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Proprioceptive Force Estimation for Quadruped Locomotion and Human-Robot Interaction

Run Wang, Xu Yang, Alapati Tuerxun, Yilin Mo

arXiv:2609.34222v1cs.RO

TL;DR

Payload forces must be accommodated during locomotion, while leash pulls can indicate desired motion. The paper jointly trains a proprioceptive force estimator and locomotion policy, using the force estimate for locomotion and leash-command generation. In simulation, the framework reduces pooled tracking and orientation error scores relative to a domain-randomized baseline.

  • Problem

    Payload loading changes what the robot must accommodate, while leash pulls can indicate desired travel, motivating a shared force estimate for locomotion and interaction.

    Source: §I · p. 1

  • Method

    A proprioceptive estimator and locomotion policy are jointly trained with supervised three-axis force outputs in newtons; the estimate conditions locomotion and generates planar-velocity and yaw-rate commands for leash guidance.

    Source: §I · p. 1

  • Results

    21.6% and 46.5% reductions in pooled tracking and orientation scores, respectively, relative to DR characterize the complete force-conditioned framework.

    Source: 1) Tracking and Payload Locomotion · p. 6

  • Takeaways & Limitations

    Go1 trials demonstrate stationary force readout, online load carrying beyond the training force magnitude, and force-driven guidance using the shared output.

    Source: §VI · p. 8, §V · p. 8

    Hardware demonstrations use a Go1 on flat terrain, with force-reference measurements during stationary loading; dynamic interactions and broader terrain and payload configurations remain for future evaluation.

    Source: §V · p. 8

Abstract

from arXiv · show

Payload forces must be accommodated during locomotion, while leash forces can specify desired motion. We investigate whether a shared three-dimensional force estimate in newtons, inferred from proprioceptive history under sustained loading, can support both tasks. An estimator and locomotion policy are jointly trained with supervised force and velocity outputs and learned latent context. The estimated force conditions locomotion and additionally generates planar-velocity and yaw-rate commands for leash guidance through an analytical map. In sustained-force simulation sweeps, temporal means of componentwise force root mean square error range from 1.44 to 2.83\,N. Compared with a domain-randomized baseline, the framework reduces velocity-tracking and base-orientation error scores by 21.6\% and 46.5\%, respectively, and increases mean survival from 68.29\% to 94.60\% in separate sustained-force tests. Unitree Go1 experiments demonstrate stationary vertical and horizontal force estimation, locomotion with an 8.5\,kg payload whose weight exceeds the 70\,N training force limit, and leash guidance using the same force-estimation interface.

I. INTRODUCTION

Payload loading must be accommodated during locomotion, while leash pulls can indicate desired travel. The paper proposes a shared proprioceptive force estimate that conditions payload locomotion and generates commands for leash guidance.

I. INTRODUCTION

  • The work addresses payload loading and leash guidance as distinct external-force roles that can share a force estimate usable by locomotion and interaction controllers.Payloads change the load the robot must accommodate; leash pulls can indicate a desired travel direction.Source: §I · p. 1
  • Go1 demonstrations cover payload-force estimation and locomotion, horizontal-force estimation, and leash-guided locomotion.The reported evidence includes sustained-force estimation in simulation and on a stationary Go1, plus load carrying beyond the training force magnitude.Source: Figure 1 · p. 1, §I · p. 1
  • The estimator predicts force, velocity, and latent context from a short observation history, with supervised regression and reinforcement learning jointly training it and the locomotion policy.Outputs update online while network weights remain fixed.Source: §I · p. 1, Figure 2 · p. 2
  • The shared interface uses a supervised three-axis force estimate in newtons to condition payload locomotion and generate continuous planar-velocity and yaw-rate commands for leash guidance.Payload commands are supplied externally, while leash commands are generated through an analytical mapping.Source: §I · p. 1, Figure 2 · p. 2

A. Proprioceptive Adaptation for Locomotion

Prior locomotion work uses latent context or estimates physical properties, while force-interaction methods vary in how they represent and use force. This paper uses a sustained-load, three-axis force estimate as an input to both locomotion and guidance, with assumptions and scope limits stated.

