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Model Predictive Control of Tensegrity Robots via Contact-Aware Graph Neural Dynamics Model

This paper presents a robust navigation framework for tensegrity robots that combines a contact-aware Graph Neural Network dynamics model with a hybrid Model Predictive Path Integral controller to achieve superior performance in complex, contact-rich environments compared to existing baselines.

Original authors: Nelson Chen, Patrick Meng, Charles Tang, Angelina Degay, Zachary Brei, Rebecca Kramer-Bottiglio, Kostas E. Bekris, Mridul Aanjaneya

Published 2026-09-09

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CC BY 4.0

Original authors: Nelson Chen, Patrick Meng, Charles Tang, Angelina Degay, Zachary Brei, Rebecca Kramer-Bottiglio, Kostas E. Bekris, Mridul Aanjaneya

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Robots that move through the world often face a fundamental dilemma: they must be strong enough to carry their own weight and push through obstacles, yet flexible enough to adapt when the ground shifts beneath them. Traditional robots, built from rigid metal frames, struggle when the terrain is uneven, rocky, or cluttered, often getting stuck or tipping over. A different approach uses structures made of rigid rods held together by a network of flexible cables. These "tensegrity" robots are lightweight and incredibly durable; if they fall, they bounce rather than break. However, controlling them is notoriously difficult. Because their movement depends on the complex interplay of tension in the cables and the way the rods touch the ground, predicting exactly how they will roll or tumble is like trying to forecast the weather with incomplete data. The robots often cannot see their own full shape or the exact angle of the ground they are touching, making it hard for a computer to plan a safe path forward.

Researchers at Rutgers University and Yale University have developed a new way to guide these bouncing robots through complex environments, including steep ramps, narrow corridors, and low-hanging obstacles. Instead of relying on a perfect mathematical formula to describe the robot's movement, they taught a computer model to learn from experience. This model uses a type of artificial intelligence known as a graph neural network, which is particularly good at understanding how different parts of a system connect to one another. In this case, the system is the robot itself, along with the walls and ground it might bump into. The researchers added a special feature to this learning system that allows it to "feel" when the robot touches a surface, whether that surface is a flat floor, a slanted ramp, or even another part of the robot's own body. This ability to sense contact is crucial, as the robot often needs to lean against a wall or squeeze under a barrier to move forward.

To put this learning model to work, the team created a control system that acts like a constant, rapid-fire planner. Imagine the robot stopping for a split second to imagine thousands of different ways it could move over the next few seconds. It simulates each possibility in its mind, checking which path leads to the goal without crashing. The system then picks the best option and executes it, only to immediately start planning the next set of moves. This process, known as model predictive control, allows the robot to react to changes in real time. However, the researchers found that the robot struggled to figure out how to turn effectively on its own. To solve this, they combined the smart planning system with a set of simple, pre-programmed turning moves. When the robot needs to change direction, it uses these reliable turns to face the right way, and then lets the smart planner take over to navigate the rest of the path.

The team tested this approach in a high-fidelity computer simulation that mimics the physics of the real world. They set up five different challenges for the robot, ranging from a simple flat course with walls to a difficult three-dimensional obstacle course that included steep inclines and tight spaces. In the most difficult test, the robot had to navigate a course it had never seen before, combining all the previous challenges into one. The results showed that the robot using the new learning system and the hybrid turning strategy was far more successful than older methods. While other approaches failed to climb the ramps or get stuck in narrow passages, the new system managed to reach its goal in the vast majority of attempts, even in the unseen environments. The robot improved as it gathered more data, becoming faster and more accurate with each round of testing.

This work suggests that by teaching robots to understand how they touch the world around them, and by giving them a mix of learned intelligence and simple, reliable moves, we can create machines capable of navigating the messy, unpredictable terrain of the real world. The researchers demonstrated that this method works well in simulation, paving the way for future tests with physical robots. While the current system is limited to flat surfaces and requires further development to handle completely unstructured environments, the success of this approach offers a promising path toward robots that can explore disaster zones, search for survivors in rubble, or traverse the rugged landscapes of other planets.

Technical Summary: Model Predictive Control of Tensegrity Robots via Contact-Aware Graph Neural Dynamics Model

Problem Statement
Tensegrity robots, composed of rigid struts and flexible cables, offer lightweight and compliant mobility suitable for unstructured terrains. However, their control is hindered by complex, contact-rich dynamics and partial observability. Traditional control approaches often avoid system dynamics by relying on geometric planning or motion primitives, while reinforcement learning policies transferred from simulation often exhibit limited locomotion capabilities. Furthermore, existing learned dynamics models based on Graph Neural Networks (GNNs) typically assume horizontal ground contacts, failing to account for non-horizontal planar terrains, environmental obstacles, or self-collisions. This work addresses the challenge of achieving robust, closed-loop navigation for tensegrity robots in complex environments where accurate modeling of contact interactions is critical.

