A robotic surgical system includes a surgical instrument and a processor. The surgical instrument includes an elongate, hollow shaft having a proximal end, a distal end, and a flexible section. The surgical instrument further includes a sensor apparatus configured to generate sensor data about the flexible section and a force transmission mechanism coupled to the proximal end of the shaft. The processor is communicatively coupled to at least the sensor apparatus. The processor is configured to receive the sensor data about the flexible section from the sensor apparatus and to combine the sensor data received from the sensor apparatus with known information regarding stiffness of the surgical instrument to derive an internal actuation force applied by the force transmission mechanism.