Stanford Seminar - Designing Origami Voxels for Robotics

Introduction to Computational Origami and Robotics

• The presentation aims to explore the application of new design techniques in computational origami to robotics, and to spark curiosity in implementing novel mechanical mechanisms to address traditional electronic or computational challenges (42s).
• An example of this concept is an origami hand made from the same kind of origami cube, which demonstrates an underactuated mechanism similar to the human hand (57s).
• Origami has emergent properties that arise from placing creases on a sheet, and there are millions of different types of origami that can be folded, with interesting mechanical properties useful for engineering applications (1m26s).
• The presentation focuses on cubic origami, which is a big design challenge due to the sealed sides and convex polyhedra, with constraints to the system (1m57s).

Exploration of Cubic Origami Designs

• The water bomb base is an ancient origami design that can be folded completely flat, but is challenging to compress without tearing the cube (2m14s).
• The square crl unit is another example that folds flat, but is difficult to fold without tearing the paper, and often requires a modified version with removed space to achieve the same motion (2m56s).
• The presentation aims to explore the possibilities of cubic origami and its applications in robotics and engineering (1m50s).

Presentation of Foldable Cube Units

• Four units of foldable cubes are presented, with one being the "saw horse molecule" that can become a cube and allow for roll, pitch, and yaw angles, and another having a minimal slit cut in the corner, allowing it to fold flat (3m48s).
• An octahedral unit cell is shown, which can be connected to others on a lattice to create a metamaterial with interesting properties (4m7s).
• A generalized cuboid is introduced, which has the most number of creases and can achieve six degrees of motion, allowing for various skew movements (4m17s).
• A cube with a diagonal slit across is also presented, which can be folded flat and is rigidly foldable (4m36s).
• Eight different cubes are shown, each with unique emergent properties, aiming to spark imagination and encourage the creation of new cubes by changing the position of creases on the surface (4m54s).

Combining Mathematical Elegance and Practical Functionality

• The goal is to combine the mathematical elegance and creative design of these foldable cubes with practical functionality for robots (5m14s).
• Mathematical elegance refers to the simplicity and beauty of a solution, and the concept can be explored further (5m25s).
• The practical functionality of the cubes is also discussed, with the idea that some cubes may be more useful than others in certain applications (5m39s).

Modular Robotics and Origami Voxels

• Modular robotics is mentioned as a potential application, with two approaches being intra-reconfigurability, where the cubes' positions are adjusted, and inter-reconfigurability, where the cubes' positions remain the same but they can still achieve motion (6m4s).
• Inter-reconfigurability is the focus of the discussion, allowing for motion in fewer degrees of freedom (6m30s).
• Audience participation is encouraged, with a question about which cube could be used to achieve reconfiguration (6m45s).
• Origami voxels can be represented by different shapes, such as the octahedral unit and the generalized cuboid, which can undergo various configurations to achieve specific goals (6m58s).

Fundamental Properties of Origami Cubes

• The fundamental properties of origami cubes include range space, which refers to the different shapes a cube can be made into and its ability to reconfigure in multiple ways (7m27s).
• Another property is flat foldability, which is the ability of a cube to fold completely flat, and is determined by the alternating angles of the cube's faces (7m37s).
• The Maekawa-Kawasaki theorem states that if the alternating angles of a 2D origami sum to zero, the paper can be folded completely flat, but this theorem is more complicated to apply to cube origami due to the 90° angle faces (7m42s).
• Self-locking is a property of some origami cubes, where they can intersect with each other and lock into place, which can be useful in robotics for designing self-locking mechanisms (8m6s).
• Most origami cubes are flat foldable, but some, such as the sawhorse molecule and the generalized cuboid, are not due to their self-locking capability (8m37s).
• Multi-stability is another property of origami cubes, where they have multiple stable end configurations, similar to the Venus fly trap, and can be useful in robotics for saving energy (9m1s).
• Origami cubes with multi-stability have an energy barrier that must be overcome to switch between the two stable end configurations, which can be useful in robotic situations with soft actuators (9m33s).

Actuation Challenges and Design Properties

• Some origami cubes are difficult to actuate due to their high energetic barrier, requiring a significant amount of force to fold the cube (10m7s).
• Origami voxels can be designed with two main properties: rigid foldability and multi-stability, which can be used as a toolkit to create different robotic systems with various properties (10m16s).
• Rigid foldability allows the sheets to fold without having an angle in them, while multi-stability enables the sheets to have different stable states (10m18s).

The Sawhorse Origami Voxel and its Applications

• The sawhorse origami voxel is a multi-stable cube that can be used to create different embodiments, such as a concave and convex surface that toggles between each other, and an alternating zigzag lattice (11m9s).
• The sawhorse voxel can also be used to create tunable joint limits, allowing it to compress to different degrees (11m43s).
• The sawhorse voxel can decompose into other cubes, such as the modified Kesling and the water bomb, by placing the vertices in different locations (11m54s).
• The decomposition of the sawhorse voxel into other cubes is called a molecule, which represents the general topological space of a specific embodiment (12m23s).

