## 3 Methods
The feedback term's gradient (\(\
abla_{\mathrm{y}}\)) with respect to the latent space vector (\(\mathrm{y}\)) represents the difference between the generated output (\(\mathrm{z}\)) and the targeted output (\(\overline{\mathrm{z}}\)). \[\mathrm{Feedback-Latent~{}vector}~{}(\overline{\mathrm{y}})=\mathrm{y-}\left[ \alpha\times\
abla_{\mathrm{y}}\mathrm{f}(\mathrm{z},\ \overline{\mathrm{z}})\right] \tag{6}\]  
An advanced design generation methodology is proposed in this study to examine and enhance both functionality and aesthetic-based preferences in designing fumigation robots. This study proposes a machine-learned multimodal and feedback-based VAE (MMF-VAE) model. This approach improves the functionality of feedback-based VAE models by refining the latent space representation and provides the desired output quality, as illustrated in Figure 1:0 In this enhanced framework, textual or image-driven prompts are given to the encoder, while a database (\(\mathrm{d}\)) with additional spraying robot training data guides the latent space. The model's refinement is achieved by combining input prompts and external datasets, reducing feedback errors, and achieving better alignment between generated output (\(\mathrm{z}\)) and desired results (\(\overline{\mathrm{z}}\)), as represented in Equation (7). The function \(\mathrm{g}\) represents the refinement function based on the database. Algorithm 1 elaborates the sequence of operations performed in the proposed MMF-VAE model to acquire the desired output. Figure 1:1  
Algorithm 1 constructs and trains an MMF-VAE using a dataset of robot attributes for fumigation services, denoted as data. These attributes include size (represented in three dimensions), weight, speed, drive type, etc. Each sample is flattened to match the specified input_dim (in this case, size, weight, battery, autonomy_type, drive_type, payload, sensors, PC, navigation_system, spraying_type, spray_system, terrain, and safety), which is then processed through an AttributeEncoder and SpecificationDecoder. The encoder outputs two vectors, \(\mathrm{\mu}\) and logvar, each of the dimension latent_dim (in this case 16). A reparameterization function draws from a normal distribution, producing a latent vector, \(\mathrm{z}\), that captures essential features of the input data. The hidden_dim parameter (in this case, 128) controls the capacity of internal layers, striking a balance between model expressiveness and computational cost. During training, batch_size controls how many samples are processed in each iteration, while num_epochs determines the total number of passes over the entire dataset. An Adam optimizer with a learning_rate (lr = 0.0001) performs gradient-based updates on the network weights. A combined VAE loss, encompassing reconstruction error, KL divergence, and any domain-specific penalties, guides the model in accurately learning the robot attribute distribution. After training, the final MMF-VAE is saved as a model file and ready to be integrated with downstream applications such as large language models. The training loop iterates until the loss, initially around 8000 (as seen in Figure 4), stabilizes below 10 after roughly 1000 iterations (though the example ran for 2000 total). Once trained, the MMF-VAE model is saved and integrated with a conversational LLM (e.g., ChatGPT/Ollama) to provide user-friendly interactions for specifying or refining robot designs. The user can submit prompts to the LLM, which queries or updates the MMF-VAE latent space and returns design suggestions or final specifications.