Spatial reasoning is a key capability in the field of artificial intelligence, especially crucial in areas such as robotics, computer vision, and natural language understanding. However, evaluating the ability of multimodal large language models(MLLMs) in complex spatial reasoning still faces challenges, particularly in scenarios requiring multi-step reasoning and precise mathematical constraints. This paper introduces ORIGAMISPACE, a new dataset and benchmark designed to evaluate the multi-step spatial reasoning ability and the capacity to handle mathematical constraints of MLLMs through origami tasks. The dataset contains 350 data instances,each comprising a strictly formatted crease pattern (CP diagram), the Compiled Flat Pattern, the complete Folding Process, and the final Folded Shape Image. We propose four evaluation tasks: Pattern Prediction, Multi-step Spatial Reasoning, Spatial Relationship Prediction, and End-to-End CP Code Generation. For the CP code generation task, we design an interactive environment and explore the possibility of using reinforcement learning methods to train MLLMs. Through experiments on existing MLLMs, we initially reveal the strengths and weaknesses of these models in handling complex spatial reasoning tasks.

But her passion is for paper--with no scissors. Today, she's a tessellation expert who teaches, invents new designs, and writes papers on the underlying math. Madonna Yoder '17 photographed in her studio Ross Mantle When Madonna Yoder '17 was eight years old, she learned how to fold a square piece of paper over and over and over again. After about 16 folds, she held a bird in her hands. The first time she pulled the tail of a flapping crane, she says, she realized: . That first piece was an origami classic, folded by kids at summer camp for generations and many people's first foray into the art form.

Deployable structures inspired by origami have provided lightweight, compact, and reconfigurable solutions for various robotic and architectural applications. However, creating an integrated structural system that can effectively balance the competing requirements of high packing efficiency, simple deployment, and precise morphing into multiple load-bearing configurations remains a significant challenge. This study introduces a new class of hyper-Yoshimura origami, which exhibits a wide range of kinematically admissible and locally metastable states, including newly discovered symmetric "self-packing" and asymmetric "pop-out" states. This metastability is achieved by breaking a design rule of Yoshimura origami that has been in place for many decades. To this end, this study derives a new set of mathematically rigorous design rules and geometric formulations. Based on this, forward and inverse kinematic strategies are developed to stack hyper-Yoshimura modules into deployable booms that can approximate complex 3D shapes. Finally, this study showcases the potential of hyper-Yoshimura with a meter-scale pop-up cellphone charging station deployed at our university's bus transit station, along with a 3D-printed, scaled prototype of a space crane that can function as an object manipulator, solar tracking device, or high-load-bearing structure. These results establish hyper-Yoshimura as a promising platform for deployable and adaptable robotic systems in both terrestrial and space environments.

The complex behavior of highly deformable mechanical metamaterials can substantially enhance the performance of soft robots. Metamaterials are rapidly emerging from electromagnetic, acoustic, or mechanical properties governed by structure rather than composition. Mechanical metamaterials, in particular, hav e been designed to show superior mechanical properties, such as ultrahigh stiffness and strength - to - weight ratio, or unusual properties, such as a negative Poisson's ratio and a negative coefficient of thermal expansion. Whereas earlier research focused on designing mechanical metamaterials with linear elastic responses, more recently, nonlinear large deformations and mechanical instabilities - typically associated with failure - have emerged as promising tools for new functionalities, including programmabl e shape transformations, tunable mechanical properties, and energy absorption (1). Ongoing advances in additive manufacturing technologies facilitate the fabrication of functional mechanical metamaterials with unprecedented complexity.

The nonlinear mechanical response of soft materials and slender structures is purposefully harnessed to program functions by design in soft robotic actuators, such as sequencing, amplified response, fast energy release, etc. However, typical designs of nonlinear actuators - e.g. balloons, inverted membranes, springs - have limited design parameters space and complex fabrication processes, hindering the achievement of more elaborated functions. Mechanical metamaterials, on the other hand, have very large design parameter spaces, which allow fine-tuning of nonlinear behaviours. In this work, we present a novel approach to fabricate nonlinear inflatables based on metamaterials and origami (Meta-Ori) as monolithic parts that can be fully 3D printed via Fused Deposition Modeling (FDM) using thermoplastic polyurethane (TPU) commercial filaments. Our design consists of a metamaterial shell with cylindrical topology and nonlinear mechanical response combined with a Kresling origami inflatable acting as a pneumatic transmitter. We develop and release a design tool in the visual programming language Grasshopper to interactively design our Meta-Ori. We characterize the mechanical response of the metashell and the origami, and the nonlinear pressure-volume curve of the Meta-Ori inflatable and, lastly, we demonstrate the actuation sequencing of a bi-segment monolithic Meta-Ori soft actuator.

