Motion frequency exploration based force separator for surgical robots interacting with a beating heart

Robotics-assisted beating heart surgery holds significant potential for application as it can reduce the risks of infection. A crucial requirement in beating heart surgery is the real-time and accurate feedback of the interaction forces between the end-effector and cardiac tissues. The primary challenge is developing a sensorless scheme to separate the beating motion-coupled force (MCF) from the robot dynamic state-coupled force (SCF). Acquiring the accurate beating frequency before surgery is often challenging, which limits the use of conventional force observers. To address these difficulties, this article proposes an online force separation scheme. Specifically, we establish a robot-cardiac tissue coupled model that considers robot dynamics, force generation mechanisms, and heart motion characteristics. Based on this, we design a motion frequency exploration-based force separator (MSEFS), utilizing an online expectation–maximization procedure for the joint estimation of the motion state and frequency parameter. Simulation results demonstrate that the proposed scheme surpasses existing force estimation schemes in performance due to its capability for motion frequency exploration.