Authors: J. Playan Garai, S. B. Djuve, C. McGreavy, M. Khadiv
Organizations: Technical University of Munich (TUM), Munich, Germany · Conseil Europ´een pour la Recherche Nucl´eaire (CERN), BE/CEM/MRO, Geneva, Switzerland
Autonomous robots can increase uptime and reduce human exposure in Big Science facilities, but strong magnetic fields needed for their operation corrupt sensors and induce pose-dependent mechanical wrenches that destabilize robots and challenge conventional reactive controllers. This paper presents a control framework for modeling, estimating, and dynamically compensating for spatially varying magnetic wrenches acting on legged robots to improve robustness in these fields. We introduce a custom physics plugin for the MuJoCo simulator to model magnetic forces on rigid-body elements, alongside an inverse field-estimation framework to infer the latent magnetic field directly from quadruped dynamic responses and any number of sensor readings. Furthermore, we develop a Magnet-Aware Model Predictive Control (MPC) and Whole-Body Control (WBC) architecture that predicts and counteracts magnetic perturbations during locomotion to increase the range of magnetic fields in which the robot can operate. The effectiveness of the framework is validated through both simulation and physical hardware experiments. We show our method increases the the maximum rejectable disturbances from magnetic field in the force space by a factor of 2.5 and and between 1.6-2 times in torque space compared to a non-compensated system. Within the proposed magnetic field, this constitutes an increase in the area in which the robot can operate by 29,34% of which 10,84% would have previously caused an immediate collapse to non-compensated controllers.
Figures & tables
Fig. 1: Robot moving through magnetic fields (dashed contour lines) experience induced disturbance wrenches due to their ferromagnetic components. Our method compensates for these disturbances (blue trace), allowing undisturbed movement and greater accessibility in magnetic field environments, where standard controllers would fail, leading to collapse (red trace)
Fig. 2: Block diagram of the proposed pipeline outlining the contributions. We present the pre-existing elements of the pipeline (grey), the components where we have applied modifications (blue, yellow, brown, purple), and the modifications themselves (green).
Fig. 3: Simulation model of our quadruped robotic system. The 12 motor joints are modeled as induced magnetic cylinders (blue disks). Four magnetometers (green) are distributed across the chassis in a tetrahedral configuration. Motion tracker markers (white) correspond to the physical experimental platform. We also represent the base frame (gray) and center of mass (red).
Field
Value
Notes
N
[0.2 0.2 0.6]
Normalized from [ 21 ]
V
7.6969\times10−5m3
Obtained from motor CAD
μr
1000
Pure iron (worst-case scenario)
TABLE I: Defined Magnetic Parameters values for Unitree GO-M8018-6 Motor
Fig. 4: Convergence results for a static magnetic field. We record the robot as it moves through a scene with a magnetic field of norm 0.07T . Optimizing over the results, we see that the algorithm eventually converges correctly to the proper magnetic field on the scene.
Fig. 5: MuJoCo simulation scene for coupled field-gradient experiments. As the Unitree Go2 traverses the spherical magnetic region towards the epicenter, spatial field gradients induce increasing physical wrenches on the leg motor assemblies.
Fig. 6: Experimental setup comparison. Right: Close-up of the MuJoCo simulation environment. Left: Physical laboratory testing ground with ground tape bounding the virtual magnetic field perimeter.
Fig. 7: Experimental results comparing uncompensated and compensated controllers. Left: Simulation performance showing maximum trajectory penetration depths into the spherical magnetic field before collapse. Right: Hardware-in-the-loop experiments demonstrating improved dynamic balance and trajectory tracking under virtual field perturbations.
Fig. 8: Simulations showing the resulting magnetic field from a proposed magnetic field for an FCC experiment. At top-down view is presented showcasing both the magnetic field norm (top) and the induced magnetic force norm expected (bottom). We present isodynamic lines at 0.1T (cyan), 0.5T (yellow), and 0.8T (magenta).
Magnetic navigation provides contact-free and line-of-sight-independent feedback for robotic systems, yet existing approaches typically rely on explicit pose estimation or direct use of raw magnetic measurements, making accurate control susceptible to modeling errors, measurement noise, and disturbances. This work presents MagServo, a hierarchical learning-based framework for robust 6-DoF magnetic servoing directly using the learned latent magnetic feature. MagServo learns uncertainty-resilient magnetic representations through masked reconstruction and captures state-dependent interaction dynamics between robot motion and latent magnetic transitions without analytical magnetic models or explicit Jacobian supervision. Based on the learned dynamics, a hierarchical controller combines nonlinear model predictive control for coarse approach with local Jacobian inversion for precise fine regulation. Extensive physical experiments demonstrate submillimeter and subdegree accuracy, achieving mean terminal errors of 0.386 mm and 0.479 degree for 6-DoF pose reaching. MagServo further outperforms a localization-based control baseline in complex trajectory tracking and maintains robust performance under unseen magnetic-source configurations without retraining. A supplementary video of the real-robot experiments is available at https://youtu.be/rZt1NUP1Mr0.
Yuhan Tan, Yameng Zhang, Pei Liu +2
Department of Bioengineering, Imperial College London, UK. · Department of Mechanical Engineering, The University of Hong Kong, Hong Kong SAR. · School of Computation, Information and Technology, Technical University of Munich, Germany.
Legged robots offer a variety of automation applications in real-world scenarios. But areas that are difficult to traverse, like slopes, caves, or scaffolding, still pose a great challenge for traversal. To tackle this problem, we propose an optimized algorithm for evaluating the full actuatable wrench polytope for arbitrary contact scenarios. With our improved analysis algorithm, the torques for each joint of the robot can be calculated within a control frequency of 49 Hz. The achieved speedup allows for deployment within a regular control loop for actuating robot poses for different contact scenarios. We evaluated our stability controller extensively in simulation scenarios and validated its applicability by deploying it on actual walking robot hardware. The proposed controller achieved stability in very complex scenarios that are currently not achievable by any other controller.
Friedrich Graaf, Elias Birkefeld, Christian Eichmann +5
FZI Research Center for Information Technology, Karlsruhe, Germany · Machine Intelligence and Robotics Lab (MaiRo), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Continuous legged manipulation requires accurate end-effector tracking while the base keeps walking. Combining reinforcement learning (RL) with model predictive control (MPC) suits this task: the learned policy provides robust locomotion, while MPC coordinates the base and arm to compensate for tracking errors. However, MPC can compensate only for base motion that it can predict, and a learned policy's command response varies with gait phase, contact, and payload. We present ReCo, a framework that couples response-consistent locomotion with policy-aware MPC for legged manipulation. Response shaping trains the policy to respond to commands consistently and repeatably across randomized dynamics. An identified closed-loop response model then lets MPC jointly plan locomotion commands and arm motion. On the simulation benchmark, ReCo reduces position and orientation root-mean-square error (RMSE) by 28.7% and 27.4% relative to the best baseline for each metric. Real-world experiments demonstrate onboard continuous legged manipulation with coordinated base and arm motion.
Kuankuan Sima, Yichao Gao, Chenxi Gu +2
Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119077, Singapore · Department of Mechanical Engineering, National University of Singapore, Singapore 119077, Singapore