A. Proprioceptive Adaptation for Locomotion

  • Unlike latent-context methods or payload-state estimators, this framework supervises resultant three-axis force without reconstructing the full payload state.Related approaches include latent-context locomotion, payload mass and center-of-mass estimation, and friction or joint-limit identification.Source: A. Proprioceptive Adaptation for… · p. 2

B. Physical Identification and Adaptive Control

  • Classical adaptive-control methods update robot or payload parameters, whereas this force output serves as a time-varying input to locomotion and guidance.Prior methods include online mass and center-of-mass estimation, disturbance estimation, and momentum observers.Source: B. Physical Identification and… · p. 2

C. Force Estimation for Physical Interaction

  • The distinguishing interface supervises force components in newtons under sustained loading, using them both to condition locomotion and to generate continuous guidance commands.An explicit force estimate alone is not unique to this approach; HAC-LOCO also provides one.Source: C. Force Estimation for Physical… · p. 2

A. Force Representation and Modeling Assumptions

  • The payload representation models resultant force from payload loading, gravity, and acceleration but omits payload-induced moments and inertia changes.Proprioceptive inference assumes forces persist long enough to produce distinguishable histories within the training distribution; unique identification is not guaranteed, and finite history and robot response limit bandwidth.Source: A. Force Representation and Modeling… · p. 2

B. Proprioceptive Force Estimation

The estimator uses proprioceptive observations, commands, and prior actions over a short history to predict velocity, force, and latent context. The history helps distinguish maneuvers from loading responses, while latent coordinates have no assigned physical meaning.

B. Proprioceptive Force Estimation

  • The observation includes base angular velocity, projected gravity, joint positions and velocities, the previous action, and the current command.Angular velocity and projected gravity are expressed in the base frame.Source: B. Proprioceptive Force Estimation · p. 3
  • The encoder stacks ten observations into a 450-dimensional history spanning 0.18 seconds at 50 Hz and predicts base linear velocity, external force, and a ten-dimensional latent representation.The history is ordered newest first.Source: B. Proprioceptive Force Estimation · p. 3
  • Previous actions and commands help distinguish maneuvers from loading responses, while latent coordinates represent context beyond the supervised outputs and have no assigned physical meaning..Source: B. Proprioceptive Force Estimation · p. 3

C. Force-Conditioned Locomotion

The actor conditions locomotion on the observation and encoder outputs, while joint optimization trains force and velocity estimation alongside the policy. Regression supervises the estimates, and policy gradients also update the encoder.

C. Force-Conditioned Locomotion

  • The actor conditions its action on the instantaneous observation and encoder outputs, then produces joint-angle targets tracked by PD control.The 12-dimensional action is scaled by 0.2 and added to nominal joint angles; torques are saturated at actuator limits.Source: C. Force-Conditioned Locomotion · p. 3

D. Joint Optimization

  • The joint objective combines PPO and supervised estimation losses, and one Adam optimizer updates all network parameters.The policy receives estimated quantities during training, and PPO gradients propagate through all 16 encoder outputs.Source: D. Joint Optimization · p. 3
  • Regression supervises six velocity and force outputs, using componentwise-normalized targets with uniform label noise.The noise half-widths are 0.1 m/s for velocity and 2 N for force; separate normalization statistics are frozen after 2 × 10^7 samples.Source: D. Joint Optimization · p. 3

E. Deployment and Interaction Interface

At deployment, the estimator and actor mean run with fixed weights and frozen normalizers. For leash guidance, the estimated horizontal force passes through a dead-zone command map, with a local bound relating force error to command error.

