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Publication Supplementary Materials: Algorithmic Design of Kinematic Trees Based on CSC Dubins Planning for Link Shapes(2024-10-08) Feshbach, Daniel Adam; Chen, Wei-Hsi; Xu, Ling; Schaumburg, Emil; Huang, Isabella; Sung, CynthiaSupplementary materials for the paper "Algorithmic Design of Kinematic Trees Based on CSC Dubins Planning for Link Shapes", presented at The 16th International Workshop on the Algorithmic Foundations of Robotics (WAFR), 2024. Paper abstract: Computational tools for robot design require algorithms moving between several layers of abstraction including task, morphology, kinematics, mechanism shapes, and actuation. In this paper we give a linear-time algorithm mapping from kinematics to mechanism shape for tree-structured linkages. Specifically, we take as input a tree whose nodes are axes of motion (lines which joints rotate about or translate along) along with types and sizes for joints on these axes, and a radius r for a tubular bound on the link shapes. Our algorithm outputs the geometry for a kinematic tree instantiating these specifications such that the neutral configuration has no self-intersection. The algorithm approach is based on understanding the mechanism design problem as a planning problem for link shapes, and arranging the joints along their axes of motion to be appropriately spaced and oriented such that feasible, non-intersecting paths exist linking them. Since link bending is restricted by its tubular radius, this is a Dubins planning problem, and to prove the correctness of our algorithm we also prove a theorem about Dubins paths: if two point-direction pairs are separated by a plane at least 2r from each, and the directions each have non-negative dot product with the plane normal, then they are connected by a radius-r CSC Dubins path with turn angles <= pi. We implement our design algorithm in code and provide a 3D printed example of a tubular kinematic tree. The results provide an existence proof of tubular-shaped kinematic trees implementing given axes of motion, and could be used as a starting point for further optimization in an automated or algorithm-assisted robot design system.Publication Kinegami: Open-source Software for Creating Kinematic Chains from Tubular Origami(Springer, 2024-07-16) Feshbach, Daniel AdamArms, legs, and fingers of animals and robots are all examples of “kinematic chains" - mechanisms with sequences of joints connected by effectively rigid links. Lightweight kinematic chains can be manufactured quickly and cheaply by folding tubes. In recent work [Chen et al. 2023], we demonstrated that origami patterns for kinematic chains with arbitrary numbers of degrees of freedom can be constructed algorithmically from a minimal kinematic specification (axes that joints rotate about or translate along). The work was founded on a catalog of tubular crease patterns for revolute joints (rotation about an axis), prismatic joints (translation along an axis), and links, which compose to form the specified design. With this paper, we release an open-source python implementation of these patterns and algorithms. Users can specify kinematic chains as a sequence of degrees of freedom or by specific joint locations and orientations. Our software uses this information to construct a single crease pattern for the corresponding chain. The software also includes functions to move or delete joints in an existing chain and regenerate the connecting links, and a visualization tool so users can check that the chain can achieve their desired configurations. This paper provides a detailed guide to the code and its usage, including an explanation of our proposed representation for tubular crease patterns. We include a number of examples to illustrate the software’s capabilities and its potential for robot and mechanism design.Publication Re-programmable Matter by Folding: Magnetically Controlled Origami that Self-Folds, Self-Unfolds, and Self-Reconfigures On-Demand(Springer, 2024-07-24) Unger, Gabriel; Sung, CynthiaWe present a reprogrammable matter system that changes shape in a controllable manner in real-time and on-demand. The system uses origami inspired fabrication for self-assembly and repeated self-reconfiguration. By writing a magnetic program onto a thin laminate and applying an external magnetic field, we control the sheet to self-fold. The magnetic program can be written at millimeter resolution over hundreds of programming cycles and folding steps. We demonstrate how the same sheet can fold and unfold into multiple shapes using a fully automated program-and-fold process. Finally, we demonstrate how electronic components can be incorporated to produce functional structures such as a foldable display. The system has advantages over existing programmable matter systems in its versatility and ability to support potentially any folding sequence.Publication Origami-Inspired Bistable Gripper with Self-Sensing Capabilities(7th IEEE-RAS International Conference on Soft Robotics (Robosoft) 2024, 2024-04) Kim, Christopher Y; Yang, Lele; Anbuchelvan, Ashwath; Garg, Raghav; Milbar, Niv; Vitale, Flavia; Sung, CynthiaAn origami-inspired bistable gripper, featuring a dual-function custom PET linear solenoid actuator that acts both as an actuator and a sensor, is presented. Movements in the permanent magnet plunger, which is directly mounted to the gripper, create induced electromotive force (emf) in the solenoid, and these induced emf measurements are used to detect snap-through actions and light contacts on the gripper. The fabrication methods for the gripper, actuator, and a gel-free soft wearable EMG electrode are outlined, and the actuator’s self-sensing method utilizing the time-integral of the induced emf measurements are explored. Because a self-sensing actuator eliminates the need for extra sensors, it allows for further miniaturization of the robot while maintaining its compactness and lightweight design. The paper also introduces a full humanin- the-loop system, allowing users to open or close the gripper with their biceps via a wearable EMG electrode. This system bridges human intent with robotic action, offering a more intuitive interaction model for robotic control.Publication Online Optimization of Soft Manipulator Mechanics via Hierarchical Control(2024) Misra, Shivangi; Sung, CynthiaActively tuning mechanical properties in soft robots is now feasible due to advancements in soft actuation technologies. In soft