Nonlinear Control using Coordinate-free and Euler Formulations: An Empirical Evaluation on a 3D Pendulum

Abstract

Pendulum dynamics are widely utilized in robotics control literature to test and evaluate novel control design techniques. They exhibit many interesting features commonly seen in real-world nonlinear systems and yet they are simple enough for quick prototyping, further analysis, and benchmarking. In this work, we study the impact of a 3D pendulum’s orientation parametrization on stabilization performance. Mainly, we show that using a global or coordinate-free formulation for dynamics and control is not only singularity-free but also more input-efficient. We validate this empirically by running over 700 stabilization simulations across the full configuration space of a 3D pendulum and compare the performance of a geometric and a Euler-parametrized controller. We show that the geometric controller is able to leverage the inherent manifold curvature and flow along geodesics for efficient stabilization.