arXiv subjects

William R. Johnson III

Publications and source records attributed to William R. Johnson III.

7 recordsLinked to original sources

arXiv2026

CableRobotGraphSim: A Graph Neural Network for Modeling Partially Observable Cable-Driven Robot Dynamics

General-purpose simulators have accelerated the development of robots. Traditional simulators based on first-principles, however, typically require full-state observability or depend on parameter search for system identification. This work presents \texttt{CableRobotGraphSim}, a novel Graph Neural Network (GNN) model for cable-driven robots that aims to address shortcomings of prior simulation solutions. By representing cable-driven robots as graphs, with the rigid-bodies as nodes and the cables and contacts as edges, this model can quickly and accurately match the properties of other simulation models and real robots, while ingesting only partially observable inputs. Accompanying the GNN model is a sim-and-real co-training procedure that promotes generalization and robustness to noisy real data. This model is further integrated with a Model Predictive Path Integral (MPPI) controller for closed-loop navigation, which showcases the model's speed and accuracy.

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arXiv2026

State and Trajectory Estimation of Tensegrity Robots via Factor Graphs and Chebyshev Polynomials

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.

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arXiv2025

An Open-Source, Reproducible Tensegrity Robot that can Navigate Among Obstacles

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.

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arXiv2025

Impact-resistant, autonomous robots inspired by tensegrity architecture

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.

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arXiv2024

Learning Differentiable Tensegrity Dynamics using Graph Neural Networks

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

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arXiv2023

Real2Sim2Real Transfer for Control of Cable-driven Robots via a Differentiable Physics Engine

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.

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arXiv2022

6N-DoF Pose Tracking for Tensegrity Robots

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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