## 5 Discussion  
In this study, we have explored the application of Deep Neural Networks (DNNs) for addressing the inverse kinematics (IK), motion control, and motion planning problems, all in the presence and absence of obstacles. These are long-standing problems, with diverse well-proved numerical and analytical solutions, but none of them are definitive. Deep Neural Networks have gained increasing popularity in recent years, and appear to be a great tool to tackle these problems. First of all, the IK problem can be easily framed as a supervised learning task. Once that is performed, the capabilities of DNNs as function approximators should make them ideal for the task of finding a suitable solution. The problem can become harder to formulate with unsupervised learning, but, if performed correctly, the computational and time cost can be reduced greatly. We have seen that simple DNNs, such as MLPs, can provide good accuracy in specified environments or settings. Newer architectures such as GANs, VAEs or GNNs are also being introduced and present acceptable results under certain conditions, though they still have considerable room to improve. DRL appears to be a good alternative as well, and is better suited for control and path planning around obstacles. Our research shows that studies are tending to focus on hybrid methods, using DNNs for fast initial IK guesses and then optimizing the solution through numerical methods, genetic algorithms or meta-heuristics such as PSO. The obstacle avoidance problem is harder to pose in a supervised learning framework. The positions of the obstacles need to be known beforehand and the trained DNN cannot adapt to changes in the environment. Additionally, introducing the constraints in the training dataset is not a trivial task. This is why there are not many results in this field, with the exception of RNNs, as they deal with time series. This model is mainly used for motion planning. In the case of motion control, the best strategy would be to select points for training that are already far from obstacles and train a simpler model, such as an MLP. Unsupervised learning appears to be a convenient option. However, constraints are still difficult to add to the framework. From both the motion control and planning perspectives, the idea is to reformulate the problem as an optimization one and then add constraints. This is why Deep Reinforcement Learning shines in this environment, as obstacles can be added intuitively to the reward function to be taken into account when training. This set of techniques are mostly used for control, but can also learn to plan trajectories. The results look promising, but more progress can still be made. Additionally, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Reference** & **Model** & **Year** & **Planning** & \
\begin{tabular}{c} **Dynamic** \\ **Environment** \\ \end{tabular} & **DOF** &
\begin{tabular}{c} **Orientation** \\ **Considered** \\ \end{tabular} & **Advantages** & **Limitations** \\ \hline
[102] & RNN & 2021 & Online & Yes & 6 & Yes & \
\begin{tabular}{c} Problem can be \\ considered a time \\ series. \\ \end{tabular} &
\begin{tabular}{c} Problem must be \\ reformulated. \\ \end{tabular} \\ \hline
[63] & GAN & 2021 & Offline & Yes & 7 & No & \
\begin{tabular}{c} Learns a distribution \\ of valid robot \\ configurations. \\ \end{tabular} &
\begin{tabular}{c} Problem must be \\ reformulated and \\ added to a larger \\ scheme. \\ \end{tabular} \\ \hline
[107] & VAE & 2022 & Offline & No & 7 & No & \
\begin{tabular}{c} Models latent space \\ of target, joint \\ positions and \\ obstacles. \\ \end{tabular} &
\begin{tabular}{c} Problem must be \\ reformulated and \\ added to a larger \\ scheme. \\ \end{tabular} \\ \hline
[114] & DRL & 2024 & Online & No & 7 & Yes &
\begin{tabular}{c} Simplest way to \\ formulate the \\ problem. \\ \end{tabular} & Sim2 real transfer. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relevant results for deep learning obstacle avoidance via motion planning.