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Feeling Through the Load: Compliant Quadruped Locomotion under Payload Interactions

Shaunak A. Mehta, Mayank Mishra, Prajit KrisshnaKumar, Sebastian Scherer, Koichiro Niinuma

arXiv:2610.08637v1cs.RO

TL;DR

Quadrupeds carrying unrestrained payloads must infer direct external interactions from onboard measurements while maintaining payload balance and stable locomotion. This work combines compliant load-carrying control with a causal force estimator and estimator-aware finetuning. Simulations and real-world experiments report compliant, force-guided behavior, with improved commanded force response over FACET-L.

  • Problem

    Forces on an unrestrained payload reach the robot through uncertain contact, so a quadruped must infer external interactions from onboard measurements while distinguishing them from ordinary motion.

    Source: §I · p. 1, §III · p. 3

  • Method

    A three-stage framework learns compliant load-carrying behavior, estimates payload forces causally from onboard measurements, and finetunes the policy with the estimator in the loop.

    Source: §I · p. 2, §VII · p. 8

  • Results

    ρcmd = 0.826 ± 0.003 for Ours, compared with 0.702±0.002 for FACET-L; real-world results show purposeful force-guided trajectory changes while preserving stable nominal locomotion.

    Source: A. Commanded Compliance and Force… · p. 6, §VI · p. 8

  • Takeaways & Limitations

    The explicit force estimate can serve as a signal for human-guided trajectory changes made by interacting directly with the payload.

    Source: §I · p. 1

Abstract

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Quadruped robots are increasingly expected to carry objects while moving through human environments. But what happens when a person interacts directly with the payload rather than with the robot? If the payload is unrestrained, the robot must distinguish intentional external interactions from ordinary payload motion, while still keeping the load balanced and maintaining stable locomotion. How can a quadruped infer and compliantly respond to such interactions using only onboard measurements? In this work, we develop a force-aware locomotion framework that treats payload interactions as commands that shape the motion of the combined robot-payload system. Our approach separates the learning of force-aware locomotion and force estimation on an unrestrained payload. We combine a compliant load-carrying policy with a causal force estimator, trained through estimator-in-the-loop data aggregation and finetuning, to predict interactions from onboard robot measurements. Our simulations and real-world experiments show that the resulting controller can maintain stable payload-carrying locomotion, yield compliantly to external interactions, and use the inferred force to support human-guided changes in the robot's trajectory.

I. INTRODUCTION

The paper addresses how a quadruped can recognize and compliantly respond to forces applied directly to an unrestrained payload while keeping the load balanced. It combines force-aware locomotion with onboard force estimation and evaluates the approach in simulation and on a real quadruped.

I. INTRODUCTION

  • Prior work addresses forces on the robot or payload adaptation, while collaborative-transport methods generally assume a mechanically coupled payload.The paper instead considers direct interaction with a payload coupled to the robot through frictional contact.Source: §I · pp. 1–2
  • A quadruped must distinguish external pushes on an unrestrained payload from ordinary payload motion, respond safely, and maintain balance during transport.The payload may slip or become imbalanced as the robot moves or a person interacts with it.Source: §I · p. 1
  • The framework treats payload forces as commands shaping combined robot-payload motion and uses a compliant load-carrying policy with a causal onboard force estimator.The three-stage learning pipeline includes estimator-aware policy finetuning and does not require sensors on the payload.Source: §I · pp. 1–2
  • Simulations and real-world experiments evaluate varied payloads, interaction forces, and impedance conditions, including human guidance of the robot through payload interaction.The inferred force is used to guide trajectory changes.Source: §I · p. 2

II. RELATED WORK

Prior work considers force-aware interaction, payload stabilization, and collaborative transportation largely as separate problems. This paper considers direct forces on an unrestrained payload, then formulates compliant response and onboard force inference under the resulting contact and control constraints.

