## 4 Discussion  
Figures of the 2D views of the set of solutions show evidence of the compromise between the different objectives since they all present a Pareto-front shape curve. Regarding robustness to the initial ankle angle, using the best solution with respect to the MSE for both MOO algorithms, we appreciated low variations, a fact which demonstrates that the system can quickly recover its position and that the performance is not affected at all during the rest of the gait cycle. As both sets of solutions show the same, we can assure robustness for initial dorsiflexion of the ankle in a range of 7 to 13 degrees.  
The parameter sets from 5 to RS produced one set with costs out of limits, and the rest of them had mean costs and standard deviations clearly worse than the solutions from SS-NSGA-II and SS-RVEA. We determined that on the established decision space, we can likely find moderate performance solutions even with short optimizations. With random selection, we would obtain parameters that surely will not even be close to the Pareto-front, and therefore optimization is necessary.  
After 300 generations, SS-RVEA resulted in 19 non-dominated solutions and 25 dominated, while SS-NSGA-II resulted in all the solutions being non-dominated. We could resume the comparison of mean and standard deviation among SS-NSGA-II and SS-RVEA as follows: for the MSE objective, values from SS-NSGA-II resulted better than the ones from SS-RVEA, but for the oscillations and energy objectives, SS-RVEA values resulted better than SS-NSGA-II values, with a more notable difference in the third objective, where the mean from SS-RVEA is 17% less than the mean from SS-NSGA-II.  
While both MOO algorithms produced varied sets of valid solutions, it is possible to observe a better balance between objectives in solutions of SS-RVEA. In contrast, SS-NSGA-II solutions tend to charge toward some objective, and therefore, the best-scored solution by MSE objective results in the worst score by other objectives.  
The present AAFO design and simulation can be used with many different operating conditions, thanks to the underlying MuJoCo engine. Other simulation efforts are mainly based on the OpenSim platform (e.g., [21]), which is very useful to obtain inverse kinematics and inverse dynamics from human motion capture data, but it is not simple to modify to emulate orthoses and exoskeletons. Unlike prior efforts that apply transfer function identification to tune a PID controller for an ankle actuator at different gait stages [10], we apply multi-objective optimization to find a set of gains that are applicable to the whole gait cycle.  
Some works have proposed to simulate exoskeletons as direct torques applied to the joints of a musculoskeletal model, like [22; 23], but assume that the actuators are massless. Our work considers masses and actuation limits that follow the specifications from a manufacturer, unlike other efforts that assume that torques are instantaneous [24].  
As for limitations of our proposed AAFO, we shall mention that the control strategy, both at the actuator level and at the FSM, is not considering walking motions over different surfaces, so at this moment, it is focused on restoring normal gait only on flat and even ground.  
Based on the results from this study, the next phase of this research will be the implementation of the AAFO design as a real prototype, using materials with mechanical properties close to their simulated counterparts and using the proposed servomotors, so that validating experiments can be conducted on a test bench.