### Homogeneous Transformation Matrices to Express Configurations in Robotics

Up to this point, we have discussed orientations in robotics, and we have become familiarized with different representations to express orientations in robotics. In this lesson, we will start with configurations, and we will learn about homogeneous transformation matrices that are great tools to express configurations (both positions and orientations) in a compact matrix form. This lesson is part of the series of lessons on foundations necessary to express robot motions. For the full comprehension of the Fundamentals of Robot Motions and the necessary tools to represent the configurations, velocities, and forces causing the motion, please read the following lessons…

### Cayley-Rodrigues Parameters to Express Orientations in Robotics

In this lesson, we will become familiarized with another representation for orientations in robotics that is called Cayley-Rodrigues Parameters. Cayley-Rodrigues parameters provide local coordinates for SO(3). They are local coordinates because the representation is not singularity-free, and not all orientations can be expressed by them. However, they have properties that make them intriguing. This lesson is part of the series of lessons on foundations necessary to express robot motions. For the full comprehension of the Fundamentals of Robot Motions and the necessary tools to represent the configurations, velocities, and forces causing the motion, please read the following lessons (note that…

### Explicit Representation of the Orientation: Exponential Coordinates

In the previous lesson, we became familiar with rotation matrices, and we saw that the nine-dimensional space of rotation matrices subject to six constraints (three unit norm constraints and three orthogonality constraints) could be used to implicitly represent the three-dimensional space of orientations. There are also methods to express the orientation with a minimum number of parameters (three in three-dimensional space). Exponential coordinates that define an axis of rotation and the angle rotated about that axis, the three-parameter Euler angles, the three-parameter roll-pitch-yaw angles, the Cayley-Rodrigues parameters, and the unit quaternions (use four variables subject to one constraint) are some of…

### Implicit Representation of the Orientation: a Rotation Matrix

In the previous lesson, we became familiar with the concept of the configuration for the robots, and we saw that the configuration of a robot could be expressed by the pair (R,p) in which R is the rotation matrix that implicitly represents the orientation of the body frame with respect to the reference frame and p is the position of the origin of the body frame relative to the space frame. In this lesson, we will focus on the orientation, and we will see that we can implicitly represent the orientation using powerful tools named rotation matrices, and we will…

### Fundamentals of Robot Motions: Configurations (Introduction)

This post is part one of the series of lessons on the fundamentals necessary to represent the robot's configuration, and it gives an introduction to what we mean when we are talking about representing a robot's configuration. In previous lessons, we learned that the robot's configuration answers the question of where the robot is, and we saw that there are two ways to represent the robot's configuration: Implicit representation, where the configuration is represented by embedding the curved space in higher-dimensional Euclidean space subject to constraints and explicit representation where configuration is represented with a minimum number of coordinates. You…

### The Future with Robots, AI, and Automation

Are you afraid that you lose your job to a robot, AI, or automation? Do you have questions about what the future will be like with current advances in technology? Do you concern about ethics when robots enter our world? If you have any of these questions, do not forget to watch Dr. Madi's discussion with the Roboticist, Michael Overstreet, on his YouTube Channel: https://www.youtube.com/watch?v=2kY8vlPv6qg Download the discussion presentation HERE! Download the free PDF of the talk containing more examples and an appendix of the professions and the degree to which they are susceptible to automation HERE. Do not forget…

### Holonomic vs. Nonholonomic Constraints for Robots

In this post, you will learn that holonomic or configuration constraints reduce the degrees of freedom (dofs) of a robot, whereas nonholonomic constraints reduce the space of possible velocities. β οΈ This post also has a video version that complements the reading. Our suggestion is to watch the video and then read the reading for a deeper understanding. Holonomic (Configuration) Constraints for Robots Letβs see this with an example. Remember our famous 4-bar linkage with one degree of freedom? If you do not, please refer to this lesson. For now, consider a 4-bar linkage that has 4 links (ground is a…

### Everything About the Degrees of Freedom of a Robot

In this post, you will learn ANYTHING that you've ever needed to know about the degrees of freedom of a robot. You will become familiarized with a general formula to find the degrees of freedom of any mechanism, not just robotic arms. The degrees of freedom of a robot is the dimension of the robot's C-space, which is the minimum number of real numbers needed to represent the robot's configuration. As we saw in the previous post, the robot's configuration is our answer to the question where is the robot? And we also saw different ways to represent the configuration…