# Reactive Balance Control for Legged Robots under Visco-Elastic Contacts
## 7 Conclusions  
This paper presented two novel control methods for balancing a legged robot on visco-elastic contacts: TSID-Flex-K and TSID-Adm. To ensure a fair comparison between novel and state-of-the-art methods we have used a unified gain-tuning procedure (except for Adm-Ctrl, which we have tuned by hand). We have performed several tests in simulation using a simple 4-DoF robot. The presented results depict a broad picture of performance for 4 controllers, across 3 contact stiffnesses and 7 gain sets each (except for Adm-Ctrl, for which we have tested only one gain set). We highlight here the main pros and cons of each controller, which are also summarized in Table 5.  
The novel controllers presented in this paper (TSID-Flex-K and TSID-Adm) perform well for soft contacts, reasonably well for medium contacts, but they have showed instability for stiff contacts and noisy simulations. TSID-Rigid has unsurprisingly shown the opposite trend, getting unstable for soft contacts (even though it was able to regain stability when introducing joint Coulomb friction), but then becoming more and more competitive as the contact stiffness increased. This is actually reasonable because the higher the contact stiffness, the more the system behaves as if contacts were rigid, which is a key assumption in TSID-Rigid. One of the main advantages of the novel controllers is their ease of gain tuning, which allows for a unified tuning of force and position feedback gains (as acceleration/jerk gains can be seen as force gains). However, the novel controllers have demonstrated a remarkable sensitivity to uncertainties. We believe that this is due to the attempt to compensate for the contact forces, which are rapidly changing (especially for stiff contacts), thus easily leading to destabilizing compensation errors. This makes these methods sensitive to low control frequencies and actuation delays, such as the ones introduced by limited joint torques bandwidth and joint Coulomb friction. Adm-Ctrl has been the only controller that was always stable, making it the most robust of them all. Despite its superior robustness, in no condition Adm-Ctrl has outperformed all the other controllers. Moreover, its gain tuning remains a heuristic procedure, and its convergence properties are not yet clearly understood. All of this makes this controller hard to use in practice, highlighting the need for more work on this subject. Overall, the case of stiff contacts was the hardest for the tested controllers: only TSID-Rigid and Adm-Ctrl remained stable, but they resulted in oscillatory trajectories, which are (at best) unpleasant on real hardware. These oscillations are due to the small contact damping, which combined with the high contact stiffness makes it hard for the controller to damp the high-frequency force oscillations. \begin{table}
\begin{tabular}{l c} \hline \hline
**PROS** & **CONS** \\ \hline \multicolumn{2}{c}{TSID-Flex-K and TSID-Adm} \\ \(\bullet\) Easy to tune (unified pos-force feedback). & \(\bullet\) Need high frequency for hard contacts. \\ \(\bullet\) Best for soft/medium contact. & \(\bullet\) Unstable for hard contact with noise. \\ \(\bullet\) Ok for hard/medium contacts. & \(\bullet\) Unstable for soft contacts. \\ \(\bullet\) Easy to tune (assuming perfect joint torque tracking). & \(\bullet\) Undesired oscillations (no force feedback). \\ Adm-Ctrl & \\ \(\bullet\) Always stable. & \(\bullet\) Hard to tune/analyze. \\ \(\bullet\) Good for soft contacts. & \(\bullet\) Never the best. \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of main features of each controller. Finally, these results show that controllers that are well supported by theoretical results and perform exquisitely in ideal conditions, can then fail miserably in realistic simulations. Thus, working on robustness issues seems paramount for future work. We believe that the subject of balance control on visco-elastic contacts still requires investigation.