II. RELATED WORK

  • Prior force-aware legged methods include compliant controllers and proprioception-based disturbance estimation, but generally address forces applied to the robot or its end effector.Payload-adaptation work estimates load properties or stabilizes an unrestrained load without considering intentional external guidance.Source: §II · p. 2
  • Collaborative-transport methods infer partner intent through a shared payload, but rely on a mechanically coupled object as the interaction interface.The paper instead considers forces applied directly to an unrestrained payload coupled to the robot through frictional contact.Source: §II · p. 2

III. PROBLEM STATEMENT

  • The desired compliant force-motion response is represented by a virtual mass-spring-damper reference, with virtual mass, stiffness, and damping specifying its behavior.Without interaction, the reference converges to nominal motion; an applied force deflects it according to the commanded impedance.Source: §III · pp. 2–3
  • Because payload forces reach the robot through uncertain frictional contact, onboard force inference must distinguish interaction effects from gait, payload-property, and ground-contact effects.The estimator is intended to remain informative using onboard measurements alone.Source: §III · p. 3
  • Force estimation and control form a feedback loop, creating a trade-off between yielding to interaction and maintaining locomotion stability and payload retention.The inferred force can also deform a nominal path for downstream trajectory guidance.Source: §III · p. 3

IV. METHOD

The method uses a three-stage training pipeline to make force-conditioned locomotion deployable with onboard observations and an estimated payload force.

IV. METHOD

  • The pipeline learns force-aware behavior from privileged state and true payload force, trains a causal force estimator from onboard measurements, then finetunes the policy on estimator-driven rollouts.The final stage accounts for errors introduced by the learned force estimate.Source: §IV · p. 3

A. External Interaction Aware Compliant Locomotion

The locomotion method combines a compliant reference, payload-retention objectives, and a policy trained to use robot-side observations and force input. Recurrent adaptation and estimator-aware rollouts address deployment without privileged state or true-force access.

A. External Interaction Aware Compliant Locomotion

  • Synchronized trunk- and payload-anchored mass-spring-damper references use true payload force during privileged training and estimated force during finetuning and deployment.The force also enters the locomotion policy, while the reference generates short-horizon position, velocity, and yaw targets.Source: A. External Interaction Aware… · p. 3
  • The reward augments FACET’s compliant tracking and stable locomotion objective with terms for payload position and motion relative to its support.Its coefficients balance compliant locomotion against payload stability.Source: A. External Interaction Aware… · p. 3
  • Payload retention penalizes normalized horizontal offset and relative motion, rewards remaining within support bounds, and encourages a level support.The offset normalization accounts for support dimensions, and the displacement penalty increases smoothly near the boundary.Source: A. External Interaction Aware… · p. 3
  • The policy receives impedance commands, robot-side measurements, and an explicit external-force channel alongside its observation history.Inputs include projected gravity, joint positions and velocities, previous actions, trunk IMU, and actuator-torque measurements.Source: A. External Interaction Aware… · p. 4
  • An asymmetric actor-critic learns the force-aware policy using a privileged latent for the actor and uncompressed privileged state for the critic, optimized with PPO.The privileged state includes reference, robot, payload, payload-property, and contact information.Source: A. External Interaction Aware… · p. 4
  • A recurrent adaptation module learns to recover the privileged latent from policy observations, then is trained on rollouts using the adapted actor’s closed-loop behavior.The actor and privileged encoder remain fixed during that adaptation stage, removing the policy’s inference-time dependency on privileged state.Source: A. External Interaction Aware… · p. 4

B. Proprioceptive Payload Force Estimation

The force estimator replaces the oracle force input with predictions from onboard measurements. Its causal recurrent design separates interaction activity, direction, and magnitude, and is trained on trajectories that include estimator-driven states.