manipulators, these novel actuators can be distributed over the robot body to allow greater control over its large number of degrees of freedom and to stabilize local deformations against a range of disturbances. In this paper, we present a hierarchical policy for stiffness control for such a class of soft manipulators. The stiffness changes induce desired deformations in each segment, thereby influencing the manipulator’s end-effector position. The algorithm can be run as an online controller to influence the manipulator’s stable states – as we demonstrate in simulation – or offline as a design algorithm to optimize stiffness distributions – as we showcase in a hardware demonstration. Our proposed hierarchical control scheme is agnostic to the stiffness actuation method and can extend to other soft manipulators with nonuniform stiffness distributions.Publication ELECTRONICS DESIGN AND VERIFICATION FOR ROBOTS WITH ACTUATION AND SENSING REQUIREMENTS(ASME, 2023-08-29) Chen, Dongsheng; Huang, Zonghao; Sung, CynthiaRobot design is a challenging problem involving a balance between the robot’s mechanical design, kinematic structure, and actuation and sensing capabilities. Recentwork in computational robot design has focused on mechanical design while assuming that the given actuators are sufficient for the task. At the same time, existing electronics design tools ignore the physical requirements of the actuators and sensors in the circuit. In this paper, we present the first system that closes the loop between the two, incorporating a robot’s mechanical requirements into its circuit design process. We show that the problem can be solved using an iterative search consisting of two parts. First, a dynamic simulator converts the mechanical design and the given task into concrete actuation and sensing requirements. Second, a circuit generator executes a branch-and-bound search to convert the design requirements into a feasible electronic design. The system iterates through both of these steps, a process that is sometimes required since the electronics components add mass that may affect the robot’s design requirements. We demonstrate this approach on two examples – a manipulator and a quadruped – showing in both cases that the system is able to generate a valid electronics design.Publication CurveQuad: A Centimeter-Scale Origami Quadruped that Leverages Curved Creases to Self-Fold and Crawl with One Motor(IEEE/RSJ, 2023-10-01) Feshbach, Daniel AdamWe present CurveQuad, a miniature curved origami quadruped that is able to self-fold and unfold, crawl, and steer, all using a single actuator. CurveQuad is designed for planar manufacturing, with parts that attach and stack sequentially on a flat body. The design uses 4 curved creases pulled by 2 pairs of tendons from opposite ends of a link on a 270° servo. It is 8 cm in the longest direction and weighs 10.9 g. Rotating the horn pulls the tendons inwards to induce folding. Continuing to rotate the horn shears the robot, enabling the robot to shuffle forward while turning in either direction. We experimentally validate the robot's ability to fold, steer, and unfold by changing the magnitude of horn rotation. We also demonstrate basic feedback control by steering towards a light source from a variety of starting positions and orientations, and swarm aggregation by having 4 robots simultaneously steer towards the light. The results demonstrate the potential of using curved crease origami in self-assembling and deployable robots with complex motions such as locomotion.Publication Density Functions for Navigation Function Based Systems(2006-12-15) Loizou, Savvas G; Jadbabaie, AliIn this paper, we present a scheme for constructing density functions for systems that are almost globally asymptotically stable (i.e., systems for which all trajectories converge to an equilibrium except for a set of measure zero) based on navigation functions. Although recently-proven converse theorems guarantee the existence of density functions for such systems, results are only existential and the construction of a density function for almost globally asymptotically stable systems remains a challenging task. We show that for a specific class of dynamical systems that are defined based on a navigation function, a density function can be easily derived from the system's underlying navigation functionPublication Approximation of the joint spectral radius using sum of squares(2008-03-18) Parillo, Pablo A; Jadbabaie, AliWe provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for an SOS polynomial that proves simultaneous contractibility of a finite set of matrices. We provide a bound on the quality of the approximation that unifies several earlier results and is independent of the number of matrices. Additionally, we present a comparison between our approximation scheme and earlier techniques, including the use of common quadratic Lyapunov functions and a method based on matrix liftings. Theoretical results and numerical investigations show that our approach yields tighter approximations.Publication Drag Coefficient Characterization of the Origami Magic Ball (Inproceedings)(2023-08-29) Chen, Guanyu; Chen, Dongsheng; Weakly, Jessica; Sung, CynthiaThe drag coefficient plays a vital role in the design and optimization of robots that move through fluids. From aircraft to underwater vehicles, their geometries are specially engineered so that the drag coefficients are as low as possible to achieve energy-efficient performances. Origami magic balls are 3-dimensional reconfigurable geometries composed of repeated simple waterbomb units. Their volumes can change as their geometries vary and we have used this concept in a recent underwater robot design. This paper characterizes the drag coefficient of an origami magic ball in a wind tunnel. Through dimensional analysis, the scenario where the robot swims underwater is equivalently transferred to the situation when it is in the wind tunnel. With experiments, we have collected and analyzed the drag force data. It is concluded that the drag coefficient of the magic ball increases from around 0.64 to 1.26 as it transforms from a slim ellipsoidal shape to an oblate spherical shape. Additionally, three different magic balls produce increases in the drag coefficient of between 57% and 86% on average compared to the smooth geometries of the same size and aspect ratio. The results will be useful in future designs of robots using waterbomb origami in fluidic environments.