Tensegrity Robotics

Unlike conventional rigid-link robots defined by discrete joints, continuum robots pose a fundamental challenge for expressing their complex continuous bending configurations for closed-loop control. Several modelling approaches have been proposed for conventional continuum robots, but tensegrity-based continuum robots remain largely open. Moreover, many of these approaches assume a continuous elastic backbone and are therefore not directly applicable to tensegrity manipulators, whose bodies are networks of rigid struts and tensioned cables. This work presents a reduced-order model for shape and posture control of a tensegrity-based continuum manipulator. The manipulator is modelled as a serially connected parallel-link mechanism. The proposed method is formulated as an optimization problem that uses geometric constraints of the tensegrity structure together with information from the Inertial Measurement Unit (IMU) sensors embedded in the strut elements. To the best of our knowledge, this work presents the first experimental demonstration of a real-time IMU-based shape estimation method on a full-scale tensegrity manipulator and demonstrates posture control using a simple Proportional-Integral (PI) controller. The results show that the proposed method can estimate the shape of both single-module tensegrity structures and multi-module tensegrity manipulators from arbitrary static configurations and achieve desired postures.

Tensegrity robots offer lightweight, compliant mobility over challenging terrain but remain difficult to model and control due to complex contact-rich dynamics and partial observability. This work presents a model predictive path integral (MPPI) controller for a three-bar tensegrity robot driven by a learned graph neural network (GNN) dynamics model. This work first extends prior GNN-based models with a differentiable contact detection module. The extension allows the dynamics model to reason over non-horizontal planar terrains, obstacles, as well as self-collisions. Then, the learned dynamics model and the MPPI controller operate in a closed data-collection loop, iteratively improving model accuracy and control performance. This work further introduces a hybrid MPPI strategy that combines MPPI with turning motion primitives to improve maneuverability. Experiments are performed in MuJoCo across five navigation tasks, which include, wall obstacles, inclines, narrow corridors, low-clearance structures, and a composite 3D obstacle course. The experiments demonstrate that the hybrid MPPI controller operating over the learned GNN dynamics model improves predictive accuracy over a flat-ground baseline model and achieves superior navigation performance compared to $A^*$-based re-planning and MPPI-only variants. Results show that the contact-aware learned dynamics combined with the sampling-based model predictive control enable robust tensegrity navigation in complex, contact-rich environments.

Robots that can change their morphologies and behaviors for different tasks and environments hold great promise for adaptable, multifunctional systems. Modular reconfigurable robots (MRRs) can achieve such functionalities by docking and rearranging individual units, but most rely on rigid modules that lack structural compliance, resulting in limited capabilities. Continuum robots offer compliance through flexible backbones, yet they cannot self-reconfigure into task-adaptive multi-robot configurations. Here, we introduce an MRR that unifies the advantages of both architectures by combining a tensegrity-based compliant body with claw-based connection mechanisms. Each robot can manipulate and locomote independently, and multiple robots can self-reconfigure into different morphologies (e.g., chains, loops, branches) for cooperative manipulation and locomotion. We demonstrate the robots' capability across diverse tasks and environments, including coordinated object manipulation and transport, multimodal locomotion, and loco-manipulation in real-world scenarios. These results lay a foundation for adaptable and multifunctional robotic collectives, with broad potential applications in manufacturing, space exploration, and search-and-rescue operations.

This paper presents a scalable, open-source visuotactile sensing system for tensegrity robots that enables six-axis wrench estimation and contact detection. The proposed endcap sensor integrates an elastomeric shell, a 3D-printed thermoplastic polyurethane (TPU) interface, and a rigid base housing an embedded camera and LED illumination ring. A novel gyroid-infill bonding technique is introduced to form a durable elastomer-TPU interface without adhesives, yielding a lightweight and modular design compatible with large-scale tensegrity structures. A tactile-to-wrench neural network maps shear vector fields to six-dimensional force and torque measurements. Experimental results demonstrate accurate and stable wrench estimation with a mean squared error (MSE) of 0.1531 on static validation data and out-of-domain generalization under dynamic motion. Furthermore, full-system integration on a 12 kg tensegrity robot confirms the sensor's ability to reliably identify ground contacts. The system substantially improves the practicality of tactile feedback for tensegrity robots, offering a low-cost, reproducible, and physically interpretable pathway toward contact-aware proprioception and state estimation. Open source files are available at github.com/Jonathan-Twz/tensegrity-gelfoot