E. Deployment and Interaction Interface

  • At 50 Hz, the history, estimator, and actor mean update online using fixed weights and frozen normalizers.Payload locomotion instead pairs online force estimates with externally supplied motion commands.Source: E. Deployment and Interaction Interface · p. 3
  • The leash map converts estimated horizontal force into planar-velocity and yaw-rate commands, returning zero commands inside a 10 N radial dead zone.Outside the dead zone, the map applies gains to the horizontal force components and force direction.Source: E. Deployment and Interaction Interface · pp. 3–4
  • For forward pulls of at least 22 N and an assumed 2 N force-error budget, deployed gains yield command-error tolerances of 0.1 m/s and 0.5 rad/s.The bound is local and assumes the specified error budget.Source: E. Deployment and Interaction Interface · p. 4

F. Reward and Domain Randomization

The shared reward combines weighted locomotion terms, while training randomizes sustained base forces, friction, and intermittent velocity pushes. A curriculum expands planar command ranges.

F. Reward and Domain Randomization

  • The shared reward sums weighted component rewards over the control interval, including tracking, posture, effort, and contact terms.The control interval is 0.02 s.Source: F. Reward and Domain Randomization · p. 4, Table II · p. 4
  • The curriculum increases forward command limits from ±0.75 to ±1.5 m/s and lateral limits from ±0.5 to ±1.0 m/s.Both planar command ranges are scaled from 0.5 to 1.0.Source: F. Reward and Domain Randomization · p. 4
  • Foot-contact and collision terms use explicit thresholds, while contact timing records the first contact after flight and corresponding air time.A foot contact indicator activates above 1 N vertical force; body collision activates above 0.1 N.Source: F. Reward and Domain Randomization · p. 4
  • Training combines sustained base forces, friction randomization, and intermittent velocity pushes.The passage specifies uniform sampling and force directions on the unit sphere, with ranges given in Table III.Source: F. Reward and Domain Randomization · p. 4, Table III · p. 4

IV. EXPERIMENTS

The experiments evaluate force-readout accuracy, locomotion under loading, and force-driven command generation for guidance. The supplied figure captions describe simulation force-error sweeps and stationary hardware force estimation.

IV. EXPERIMENTS

  • Fig. 3 reports simulation force-estimation errors under sustained base forces along each axis, with all three force components entering each score.Curves and bands show the mean and one temporal standard deviation.Source: §IV · p. 4, Figure 3 · p. 5
  • Fig. 4 depicts stationary hardware estimates while a 5 kg dumbbell is placed on and removed from the robot, using payload gravity as the settled vertical reference.The evaluation questions also include locomotion performance under loading and force-driven guidance commands.Source: §IV · p. 4, Figure 4 · p. 5

A. Simulation Setup

Policies are trained in parallel simulated environments, then evaluated against three proprioceptive controllers and a privileged reference. The evaluation also specifies separate simulation and hardware protocols.

A. Simulation Setup

  • Training uses Isaac Gym and Legged Gym with 4,096 parallel flat-terrain environments; PPO runs for 2,000 iterations and takes approximately one hour on an RTX 4090.All controllers share reward weights, domain randomization, and network hidden widths.Source: A. Simulation Setup · p. 5

B. Evaluation Protocol

  • The comparison includes DR, history-based IA, Ours, and an Oracle receiving ground-truth force and velocity.IA uses a VAE with KL regularization weight β = 1 and has no explicit velocity head; Oracle is a privileged empirical reference.Source: B. Evaluation Protocol · p. 5
  • Simulation rollouts last 30 s, with commands resampled every 5 s unless standing; hardware Go1 trials use 50 Hz onboard inference and spring-scale or payload-gravity references.Payload trials give both controllers identical supplied commands, while leash trials use force-generated commands.Source: B. Evaluation Protocol · p. 5

C. Metrics

The section defines composite tracking, orientation, and force-error measures, then reports sustained-force estimation results in simulation and stationary Go1 trials.

