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Magnet-Aware Control of Legged Robots

J. Playan Garai, S. B. Djuve, C. McGreavy, M. Khadiv

arXiv:2610.08653v1cs.RO

TL;DR

Strong magnetic fields induce forces and torques on ferromagnetic robot components and disrupt sensing, challenging legged-robot operation. The paper models and estimates these magnetic effects and compensates for them during locomotion; the reported compensation raises tolerated disturbance thresholds and expands the operational range.

  • Problem

    Strong magnetic fields can disrupt robot sensing and induce magnetic forces and torques on ferromagnetic components, creating challenges for legged-robot operation.

    Source: §I · p. 1

  • Method

    The framework models magnetic wrenches, estimates field conditions from robot dynamics and sensor readings, and incorporates predicted wrenches into MPC and WBC.

    Source: §I · p. 2, A. Centroidal Dynamics in MPC · p. 4

  • Results

    Compensation increased the tolerated disturbance force threshold by a factor of 2.5 and the disturbance torque threshold by a factor of 1.6-2.

    Source: §VII · p. 8

  • Takeaways & Limitations

    Active compensation expanded the robot’s safe operational range within the target high-field facilities.

    Source: §VII · p. 8

    In HIL tests, perturbation wrenches were injected numerically rather than applied as physical forces on structural leg masses, unlike in full-physics simulations.

    Source: D. Performance Evaluation · p. 7

Abstract

from arXiv · show

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.

I. INTRODUCTION

Strong magnetic fields in Big Science facilities induce forces and torques on ferromagnetic robot components and disrupt sensing, challenging reliable legged-robot operation. The paper addresses this with magnetic-wrench modeling, field estimation, and predictive compensation for locomotion.

I. INTRODUCTION

  • Magnetic fields can pull unequipped robots toward field origins, while sensor corruption and parasitic currents threaten control, electronics, and task completion.Hall-effect encoders can fail in high fields, and steep flux gradients induce currents in unshielded wiring.Source: §I · p. 1
  • Existing reactive disturbance methods struggle with continuous, pose- and gradient-dependent magnetic wrenches, while magnetic effects can be masked in ground-reaction-force measurements.Projection methods are also vulnerable to modeling inaccuracies, foot slip, and contact compliance.Source: §I · pp. 1–2
  • The paper identifies a need for a legged-robot control framework that models magnetic fields and their effects on ferromagnetic components to support robust dynamic balance.Source: §I · p. 2
  • The contributions are a MuJoCo magnetic-wrench plugin, an inverse field-estimation framework using robot dynamics and sensor readings, and a Magnet-Aware framework that predicts and compensates for locomotion perturbations.Source: §I · p. 2

II. BACKGROUND

The notation defines generalized configuration, velocity, and acceleration vectors for a floating-base legged system. It also specifies properties of the magnetic-field gradient in source-free regions.

A. Notation

  • The generalized configuration q, velocity qdot, and acceleration qddot describe a floating-base legged system.Their components include base and joint quantities.Source: A. Notation · p. 2
  • The base quantities include position, orientation, linear and angular velocity, and linear and angular acceleration; joint vectors contain positions, velocities, and accelerations.Source: A. Notation · p. 2
  • In source-free regions, the magnetic-field gradient G is symmetric and traceless because the field is curl-free and divergence-free.Source: A. Notation · p. 2

B. Dynamics of legged robots

The section presents floating-base robot dynamics and an anisotropic induced-magnetic model. The model accounts for magnetic forces and torques on elements whose magnetization is not aligned with the external field.

B. Dynamics of legged robots

  • The floating-base dynamics balance inertia and nonlinear effects against actuated-joint torques and contact forces.The nonlinear terms include Coriolis, centrifugal, and gravitational effects; the contact Jacobian maps contact forces into generalized coordinates.Source: B. Dynamics of legged robots · pp. 2–3

C. Anisotropic Induced Magnetic Model

  • An anisotropic magnetic model uses tensor susceptibility and permeability to represent asymmetric, non-homogeneous magnetization.The demagnetizing matrix captures geometric asymmetries, and the model incorporates element volume and vacuum permeability into magnetic polarizability.Source: C. Anisotropic Induced Magnetic Model · p. 3
  • The model transforms magnetic polarizability from the body frame to the inertial frame and defines the induced moment assuming a uniform field across the element.Source: C. Anisotropic Induced Magnetic Model · p. 3
  • Because an anisotropic element's induced moment can be non-collinear with the field, it experiences both a gradient force and a magnetic torque.The wrench is quadratic in the field for torque and bilinear in the field gradient and field for force.Source: C. Anisotropic Induced Magnetic Model · p. 3

III. PHYSICS SIMULATION

The physics simulation contribution is a MuJoCo plugin that models magnetic forces on rigid-body elements. It evaluates specified field distributions at magnetic-body centers of mass and uses material parameters to compute local field effects.

