  Non-contact laser ablation, a precise thermal technique, simultaneously cuts
and coagulates tissue without the insertion errors associated with rigid
needles. Human organ motions, such as those in the liver, exhibit rhythmic
components influenced by respiratory and cardiac cycles, making effective laser
energy delivery to target lesions while compensating for tumor motion crucial.
This research introduces a data-driven method to derive surrogate models of a
soft manipulator. These low-dimensional models offer computational efficiency
when integrated into the Model Predictive Control (MPC) framework, while still
capturing the manipulator's dynamics with and without control input. Spectral
Submanifolds (SSM) theory models the manipulator's autonomous dynamics,
acknowledging its tendency to reach equilibrium when external forces are
removed. Preliminary results show that the MPC controller using the surrogate
model outperforms two other models within the same MPC framework. The
data-driven MPC controller also supports a design-agnostic feature, allowing
the interchangeability of different soft manipulators within the laser ablation
surgery robot system.
