  We present a method for system identification of flexible objects by
measuring forces and displacement during interaction with a manipulating arm.
We model the object's structure and flexibility by a chain of rigid bodies
connected by torsional springs. Unlike previous work, the proposed optimal
control approach using variational integrators allows identification of closed
loops, which include the robot arm itself. This allows using the resulting
models for planning in configuration space of the robot. In order to solve the
resulting problem efficiently, we develop a novel method for fast discrete-time
adjoint-based gradient calculation. The feasibility of the approach is
demonstrated using full physics simulation in trep and using data recorded from
a 7-DOF series elastic robot arm.
