Tensegrity robots, composed of rigid struts and elastic tendons, provide impact resistance, low mass, and adaptability to unstructured terrain. Their compliance and complex, coupled dynamics, however, present modeling and control challenges, hindering path planning and obstacle avoidance. This paper presents a complete, open-source, and reproducible system that enables navigation for a 3-bar tensegrity robot. The system comprises: (i) an inexpensive, open-source hardware design, and (ii) an integrated, open-source software stack for physics-based modeling, system identification, state estimation, path planning, and control. All hardware and software are publicly available at https://sites.google.com/view/tensegrity-navigation/. The proposed system tracks the robot's pose and executes collision-free paths to a specified goal among known obstacle locations. System robustness is demonstrated through experiments involving unmodeled environmental challenges, including a vertical drop, an incline, and granular media, culminating in an outdoor field demonstration. To validate reproducibility, experiments were conducted using robot instances at two different laboratories. This work provides the robotics community with a complete navigation system for a compliant, impact-resistant, and shape-morphing robot. This system is intended to serve as a springboard for advancing the navigation capabilities of other unconventional robotic platforms.

Recent studies have demonstrated that the dynamics of physical systems can be utilized for the desired information processing under the framework of physical reservoir computing (PRC). Robots with soft bodies are examples of such physical systems, and their nonlinear body-environment dynamics can be used to compute and generate the motor signals necessary for the control of their own behavior. In this simulation study, we extend this approach to control and embed not only one but also multiple behaviors into a type of soft robot called a tensegrity robot. The resulting system, consisting of the robot and the environment, is a multistable dynamical system that converges to different attractors from varying initial conditions. Furthermore, attractor analysis reveals that there exist "untrained attractors" in the state space of the system outside the training data. These untrained attractors reflect the intrinsic properties and structures of the tensegrity robot and its interactions with the environment. The impacts of these recent findings in PRC remain unexplored in embodied AI research. We here illustrate their potential to understand various features of embodied cognition that have not been fully addressed to date.

ACCEPTED MARCH, 2025 1 Real-Time Shape Estimation of Tensegrity Structures Using Strut Inclination Angles Tufail Ahmad Bhat 1, Y uhei Y oshimitsu 1, Kazuki Wada 1, Shuhei Ikemoto 1 Abstract --T ensegrity structures are becoming widely used in robotics, such as continuously bending soft manipulators and mobile robots to explore unknown and uneven environments dynamically. Estimating their shape, which is the foundation of their state, is essential for establishing control. However, on-board sensor-based shape estimation remains difficult despite its importance, because tensegrity structures lack well-defined joint structures, which makes it challenging to use conventional angle sensors such as potentiometers or encoders for shape estimation. T o our knowledge, no existing work has successfully achieved shape estimation using only onboard sensors such as Inertial Measurement Units (IMUs). This study addresses this issue by proposing a novel approach that uses energy minimization to estimate the shape. We validated our method through experiments on a simple Class 1 tensegrity structure, and the results show that the proposed algorithm can estimate the real-time shape of the structure using onboard sensors, even in the presence of external disturbances. I NTRODUCTION T HE concept of "tensegrity" is coined by the iconoclastic architect R. Buckminster Fuller. It describes structures that achieve stability through a balance of forces: specific components, known as "cables" are always in tension, while others, known as "struts" are constantly under compression [1]. In tensegrity, the cables of the structure are always under continuous tension, a condition known as "prestress".

Future robots will navigate perilous, remote environments with resilience and autonomy. Researchers have proposed building robots with compliant bodies to enhance robustness, but this approach often sacrifices the autonomous capabilities expected of rigid robots. Inspired by tensegrity architecture, we introduce a tensegrity robot -- a hybrid robot made from rigid struts and elastic tendons -- that demonstrates the advantages of compliance and the autonomy necessary for task performance. This robot boasts impact resistance and autonomy in a field environment and additional advances in the state of the art, including surviving harsh impacts from drops (at least 5.7 m), accurately reconstructing its shape and orientation using on-board sensors, achieving high locomotion speeds (18 bar lengths per minute), and climbing the steepest incline of any tensegrity robot (28 degrees). We characterize the robot's locomotion on unstructured terrain, showcase its autonomous capabilities in navigation tasks, and demonstrate its robustness by rolling it off a cliff.