III. PHYSICS SIMULATION

  • The custom MuJoCo plugin simulates magnetic forces on passive ferromagnetic materials and allows rigid bodies to be designated as magnetic.Source: §III · p. 3
  • Users specify material properties and an analytical spatial field; the plugin evaluates local field vectors and gradients at each magnetic body's center of mass.Source: §III · p. 3
  • The simulator tests linear fields with constant gradient and spherical fields whose magnitude rises quadratically from the boundary to a central peak.Source: §III · p. 3
  • The quadruped model represents all 12 motor assemblies as cylinders, but assumes pure iron (µr = 1000) because the assemblies' effective permeability is difficult to measure.This conservative assumption maximizes predicted magnetic wrench; an accurate representative motor magnetic moment remains an open research issue.Source: §III · pp. 3–4

IV. DYNAMIC COMPENSATION

The MPC augments centroidal dynamics with magnetic forces and torques to predict their effects alongside contact forces. Its optimization uses robot state and control inputs while enforcing contact, friction, swing-foot, and operational constraints.

A. Centroidal Dynamics in MPC

  • Magnetic forces and torques are added to centroidal dynamics alongside ground-reaction forces and moments to predict their effects on robot momentum.The modeled magnetic wrenches use motor material properties and localized field values.Source: A. Centroidal Dynamics in MPC · p. 4
  • The optimization enforces friction cones, zero swing-foot forces, swing-foot tracking, and stance-contact conditions.It also includes initial-state, tracking, and state-input bound constraints.Source: A. Centroidal Dynamics in MPC · p. 4
  • The MPC state stacks normalized centroidal momentum with generalized coordinates, while its inputs combine ground-reaction forces and joint velocities.Source: A. Centroidal Dynamics in MPC · p. 4

B. Whole-Body Dynamics in WBC

The WBC maps MPC trajectories to joint torques by augmenting rigid-body dynamics with magnetic wrenches projected into generalized coordinates. Magnetic fields are locally approximated for trajectory evaluation, while compensation remains bounded by friction and actuator limits.

B. Whole-Body Dynamics in WBC

  • The WBC augments floating-base rigid-body dynamics with magnetic wrenches projected into generalized coordinates to map MPC trajectories to joint torques.The formulation stacks motor-body Jacobians and magnetic wrenches.Source: B. Whole-Body Dynamics in WBC · p. 4
  • Spatial field distributions are approximated locally with a first-order Taylor expansion to evaluate magnetic wrenches across predicted MPC trajectories.Source: B. Whole-Body Dynamics in WBC · p. 4
  • Compensation cannot prevent collapse when magnetic forces or torques exceed friction or actuator limits.Operational boundaries depend on maximum joint torque limits, system weight, and perturbation direction.Source: B. Whole-Body Dynamics in WBC · p. 4
  • The WBC decision vector combines generalized accelerations, ground-reaction forces, and joint torques, with motor torque bounds among its constraints.Source: B. Whole-Body Dynamics in WBC · p. 5

V. MAGNETIC FIELD ESTIMATION

The field-estimation method fits candidate magnetic-field parameters to quadruped motion and sensor observations using forward simulation. It avoids relying on noisy joint-acceleration estimates, and simulations show convergence under a static 0.07 T field, with noise and limited sensor data affecting optimization.

V. MAGNETIC FIELD ESTIMATION

  • Quadruped floating-base dynamics and contact interactions make external disturbance forces difficult to isolate from contact dynamics and gravity.Source: §V · p. 5
  • The estimator optimizes candidate field parameters against recorded joint torques and quadruped base-motion trajectories using forward simulation.The field can be optimized alone or jointly with model parameters, with greater complexity in the latter case.Source: §V · p. 5
  • Instead of minimizing joint-acceleration errors, the objective compares simulated and measured base accelerations and sensor observations because reliable joint accelerations require noisy double differentiation.Source: §V · p. 5
  • Base accelerations are available from an onboard IMU, while angular accelerations can be estimated with low-pass-filtered gyroscope finite differences.Source: §V · p. 5
  • Under a static 0.07 T field, the algorithm eventually converges to the proper field; high noise or insufficient sensor data can affect optimization.The reported simulation uses a linear field with constant diagonal gradient and a field at the origin.Source: Figure 4 · p. 5

VI. RESULTS

The paper evaluates its modeling, estimation, and compensation methods in simulation and on physical hardware. Experiments are structured to assess the isolated and coupled effects of field vectors and gradients on controller performance.

