Cloth folding stands as an intricate subject in robot manipulation, requiring robots to fold diverse fabrics into different configurations according to human intentions. Previous work in this area falls into three primary categories: imitation learning, reinforcement learning, and geometric model-based planning methods. While each paradigm has its merits, they generally lack inherent multi-step reasoning ability and struggle to generalize to novel cloth appearances and tasks. To tackle these problems, our key insight is incorporating the common sense reasoning and generalization abilities of Large Language Models (LLMs) into cloth manipulation, while addressing the limitations of LLMs in manipulating deformable objects, which involves an effective grounding module and rational planning hierarchy. To this end, we present PolyFold, a novel language-conditioned bimanual cloth folding framework that leverages the parameterized polygon model as an effective abstraction and grounding module for cloth representation. Moreover, PolyFold enables LLMs to infer an intermediate-level action—specifically, the symmetrical fold line, while delegating the pick-and-place calculations to a fold-line-guided downstream policy, which is learned through self-supervision using random data. Experiments on 70 cloth folding tasks and 4 cloth types show that PolyFold excels in zero-shot generalization and inherent multi-step reasoning capability, while also operating in a sample-efficient expert-demonstration-free manner, surpassing previous SOTA vision-conditioned and language-conditioned methods. Our method can also be directly deployed in real-world scenarios. Videos, code and appendix are available at our project webpage: https://sites.google.com/view/polyfold.

Pose registration is critical in vision and robotics. This article focuses on the challenging task of initialization-free pose registration up to 7DoF for homogeneous and heterogeneous measurements. While recent learning-based methods show promise using differentiable solvers, they either rely on heuristically defined correspondences or require initialization. Phase correlation seeks solutions in the spectral domain and is correspondence-free and initialization-free. Following this, we propose a differentiable solver and combine it with simple feature extraction networks, namely DPCN++. It can perform registration for homo/hetero inputs and generalizes well on unseen objects. Specifically, the feature extraction networks first learn dense feature grids from a pair of homogeneous/heterogeneous measurements. These feature grids are then transformed into a translation and scale invariant spectrum representation based on Fourier transform and spherical radial aggregation, decoupling translation and scale from rotation. Next, the rotation, scale, and translation are independently and efficiently estimated in the spectrum step-by-step. The entire pipeline is differentiable and trained end-to-end. We evaluate DCPN++ on a wide range of tasks taking different input modalities, including 2D bird's-eye view images, 3D object and scene measurements, and medical images. Experimental results demonstrate that DCPN++ outperforms both classical and learning-based baselines, especially on partially observed and heterogeneous measurements.