# Dynamic Modeling and Simulation of a Robotic Lander Based on Variable Radius Drums
## 5 Discussion
### Case (1): Simulation on Horizontal Surface  
Figure 7 reports the evolution of the state of the lander MBS during the simulation time. In Figure 7a the loss of height can be seen; Figure 7b shows the evolution and the changes of speed the lander is subjected; finally Figure 7c describes the acceleration of the lander. From these figures it can be seen that at \(t\approx 0.3\) s, the lander impact the ground with a speed \(v\approx 3.0\) m s\({}^{-1}\). Moreover, some sudden changes in  
Figure 15: (**a**) The lander structure center mass rotation around its vertical axis and (**b**) its angular speed around the same axis.  
speed are observed, which identifies the bounces of the lander after impact. The oscillation speed and amplitude decreases due to the dissipative forces defined in the contact problem. It can be seen that the lander is subjected to peaks of deceleration having amplitude \(|a|\in[3,3.5]g\). It is important to report that the evolution of the acceleration has been slightly filtered in order to cut out the high-frequency peaks of deceleration taking place in specific instants of time due to numerical instabilities. Disregarding these is allowed from a simulation perspective, as their impact on the landing behavior is low and they can easily be filtered out with dampers on the payload attachment points.  
When the lander impacts with the soil its legs start to rotate due to the torque generated by the contact force with the ground. As expected, for an impact simulation on an horizontal surface, the legs of the lander rotate uniformly, until the maximum angle \(\theta\approx 30^{\circ}\) for each leg. The reactive torques generated have the same trend. These aspects can be observed in Figure 8a,b. From the same figures, the action of the ratchets can be observed. More precisely, when the leg rotation reaches its maximum value, the leg starts to rotate back to the original position. However, the ratchet almost immediately engages and limits this motion, effectively stopping the leg orientation at the current angle; to this angle a fixed torque of \(T\approx 1.5\,\mathrm{N}\,\mathrm{m}\) is naturally associated. Finally, in Figure 8c the contact forces acting between the soil and the lander leg are shown. In a way similar to the case of acceleration, the contact forces have been slightly filtered in order to remove the high-frequency spikes. In this figure the bounces can be seen and, as expected, the contact force has the same trend as the joint rotation. By looking again at the figure we can say that the first peak of the contact force is the one responsible of dissipating most of the energy of the system, as can be seen in Figure 9b, which represents the kinetic energy of the lander MBS during the whole impact simulation. The other spikes are about the lander stabilizing on the soil surface. However, the amplitude of the contact force is \(|F|\in[5.0,8.7]\mathrm{N}\). Finally, Figure 9a reports the rotation of the ratchet structure revolute joint. The high peaks represent the instants at which the ratchet overcomes the tooth present on the side of the leg, and thus moving to the next tooth. In this case, the ratchet overcomes four teeth. The low peaks instead are due to the leg trying to rotate in the opposite direction, against the engaged ratchet.