VI. RESULTS

  • The evaluation uses both simulation and physical hardware experiments for the modeling, estimation, and compensation strategies.Source: §VI · p. 5
  • The experimental design separates and combines the effects of magnetic field vectors and spatial gradients on controller performance.Source: §VI · p. 5
  • The MPC and WBC pipelines use Pinocchio and CasADi for dynamics and Jacobians, Acados for MPC, and qpOASES for the WBC quadratic program.Source: §VI · p. 5

A. Estimation validation

The estimation algorithm converges in simulation, though noise, sparse sensor data, and field-model complexity constrain estimation. Simulated compensation improves balance under magnetic disturbances, including coupled field gradients.

A. Estimation validation

  • The estimation algorithm converges in simulation, but high noise and insufficient sensor data can substantially affect optimization.The validation uses a linear field with constant diagonal gradient and a field at the origin; more complex fields require scaled models or feasible approximations.Source: A. Estimation validation · p. 5

B. Simulated Compensation Studies

  • 10 N m of continuous disturbance torque is tolerated with compensation, versus 6 N m under standard control; the compensated controller reaches saturation around 12 N m.Without compensation, heading error reaches 10° at B ≈0.1 T before controller collapse at higher field strengths.Source: B. Simulated Compensation Studies · p. 6
  • The coupled-gradient experiment sends the quadruped through a 2 m-radius spherical field, where forces and torques increase toward the center.The simulated scene depicts increasing physical wrenches on leg motor assemblies as the Go2 approaches the epicenter.Source: B. Simulated Compensation Studies · p. 6, Figure 5 · p. 6

C. Hardware-in-the-Loop Validation

Hardware-in-the-loop testing injects simulated magnetic perturbations into a physical Go2’s controller, while full-physics simulation evaluates physical effects. Compensation improves disturbance tolerance, but HIL does not reproduce structural loading on the robot.

C. Hardware-in-the-Loop Validation

  • HIL tests update the physical Go2’s state in MuJoCo, use four tetrahedrally arranged virtual magnetometers, and inject a feedforward wrench into the whole-body controller.The wrench is computed from noisy magnetometer feedback using a first-order Taylor-series expansion; numerical injection yields realistic torque distribution and contact-force reallocation through floating-base dynamics.Source: C. Hardware-in-the-Loop Validation · p. 6

D. Performance Evaluation

  • Compensation tolerates peak perturbation forces up to 50 N, compared with reliable locomotion failure at 20 N under standard control; yaw deviation falls from up to 5° to <1°.The comparison is shown across simulation penetration depths and HIL balance and trajectory tracking.Source: Figure 7 · p. 7, D. Performance Evaluation · p. 7
  • HIL wrenches are injected numerically rather than applied as physical forces on leg structures, so HIL traversals do not test external structural loading or physical joint binding.In full-physics simulation, the robot falls when physical leg forces exceed friction limits.Source: D. Performance Evaluation · p. 7
  • Fig. 8 maps field norm and expected induced-force norm, with isodynamic contours at 0.1 T, 0.5 T, and 0.8 T, alongside the expanded traversable workspace.The workspace is compared with the uncompensated baseline.Source: Figure 8 · p. 7, D. Performance Evaluation · p. 7

VII. CONCLUSIONS

The paper presents a framework to model, estimate, and compensate for magnetic perturbations in legged-robot locomotion. Compensation raises tolerated disturbance thresholds, and field parameters can be inferred from base-acceleration measurements.

VII. CONCLUSIONS

  • The framework models magnetic wrenches with a MuJoCo plugin and compensates for them through a two-stage MPC/WBC pipeline during locomotion.It also addresses inverse field estimation.Source: §VII · pp. 7–8
  • 2.5x higher disturbance-force thresholds and 1.6–2x higher disturbance-torque thresholds are reported with compensation in simulation and HIL experiments.The reported operational-area increase is 29, 34%, including 10, 84% that would previously have caused critical collapse.Source: §VII · p. 8
  • When magnetometers are unavailable, noisy, or spatially constrained, system identification can infer B0 and G by minimizing discrepancies between simulated and measured base accelerations.The optimization does not require noisy joint-acceleration signals.Source: §VII · p. 8
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