Configuration of a Robot
By: Khalil Idrissi
Tags: Robotics, Configuration, Robot, C Space

Hello everyone. This is my first story on medium .Today’s lesson is the first lesson in the course of Robotics. Before we dive in practice directly , we should first get some theoretical knowledge about a bunch of fundamental notions and concepts that will help us in the practical part. So let’s start .

A robot is a machine composed of hardware and software parts capable of performing complex tasks such as mimicking humans ( walking , thinking , … etc ) to interact with the environment .On this course we will focus on the hardware part.

The majority of robots consist of multiple mechanisms to complete a task.A mechanism is a composition of links and joints. A link is a rigid body ( rigid body means a body where we omit deformations and elasticity ,in other words , a solid body and not soft like a pillow) integrated in the robot’s mechanism. And a joint is a mechanical part responsible of joining 2 links .

MODERN ROBOTICS MECHANICS by Kevin M. Lynch and Frank C. Park

As you can see in the picture above , it is a four-bar linkage mechanism .The blue circles are joints ( here we have 4 joints ) and the red arrows are links ( 3+ the ground that is 4 links ).

After this introduction ,let’s move to some theory .

One of the most important questions in robotics is where is it (localization )? The answer of that question is given by the configuration of the robot .

The configuration of the robot is a specification of the position of all points of the robot . ( since a rigid body is a composition of multiple material points)

Let’s take an example :

If i ask you where is the green point in the plane of 2 dimensions IR² ( x-axis + y-axis )? You would respond automatically the position of the green point is (2,1) . Here without knowing ,you specified a configuration of the green point. In general ,the configuration of a point laying on a plane (2 dimensions : x-axis and y-axis or 2 coordinates) is q=(x,y) .

Let’s look at another example to see if you get the idea of configuration :

Above , we want to localize the coin when it is moving .In other words , we want to find a way or to be precise , a configuration to specify the position of all points constituting the coin ,thus the position of the coin . To do that , we start by choosing randomly any point from the coin here we chose the green point (3,2). Then we see that a choice of 2 coordinates (x,y) is a good option but it is not enough .The image below explains why something is still missing :

If we turn the coin ( changing orientation ) and keep the intial position of our green point , we will have different positions of the coin and the same position of the green point .So we need another coordinate responsible of the orientation :

Angle theta responsible of the orientation angle

We finish with 3 coordinates that describes the configuration of our coin : (x,y) and theta . Consequently , a configuration of our coin is q =(x,y,theta).

Summary : the configuration of a robot is a complete specification of the position of every point of the robot .

reference:

MODERN ROBOTICS MECHANICS, PLANNING, AND CONTROL by Kevin M. Lynch and Frank C. Park May 3, 2017