# Compensating Uncertainties in Force Sensing for Robotic-Assisted Palpation
## 1 Introduction
Finite element method (FEM) simulation is recognized as a proper approach to extract objective and quantitative information of inhomogeneous abnormal tissue, but this method is highly time consuming and normally has been used to simulate the mechanical property of soft tissue deformation from a scientific research point of view [25; 26]. The Young's or elastic modulus is recently widely used to evaluate the perceived stiffness of the soft tissue, which takes into account the tool-tissue interaction and the indentation tip size as used in [22; 27]. To calculate the perceived stiffness of soft tissue, the interaction force must be measured. Although it is possible to obtain the interaction force with a non-sensory based approach as shown in [28], the sensitivity of this development is notably lower, which makes it less favorable. In order to better estimate the interaction force of soft tissue, a sensor-based approach is usually adopted. Considering the surgical application, sometimes the sensors cannot be used to directly contact the patient body for proper operation, thus the sensor is normally arranged at the end of the surgical tools. During the operation, the surgical tool is manipulated in a dynamic manner, and possibly causes measurement uncertainties (such as noise, inertial force, friction etc. ), thus potentially providing wrong or inaccurate diagnoses, for instance, the force-based palpation. The inertial force of the sensor based robotic-environment interaction has been investigated recently within industrial robotic applications, which presents a major issue for force-guided or force-guaranteed robotic manipulations. In [29], a variant of the recursive instrumental variables method is used to online estimate the inertial parameter of the payload on the robotic system, and then an improved force control performance can be achieved. After that, in [30], the authors extended the recursive instrumental variables method to bilateral teleoperation tasks to eliminate and/or scale the non-contact force (including inertial force caused by payload). In view of the non-negligible effect of inertial force from sensor measurements, which potentially degrades the performance of interaction control, in [31] an observer was developed with two different approaches: The extended Kalmanfilter (EKF) and unscented Kalman filter (UKF), for both type of observers, different measurement vectors were considered with the first one only using pose and force/torque measurement, and the second one also considering acceleration measurement. Another work presented in [32] investigates the inertial force compensation with the industrial robot by using a quaternion-based Kalman filter for safer human-robot interaction. All these works analyze the main factors such as velocity, position, and accelerations of the inertial force caused by the sensor measurement, which highly relies on the accuracy of the inertial force model, and mainly only considers the industrial application with a heavy payload. Having reviewed the previous related works, to the best knowledge of the authors, there is no reported work on the inertial force analysis and compensation in robotic-assisted palpation. Force sensing is the most important factor to be used to analyze the mechanical property of soft tissue, and it is normally measured by the force sensor. Consequently, the inertial force will appear during the data collection process and possibly degrade the detection of tissue and may even be a risk to safety during palpation. In this paper, we investigate the effect of inertial force for robotic palpation with a probe on the force sensor, a neural-network-based method is utilized to model the inertial force during the palpation, and after that the inertial force will be compensated in an online way during the data collection process. To demonstrate the effectiveness of the proposed approach, the perceived stiffness of the soft tissue is calculated before and after the inertial force compensation and compared with each other.