Tensegrity robots, characterized by a synergistic assembly of rigid rods and elastic cables, form robust structures that are resistant to impacts. However, this design introduces complexities in kinematics and dynamics, complicating control and state estimation. This work presents a novel proprioceptive state estimator for tensegrity robots. The estimator initially uses the geometric constraints of 3-bar prism tensegrity structures, combined with IMU and motor encoder measurements, to reconstruct the robot's shape and orientation. It then employs a contact-aided invariant extended Kalman filter with forward kinematics to estimate the global position and orientation of the tensegrity robot. The state estimator's accuracy is assessed against ground truth data in both simulated environments and real-world tensegrity robot applications. It achieves an average drift percentage of 4.2%, comparable to the state estimation performance of traditional rigid robots. This state estimator advances the state of the art in tensegrity robot state estimation and has the potential to run in real-time using onboard sensors, paving the way for full autonomy of tensegrity robots in unstructured environments.

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 excel in tasks requiring extreme levels of deformability and robustness. However, there are challenges in state estimation and payload versatility due to their high number of degrees of freedom and unconventional shape. This paper introduces a modular three-bar tensegrity robot featuring a customizable payload design. Our tensegrity robot employs a novel Quasi-Direct Drive (QDD) cable actuator paired with low-stretch polymer cables to achieve accurate proprioception without the need for external force or torque sensors. The design allows for on-the-fly stiffness tuning for better environment and payload adaptability. In this paper, we present the design, fabrication, assembly, and experimental results of the robot. Experimental data demonstrates the high accuracy cable length estimation (<1% error relative to bar length) and variable stiffness control of the cable actuator up to 7 times the minimum stiffness for self support. The presented tensegrity robot serves as a platform for future advancements in autonomous operation and open-source module design.

Tensegrities synergistically combine tensile (cable) and rigid (link) elements to achieve structural integrity, making them lightweight, packable, and impact resistant. Consequently, they have high potential for locomotion in unstructured environments. This research presents geometric modeling of a Tensegrity eXploratory Robot (TeXploR) comprised of two semi-circular, curved links held together by 12 prestressed cables and actuated with an internal mass shifting along each link. This design allows for efficient rolling with stability (e.g., tip-over on an incline). However, the unique design poses static and dynamic modeling challenges given the discontinuous nature of the semi-circular, curved links, two changing points of contact with the surface plane, and instantaneous movement of the masses along the links. The robot is modeled using a geometric approach where the holonomic constraints confirm the experimentally observed four-state hybrid system, proving TeXploR rolls along one link while pivoting about the end of the other. It also identifies the quasi-static state transition boundaries that enable a continuous change in the robot states via internal mass shifting. This is the first time in literature a non-spherical two-point contact system is kinematically and geometrically modeled. Furthermore, the static solutions are closed-form and do not require numerical exploration of the solution. The MATLAB simulations are experimentally validated on a tetherless prototype with mean absolute error of 4.36{\deg}.

Abstract-- A tensegrity-based system is a promising approach for dynamic exploration of uneven and unpredictable environments, particularly, space exploration. However, implementing such systems presents challenges in terms of intelligent aspects: state recognition, wireless monitoring, human interaction, and smart analyzing and advising function. Here, we introduce a 6-strut tensegrity integrate with 24 multimodal strain sensors by leveraging both deep learning model and large language models to realize smart tensegrity. Using conductive flexible tendons assisted by long short-term memory model, the tensegrity achieves the self-shape reconstruction without extern sensors. Finally, human interaction system of the tensegrity helps human obtain necessary information of tensegrity from the aspect of human language. The concept of using tensegrity structures in space exploration is an innovative approach that offers several advantages due to the unique properties of tensegrity systems. One famous example is the "Super Ball Bot" developed by NASA (National Aeronautics and Space Administration) [1][2]. Tensegrity structures are composed of solid compression components (rods/struts) connected by tension elements (cables/strings).

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.