C. Metrics

  • Tracking scores combine planar-velocity and yaw-rate errors using 1 m/s and 1 rad/s reference scales; orientation error is dimensionless and force error is componentwise RMSE in newtons.Simulation summaries apply a 1.5-factor IQR outlier filter separately by method, force condition, and metric; overall scores pool per-time errors across force conditions.Source: C. Metrics · p. 5

D. Q1: External-Force Estimation

  • 1.44–2.83 N is the range of temporal means of componentwise force RMSE in sustained-force simulation sweeps, including errors on unloaded axes.Forces span −50 to 50 N in 5 N increments, within the 70 N training range.Source: D. Q1: External-Force Estimation · p. 6
  • The 5 kg stationary payload produced a near-steady vertical estimate of −45.9 N versus a −49 N gravitational reference, a 3.1 N (6.3%) difference.Horizontal estimates remained near zero; the approximately 1 s response reflects combined robot–estimator dynamics beyond the 0.18 s history span.Source: D. Q1: External-Force Estimation · p. 6
  • At t = 11 s, the x-axis estimate was −39.7 N against −41 N, an absolute error of 1.3 N (3.2%); at t = 24 s, the y-axis estimate was −50.1 N against −45 N, an error of 5.1 N (11.3%).The references came from separate pulls along the negative base x and y axes.Source: D. Q1: External-Force Estimation · p. 6

E. Q2: Locomotion Performance and Robustness

Ours reduces simulation tracking and orientation error scores relative to DR, while hardware trials show load carrying with a payload beyond the training force range. The section also reports training-reward and leash-guidance demonstrations.

1) Tracking and Payload Locomotion:

  • Ours approaches the Oracle reward trace in recorded training runs, while DR and IA reach lower rewards.All methods improve rapidly at first.Source: 1) Tracking and Payload Locomotion · p. 6
  • 21.6% and 46.5% are Ours' reductions in pooled tracking and orientation scores relative to DR under x-axis forces from −50 to 50 N.The comparison evaluates the complete force-conditioned framework.Source: 1) Tracking and Payload Locomotion · p. 6
  • The hardware leash-guidance sequence includes forward motion, a 180° turn, and small-radius turning, with heading reference reconstructed offline from force estimates and measured yaw.The plotted figure shows simulated transient response in planar velocity, yaw rate, and applied versus estimated force.Source: Figure 10 · p. 7, Figure 9 · p. 7
  • The 8.5 kg payload weighs approximately 83 N, exceeding the 70 N training range, and the trial demonstrates online force-conditioned load carrying despite changed mass distribution and inertia.During backward stepping, hind-knee ground contacts occur in the displayed DR sequence and are absent in Ours; the reported pitches are −11.3° and −3.3°, respectively.Source: 1) Tracking and Payload Locomotion · pp. 6–7

2) Survival and Transient Response:

Under sustained forces, Ours achieves higher survival than DR and returns toward stationary commands after force onset. The same force output supports leash guidance, while the hardware demonstrations and force-reference measurements remain limited in scope.

2) Survival and Transient Response:

  • Mean survival is 94.60% for Ours versus 68.29% for DR; under force onset, Ours and Oracle return toward the stationary command while DR and IA oscillate more.The survival tests use continuous forces of 80 N along x or z and 60 N along y; the 80 N cases exceed the training force magnitude.Source: 2) Survival and Transient Response · p. 7

F. Q3: Leash-Guided Control

  • With an elastic tether, the same force output generates motion commands for following pulls through forward locomotion, a 180° turn, and small-radius turning.The command map uses K1 = K2 = 0.05 m s−1 N−1 and K3 = 5 s−1.Source: F. Q3: Leash-Guided Control · p. 7

V. DISCUSSION AND LIMITATIONS

  • Hardware demonstrations use a Go1 on flat terrain, and force-reference measurements are obtained during stationary loading.Further work is proposed on component contributions, dynamic-interaction force estimation, and evaluation across terrains and payload configurations.Source: §V · p. 8

VI. CONCLUSION

  • The complete framework improves reported simulation tracking and survival metrics, while Go1 trials demonstrate stationary force readout, load carrying beyond the training force magnitude, and force-driven guidance.The shared proprioceptive estimate is in newtons and conditions locomotion as well as generating interaction commands.Source: §VI · p. 8
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