Calibration and transformation of a camera system's coordinate system

A method for determining a transformation between a robot's coordinate system and a camera system's coordinate system, wherein the robot includes a movable arm having the camera system mounted thereto, the robot's coordinate system defines a position of the movable arm, and the camera system's coordinate system defines a position of a target within a field of view of the camera system, the method comprising:

• positioning the movable arm about the target to three or more image-capture locations such that the target is within the field of view of the camera system at individual image-capture locations and the movable arm is rotated about and translated relative to the target from one image-capture location to another image-capture location;
• at the individual image-capture locations, capturing a set of images of the target using the camera system and recording, in the robot's coordinate system, a position of the movable arm;
• determining, in the camera system's coordinate system, coordinates of a set of two or more calibration features of the target identified in the set of images;
• and
• determining, based on the position of the movable arm and the coordinates of the set of two or more calibration features at the individual image-capture locations, the transformation between the robot's coordinate system and the camera system's coordinate system,
• wherein a position of the target is fixed and the step of determining the transformation between the robot's coordinate system and the camera system's coordinate system comprises iteratively selecting a value for the transformation between the robot's coordinate system and the camera system's coordinate system and comparing (A) a product of the selected value for the transformation, a position of the movable arm, and coordinates of a calibration feature at one image-capture location and (B) a product of the selected value for the transformation, a position of the movable arm, and coordinates of the corresponding calibration feature at another image-capture location to determine a value for the transformation that minimizes a difference between (A) and (B).