Model-Based Error Correction for Instrument Flexion in Robotic Surgery

Surgical robots can improve the safety of minimally invasive surgeries through image guidance and motion filtering, but design choices that reduce patient trauma (e.g., thin instrument shafts) lead to intraoperative variation in kinematic parameters. The resulting kinematic errors can degrade image-guidance methods and cause instrument motions in undesired directions. This work addresses the most significant kinematic errors: quasi-static instrument shaft flexion and motion of the port through which the instrument is introduced into the patient.

First, a metric is presented to determine the impact of kinematic errors on instrument motions. The metric quantifies how closely an erroneous robot controller will move the instrument to its desired position in a single step, as well as the worst-case angular difference between desired motions and actual motions. Simulations and experiments demonstrate results for kinematic errors due to port motion. Uses for the measure include predicting monotonic convergence, path planning, and robot design.

Second, a model-based controller is proposed to correct the instrument motions. The controller models quasi-static instrument flexion and port motion as a pinned-pinned beam with a point load at the port. The proposed controller is evaluated using the above metric, for various instrument lengths, flexion, and sensor noise, and is compared with a controller assuming a straight instrument shaft. Through 2D quasi-static simulations and experiments, the proposed controller’s motion errors are shown to be half the size of errors for the straight shaft controller. Additionally, the ability to implement the model using various sensors is demonstrated in dynamic experiments using two different sensor modalities, electromagnetic position/orientation sensors compared with strain gage force sensors.

Third, the benefits of more accurate kinematics are compared relative to the benefits from directly measuring the instrument tip’s position. Four controllers are developed, two with the proposed flexion kinematic model and two with tip tracking. A user study determines the performance of these four controllers in a 3D image guided teleoperation task involving instrument shaft flexion. Using either improved kinematics or tip tracking reduces motion errors compared with the current standard controller, but the best performance is with the proposed controller, which uses both enhancements.