lecnotes - Lecture 2 Robot description and state Robotics...

Lecture 2
Robot description and state
Robotics: Design, Manufacturing, and Control EE209AS – Fall 2016
Prof. Ankur Mehta Transcribed by: Tianrui Zhang
2.1 Task Description of a Robot
The task description of a robot defines the goals of a robot, which includes sensing, decision making, and
actuation. Often, the sensing and actuation goals of the description requires the robot to properly define the
physical states of its own mechanical structure and any objects that it must interact with in the environment.
Example:
Move the paddle to the location of the ping-pong ball (see Fig. 2.1).
Figure 2.1: KUKA robot and Ping-Pong ball. From [2]
2.2 State description of a rigid body
The physical states of any rigid body is represented by its location and orientation/pose. For a rigid body
that can be abstracted as a point mass, the description of its location is sufficient.
Examples:
1. The ping-pong ball can be viewed as a point mass, and its state is its location.
2. The state of the paddle contains both its location and orientation (e.g. If the paddle exists in 2D space,
the orientation can be its rotation angle from a reference axis).
2-1

Lecture 2. Robot description and state EE209AS – Fall 2016
2.3 Mathematical Representation of the State
For the mathematical representation, we can borrow some concepts from linear algebra and geometry to
help us describe the states.
• A reference frame contains an origin point, a set of orthogonal axes, and a unit length. These entities
describe a set of physical reference points that uniquely defines a coordinate system and measurements
within it.
• A vector is an ordered list of numbers that characterizes a point within a coordinate system. It has
both a direction and a magnitude (length).
There may be a number of reference frames of interest. In particular, we will consider the following:
• World / global reference frame : A static, unchanging reference frame typically describing the
environment that the rigid body exists in.
• Body reference frame : A reference frame with its origin and axes fixed relative to rigid body.
With these, we can define the state of the rigid body using the following values:
• Position : a vector describing the coordinates of the origin of body frame with respect to the world
frame
• Orientation : a set of values describing the rotation of the body frame relative to the world frame.
In 2D space, this can be the single angle, between corresponding axes in the body and world frames.
In 3D space, this can be expressed in several different ways including: a rotation (or direction cosine)
matrix, Euler angles, and a quaternion, which will be explained in Section 2.4 below.
Example:
Let o
0
x
, o
0
y
, o
0
z
denote the x, y, z coordinates of the origin of the body frame associated with the paddle in
the coordinate system of the world frame (see Fig. 2.2). Then, the position vector o
0
of the paddle is given
by:
o
0
=


o 0
x
o
0
y
o
0
z


.