Dynamic virtual fixture on the Euclidean group for admittance-type manipulator in deforming environments

In a deforming anatomic environment, the motion of an instrument suffers from complex geometrical and dynamic constraints, robot assisted minimally invasive surgery therefore requires more sophisticated skills for surgeons. This paper proposes a novel dynamic virtual fixture (DVF) to enhance the surgical operation accuracy of admittance-type medical robotics in the deforming environment.

A framework for DVF on the Euclidean Group SE(3) is presented, which unites rotation and translation in a compact form. First, we constructed the holonomic/non-holonomic constraints, and then searched for the corresponded reference to make a distinction between preferred and non-preferred directions. Second, different control strategies are employed to deal with the tasks along the distinguished directions. The desired spatial compliance matrix is synthesized from an allowable motion screw set to filter out the task unrelated components from manual input, the operator has complete control over the preferred directions; while the relative motion between the surgical instrument and the anatomy structures is actively tracked and cancelled, the deviation relative to the reference is compensated jointly by the operator and DVF controllers. The operator, haptic device, admittance-type proxy and virtual deforming environment are involved in a hardware-in-the-loop experiment, human-robot cooperation with the assistance of DVF controller is carried out on a deforming sphere to simulate beating heart surgery, performance of the proposed DVF on admittance-type proxy is evaluated, and both human factors and control parameters are analyzed.

The DVF can improve the dynamic properties of human-robot cooperation in a low-frequency (0 ~ 40 rad/sec) deforming environment, and maintain synergy of orientation and translation during the operation. Statistical analysis reveals that the operator has intuitive control over the preferred directions, human and the DVF controller jointly control the motion along the non-preferred directions, the target deformation is tracked actively.

The proposed DVF for an admittance-type manipulator is capable of assisting the operator to deal with skilled operations in a deforming environment.