Forward and Back

To control a robot arm we must often work in the joint space, for example if we only care about how some specific joints are oriented, or in the task space if we care about the coordinates of the tool. Going back and forth between these two spaces is the job of Forward and Inverse Kinematics. A set of mathematical equations that allow us to translate freely from one space to the other, so placing the robot's joints at specific angles will tell us the resulting cartesian coordinates. Inversely placing the tool at specific coordinates will tell us the resulting joint values each motor should reach to position the tool where we desire. Luckily all of that is handled internally by the robot controller and we usually never have to bother with the complexities of robot kinematics, but it is important to understand that ultimately the robot can only ever move around by moving in the joint space while we usually desire to move it in the task space and this translation from one to the other via forward and inverse kinematics is where robot arms derive a lot of their power.