Representing Positions
Alarge part of robot kinematics is concerned with the establishment of various coordinate
systems to represent the positions and orientations of rigid object sand with transformations
among the secoordinate systems
the geometry of three-dimensional space and of
rigid motions plays a central role in all aspects of robotic manipulation
it is instructive to dis-tinguish between the two fundamental approaches to geometric reasoning: the
synthetic approach and the analytic approach
synthetic approach reasons directly about geomet-ric entities(e.g.,pointsorlines)
while synthetic approach represents these entities using
coordinates or equations, and reasoning is performed via algebraic manipulations.
In robotics,one typically uses analytic reasoning, since robot tasks are often defined ina
Cartesian workspace,using Cartesian coordinates.
Frame Rotations
Euler angles are a method to determine and represent the rotation of a body as expressed in a given
coordinate frame.
They are defined as three (chained) rotations relative to the three major axes of the coordinate frame.
Euler angles are typically representes as phi (φ) for x-axis rotation, theta (θ) for y-axis rotation, and psi ) for x-axis rotation, theta (θ) for y-axis rotation, and psi ) for y-axis rotation, and psi
(,) for z-axis rotation. Any orientation can be described through a combination of these angles.
Euler angles represented for a multirotor aerial robot.
