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1. 6N-DoF Pose Tracking for Tensegrity Robots

   Lu, S. ; Johnson, W. ; Wang, K. ; Huang, X. ; Booth, J. ; Kramer-Bottiglio, R. ; Bekris, K. E. ( January 2022 , International Symposium on Robotics Research (ISRR))

   Tensegrity robots, which are composed of compressive elements (rods) and flexible tensile elements (e.g., cables), have a variety of advantages, including flexibility, low weight, and resistance to mechanical impact. Nevertheless, the hybrid soft-rigid nature of these robots also complicates the ability to localize and track their state. This work aims to address what has been recognized as a grand challenge in this domain, i.e., the state estimation of tensegrity robots through a markerless, vision-based method, as well as novel, onboard sensors that can measure the length of the robot's cables. In particular, an iterative optimization process is proposed to track the 6-DoF pose of each rigid element of a tensegrity robot from an RGB-D video as well as endcap distance measurements from the cable sensors. To ensure that the pose estimates of rigid elements are physically feasible, i.e., they are not resulting in collisions between rods or with the environment, physical constraints are introduced during the optimization. Real-world experiments are performed with a 3-bar tensegrity robot, which performs locomotion gaits. Given ground truth data from a motion capture system, the proposed method achieves less than 1~cm translation error and 3 degrees rotation error, which significantly outperforms alternatives. At the same time, the approach can provide accurate pose estimation throughout the robot's motion, while motion capture often fails due to occlusions. 

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2. A Shape-Changing Wheeling and Jumping Robot Using Tensegrity Wheels and Bistable Mechanism

   https://doi.org/10.1109/TMECH.2023.3276933  

   Spiegel, Sydney ; Sun, Jiefeng ; Zhao, Jianguo ( August 2023 , IEEE/ASME Transactions on Mechatronics)

   Tensegrity structures made from rigid rods and elastic cables have unique characteristics, such as being lightweight, easy to fabricate, and high load-carrying to weight capacity. In this article, we leverage tensegrity structures as wheels for a mobile robot that can actively change its shape by expanding or collapsing the wheels. Besides the shape-changing capability, using tensegrity as wheels offers several advantages over traditional wheels of similar sizes, such as a shock-absorbing capability without added mass since tensegrity wheels are both lightweight and highly compliant. We show that a robot with two icosahedron tensegrity wheels can reduce its width from 400 to 180 mm, and simultaneously, increase its height from 75 to 95 mm by changing the expanded tensegrity wheels to collapsed disk-like ones. The tensegrity wheels enable the robot to overcome steps with heights up to 110 and 150 mm with the expanded and collapsed configuration, respectively. We establish design guidelines for robots with tensegrity wheels by analyzing the maximum step height that can be overcome by the robot and the force required to collapse the wheel. The robot can also jump onto obstacles up to 300-mm high with a bistable mechanism that can gradually store but quickly release energy. We demonstrate the robot's locomotion capability in indoor and outdoor environments, including various natural terrains, like sand, grass, rocks, ice, and snow. Our results suggest that using tensegrity structures as wheels for mobile robots can enhance their capability to overcome obstacles, traverse challenging terrains, and survive falls from heights. When combined with other locomotion modes (e.g., jumping), such shape-changing robots can have broad applications for search-and-rescue after disasters or surveillance and monitoring in unstructured environments. 

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3. A Recurrent Differentiable Engine for Modeling Tensegrity Robots Trainable with Low-Frequency Data

   https://doi.org/10.1109/ICRA46639.2022.9812135  

   Wang, Kun ; Aanjaneya, Mridul ; Bekris, Kostas ( May 2022 , 2022 International Conference on Robotics and Automation (ICRA))

