Robotic Tool Tracking under Partially Visible Kinematic Chain: A Unified Approach

Anytime a robot manipulator is controlled via visual feedback, the transformation between the robot and camera frame must be known. However, in the case where cameras can only capture a portion of the robot manipulator in order to better perceive the environment being interacted with, there is greater sensitivity to errors in calibration of the base-to-camera transform. A secondary source of uncertainty during robotic control are inaccuracies in joint angle measurements which can be caused by biases in positioning and complex transmission effects such as backlash and cable stretch. In this work, we bring together these two sets of unknown parameters into a unified problem formulation when the kinematic chain is partially visible in the camera view. We prove that these parameters are non-identifiable implying that explicit estimation of them is infeasible. To overcome this, we derive a smaller set of parameters we call Lumped Error since it lumps together the errors of calibration and joint angle measurements. A particle filter method is presented and tested in simulation and on two real world robots to estimate the Lumped Error and show the efficiency of this parameter reduction.