2012/11/19 by Taeyoung Lee, Lee, Taeyoung, Melvin Leok +3
Engineering · #Control and Dynamics of Mobile Robots #Control and Stability of Dynamical Systems #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1211.4604
openalex publication_date 2012/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of n rigid links connected by spherical joints, that is attached to a rigid cart. The cart can translate in a horizontal plane acted on by a horizontal control force while the chain pendulum can undergo complex motion in 3D due to gravity. The configuration of the system is in (\Sph2)n × \Re2. We examine the rich structure of the uncontrolled system dynamics: the equilibria of the system correspond to any one of 2n different chain pendulum configurations and any cart location. A linearization about each equilibrium, and the corresponding controllability criterion is provided. We also show that any equilibrium can be asymptotically stabilized by using a proportional-derivative type controller, and we provide a few numerical examples.