Density-based Feasibility Learning with Normalizing Flows for Introspective Robotic Assembly

Question

1. How can feasibility learning be addressed in RASP?

2. What is the main focus of feasibility learning in TAMP?

3. What are the advantages of Normalizing Flows (NF) for OOD detection?

4. How is the problem formulated for predicting assembly feasibility?

Accepted Answer

Feasibility learning in RASP can be addressed by modeling the feasibility of an assembly with NF models trained on feasible assemblies alone. This approach estimates the density of In-Distribution (ID) data, allowing infeasible assemblies to be detected via a lower predicted likelihood as Out-of-Distribution (OOD). In a robotic assembly use case, NF models were trained on features of only feasible assemblies extracted from the Graph Assembly Processing Networks (GRACE) proposed in [2]. The NF model predicts the likelihood of test data, including both feasible and infeasible assemblies. By selecting a threshold on a validation set, infeasible assemblies can be detected. Empirical results show better performance with the proposed method compared to other baselines in terms of AUROC when only feasible assemblies are available. Additionally, the major contributing factors of NF were investigated, leading to a decrease in memory costs by employing a more elaborate base distribution [17].

Accepted Answer

The main focus of feasibility learning in TAMP is plan or action feasibility learning. This involves training models to predict the feasibility of an action sequence based on experience. However, scaling this approach to scenarios with different numbers and types of objects is challenging. Wells et al. [19] developed a feature-based SVM model for this purpose, but it struggles with scalability. Driess et al. [6] and a recent follow-up [20] predict the feasibility of a mixed-integer program based on visual input. Yang et al. [21] used a transformer-based architecture with multi-model input embeddings to predict plan feasibility. Atad et al. [2] introduced GRACE, a graph-based feature extractor for assemblies, which can identify infeasible assemblies when trained with both feasible and infeasible cases. These methods differ from our approach as they operate in a two-class setting, requiring the inclusion of failing action sequences in the training set and using binary feasibility classifiers.

Accepted Answer

Normalizing Flows (NF) offer several advantages for Out-of-Distribution (OOD) detection. Firstly, NF is a family of deep generative models with expressive modeling capability for complex data distributions. They allow efficient and exact sampling and density evaluation. Affine Coupling Flows, a subset of NF, have gained popularity due to their scalability to big data with high dimensionality and efficiency for both forward and inverse evaluation. Compared to other uncertainty estimation methods, NF provides a more practical advantage for OOD detection. Additionally, the use of PostNet operating on feature embeddings enhances the modeling ability for task-relevant OOD detection. The potentials of NF for OOD detection have been demonstrated in various domains, inspiring further research and application in feasibility learning.

Accepted Answer

The problem is formulated as an Out-Of-Distribution (OOD) detection. Given a dataset D of N feature embeddings of feasible assemblies, a density estimator approximates the true probability density function (PDF) of feasible assemblies. During inference, a test assembly's feature is classified as OOD (infeasible) if the density estimator's output is below a threshold, otherwise as ID (feasible). This approach allows for predicting the feasibility of assemblies based on the distribution of feasible ones.

Accepted Answer

In this work, NF are utilized to estimate the density of feasible assemblies by transforming a base distribution to the data distribution. The likelihood of an assembly embedding is obtained through an optimized MLE based on feasible data, using the Change-of-Variables formula. The inverse flow and log determinant of the Jacobian are essential for tractability and efficiency. Real-NVP, composed of multiple layers of affine coupling flows, is employed as the NF. A dataset of feature embeddings for feasible assemblies is extracted from a pre-trained GRACE, representing each assembly structure as a graph of its parts and surfaces. Channelwise mean pooling is applied to create a single feature embedding per assembly, independent of the number of assembly parts. During inference, the trained NF predicts a log-likelihood score and determines feasibility based on a pre-defined threshold.

Accepted Answer

The data-set consists of 6036 5-parts and 2865 6-parts assemblies. These assemblies were generated using the in-house simulation software MediView, which randomly created synthetic structures with aluminum parts. The software used a brute-force search method while considering geometry restrictions and the capabilities of the dual-armed robotic system KUKA LBR Med. The resulting assemblies were labeled as feasible or infeasible based on successful assembly. The training set used only feasible labeled assemblies, while the validation and testing sets were balanced with both feasible and infeasible assemblies.

Accepted Answer

GRACE was pre-trained with its default parameters to retrieve a 94-dimensions embedding per assembly. This embedding was used for implementing the NF model, which involved experimenting with Gaussian and Resampling base distributions. The NF model was trained using a batch size of 32, a learning rate of 1e-5, and the Adam optimizer. The number of coupling flows was determined through hyper-parameter search on a validation set. Each affine coupling flow contained 4 layers with 94 hidden channels per layer. The feasibility classes were measured using binary classification metrics, including False Positive Rate (FPR) and True Positive Rate (TPR), to derive an AUROC score. In this setting, a positive instance represents a feasible assembly, while a negative instance represents an infeasible one.

Accepted Answer

The NF model with Gaussian base distribution achieves the highest score, outperforming One-class SVM (OC-SVM) and naive GRACE. It uses a deep 749-layered network for better results. Additionally, the NF variant with the more expressive Resampling base distribution reaches comparable results with a smaller network (109 layers), making it more memory-efficient for robotic systems with limited computation resources. Unlike GRACE, the NF model only requires a single-pass through the feature-extraction pipeline, allowing for the feasibility determination of multiple batched assemblies simultaneously.

Accepted Answer

The NF log-likelihood estimation consists of two terms: the density of the base distribution and the log-determinant of the Jacobian of the flow transformation. The determinants play a significant role in the final scores, while the base distribution values act as a normalization term. This combination helps in estimating the likelihood of feasible and infeasible assemblies. Additionally, the flow transformation 'normalizes' the inputs in terms of both likelihood computation and geometrical coordinates, as observed in the t-SNE visualization and similarity matrices. This normalization contributes to better OOD detection performance in the flow latent space, which can be further improved by enhancing the feature extractor's ability to capture semantics related to feasibility.

Accepted Answer

The purpose of the density-based OOD detection formulation is to develop an effective feasibility prediction algorithm based on feature embeddings from a pre-trained processing network. This formulation aims to address feasibility prediction for data-driven methods in RASP with NF relying only on feasible examples. By utilizing this approach, the algorithm can detect infeasible assemblies in simulation, providing promising results that outperform baselines. Additionally, the internal working mechanism of NF is explored, offering insightful observations for further improvements in this research area.

Density-based Feasibility Learning with Normalizing Flows for Introspective Robotic Assembly

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Most frequently asked questions

1. How can feasibility learning be addressed in RASP?

2. What is the main focus of feasibility learning in TAMP?

3. What are the advantages of Normalizing Flows (NF) for OOD detection?

4. How is the problem formulated for predicting assembly feasibility?

5. How are NF used to estimate assembly density?

6. How many 5-parts and 6-parts assemblies were generated?

7. What parameters were used for pre-training GRACE?

8. How does the NF model with Gaussian base distribution compare to baselines?

9. What factors contribute to NF log-likelihood estimation?

10. What is the purpose of the density-based OOD detection formulation?

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