*3.5. Pull Back and Payload Weighing*

Once the excavation is finished, the bucket gets fully retracted and the vehicle is driven backwards, using the same "guidance" navigation module from the positioning step. A predefined time limit is assigned to this step (in the experiments, 60 s were used). If a timeout occurs, the system is put in the loading assistance state from Figure 6.

After a predefined distance has been covered within the aforementioned time limit, the bucket is commanded to perform short downward and upward tilting movements, known as the "bucket shake". Then, the bucket is lifted up to a fixed angle (*βweigh*), and the pressure sensors in the boom hydraulic line are used to estimate the bucket fill factor. A fill factor is used instead of the mass weight, since it simplifies calibration, while providing the same information for the evaluation process. The relationship between the lift cylinder pressure (*P*) and the fill factor was found experimentally and corresponds to the following affine model:

$$f\_{f\text{ill}} = mP - n \tag{9}$$

where *f fill* is the relative fill factor (0 for an empty bucket and 1 for a full bucket), and *m* and *n* are the constants to be calibrated through experimentation. Table 2 shows the parameters used for the particular conditions of the field trials presented in this work (machine and rock characteristics).

**Figure 19.** Pseudo code of the excavation algorithm.

**Table 1.** Excavation method parameters used for the full-scale validation.



**Table 2.** Weight model parameters used for the full-scale validation.
