3 research outputs found
A Separation Principle on Lie Groups
For linear time-invariant systems, a separation principle holds: stable
observer and stable state feedback can be designed for the time-invariant
system, and the combined observer and feedback will be stable. For non-linear
systems, a local separation principle holds around steady-states, as the
linearized system is time-invariant. This paper addresses the issue of a
non-linear separation principle on Lie groups. For invariant systems on Lie
groups, we prove there exists a large set of (time-varying) trajectories around
which the linearized observer-controler system is time-invariant, as soon as a
symmetry-preserving observer is used. Thus a separation principle holds around
those trajectories. The theory is illustrated by a mobile robot example, and
the developed ideas are then extended to a class of Lagrangian mechanical
systems on Lie groups described by Euler-Poincare equations.Comment: Submitted to IFAC 201
Intrinsic Optimal Control for Mechanical Systems on Lie Group
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