B. Proprioceptive Payload Force Estimation

  • The estimator removes the oracle-force dependency by predicting payload interactions from onboard robot measurements.The predicted force is supplied to both the compliant reference and the policy force channel.Source: B. Proprioceptive Payload Force… · p. 4
  • Inputs include robot-side proprioceptive, inertial, actuator, and foot-load measurements, but exclude the force channel, ground-truth force, payload pose, and payload properties.A recurrent encoder summarizes these measurements.Source: B. Proprioceptive Payload Force… · p. 4
  • Separate recurrent heads predict interaction probability, force direction, and magnitude, which combine into a conditional force estimate.The probability estimates whether force exceeds the actionable threshold; direction is unit length and magnitude is predicted separately.Source: B. Proprioceptive Payload Force… · p. 4
  • At inference, a causal hysteresis gate suppresses predictions when no actionable interaction is detected without attenuating active-force magnitude.The resulting force estimate is supplied to both the compliant reference and policy force channel.Source: B. Proprioceptive Payload Force… · p. 4
  • Estimator training uses balanced interaction classification, active-sample force supervision, and a training-only payload-mass prediction head to distinguish inertia changes from external interaction.The objective also suppresses confident nonzero predictions during ordinary locomotion.Source: B. Proprioceptive Payload Force… · pp. 4–5
  • Mixed-distribution DAgger combines blind, oracle-force, and estimator-in-the-loop trajectories so training includes states induced by the estimator’s own predictions.The experiments use one estimator-in-the-loop aggregation round.Source: B. Proprioceptive Payload Force… · p. 5

C. Estimator-Aware Policy Finetuning

Because estimation introduces force magnitude, direction, gating, and timing errors, the actor is finetuned under estimator-driven rollouts. Behavioral anchoring helps retain the compliant behavior learned with oracle force.

C. Estimator-Aware Policy Finetuning

  • Estimation introduces magnitude, direction, gating, and timing errors absent during oracle-force adaptation.These errors motivate finetuning under estimator-driven rollouts.Source: C. Estimator-Aware Policy Finetuning · p. 5
  • PPO finetunes an actor initialized from the oracle force-adapted policy while the estimator and recurrent adaptation module remain frozen.Estimated force drives both the compliant reference and policy force channel; the critic also receives privileged state.Source: C. Estimator-Aware Policy Finetuning · p. 5
  • Behavioral anchoring regularizes the finetuned actor toward the frozen oracle actor because PPO robustness updates may weaken compliant behavior.Both actors receive the same estimated-force observation and adaptation latent, while true force is used only for the training-time label.Source: C. Estimator-Aware Policy Finetuning · p. 5
  • At deployment, simulator-only supervision, aggregation, and anchor-weighting quantities are removed, leaving only deployable observations for the controller.The policy is optimized under the estimator-induced state distribution while remaining close to the oracle-force compliant behavior.Source: C. Estimator-Aware Policy Finetuning · p. 5

V. SIMULATIONS

The simulation evaluation examines whether the controller realizes commanded compliant responses to payload interactions and whether estimated force can guide trajectory correction. The setup uses a simulated quadruped carrying an unrestrained payload.

V. SIMULATIONS

  • The simulations evaluate commanded compliant responses to payload interactions and whether force estimates can guide downstream trajectory correction.Source: §V · pp. 5–6
  • Table I covers aggregate compliance response and full-grid termination, with column values reported as means and standard deviations across five seeds.Source: Table I · p. 6
  • Table II is identified as a quantitative analysis of the force estimator.Source: Table II · p. 6
  • The setup simulates a Unitree Go2 carrying a rigid, unrestrained payload on a trunk-mounted support, with randomized payload, contact, robot, actuator, and initial-condition properties.The payload is 0.20 m tall, bottom-heavy, and has footprints from 0.18 × 0.18 m to 0.35 × 0.25 m.Source: §V · p. 6

A. Commanded Compliance and Force Response

The evaluation tests force-aware compliance across payload masses, applied forces, and commanded stiffnesses. The learned approach approaches the oracle response, improves over FACET-L, and varies its response with force and stiffness.

