TY - JOUR
T1 - Intrinsic Optimal Control for Mechanical Systems on Lie Group
AU - Liu, Chao
AU - Tang, Shengjing
AU - Guo, Jie
N1 - Publisher Copyright:
© 2017 Chao Liu et al.
PY - 2017
Y1 - 2017
N2 - The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.
AB - The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.
UR - http://www.scopus.com/inward/record.url?scp=85026538839&partnerID=8YFLogxK
U2 - 10.1155/2017/6302430
DO - 10.1155/2017/6302430
M3 - Article
AN - SCOPUS:85026538839
SN - 1687-9120
VL - 2017
JO - Advances in Mathematical Physics
JF - Advances in Mathematical Physics
M1 - 6302430
ER -