Exploration of kinematic optimal control on the lie group 50(3)

• Type: Article in International Conference Proceedings Book
• Date: 2010

Authors

Saccon, A (Author) Other; Hauser, J (Author) Other; Pedro Aguiar, A (Author) Other

Conference proceedings International

Title: IFAC Proceedings Volumes (IFAC-PapersOnline)

Pages: 1302-1307

8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010

Bologna, 1 September 2010 through 3 September 2010

Indexing

ISI Web of Knowledge

Scopus - 9 Citations

Other information

Authenticus ID: P-007-ZQ4

DOI: 10.3182/20100901-3-it-2016.00237

Abstract (EN): In this paper, we investigate a generalization of the infinite time horizon linear quadratic regulator (LQR) for systems evolving on the special orthogonal group SO(3). Using Pontryagin's Maximum Principle, we derive the necessary conditions for optimality and the associated Hamiltonian equations. For a special class of weighting matrices, we show that the optimal feedback can be computed explicitly and we prove that the non differentiable value function is the viscosity solution of an appropriate Hamiltn-Jacobi-Bellman equation on SO(3). For arbitrary positive definite weighting matrices, numerical simulations allow us to explore the relationship between the optimal trajectories and weighting matrices, and in particular to highlight nontrivial non differentiability properties of the value function. © 2010 IFAC.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 6