Methodology
The proposed framework integrates a learned GNN dynamics model with a Model Predictive Path Integral (MPPI) controller, operating within an iterative data-collection loop.

Contact-Aware GNN Dynamics Model:
- The core of the approach is an extension of prior GNN-based dynamics models. The authors introduce a differentiable contact detection module implemented in PyTorch.
- This module generates contact features representing interactions between the robot's end-caps and non-horizontal planar surfaces (e.g., ramps, walls), as well as self-collisions between the robot's cylindrical rods.
- These interactions are encoded as node features (signed distances) and edge features (relative velocities, surface normals, and distances) within the graph. This allows the model to predict state changes (rod velocities and cable rest lengths) under partial observations in environments with complex contact constraints.
Hybrid MPPI Controller:
- The controller utilizes the learned GNN as its internal predictive model to perform sampling-based optimal control.
- To address the difficulty of sampling effective turning behaviors for the three-bar tensegrity robot (which requires long horizons and many samples), a hybrid strategy is employed.
- The system evaluates the robot's heading relative to the local cost gradient. If the heading is aligned with the goal direction (within a threshold $\alpha$ ), the MPPI controller executes. If misaligned, the system switches to human-engineered turning motion primitives (clockwise or counter-clockwise) to reorient the robot before resuming MPPI control.
- The cost function utilizes an obstacle-aware, wave-front heuristic constructed on a grid. This avoids the pitfalls of Euclidean distance metrics in cluttered environments by propagating obstacle-aware distance estimates from the goal.
Iterative Data-Collection Loop:
- The system operates in a closed loop where the MPPI controller executes tasks, generating new trajectory data.
- This data is added to the training set to retrain the GNN dynamics model, which in turn improves the controller's predictive accuracy and performance in subsequent iterations. The process begins with data from human-designed primitives and evolves through successive training cycles.

Key Contributions

Extended GNN Dynamics Model: A learned model incorporating differentiable contact detection to handle non-horizontal planar terrains, environmental obstacles, and self-collisions, extending beyond prior flat-ground assumptions.
Iterative MPC Framework: An MPC framework using MPPI over the learned GNN that facilitates an iterative loop for improving both the dynamics model and control performance simultaneously.
Hybrid Control Strategy: A solution combining MPPI with turning motion primitives to enhance maneuverability and overcome the sampling inefficiencies of pure MPPI for turning maneuvers.
Comprehensive Evaluation: Experimental validation in MuJoCo across five diverse navigation tasks, including inclines, narrow corridors, low-clearance structures, and a composite 3D obstacle course.

Results
Experiments were conducted across five navigation scenarios: a flat obstacle course, a 5° incline, a narrow corner/passageway, a low-clearance structure, and a composite 3D obstacle course (the latter serving as an unseen test environment).

Model Accuracy: The contact-aware GNN model consistently outperformed a baseline GNN (assuming flat ground) in predicting center-of-mass position and rod orientation. Prediction errors decreased across training iterations as the dataset grew with controller-generated data.
Navigation Performance:
- Flat Obstacle Course: The Hybrid MPPI achieved 100% success rate from the first iteration, outperforming MPPI-only (which struggled with turning) and matching the final performance of A* re-planning baselines.
- Incline: A* baselines failed completely due to drift in heading dynamics. MPPI-only achieved limited success (33%), while Hybrid MPPI achieved 100% success from the first iteration.
- Narrow Corridor & Low Clearance: These tasks required intentional contact with obstacles, which A* baselines could not plan. Hybrid MPPI significantly outperformed MPPI-only, achieving higher success rates and faster convergence.
- 3D Obstacle Course (Unseen): The Hybrid MPPI strategy demonstrated strong generalization, achieving an 84% success rate by the final iteration, compared to 35% for MPPI-only.
Ablation Studies: Results indicated that distance-to-contact node features had a larger impact on prediction accuracy than contact edges alone, highlighting the importance of explicit proximity information.

Significance and Claims
The paper claims that the combination of contact-aware learned dynamics and sampling-based model predictive control enables robust tensegrity navigation in complex, contact-rich environments where traditional geometric planning or pure reinforcement learning fails. The authors emphasize that the iterative data-collection loop is crucial for refining the model's ability to handle partial observability and complex contact physics.

The work is modest regarding its current scope, acknowledging that the approach is currently restricted to planar surface representations and that the turning primitives are hand-engineered. The authors identify future work in extending the model to fully unstructured terrains, learning turning primitives directly from data, and demonstrating the iterative improvement loop on a physical three-bar tensegrity robot.

Technical Summary: Model Predictive Control of Tensegrity Robots via Contact-Aware Graph Neural Dynamics Model

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