Fabrication and Energetic Properties of Origami Voxels

• The origami voxels can be made from thin deformable panels or thick rigid panels, but the latter is more challenging due to the intersection of the panels (12m39s).
• The energetic barrier of the origami voxels is an important property that determines how difficult it is to compress or expand the voxel, and it can be affected by the stiffness of the hinges and the rigidity of the panels (12m59s).
• The study examined the properties of origami voxels, specifically the face material and hinge material, to determine the effects of rigid versus flexible and stretchy versus non-stretchy hinges on the energetic curve of the voxel (13m41s).
• Mathematical models were created to accommodate both face bending and hinge bending, and the results showed that non-stretchy hinges have a linear curve, while stretchy hinges have an exponential curve (13m57s).
• Experimental results confirmed that the contribution of stretchy hinges is minimal at small displacements but becomes significant at larger displacements (14m24s).
• The geometry of the block was also studied, and it was found that more twist causes a higher energetic barrier (14m48s).
• A larger range of the H parameter results in more energy dissipation, and the voxels follow a specific order when subjected to a constant force (15m1s).
• The study also found that material degradation occurs after repeated cycling of the block, with the energy barrier decreasing after around 100 cycles (15m58s).

Minimal Cuts and Foldability

• The addition of a minimal slit to the block can make it foldable, as shown by the work of Couchi in 1813 and Abel in 2014 (16m41s).
• A minimal cut size can be added to rigidly flatten a tetrahedron, allowing it to be completely removed (17m7s).
• A super large energy barrier can be reduced by making a minimal small cut, and a block with a large diagonal cut can be compared to one with a super small cut to achieve this reduction (17m16s).
• By parameterizing a cube and solving for the minimal cut size, it is found that the optimal cut size is 88.6% of the edge length, which is much smaller than the large diagonal cut (17m46s).
• The minimal cut size allows the block to fold without separating the end points more than the original distance, and changing the number of cuts in each cube can also reduce the energetic barrier (18m12s).
• Adding more cuts to the block can make it programmable and multi-able, and having all four cuts makes the block both theoretically rigidly foldable and experimentally shown to be effective (18m41s).

Reconfiguration and Tessellations of Origami Blocks

• Combining multiple blocks together, such as the octahedral unit cell, allows for reconfiguration and tessellations, and there are three pathways for individual reconfiguration: compressing in the X, Y, or Z direction (18m55s).
• The internal structure of the block prevents it from being compressed in all directions, and a kinematic model is needed to create tessellations, but it is challenging due to the complexity of the system (19m41s).
• A possible solution to this complexity is to look at the geometry of a sphere passing through a plane, which can be used to solve the problem of multiple states for a given height (20m7s).
• A system can be created by placing the four corners of a cube at the intersecting plane and a vertex at the center of a sphere, allowing for the same system to be achieved when the block moves around, satisfying the property of making a tube shape and a center shape by moving the position of the C vertices around the intersecting circle (20m34s).
• This system can be used to understand how complex geometry can be simplified, and generative modeling can be used to create different structures with various properties, such as compressibility and rigidity (21m10s).
• Examples of generative models include a structure that can compress in all three directions, a fully rigid structure, and a structure with a unique folding method that can only fold in one direction (21m18s).

3D Shape Matching and Evolutionary Design

• The challenge of 3D shape matching is a significant problem, where a robot needs to be able to change shape while maintaining energetic minimality, and this can be achieved through the use of coupled systems (21m55s).
• Another potential application is the evolutionary design of robots, where cubes with different properties can be used to create complex systems, such as running robots, using evolutionary algorithms (22m17s).
• The use of modular design, where a single shape is repeated to create a larger structure, can be used to create robots that can move and show micro-mobility, and this design can be used to consider the construction of structures (23m8s).
• The model can also be used to look at the number of points of connectivity between blocks, which can affect the strength of the connection, and this can be used to design more robust structures (23m46s).
• The system can also be used to consider damage to some of the modules, and how this can affect the overall structure, by looking at the points of connectivity and the strength of the connections (23m44s).
• The total number of connection points for each individual block can be used as a proxy to determine if a structure is rigid or not, and blocks with too few connection points are discarded for being structurally unstable (24m11s).

Controlling Origami Robots and Actuation Strategies

• Controlling robots made of origami cubes is a goal, with the aim of using as few actuators as possible, and one way to achieve this is by routing a tendon through the structure (24m30s).
• Individually controlling each cube would require a separate actuator for each one, which could be difficult, especially in bulk (25m0s).
• Connection points for each shape are typically set in advance, but there is no automatic way to reconfigure them on the fly, and a locking mechanism would be needed to attach and detach cubes (25m11s).
• The generative design process uses a grammar with eight different options for connecting cubes, but this is limited to design time and does not allow for automatic reconfiguration (25m49s).

Soft Robotics and Design Challenges

• Soft robotics research has made progress in delivering medicine, with a recent test using a six-hexagon version of the Kesling unit to magnetically deliver medicine to a pig (26m28s).
• Theoretically, a single cube could be designed to transform into any type of shape, but manufacturing challenges arise when adding multiple crease patterns to a single cube (27m2s).
• The more creases added to a cube, the more difficult it becomes to manufacture, especially if using certain materials (27m27s).
• Designing origami voxels for robotics involves finding the simplest crease pattern possible to achieve a specific application, with the goal of using as few creases as possible (27m45s).
• A challenge in designing origami voxels is approaching the problem from a heterogeneous perspective, which can be difficult, but a grammar-based and evolutionary approach may be effective (28m54s).
• The cbard voxel is a promising design that can accommodate more complex shape changes and reach a wider space, making it a potential area of future research (29m8s).

Fabrication Strategies and Future Research

• The saw horse voxel is a design that gets its name from the saw horse molecule in organic chemistry, due to the similarity in the connection between the creases and the atoms in the molecule (29m51s).
• The best fabrication strategies for origami voxels include heat lamination, using double-sided adhesive, and potentially using metal hinges for added robustness (30m31s).
• Cynthia Sun's work on optimization and the use of the Oregon and Cube as a primitive design element were mentioned as relevant to the topic of origami voxel design (28m4s).