The wrist plays a pivotal role in facilitating motion dexterity and hand functions. Wrist orthoses, from passive braces to active exoskeletons, provide an effective solution for the assistance and rehabilitation of motor abilities. However, the type of motions facilitated by currently available orthoses is limited, with little emphasis on personalised design. To address these gaps, this paper proposes a novel wrist orthosis design inspired by the Kresling origami. The design can be adapted to accommodate various individual shape parameters, which benefits from the topological variations and intrinsic compliance of origami. Heat-sealable fabrics are used to replicate the non-rigid nature of the Kresling origami. The orthosis is capable of six distinct motion modes with a detachable tendon-based actuation system. Experimental characterisation of the workspace has been conducted by activating tendons individually. The maximum bending angle in each direction ranges from 18.81{\deg} to 32.63{\deg}. When tendons are pulled in combination, the maximum bending angles in the dorsal, palmar, radial, and ulnar directions are 31.66{\deg}, 30.38{\deg}, 27.14{\deg}, and 14.92{\deg}, respectively. The capability to generate complex motions such as the dart-throwing motion and circumduction has also been experimentally validated. The work presents a promising foundation for the development of personalised wrist orthoses for training and rehabilitation.

Despite the popularity and widespread use of semi-structured data formats such as JSON, end-to-end supervised learning applied directly to such data remains underexplored. We present ORIGAMI (Object RepresentatIon via Generative Autoregressive ModellIng), a transformer-based architecture that directly processes nested key/value pairs while preserving their hierarchical semantics. Our key technical contributions include: (1) a structure-preserving tokenizer, (2) a novel key/value position encoding scheme, and (3) a grammar-constrained training and inference framework that ensures valid outputs and accelerates training convergence. These enhancements enable efficient end-to-end modeling of semi-structured data. By reformulating classification as next-token prediction, ORIGAMI naturally handles both single-label and multi-label tasks without architectural modifications. Empirical evaluation across diverse domains demonstrates ORIGAMI's effectiveness: On standard tabular benchmarks converted to JSON, ORIGAMI remains competitive with classical and state-of-the-art approaches. On native JSON datasets, we outperform baselines on multi-label classification and specialized models such as convolutional and graph neural networks on a code classification task. Through extensive ablation studies, we validate the impact of each architectural component and establish ORIGAMI as a robust framework for end-to-end learning on semi-structured data.

With the increasing adoption of large language models (LLMs) in education, concerns about inherent biases in these models have gained prominence. We evaluate LLMs for bias in the personalized educational setting, specifically focusing on the models' roles as "teachers". We reveal significant biases in how models generate and select educational content tailored to different demographic groups, including race, ethnicity, sex, gender, disability status, income, and national origin. We introduce and apply two bias score metrics--Mean Absolute Bias (MAB) and Maximum Difference Bias (MDB)--to analyze 9 open and closed state-of-the-art LLMs. Our experiments, which utilize over 17,000 educational explanations across multiple difficulty levels and topics, uncover that models perpetuate both typical and inverted harmful stereotypes.

Airships, best recognized for their unique quality of payload/energy ratio, present a fascinating challenge for the field of engineering. Their construction and operation require a delicate balance of materials and rules, making them a compelling object of study. They embody a distinct intersection of physics, design, and innovation, offering a wide array of possibilities for future transportation and exploration. Thanks to their long-flight endurance, they are suited for long-term missions. To operate in complex environments such as indoor cluttered spaces, their membrane and mechatronics need to be protected from impacts. This paper presents a new indoor airship design inspired by origami and the Kresling pattern. The airship structure combines a carbon fiber exoskeleton and UV resin micro-lattices for shock absorption. Our design strengthens the robot while granting the ability to access narrow spaces by folding the structure - up to a volume expansion ratio of 19.8. To optimize the numerous parameters of the airship, we present a pipeline for design, manufacture, and assembly. It takes into account manufacturing constraints, dimensions of the target deployment area, and aerostatics, allowing for easy and quick testing of new configurations. We also present unique features made possible by combining origami with airship design, which reduces the chances of mission-compromising failures. We demonstrate the potential of the design with a complete simulation including an effective control strategy leveraging lightweight mechatronics to optimize flight autonomy in exploration missions of unstructured environments.

Origami designs and structures have been widely used in many fields, such as morphing structures, robotics, and metamaterials. However, the design and fabrication of origami structures rely on human experiences and skills, which are both time and labor-consuming. In this paper, we present a rapid design and fabrication method for string-driven origami structures and robots. We developed an origami design software to generate desired crease patterns based on analytical models and Evolution Strategies (ES). Additionally, the software can automatically produce 3D models of origami designs. We then used a dual-material 3D printer to fabricate those wrapping-based origami structures with the required mechanical properties. We utilized Twisted String Actuators (TSAs) to fold the target 3D structures from flat plates. To demonstrate the capability of these techniques, we built and tested an origami crawling robot and an origami robotic arm using 3D-printed origami structures driven by TSAs.