  In this report we explore the application of the Lagrange-Newton method to
the SAM (smoothing-and-mapping) problem in mobile robotics. In Lagrange-Newton
SAM, the angular component of each pose vector is expressed by orientation
vectors and treated through Lagrange constraints. This is different from the
typical Gauss-Newton approach where variations need to be mapped back and forth
between Euclidean space and a manifold suitable for rotational components. We
derive equations for five different types of measurements between robot poses:
translation, distance, and rotation from odometry in the plane, as well as
home-vector angle and compass angle from visual homing. We demonstrate the
feasibility of the Lagrange-Newton approach for a simple example related to a
cleaning robot scenario.
