An efficient method of correcting position mismatch between a haptic device and a robot-assisted tool

In robot-assisted surgery, a critical factor is to handle pose (position and orientation) mismatch between a stylus-style hand controller and a surgical tool (robot-assisted tool) attached to the end-effector of a robot. The mismatch has similar characteristics as robot calibration in industrial settings. Nevertheless, any methods for correcting the mismatch need to meet certain computation and accuracy requirements, which are derived from the constraints of a robot-assisted surgical system. On a virtual reality simulator, we use a haptic device (PHANToM Premium 1.5/6DOF) as the hand controller to actuate a robot-assisted surgical tool via neuroArm - a robotic system in microscopic neurosurgery. Within the workspace of the tool, we have defined the computation and accuracy requirements of correction as 1.0 ms and 30.0 μm, respectively. Towards the correction of the pose mismatch, this current work first assesses the suitability of the Newton-Raphson (NR) method for addressing the position mismatch between the haptic interface point (HIP) of the haptic device and the tooltip of the surgical tool. For fast computation, we have modified the NR method to take advantage of its quadratic rate of convergence. This modification adds a feedback loop for selecting appropriate initial values. As well, we have verified the non-singularities of the workspace where the position mismatch needs to be corrected. Assessed in the workspace of 90 targets, the modified NR method achieves an accuracy between the HIP and the tooltip at about 1.0 μm in less than 64 μs - meeting both requirements of correction. Thus, this work confirms the suitability of the modified NR method to efficiently correct the position mismatch between the HIP and the tooltip on neuroArm.