# Dynamic Modeling and Simulation of a Robotic Lander Based on Variable Radius Drums
## 5 Discussion
### Comparison with the Theoretical Model
However, at the beginning of the impact, the analytical curve has a greater peak with respect to the ADAMS ones; this is because at that stage the contact point is further from \(l_{m}\), and as the impact time goes on, and the legs rotates the contact point comes closer to the mean point until the minimum distance \(l_{c}\) is reached. Figure 14: Comparison between ADAMS simulations with and without ratchets and the MATLAB-based analytical simulation for two leg length parameter chosen: in the top row the lander acceleration, in the middle row the contact force between soil and lander pad, and in the bottom layer the evolution of the leg joint rotation. By comparing the black curves with the blue curves in Figure 14 it can be clearly seen the influence of the ratchet to the global dynamics of the lander. In particular, from the force and acceleration graphs small humps in the curves can be recognized due to the presence of the ratchet. From the angle graphs, instead, it can be clearly seen the influence of the ratchet: in particular as it exerts a reactive torque which opposes to the leg opening during landing, this leads to the leg opening with a lower angle. It is important to remark that the ratchet has been modeled in order to easily deflect, so in this case the influence of the ratchet is present but it does influence to a lesser extent the global dynamics of the lander. The stiffer the ratchet is, the more it influences the dynamics of the lander, even leading to the limit case of no opening of the legs at all thus imposing enormous vertical accelerations to the structure and the payload. An other cause which we can address the discrepancies between the MATLAB-based analytical simulation and ADAMS ones is one which is due to the limit that the analytical model is a purely bidimensional model, thus unable to catch 3D related phenomenon. Of particular note is that during the soft-landing the lander structure body slightly rotates around it's vertical axis (allowed given the lander legs configuration), thus part of the lander energy is split into rotational energy and therefore dissipated through lateral friction forces. This just being said can be seen from Figure 15 which shows in the left the lander rotation and in the right its rotational speed during the impact stage. During this stage can be recognized that in 0.15 s the lander rotational energy is almost completely dissipated. Moreover, an other factor which causes discrepancies between the models is that ADAMS implements a nonlinear damper in the contact model; while the analytical model implements a linear damper. This fact causes differences at the initial stage of the contact. In fact the purely linear damper causes greater damping forces in the moment of contact. Namely, the combination of all the factors mentioned above leads to discrepancies between the analytical model and the ADAMS simulations. However, despite the discrepancies between the ADAMS simulations and the analytical model, which after all is a bidimensional idealization of a three dimensional lander, the results of the two models show remarkable adherence, thus validating the approach.