A. Commanded Compliance and Force Response

  • The comparison includes Ours, FACET, FACET-L, Oracle, and Ours-Analytic across payload masses of 2–6 kg, forces of 6–30 N, and stiffnesses of 6–30 N/m.Each condition is tested in 32 randomized simulation instances; compliance metrics use conditions where Oracle succeeds in at least 95% of trials, while termination covers the full grid.Source: A. Commanded Compliance and Force… · p. 6
  • Ours reaches ρcmd = 0.826 ± 0.003 versus 0.702±0.002 for FACET-L, approximately halves direction error, and keeps full-grid termination near Oracle.The largest failure rates occur under high forces on light payloads.Source: A. Commanded Compliance and Force… · p. 6
  • The learned estimator recovers more applied force, detects interactions more consistently, and responds with less delay than the analytic estimate.Ours follows the Oracle trend: larger forces produce the corresponding compliant response, while increasing Kp reduces displacement.Source: A. Commanded Compliance and Force… · p. 6, Figure 3 · p. 6

B. Force-Guided Trajectory Correction

The study tests whether estimated payload force can guide obstacle avoidance. Ours uses onboard measurements to correct the route, with reported clearance and joint success below the oracle-force ceiling.

B. Force-Guided Trajectory Correction

  • Ours achieves 77.1% clearance and 76.9% joint success, compared with the Oracle true-force ceiling of 92.4%; Ours-Analytic clears 34.8%.FACET-L cannot deliberately alter its route, and the small clearance-to-joint-success gap indicates successful avoidance generally also preserves the payload and reaches the goal.Source: B. Force-Guided Trajectory Correction · pp. 6–7, Table III · p. 7
  • The experiment maps signed lateral impulse to a bounded minimum-jerk path deformation that selects an avoidance side and smoothly returns to the nominal route.The comparison spans forces of 10, 13, 16, and 20 N, payload masses of 2, 4, and 6 kg, and both lateral directions.Source: B. Force-Guided Trajectory Correction · p. 6
  • The same trajectory-correction rule receives different force inputs across methods, while physical displacement during yielding is excluded from commanded trajectory deformation.The table reports mean and standard deviation across five seeds.Source: B. Force-Guided Trajectory Correction · p. 6, Table III · p. 7

VI. REAL-WORLD EXPERIMENTS

Real-world trials on a Go2 carrying an unrestrained 4 kg payload assess nominal walking and human-guided route correction. The robot yields to payload interactions and uses the estimated force for purposeful trajectory changes while maintaining stable locomotion.

VI. REAL-WORLD EXPERIMENTS

  • The Go2 carries an unrestrained 4 kg payload at a commanded speed of 0.25 m/s over 6 m; human-guided replanning begins after an interaction persists for at least one second.Motion capture tracks the robot but is not an input to the policy or force estimator; the experiments evaluate resulting motion, not ground-truth forces.Source: §VI · p. 7
  • During straight-line walking, Ours closely tracks commanded speed with near-zero lateral speed, while FACET-L has lower mean lateral deviation: 0.025 ± 0.017 m versus 0.045 ± 0.020 m.Ours has lower mean tilt but higher peak tilt; the authors hypothesize its larger path deviation and peak tilt reflect corrective motions triggered by detected payload movement.Source: §VI · p. 7, Table IV · p. 8
  • Across ten trials, Ours yields more laterally than FACET-L during interaction, reaches the goal more accurately, and produces 0.345 ± 0.081 m average lateral displacement beyond the displaced pose.Median trunk tilt was 3.44° and median speed was 0.25 m/s; speed reduced during interaction and resumed after a new path was available.Source: §VI · pp. 7–8, Figure 4 · p. 7

VII. CONCLUSION

The conclusion presents a force-aware locomotion framework for unrestrained payloads, combining compliant load-carrying behavior with force estimation from onboard measurements. Experiments suggest stable carrying and compliant yielding, with estimated forces also supporting human-guided trajectory changes.

VII. CONCLUSION

  • The framework addresses forces applied directly to an unrestrained payload coupled to the robot through frictional contact, rather than forces on the robot or a rigidly connected load.The learning stages are separated: the compliant load-carrying behavior is learned first, followed by a causal estimator and policy finetuning with that estimator in the loop.Source: §VII · p. 8
  • Simulations and real-world experiments suggest stable load-carrying locomotion while yielding compliantly, and show that estimated force can support human-guided trajectory changes.Source: §VII · p. 8
  • The formulation is limited to planar payload interactions and assumes the payload remains in contact with its support, though sufficiently large forces may still cause payload loss.Future work is aimed at three-dimensional interactions and a broader range of payloads and terrains.Source: §VII · p. 8
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