Model Predictive Control of Tensegrity Robots via Contact-Aware Graph Neural Dynamics Model
Authors: Nelson Chen, Patrick Meng, Charles Tang, Angelina Degay, Zachary Brei, Rebecca Kramer-Bottiglio, Kostas E. Bekris, Mridul Aanjaneya
Abstract
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.
This study proposes a novel Model Predictive Path Integral (MPPI)-based task-space control framework. The proposed framework explicitly solves rigid-body dynamics within a real-time MPC formulation and enforces safety constraints, enabling accurate motion and force control that yields compliant behaviors for safe and effective physical interaction of robotic manipulators in unstructured environments. By leveraging MPPI, the proposed framework efficiently handles nonlinear dynamics that are difficult to solve with conventional MPC approaches in real-time. Furthermore, we develop a torque-sampling-based control architecture that enables efficient exploitation of GPU-based parallelization, resulting in effective compliant and force-aware behaviors. As a result, the proposed framework achieves a solver update rate of over 166 Hz with a 0.18 s prediction horizon, and its performance is validated through real-world experiments on a 7-DoF manipulator.
We present a learnable physics-based model that predicts motion of the robot end effector and reaction force-torque in contact-rich manipulation. The model represents the end effector and the environment as interacting meshes in a graph structure, and conditions its prediction explicitly on the applied control input. It predicts object-level pose update directly, while the reaction torque emerges from a per-vertex force field. Training is self-supervised using only joint encoder and force-torque data while the robot is randomly touching the environment without task context. In simulation, our model transfers to peg insertion with unseen concave geometry, where an MPC agent using it reaches up to 98% success rate, and after fine-tuning on self-collected data matches an agent planning with the ground truth dynamics at the tightest 1 mm clearance. In the real world, it outperforms the system-identified MuJoCo model by 45% in position and by 74% and 63% in force and torque error.
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 \href{https://github.com/Jonathan-Twz/tensegrity-gelfoot}{github.com/Jonathan-Twz/tensegrity-gelfoot}