System and method for controlling work machine

A system for controlling a work machine including

• a vehicle body,
• a work implement frame including a first frame including a first body connecting portion connected to the vehicle body, and a second frame disposed apart from the first frame in a left-right direction and including a second body connecting portion connected to the vehicle body,
• a work implement including a first frame connecting portion connected to the first frame, a second frame connecting portion disposed apart from the first frame connecting portion in the left-right direction and connected to the second frame, and a predetermined portion,
• a first actuator configured to operate the first frame relative to the vehicle body, and
• a second actuator configured to operate the second frame relative to the vehicle body,
• a yaw angle of the work implement with respect to the vehicle body when the work implement is in a first posture being different from a yaw angle of the work implement when the work implement is in a second posture different from the first posture,
• the system comprising:
• a work implement sensor attached to the work implement to detect a roll angle and a pitch angle of the work implement;
• and
• a controller configured to
• acquire an actual frame length indicating a distance between the first body connecting portion and the first frame connecting portion,
• acquire a position of the first body connecting portion,
• acquire the roll angle and the pitch angle of the work implement,
• calculate an assumed position of the first frame connecting portion when the yaw angle is assumed to be a predetermined angle based on the roll angle and the pitch angle of the work implement when the work implement is in the first posture,
• calculate an assumed frame length indicating a distance between the assumed position of the first frame connecting portion and the first body connecting portion,
• calculate the yaw angle of the work implement in the first posture based on a difference between the actual frame length and the assumed frame length, and
• calculate a position of the predetermined portion of the work implement based on the roll angle and the pitch angle of the work implement and the yaw angle of the work implement in the first posture.