Energy shaping nonlinear control of underactuated needle insertion

This work investigates the position control of an underactuated mechatronic system for straight needle insertions in soft tissues. The system consists of a pneumatic cylinder pushing a slender needle supported at the base and subject to external forces at the tip due to interactions with soft tissues. The system dynamics is described by a rigid-link underactuated model for controller design purposes. The main contribution of this work is a new energy shaping control law that: (i) does not rely on the analytical solution of partial differential equations, which is a major hurdle in energy shaping techniques, and does not require partial feedback linearization, which is known to be sensitive to model uncertainties; (ii) accounts for the work of the friction forces on the pneumatic cylinder and of the lateral forces acting on the needle tip, which are estimated adaptively with nonlinear observers. For comparison purposes, an alternative controller that employs feedback linearization is also presented. Simulations and experiments on silicone rubber phantoms using a needle with axial-symmetric tip indicate that the proposed controller can reduce the needle tip rotation and the corresponding deflection compared to a PID algorithm. In case of larger insertion forces, the controller can limit the insertion depth to prevent large needle deflections: this behavior can be influenced by acting on a specific tuning parameter, thus providing additional flexibility compared to previous implementations. Finally, the proposed solution is less sensitive to parameter uncertainties than the alternative controller.