;}
float getTimeConst() const {return timeConst;}
void setTimeConst(float value) {timeConst = value;}

private:
tf::Vector3 accel;
tf::Vector3 magnet;
tf::Vector3 gyro;

tf::Vector3 angularVel;
tf::Quaternion q;
double prevt;
double dt;
float timeConst;
float filterCoeff;
};



# 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. 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;
msg_fsrs.data = (int16_t *)malloc(sizeof(int16_t)*numOfFSRs);

nh.initNode();

// Wait until connected
while (!nh.connected())
nh.spinOnce();

Wire.begin();

// 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.enableDefault();

// 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!");
}
gyro.enableDefault();

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

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

if (compass.a.z < 0)
signOfz = -1;
else
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
//
// http://www.analog.com/media/en/technical-documentation/application-notes/AN-1057.pdf
//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:
// http://www.freescale.com/files/sensors/doc/app_note/AN3461.pdf
// 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;
}
else
{
// 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;

pub_fsrs.publish(&msg_fsrs);
pub_rpy.publish(&msg_rpy);

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;
else
LEDTimer = millis() + 2000;
}

nh.spinOnce();
}



# 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!