* **READING: <a href="/content/topics/homeworks/hw_readings_119/150_hw_119_chapter8/">Read PRR Chapter 8</a>** *Reminder: Readings are your responsibility. You will be expected to come to class prepared, having read the material, and ready to participate in the discussion* <slide_break></slide_break> ## Coordinate systems * Review of Chapters up to <a href="/content/topics/robotics/ros_book/80_prr_teleop_bot/">8: Teleop-bot</a> * Who has implemented and run it? * Where is a robot? How do we designate the location? * If it's a surface moving mobile robot, then an x,y coordinate would seem to be sufficient * We need to determine the units: for us, usually Meters * We need to designate the origin * Anything else? <slide_break></slide_break> ### What about the "real world"? * Where is that 0,0? * Does it matter? <slide_break></slide_break> ### What part of the robot? * What part of the robot are we talking about? * The "middle"? * Who says where the middle is? * Does it matter how high off the ground it is? <slide_break></slide_break> ### Orientation * What about where it is pointing? * Is that part of the orientation? * What does it mean to tell the robot to rotate right or left? * Is that direction also part of the orientation in space? * When would that matter? <slide_break></slide_break> ### Demo <slide_break></slide_break> ### What else? * What other aspects of orientation in space? * If the Robot has a camera mounted on it? * If there is an arm? * Robot pushing an elevator button <slide_break></slide_break> ### Actions * Taking action based on orientation. Think about: * Turn Right * Turn North * Point camera in the direction of the sound <slide_break></slide_break> ### "Pose" * The combination of the robot's position and orientation (direction it is pointing) * Each one has 3 dimensions: x,y,z and r,p,y * x,y,z are cartesian coordinates (position) * r,p,y are Euler coordinates (orientation) <slide_break></slide_break> ### Multiple Coordinate systems * Each component of the robot potentially has a coordinate system * Many of them have a fixed relationship to each other * Point 0,0 for the robot's tf might be Point 10,0 for the camera's tf * There are coordinate systems attached to (each) robot * But also to the rest of the "world" the robot knows about <slide_break></slide_break> ### Conversions * Converting between coordinate systems * Very common calculation is to convert a certain actual point * From one coordinate system to another <slide_break></slide_break> ### ROS Units and data types (see [Rep 103](https://www.ros.org/reps/rep-0103.html)) * In ROS, we use the following units: 1. Distance: Meter 2. Velocity: Meters/Second 3. Angles: Radians (sometimes degrees) 4. Orientation: Euler angles (roll pitch yaw) or Quaternions 5. Right Hand Rule 6. "RPG" Mnemonic <slide_break></slide_break> ### Euler Angles * Conventional way to represent orientation * Pitch, Roll, Yaw (from airplanes) * Can be radians or angles, but for ROS poses, it's radians * Reminder: Radians go from 0 (0 degrees) to 2 * PI (360 degrees == 0 degrees) * Howevever you will encounter negative radians for poses * Be careful when you add angles together (modulo!) <slide_break></slide_break> ### Quaternions * Quaternion represents the same, but with 4 numbers * There's an exact conversion between Euler angles and Quaternions * For subtle mathematical reasons, when combining a series of rotations, Quaternions work better * Don't try to interpret the x,y,z,r of a quaternion, it doesn't have an intuitive mapping to x,y and z euler angles. <pre><code class="language-python"> # type(pose) = geometry_msgs.msg.Pose # convert from euler to quaternion quaternion = tf.transformations.quaternion_from_euler(roll, pitch, yaw) pose.orientation.x = quaternion[0] pose.orientation.y = quaternion[1] pose.orientation.z = quaternion[2] pose.orientation.w = quaternion[3] # type(pose) = geometry_msgs.msg.Pose # convert from quaternion to euler quaternion = ( pose.orientation.x, pose.orientation.y, pose.orientation.z, pose.orientation.w) euler = tf.transformations.euler_from_quaternion(quaternion) roll = euler[0] pitch = euler[1] yaw = euler[2] </code></pre> <slide_break></slide_break> ## Datatypes in ROS * ROS "messages", also *.msg files * Really amount to a C `struct` <slide_break></slide_break> ### Point * Point (geometry_msgs/Point.msg) * x,y,z: float64 * A point in 3D space * Right hand rule * positive x-forward, positive y-left, positive z-up <slide_break></slide_break> ### Vector3 * Vector3 (geometry_msgs/Vector3.msg) * x, y, z: float64 * Simple, generic representation of 3 float64 <slide_break></slide_break> ### Quaternion * Orientation (geometry_msgs/Quaternion.msg) * x, y, z, w: float64 * An orientation in space, in quaternion form * Quaternions are another way to express orientation <slide_break></slide_break> ### Pose * Pose (geometry_msgs/Pose.msg) * position: Point * orientation: Quaternion * A combination of "where" and "facing what way" <slide_break></slide_break> ### Twist * Velocity in free space, broken into linear and angular * Twist (geometry_msgs/Twist.msg) * linear, angular: Vector3 <slide_break></slide_break> <h2 class="shadow p-3 bg-white rounded">Thank you. Questions?<img class="img-fluid w-100" src="https://picsum.photos/800/100.jpg" /> <small> (random Image from picsum.photos)</small></h2>