CS223A - Introduction to Robotics-lecture02
Topics: Spatial Descriptions, Generalized Coordinates, Operational Coordinates, Rotation Matrix, Example - Rotation Matrix, Translations, Example - Homogeneous Transform, Operators, General Operators Instructor (Oussama Khatib):Okay. Let's get started. So as always, the lecture starts with a video segment, and today's video segment comes from 1991, and from the group at the British Columbia and it deals with Bibet walking so there should be some sound. [Video playing] [Inaudible] Instructor (Oussama Khatib):Well, maybe we need some motors, right. Okay. So today we're going to start covering kinematics and kinematics, as I mentioned last time, kinematics is very, very important, the models that describe the robot position, the robot frames, and links, and joints. So we're going to go over the basics in describing a task, the models that we can use to determine the position and orientation of the end-effector. Then obviously when we determine the location of a link we need to be able to transform that description to the next link or to describe the position and orientation of the end- effector in our previously link so we need really to handle transformations. Then we need to discuss how we represent the position and orientation. There are many different ways through which we can describe a position or an orientation, and we will discuss a few different representations. And I'm going also to describe a little bit what is manipulated, what is a robot arm, and then what are these joints, what are the degrees of freedom of a manipulator, how we can represent the position of a manipulator. So a manipulator is defined by a set of links connected through joints. The first one, the first of the thing is fixed. We call it the base. And the last one is actually this gripper. The whole purpose of the manipulator is really to move this gripper and place it in space to do manipulation. Obviously later, we will see that it is possible to use the body, the links themselves, to do manipulation. We call it whole body manipulation. But for now, we are really interested in locating this end-effector at the same time locating any other links that is moving. So we will see that there are two types of joints that we are going to consider. There will be other possible types of joints, but we can see that any set of joints could be reduced to those two types of joints, the revolute joints and the prismatic joints. A revolute joint allows you to rotate about a fixed axis, and a prismatic joint allows you to translate about a fixed axis. And this motion is done along or about one axis so it is one degree of freedom motion. So as I said we have links and those links are a number of n. We are going to call n is the number of moving links plus one base link, the fixed link, and we have joints of two types, revolute joints and prismatic joints. So the idea is, we are going to work with one degree of freedom and this is interesting because knowing that we have only one degree of freedom joints then we will be able to connect to this to the last coordinates, as we will see. And as I said, if we have a joint like a spherical joint, would you know how many degrees of freedom a spherical joint would have? Student:Two. Student:Three. Instructor (Oussama Khatib):Three, yeah. Three. So what we would do is we will then use three revolute joints with zero links length, and then we will introduce these joints and links to represent a spherical joint. Okay. Now, we have this manipulator in this configuration and the question is how can we represent the configuration of the manipulator? What would be a good way to represent the configuration because we need to know where the manipulator is in space with respect to a fixed frame? So there are many different ways. We can go to each link and try to fix that link. So we can take maybe a given link and say we are going to locate this link with several vectors, lock it there. So if we use like three vectors and three different points the link is defined, and that would give us the configuration of that link. Now we are going to use in that case three vectors, each vector has three parameters in 3D, so we have nine parameters to describe each link, and we have n links, moving links, so we will need nine ends. A lot of parameters. And this would be one of the representations. So the description of the position using a set of configuration parameters can involve a large number of parameters, and each of them is fine. So any set of parameters that describe fully the configuration is called a set of configuration parameters. So in this case here we have nine parameters per link. Now we are really interested in a particular set of parameters – configuration parameters that has minimal number of parameters involved. We don't need all these parameters in that three vectors, three points because the points are fixed so there is a contrast betw
Topics: Spatial Descriptions, Generalized Coordinates, Operational Coordinates, Rotation Matrix, Example - Rotation Matrix, Translations, Example - Homogeneous Transform, Operators, General Operators Instructor (Oussama Khatib):Okay. Let's get started. So as always, the lecture starts with a video segment, and today's video segment comes from 1991, and from the group at the British Columbia and it deals with Bibet walking so there should be some sound. [Video playing] [Inaudible] Instructor (Oussama Khatib):Well, maybe we need some motors, right. Okay. So today we're going to start covering kinematics and kinematics, as I mentioned last time, kinematics is very, very important, the models that describe the robot position, the robot frames, and links, and joints. So we're going to go over the basics in describing a task, the models that we can use to determine the position and orientation of the end-effector. Then obviously when we determine the location of a link we need to be able to transform that description to the next link or to describe the position and orientation of the end- effector in our previously link so we need really to handle transformations. Then we need to discuss how we represent the position and orientation. There are many different ways through which we can describe a position or an orientation, and we will discuss a few different representations. And I'm going also to describe a little bit what is manipulated, what is a robot arm, and then what are these joints, what are the degrees of freedom of a manipulator, how we can represent the position of a manipulator. So a manipulator is defined by a set of links connected through joints. The first one, the first of the thing is fixed. We call it the base. And the last one is actually this gripper. The whole purpose of the manipulator is really to move this gripper and place it in space to do manipulation. Obviously later, we will see that it is possible to use the body, the links themselves, to do manipulation. We call it whole body manipulation. But for now, we are really interested in locating this end-effector at the same time locating any other links that is moving. So we will see that there are two types of joints that we are going to consider. There will be other possible types of joints, but we can see that any set of joints could be reduced to those two types of joints, the revolute joints and the prismatic joints. A revolute joint allows you to rotate about a fixed axis, and a prismatic joint allows you to translate about a fixed axis. And this motion is done along or about one axis so it is one degree of freedom motion. So as I said we have links and those links are a number of n. We are going to call n is the number of moving links plus one base link, the fixed link, and we have joints of two types, revolute joints and prismatic joints. So the idea is, we are going to work with one degree of freedom and this is interesting because knowing that we have only one degree of freedom joints then we will be able to connect to this to the last coordinates, as we will see. And as I said, if we have a joint like a spherical joint, would you know how many degrees of freedom a spherical joint would have? Student:Two. Student:Three. Instructor (Oussama Khatib):Three, yeah. Three. So what we would do is we will then use three revolute joints with zero links length, and then we will introduce these joints and links to represent a spherical joint. Okay. Now, we have this manipulator in this configuration and the question is how can we represent the configuration of the manipulator? What would be a good way to represent the configuration because we need to know where the manipulator is in space with respect to a fixed frame? So there are many different ways. We can go to each link and try to fix that link. So we can take maybe a given link and say we are going to locate this link with several vectors, lock it there. So if we use like three vectors and three different points the link is defined, and that would give us the configuration of that link. Now we are going to use in that case three vectors, each vector has three parameters in 3D, so we have nine parameters to describe each link, and we have n links, moving links, so we will need nine ends. A lot of parameters. And this would be one of the representations. So the description of the position using a set of configuration parameters can involve a large number of parameters, and each of them is fine. So any set of parameters that describe fully the configuration is called a set of configuration parameters. So in this case here we have nine parameters per link. Now we are really interested in a particular set of parameters – configuration parameters that has minimal number of parameters involved. We don't need all these parameters in that three vectors, three points because the points are fixed so there is a contrast betw