Krang Kinematics: A Denavit-Hartenberg Parameterization

Krang is a 19 degree of freedom robot with actuators along three different major axes with a unique physical structure. Moreover, in comparison to most robots on which kinematics is studied, Krang is neither a stationary robot with a fixed base nor is it a legged humanoid for which somewhat a standard has been established. Still, we would like the kinematics for Krang to be easy to understand, regenerate and implement. To this end, we choose the well-established Denavit-Hartenberg (DH) parameterization. In the following, we will describe the DH parameterization for Krang. To do so, we will first present a refresher on DH and the specific rules we follow. With the advantage of DH being adopted for the last 60 years comes the disadvantage that different interpretations arose within the standard over the years. We follow one of the most popular and well-documented interpretations, and also describe it here. After the tutorial, we will focus on the specific parameterization of Krang in three sections: wheels to torso, torso to left arm and torso to right arm. We separate the kinematics in this way because (1) the lower body of Krang, from wheels to the torso module, is significantly different than the upper body and (2) once lower body is established, left and right arms are quite similar to each other. Lastly, we will discuss the inverse kinematics for the arms. The discussion will be mostly based on [2] where we will delve into the details of the technical work and relate it to the Krang’s parameterization.