   Tensegrity robots, composed of rigid rods and flexible cables, are difficult to accurately model and control given the presence of complex dynamics and high number of DoFs. Differentiable physics engines have been recently proposed as a data-driven approach for model identification of such complex robotic systems. These engines are often executed at a high-frequency to achieve accurate simulation. Ground truth trajectories for training differentiable engines, however, are not typically available at such high frequencies due to limitations of real-world sensors. The present work focuses on this frequency mismatch, which impacts the modeling accuracy. We proposed a recurrent structure for a differentiable physics engine of tensegrity robots, which can be trained effectively even with low-frequency trajectories. To train this new recurrent engine in a robust way, this work introduces relative to prior work: (i) a new implicit integration scheme, (ii) a progressive training pipeline, and (iii) a differentiable collision checker. A model of NASA's icosahedron SUPERballBot on MuJoCo is used as the ground truth system to collect training data. Simulated experiments show that once the recurrent differentiable engine has been trained given the low-frequency trajectories from MuJoCo, it is able to match the behavior of MuJoCo's system. The criterion for success is whether a locomotion strategy learned using the differentiable engine can be transferred back to the ground-truth system and result in a similar motion. Notably, the amount of ground truth data needed to train the differentiable engine, such that the policy is transferable to the ground truth system, is 1% of the data needed to train the policy directly on the ground-truth system. 

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4. A Recurrent Differentiable Engine for Modeling Tensegrity Robots Trainable with Low-Frequency Data

   Wang, K. ; Aanjaneya, M. ; Bekris, K. E. ( January 2022 , IEEE International Conference on Robotics and Automation (ICRA))

   Tensegrity robots, composed of rigid rods and flexible cables, are difficult to accurately model and control given the presence of complex dynamics and high number of DoFs. Differentiable physics engines have been recently proposed as a data-driven approach for model identification of such complex robotic systems. These engines are often executed at a high-frequency to achieve accurate simulation. Ground truth trajectories for training differentiable engines, however, are not typically available at such high frequencies due to limitations of real-world sensors. The present work focuses on this frequency mismatch, which impacts the modeling accuracy. We proposed a recurrent structure for a differentiable physics engine of tensegrity robots, which can be trained effectively even with low-frequency trajectories. To train this new recurrent engine in a robust way, this work introduces relative to prior work: (i) a new implicit integration scheme, (ii) a progressive training pipeline, and (iii) a differentiable collision checker. A model of NASA's icosahedron SUPERballBot on MuJoCo is used as the ground truth system to collect training data. Simulated experiments show that once the recurrent differentiable engine has been trained given the low-frequency trajectories from MuJoCo, it is able to match the behavior of MuJoCo's system. The criterion for success is whether a locomotion strategy learned using the differentiable engine can be transferred back to the ground-truth system and result in a similar motion. Notably, the amount of ground truth data needed to train the differentiable engine, such that the policy is transferable to the ground truth system, is 1% of the data needed to train the policy directly on the ground-truth system. 

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5. Prototype Design and Manufacture of a Deployable Tensegrity Microrobot

   https://doi.org/10.1115/IMECE2022-93929  

   Kazoleas, Christian ; Mehta, Kaushik ; Yuan, Sichen ( October 2022 , ASME 2022 International Mechanical Engineering Congress and Exposition)

   Micro-, and milli-scale robots have been of great R&D interest, due to their ability to accomplish difficult tasks such as minimally invasive diagnosis and treatment for human bodies, and underground or deep-sea tests for environment monitoring. A good solution to this design need is a multi-unit deployable tensegrity microrobot. The microrobot can be folded to only 15% of its deployed length, so as to easily enter a desired working area with a small entrance. When deployed, the tensegrity body of the robot displays lightweight and high stiffness to sustain loads and prevent damage when burrowing through tightly packed tissues or high-pressure environments. In this work, topology, initial configuration and locomotion of a deployable tensegrity microrobot are determined optimally. Based on the design, a centimeter-scale prototype is manufactured by using a fused deposition modelling advanced additive manufacturing or 3-D printing system for proof of concept. As shown in experimental results, the deployable tensegrity microrobot prototype designed and manufactured can achieve an extremely high folding ratio, while be lightweight and rigid. The locomotion design, that mimics a crawling motion of an earthworm, is proved to be efficient by the prototype equipped with stepper motors, actuation cables, control boards and a braking system. 

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