Abstract

No abstract

Abstract-We present a novel approach for incorporating collision avoidance into trajectory optimization as a method of solving robotic motion planning problems. At the core of our approach are (i) A sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary. (ii) An efficient formulation of the no-collisions constraint that directly considers continuous-time safety and enables the algorithm to reliably solve motion planning problems, including problems involving thin and complex obstacles.We benchmarked our algorithm against several other motion planning algorithms, solving a suite of 7-degree-of-freedom (DOF) arm-planning problems and 18-DOF full-body planning problems. We compared against sampling-based planners from OMPL, and we also compared to CHOMP, a leading approach for trajectory optimization. Our algorithm was faster than the alternatives, solved more problems, and yielded higher quality paths.Experimental evaluation on the following additional problem types also confirmed the speed and effectiveness of our approach: (i) Planning foot placements with 34 degrees of freedom (28 joints + 6 DOF pose) of the Atlas humanoid robot as it maintains static stability and has to negotiate environmental constraints.(ii) Industrial box picking. (iii) Real-world motion planning for the PR2 that requires considering all degrees of freedom at the same time.

We present SR3, an approach to image Super-Resolution via Repeated Refinement. SR3 adapts denoising diffusion probabilistic models [1], [2] to image-to-image translation, and performs super-resolution through a stochastic iterative denoising process. Output images are initialized with pure Gaussian noise and iteratively refined using a U-Net architecture that is trained on denoising at various noise levels, conditioned on a low-resolution input image. SR3 exhibits strong performance on super-resolution tasks at different magnification factors, on faces and natural images. We conduct human evaluation on a standard 8× face super-resolution task on CelebA-HQ for which SR3 achieves a fool rate close to 50%, suggesting photo-realistic outputs, while GAN baselines do not exceed a fool rate of 34%. We evaluate SR3 on a 4× super-resolution task on ImageNet, where SR3 outperforms baselines in human evaluation and classification accuracy of a ResNet-50 classifier trained on high-resolution images. We further show the effectiveness of SR3 in cascaded image generation, where a generative model is chained with super-resolution models to synthesize high-resolution images with competitive FID scores on the class-conditional 256×256 ImageNet generation challenge.

We propose Axial Transformers, a self-attention-based autoregressive model for images and other data organized as high dimensional tensors. Existing autoregressive models either suffer from excessively large computational resource requirements for high dimensional data, or make compromises in terms of distribution expressiveness or ease of implementation in order to decrease resource requirements. Our architecture, by contrast, maintains both full expressiveness over joint distributions over data and ease of implementation with standard deep learning frameworks, while requiring reasonable memory and computation and achieving state-of-the-art results on standard generative modeling benchmarks. Our models are based on axial attention, a simple generalization of self-attention that naturally aligns with the multiple dimensions of the tensors in both the encoding and the decoding settings. Notably the proposed structure of the layers allows for the vast majority of the context to be computed in parallel during decoding without introducing any independence assumptions. This semi-parallel structure goes a long way to making decoding from even a very large Axial Transformer broadly applicable. We demonstrate state-of-the-art results for the Axial Transformer on the ImageNet-32 and ImageNet-64 image benchmarks as well as on the BAIR Robotic Pushing video benchmark. We open source the implementation of Axial Transformers.