## 4 Simulation and Experiments  
The 6-wheel robot was designed and optimized by the Taguchi method. Tables 1 and 6 show the initial and optimized robot parameters. The simulation and experiments were carried out during climbing up and down steps of (\(6\times 17\)) cm, (\(7.5\times 25\)) cm, and (\(11\times 27\)) cm. The sensors for measuring the contact angle between the wheel-ground are encoders in each bogie, LiDAR sensor in each side of the robot, and IMU in the chassis. Each wheel has an independent actuator and one position-controlled motor in the chassis; To maintain the delivery package horizontal with respect to the ground, the IMU senses the rotation of the chassis. Then the motor rotates at the same angle in the opposite direction to the inclination of the chassis  
Figure 11 shows the initial design (Figure 11a,b) and the optimal design using the Taguchi method (Figure 11c-f). The initial design can climb up stairs measuring (\(6\times 17\)) cm and (\(7\times 25\)) cm. However, The robot had problems while climbing up the stair measuring (\(11\times 27\)) cm, and during the robot's descent, only the (\(6\times 17\)) cm step succeeded while the other two stairs resulted in falls; for that reason, we were motivated to optimize the robot design by the Taguchi method, then, we obtained the optimal parameters and created the new design. The optimal design can climb up the three stairs safely. However, climbing down (\(7\times 25\)) cm and (\(11\times 27\)) cm steps remains a problem due to the length of the robot from the front to the rear wheel being \(28\) cm, and based on the kinematic constraints to climbing  
Figure 10: Schematic of emergency control when the wheel loses contact with the ground. down, the three wheels need to touch the step. Thus, the problem remains because the steps have 25 cm and 27 cm in length. Another solution is reduce the chassis length, which is 22 cm, but this parameter was not included in the Taguchi method because we cannot reduce the chassis space for the computer and sensors. Then, the emergency control helps the robot climb up and down safely without reducing the length of the chassis. The case when emergency control work is when the front wheel loses contact with the ground. We detect this case using the contact angle method by the laser scanner sensor Equation (10). Figure 12 shows the contact angle between wheel-ground. The front, middle, and rear wheels are the lines colored cyan, magenta, and blue, respectively. In Figure 12a,b, the robot climbs up steps of (6 \(\times\) 17) cm, in Figure 12c,d, the robot descends steps of (7.5 \(\times\) 25) cm, and in Figure 12e,f, the robot descends steps of (11 \(\times\) 27) cm. In Figure 12a,b, in simulation and experiment, it can be seen that the robot does not lose contact with the ground; for that reason, the lines are continuous. It can also be seen that when the robot is rising, the contact angle is 90 degrees. On the edges, it drops from 90 to 1 degree, and on the flat surface, it is zero degrees. Figure 12c-f) shows the descent of the robot on the (7.5 \(\times\) 25) and (11 \(\times\) 27) cm  
Figure 11: Simulation and experiment while climbing up and down stairs. (**a**,**b**) climbing up a step of (6 \(\times\) 17) cm; (**c**,**d**) Climbing down a step of (7.5 \(\times\) 25) cm; (**e**,**f**) climbing down a step of (11 \(\times\) 27) cm. steps. The contact angle on the edge of the step goes up to 90 degrees, and when the wheel touches the vertical surface of the step, it is 90 degrees. The contact angle is zero when the wheel touches a flat surface or when it loses contact with the ground. In the second case, the emergency controller kicks in (Figure 13) when descending steps of (11 \(\times\) 27) cm, where \(\alpha_{2}\) denotes the angle between \(l_{2}\) and the global horizontal axis, this is the parameter controlled to prevent the robot from falling.