2008/05/06 by Taeyoung Lee, Lee, Taeyoung, Melvin Leok +3
Engineering · #Aerospace Engineering and Control Systems #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Robotic Mechanisms and Dynamics
paper · pdf · doi:10.48550/arxiv.0805.0639
openalex publication_date 2008/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each rigid body is viewed as evolving on a configuration manifold that is a Lie group. Discrete-time dynamics of each rigid body are developed that evolve on the configuration manifold according to a discrete version of Hamilton's principle so that the computations preserve geometric features of the dynamics and guarantee evolution on the configuration manifold; these discrete-time dynamics are referred to as Lie group variational integrators. Rigid body optimal control problems are formulated as discrete-time optimization problems for discrete Lagrangian/Hamiltonian dynamics, to which standard numerical optimization algorithms can be applied. This general approach is illustrated by presenting results for several different optimal control problems for a single rigid body and for multiple interacting rigid bodies. The computational advantages of the approach, that arise from correctly modeling the geometry, are discussed.