Abstract by Jesse Friedbaum
Stability and Robustness of Several Linear Approximation Techniques used for Robotics Control
Historically robots have been relegated to a very limited variety of tasks primarily in manufacturing, however engineers at the BYU Robotics and Dynamics Laboratory (RAD Lab) are attempting to create robots and control systems capable of participating in a greater variety of activities, especially the medical field. In order to carry out these more delicate tasks the RAD Lab uses the Model Predictive Control (MPC) algorithm. In order to make this algorithm computationally tractable, it is necessary to simplify the equations of motion of our robotic system to a linear approximation.
We examine the numerical stability and robustness to perturbation of three linearization techniques: the standard Jacobian Linearization technique, as well as an engineering technique the “Fixed State” approximation that assumes the dynamics matrix remains constant between time steps, and finally a novel technique “Coupling Torque,” which assumes all coupling terms between variables is constant. The Coupling Torque technique especially presents promise as it allows the control algorithm to be parallelized which allows it to be applied to mush more complex robots.