Inverse Kinematics (IK) is to find the robot's configurations that satisfy the target pose of the end effector. In motion planning, diverse configurations were required in case a feasible trajectory was not found. Meanwhile, collision checking (CC), e.g. Oriented bounding box (OBB), Discrete Oriented Polytope (DOP), and Quickhull \cite{quickhull}, needs to be done for each configuration provided by the IK solver to ensure every goal configuration for motion planning is available. This means the classical IK solver and CC algorithm should be executed repeatedly for every configuration. Thus, the preparation time is long when the required number of goal configurations is large, e.g. motion planning in cluster environments. Moreover, structured maps, which might be difficult to obtain, were required by classical collision-checking algorithms. To sidestep such two issues, we propose a flow-based vision method that can output diverse available configurations by fusing inverse kinematics and collision checking, named Vision Inverse Kinematics solver (ViIK). Moreover, ViIK uses RGB images as the perception of environments. ViIK can output 1000 configurations within 40 ms, and the accuracy is about 3 millimeters and 1.5 degrees. The higher accuracy can be obtained by being refined by the classical IK solver within a few iterations. The self-collision rates can be lower than 2%. The collision-with-env rates can be lower than 10% in most scenes. The code is available at: https://github.com/AdamQLMeng/ViIK.

Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues: 1) If the target distribution is manifold, due to the unmatch between the dimensions of the latent target distribution and the data distribution, flow-based models might perform badly. 2) Discrete data might make flow-based models collapse into a degenerate mixture of point masses. To sidestep such two issues, we propose PaddingFlow, a novel dequantization method, which improves normalizing flows with padding-dimensional noise. To implement PaddingFlow, only the dimension of normalizing flows needs to be modified. Thus, our method is easy to implement and computationally cheap. Moreover, the padding-dimensional noise is only added to the padding dimension, which means PaddingFlow can dequantize without changing data distributions. Implementing existing dequantization methods needs to change data distributions, which might degrade performance. We validate our method on the main benchmarks of unconditional density estimation, including five tabular datasets and four image datasets for Variational Autoencoder (VAE) models, and the Inverse Kinematics (IK) experiments which are conditional density estimation. The results show that PaddingFlow can perform better in all experiments in this paper, which means PaddingFlow is widely suitable for various tasks. The code is available at: https://github.com/AdamQLMeng/PaddingFlow.