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Robotics, Vision and Control

Fundamental algorithms in MATLAB: Second Edition

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I. Fundamentals

This part discusses what the word robot means to roboticists and the wider public, the history of the field, and the different forms that robots take today. A definition that will serve us well is:


a goal oriented machine that can senseplan and act


We then move on to cover how we can represent the position and orientation of objects in 2- or 3-dimensional environments in terms of graphical coordinate frames. The objects might be robots, cameras, objects or obstacles. In order to use these frames in a computer program we need an appropriate representation and we discuss vectors, orthonormal rotation matrices, triple angles, homogeneous transformation matrices and quaterions.

Finally we discuss motion, how to generate a sequence of coordinate frames that represent smooth motion from one pose to another. We also consider how to process information from sensors on a moving frame to determine the pose of that frame.

  1. Representing position & orientation
    • Pose in 2-dimensions
    • Pose in 3-dimensions
    • Orthonormal rotation matrices, homogeneous transformation matrices
    • Euler angles, roll-pitch-yaw angles, gimbal lock, quaternions
  2. Time & motion
    • Trajectories: 1-dimensional, multi-dimensional, multi-segment
    • Interpolation of rotation
    • Smooth Cartesian motion
    • Time-varying coordinate frames, angular velocity
    • Inertial navigation solution