  Force modulation of robotic manipulators has been extensively studied for
several decades but is not yet commonly used in safety-critical applications
due to a lack of accurate interaction contact modeling and weak performance
guarantees - a large proportion of them concerning the modulation of
interaction forces. This study presents a high-level framework for simultaneous
trajectory optimization and force control of the interaction between
manipulator and soft environments. Sliding friction and normal contact force
are taken into account. The dynamics of the soft contact model and the
manipulator dynamics are simultaneously incorporated in the trajectory
optimizer to generate desired motion and force profiles. A constraint
optimization framework based on Differential Dynamic Programming and
Alternative Direction Method of Multipliers has been employed to generate
optimal control input and high-dimensional state trajectories. Experimental
validation of the model performance is conducted on a soft substrate with known
material properties using Cartesian space force control mode. Results show a
comparison of ground truth and predicted model based contact force states for a
few cartesian motions and the validity range of the friction model. Potential
applications include high-level task planning of medical tasks involving
manipulation of compliant, delicate, and deformable tissues.
