Kinematic and Dynamic Modeling of the PhantomX AX Metal Hexapod Mark III Robot using Quaternions

Abstract

For years, hexapod robots have been the subject of study due to their many applications of use. Among their different characteristics, the great adaptability of locomotion and stability to hostile terrains are the main features that stand out the most. For that reason, it is fundamental to obtain its kinematic and dynamic model. For the development of its mathematical modeling, traditional spatial location tools are usually used, which leads to high computational costs, as well as a high complexity in its control system. In this context, this research developed the kinematic and dynamic modeling of the PhantomX AX Metal Hexapod Mark III Robot using quaternions; likewise, the modeling was carried out using the homogeneous transformation matrix for its comparison, both models were finally validated in a robotic simulation software CoppeliaSim. The RMSE was used as an error indicator, obtaining values not greater than 1.27 mm in the validation of the kinematics and values in the range of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> Nm in the validation of the dynamics, showing that both models were valid. One of the most important conclusions is that an adaptation of Newton Euler's algorithm for the calculation of dynamics using quaternions is obtained, applied to different types of open kinematic chain robots. Finally, the computational cost of the models using quaternions and the homogeneous transformation matrix was compared, a reduction of 21.4% was obtained with the use of quaternions in kinematic modeling; however, in dynamic modeling with Newton Euler, a reduction of 27% was obtained with the use of homogeneous transformation matrices.