Tensegrity robots offer compliance and adaptability, but their nonlinear, and underconstrained dynamics make state estimation challenging. Reliable continuous-time estimation of all rigid links is crucial for closed-loop control, system identification, and machine learning; however, conventional methods often fall short. This paper proposes a two-stage approach for robust state or trajectory estimation (i.e., filtering or smoothing) of a cable-driven tensegrity robot. For online state estimation, this work introduces a factor-graph-based method, which fuses measurements from an RGB-D camera with on-board cable length sensors. To the best of the authors' knowledge, this is the first application of factor graphs in this domain. Factor graphs are a natural choice, as they exploit the robot's structural properties and provide effective sensor fusion solutions capable of handling nonlinearities in practice. Both the Mahalanobis distance-based clustering algorithm, used to handle noise, and the Chebyshev polynomial method, used to estimate the most probable velocities and intermediate states, are shown to perform well on simulated and real-world data, compared to an ICP-based algorithm. Results show that the approach provides high fidelity, continuous-time state and trajectory estimates for complex tensegrity robot motions.

Conventional mobile tensegrity robots constructed with straight links offer mobility at the cost of locomotion speed. While spherical robots provide highly effective rolling behavior, they often lack the stability required for navigating unstructured terrain common in many space exploration environments. This research presents a solution with a semi-circular, curved-link tensegrity robot that strikes a balance between efficient rolling locomotion and controlled stability, enabled by discontinuities present at the arc endpoints. Building upon an existing geometric static modeling framework [1], this work presents the system design of an improved Tensegrity eXploratory Robot 2 (TeXploR2). Internal shifting masses instantaneously roll along each curved-link, dynamically altering the two points of contact with the ground plane. Simulations of quasistatic, piecewise continuous locomotion sequences reveal new insights into the positional displacement between inertial and body frames. Non-intuitive rolling behaviors are identified and experimentally validated using a tetherless prototype, demonstrating successful dynamic locomotion. A preliminary impact test highlights the tensegrity structure's inherent shock absorption capabilities and conformability. Future work will focus on finalizing a dynamic model that is experimentally validated with extended testing in real-world environments as well as further refinement of the prototype to incorporate additional curved-links and subsequent ground contact points for increased controllability.

Shape estimation is fundamental for controlling continuously bending tensegrity manipulators, yet achieving it remains a challenge. Although using exteroceptive sensors makes the implementation straightforward, it is costly and limited to specific environments. Proprioceptive approaches, by contrast, do not suffer from these limitations. So far, several methods have been proposed; however, to our knowledge, there are no proven examples of large-scale tensegrity structures used as manipulators. This paper demonstrates that shape estimation of the entire tensegrity manipulator can be achieved using only the inclination angle information relative to gravity for each strut. Inclination angle information is intrinsic sensory data that can be obtained simply by attaching an inertial measurement unit (IMU) to each strut. Experiments conducted on a five-layer tensegrity manipulator with 20 struts and a total length of 1160 mm demonstrate that the proposed method can estimate the shape with an accuracy of 2.1 % of the total manipulator length, from arbitrary initial conditions under both static conditions and maintains stable shape estimation under external disturbances.

Tensegrity robots possess lightweight and resilient structures but present significant challenges for state estimation due to compliant and distributed ground contacts. This paper introduces a symmetry-aware heterogeneous graph neural network (Sym-HGNN) that infers contact states directly from proprioceptive measurements, including IMU and cable-length histories, without dedicated contact sensors. The network incorporates the robot's dihedral symmetry $D_3$ into the message-passing process to enhance sample efficiency and generalization. The predicted contacts are integrated into a state-of-the-art contact-aided invariant extended Kalman filter (InEKF) for improved pose estimation. Simulation results demonstrate that the proposed method achieves up to 15% higher accuracy and 5% higher F1-score using only 20% of the training data compared to the CNN and MI-HGNN baselines, while maintaining low-drift and physically consistent state estimation results comparable to ground truth contacts. This work highlights the potential of fully proprioceptive sensing for accurate and robust state estimation in tensegrity robots. Code available at: https://github.com/Jonathan-Twz/Tensegrity-Sym-HGNN