Lecture 2Robot description and stateRobotics: Design, Manufacturing, and ControlEE209AS – Fall 2016Prof. Ankur MehtaTranscribed by: Tianrui Zhang2.1Task Description of a RobotThe task description of a robot defines the goals of a robot, which includes sensing, decision making, andactuation. Often, the sensing and actuation goals of the description requires the robot to properly define thephysical 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 2.2State description of a rigid bodyThe physical states of any rigid body is represented by its location and orientation/pose. For a rigid bodythat 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 stateEE209AS – Fall 20162.3Mathematical Representation of the StateFor the mathematical representation, we can borrow some concepts from linear algebra and geometry tohelp us describe the states.•Areference framecontains an origin point, a set of orthogonal axes, and a unit length. These entitiesdescribe a set of physical reference points that uniquely defines a coordinate system and measurementswithin it.•Avectoris an ordered list of numbers that characterizes a point within a coordinate system. It hasboth 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 theenvironment 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 worldframe•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:Leto0x, o0y, o0zdenote thex, y, zcoordinates of the origin of the body frame associated with the paddle inthe coordinate system of the world frame (see Fig. 2.2). Then, the position vectoro0of the paddle is givenby:o0=o0xo0yo0z.
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reference frame, joint space, Prof. Ankur Mehta, Tianrui Zhang