Robotic sensing is used in many sectors to improve the inspection of large and/or complex parts, enhancing data acquisition speed, part coverage and inspection reliability. Several automated or semi-automated solutions have been proposed to enable the automated deployment of specific types of sensors. The trajectory to be followed by a robotic manipulator is typically obtained through the offline programmed tool paths for the inspection of a part. This method is acceptable for a part with known geometry in a well-structured and controlled environment. The part undergoing assessment needs to be precisely registered with respect to the robot reference system. It implies the need for a setup preparation phase for each new part, which can be very laborious and reliant on the human experience. This work combines real-time robot control and live sensor data to confer full autonomy to robotic sensing applications. It presents a novel framework that enables fully autonomous single-pass geometric and volumetric inspection of complex parts using one single robotised sensor. A practical and robust robot control sequence allows the autonomous correction of the sensor orientation and position to maximise the sensor signal amplitude. It is accompanied by an autonomous in-process path planning method, capable of keeping the inspection resolution uniform throughout the full extension of the free-form parts. Last but not least, a by-product of the framework is the progressive construction of the digital model of the part surface throughout the inspection process. The introduced framework is scalable and applicable to widely different fields.