  We present a contact-implicit trajectory optimization framework that can plan
contact-interaction trajectories for different robot architectures and tasks
using a trivial initial guess and without requiring any parameter tuning. This
is achieved by using a relaxed contact model along with an automatic penalty
adjustment loop for suppressing the relaxation. Moreover, the structure of the
problem enables us to exploit the contact information implied by the use of
relaxation in the previous iteration, such that the solution is explicitly
improved with little computational overhead. We test the proposed approach in
simulation experiments for non-prehensile manipulation using a 7-DOF arm and a
mobile robot and for planar locomotion using a humanoid-like robot in zero
gravity. The results demonstrate that our method provides an out-of-the-box
solution with good performance for a wide range of applications.
