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Tensegrity robots are composed of rigid struts and flexible cables. They constitute an emerging class of hybrid rigid-soft robotic systems and are promising systems for a wide array of applications, ranging from locomotion to assembly. They are difficult to control and model accurately, however, due to their compliance and high number of degrees of freedom. To address this issue, prior work has introduced a differentiable physics engine designed for tensegrity robots based on first principles. In contrast, this work proposes the use of graph neural networks to model contact dynamics over a graph representation of tensegrity robots, which leverages their natural graph-like cable connectivity between end caps of rigid rods. This learned simulator can accurately model 3-bar and 6-bar tensegrity robot dynamics in simulation-to-simulation experiments where MuJoCo is used as the ground truth. It can also achieve higher accuracy than the previous differentiable engine for a real 3-bar tensegrity robot, for which the robot state is only partially observable. When compared against direct applications of recent mesh-based graph neural network simulators, the proposed approach is computationally more efficient, both for training and inference, while achieving higher accuracy. Code and data are available at https://github.com/nchen9191/tensegrity_gnn_simulator_public 

Tensegrity robots, composed of rigid rods and flexible cables, exhibit high strength-to-weight ratios and significant deformations, which enable them to navigate unstructured terrains and survive harsh impacts. They are hard to control, however, due to high dimensionality, complex dynamics, and a coupled architecture. Physics-based simulation is a promising avenue for developing locomotion policies that can be transferred to real robots. Nevertheless, modeling tensegrity robots is a complex task due to a substantial sim2real gap. To address this issue, this paper describes a Real2Sim2Real (R2S2R) strategy for tensegrity robots. This strategy is based on a differentiable physics engine that can be trained given limited data from a real robot. These data include offline measurements of physical properties, such as mass and geometry for various robot components, and the observation of a trajectory using a random control policy. With the data from the real robot, the engine can be iteratively refined and used to discover locomotion policies that are directly transferable to the real robot. Beyond the R2S2R pipeline, key contributions of this work include computing non-zero gradients at contact points, a loss function for matching tensegrity locomotion gaits, and a trajectory segmentation technique that avoids conflicts in gradient evaluation during training. Multiple iterations of the R2S2R process are demonstrated and evaluated on a real 3-bar tensegrity robot. 

Numerous recent advances in robotics have been inspired by the biological principle of tensile integrity — or “tensegrity”— to achieve remarkable feats of dexterity and resilience. Tensegrity robots contain compliant networks of rigid struts and soft cables, allowing them to change their shape by adjusting their internal tension. Local rigidity along the struts provides support to carry electronics and scientific payloads, while global compliance enabled by the flexible interconnections of struts and cables allows a tensegrity to distribute impacts and prevent damage. Numerous techniques have been proposed for designing and simulating tensegrity robots, giving rise to a wide range of locomotion modes including rolling, vibrating, hopping, and crawling. Here, we review progress in the burgeoning field of tensegrity robotics, highlighting several emerging challenges, including automated design, state sensing, and kinodynamic motion planning. 

Dynamic tensegrity robots are inspired by tensegrity structures in architecture; arrangements of rigid rods and flexible elements allow the robots to deform. This work proposes the use of multiple, modular, tensegrity robots that can move and compliantly connect to assemble larger, compliant, lightweight, strong structures and scaffolding. The focus is on proof-of-concept designs for the modular robots themselves and their docking mechanisms, which can allow the easy deployment of structures in unstructured environments. These mechanisms include (electro)magnets to allow each individual robot to connect and disconnect on cue. An exciting direction is the design of specific module and structure designs to fit the mission at hand. For example, this work highlights how the considered three bar structures could stack to form a column or deform on one side to create an arch. A critical component of future work will involve the development of algorithms for automatic design and layout of modules in structures. 

Learning policies in simulation is promising for reducing human effort when training robot controllers. This is especially true for soft robots that are more adaptive and safe but also more difficult to accurately model and control. The sim2real gap is the main barrier to successfully transfer policies from simulation to a real robot. System identification can be applied to reduce this gap but traditional identification methods require a lot of manual tuning. Data-driven alternatives can tune dynamical models directly from data but are often data hungry, which also incorporates human effort in collecting data. This work proposes a data-driven, end-to-end differentiable simulator focused on the exciting but challenging domain of tensegrity robots. To the best of the authors’ knowledge, this is the first differentiable physics engine for tensegrity robots that supports cable, contact, and actuation modeling. The aim is to develop a reasonably simplified, data-driven simulation, which can learn approximate dynamics with limited ground truth data. The dynamics must be accurate enough to generate policies that can be transferred back to the ground-truth system. As a first step in this direction, the current work demonstrates sim2sim transfer, where the unknown physical model of MuJoCo acts as a ground truth system. Two different tensegrity robots are used for evaluation and learning of locomotion policies, a 6-bar and a 3-bar tensegrity. The results indicate that only 0.25% of ground truth data are needed to train a policy that works on the ground truth system when the differentiable engine is used for training against training the policy directly on the ground truth system.