Robotics and the Geometry of Motion

This course is about understanding robotics and the geometry of motion, and covers kinematics and differential relations. You will start the course by learning how a homogeneous matrix maps frame K coordinates to (k-1) coordinates, along with the four fundamental operations that are involved in making (k-1) frame coincident with k frame. You will also learn how, given the values of joint variables, you can solve for the end-effector location in the Cartesian space of the robot base frame. You will be taught how to find the position and the orientation of the tool at the soft home position of, for instance, the six-axis articulated arm, Intelledex 660T, which involves three steps. Consider how to assign the coordinate frame, calculate the DH (Diffie-Helmann) parameters and, finally, find the arm matrix. The course will cover the formulation of manipulator tasks whether a systematic closed form solution applicable to robots in general is available.

Next, you will learn how to solve a manipulator if all the sets of joint variables can be found corresponding to a given end-effector location, subject to three conditions. Analyze how these conditions relate to tool points within the workspace, what values a number has to have to have any arbitrary orientation of a tool, and how the status of joint limitations is important. You will be taught the complex differences between a closed form solution and a unique solution, as well as the difference mathematical approaches for deriving closed form solutions.

Finally, you will learn that the robot path planning problem is formulated in a tool-configuration space, and the robot motion is controlled at the joint space. What do you need to calculate the Jacobian? What is one of potential problems for solving for joint space velocity? When does a Jacobian lose rank in joint space? You will also be taught why the interior singularity is potentially troublesome and how it is formed. Students of mechanical engineering, especially those specializing in robotics, will find this course particularly interesting. Start this course how and better your understanding of robotics and the geometry of motion today.