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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 a trajectory optimizer to generate desired motion and force profiles. A constrained optimization framework based on Differential Dynamic Programming and Alternative Direction Method of Multipliers has been employed to generate optimal control inputs and high-dimensional state trajectories. Experimental validation of the model performance is conducted on a soft substrate with known material properties using a Cartesian space force control mode. Results show a comparison of ground truth and predicted model based contact force states for multiple Cartesian motions and the validity range of the friction model. The proposed high-level planning has the potential to be leveraged for medical tasks involving manipulation of compliant, delicate, and deformable tissues.

Simultaneous Trajectory Optimization and Force Control with Soft Contact Mechanics