## 7 Discussion and Conclusions
The fact that we are able to generate walking in different styles in an automated way already presents a significant difference from the classical walking generation methods using the simple models for which all outcomes look very similar. * The resulting motions are still not close to biological motion, but they have made significant progress in the right direction. In particular, the motions show variations in the height of the CoM. See the discussion below for making optimized walking motions more biological or \"human-like\". As discussed in the Introduction, optimization can be a very helpful tool to bring humanoid robots to their technical limits, i.e., to make the most out of given robot hardware. This requires that suitable optimization criteria targeting an improvement of performance be used, which has not been done so far in this study. In current research, we are also looking at step length, step frequency and walking speed maximization. The objective functions used in this study targeted the smoothness of motions, as well as measures of efficiency. We are also interested in using human-inspired criteria for generating humanoid motions. For this, we can rely on the results of inverse optimal control studies, which identify criteria underlying human motions from motion capture data. These criteria can then be applied to humanoid models in optimal control problem formulations as the one presented in this paper. We have demonstrated a similar approach based on simpler template models of human and humanoid walking in [19], also for the HeiCub, but it would be new to apply this concept of transferring bio-inspired optimization criteria to whole-body models of the HeiCub robot. There are several characteristics of the robot and its inherent control approaches that limit the performance. The fact that the robot has no arms and all counteraction to the lower limb angular momentum has to be done by the torso already prevents it from acting in a fully-human-like manner. While humans exhibit a strongly stabilized head and torso while walking forward on flat ground, such a criterion induces strong limitations to the motion if no actions of the arms are possible. In this context, also the extension of the work to the full iCub model would be interesting to see how the arms are used for angular momentum compensation. As discussed before, the HeiCub and iCub robots also have several limitations in the joint angles, the angular velocities and the joint torques that prevent them from coming close to human performance. In addition, the current foot shape and controllers impose that the robot, as most contemporary robots, walks with flat feet and cannot, e.g., have heel only or toe only contact as humans can, resulting in limited step lengths and step heights (the latter on stairs). The optimal control approach presented in this paper could also serve to generate walking motions with partial or more flexible foot contact, as soon as the hardware allows it. While optimization can help to exploit the capabilities of the robot hardware, it is best to simultaneously also improve the hardware to have an overall performance improvement. As mentioned in Section 2, the robot is equipped with series elastic actuators. The model of the robot with a reduced number of DOF, but including elasticity has been used in optimal control frameworks for the generation of squat and push recovery motions [40; 41]; the current framework for walking will be extended to include also the elasticity of the elastic actuators, which will be mounted for the experimental validations. The optimal control problem including elasticity is a larger nonlinear problem with respect to the one described in this work, which will require longer computation times. On the hardware side, a proper control for the SEA needs to be implemented.