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ReCo: Response-Consistent Locomotion with Policy-Aware MPC for Legged Manipulation

Kuankuan Sima, Yichao Gao, Chenxi Gu, Kefan Zhao, Lin Zhao

arXiv:2610.01612v1cs.RO

TL;DR

Continuous legged manipulation needs accurate end-effector tracking while the base walks, but the command response of a learned locomotion policy varies with gait phase, contact, and payload. ReCo shapes policy responses and uses an identified closed-loop model in MPC for joint base-and-arm planning; on a selected trajectory it achieves lower position and orientation errors than two baselines.

  • Problem

    Continuous legged manipulation requires tracking a world-frame end-effector trajectory while walking, but the learned base response varies with gait phase, contact, and payload.

    Source: §I · p. 1

  • Method

    ReCo shapes the locomotion policy for predictable command responses, identifies its closed-loop response model, and uses that model in MPC to jointly plan locomotion commands and arm motion.

    Source: §I · pp. 1–2

  • Results

    On a selected 3.43 m trajectory, ReCo achieves 0.0695 m position RMSE and 8.20° orientation RMSE, less than half the error of either Pure MPC or Ma et al. on both metrics.

    Source: B. Trajectory Tracking Performance · p. 5

  • Takeaways & Limitations

    A repeatable base response lets a planner use locomotion for sustained displacement and the arm for fast local corrections within its workspace and actuator limits.

    Source: §I · p. 1

    The tested impulse disturbance covers only one direction, duration, and application schedule.

    Source: B. Trajectory Tracking Performance · p. 5

Abstract

from arXiv · show

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.

I. INTRODUCTION

Continuous legged manipulation requires end-effector tracking while the base walks, but policy-controlled base motion can vary with gait phase, contact, and payload. ReCo shapes the locomotion policy for predictable responses and uses an identified response model in MPC to plan locomotion commands and arm motion together.

I. INTRODUCTION

  • Tracking a world-frame end-effector trajectory while walking requires coordination because base translation, attitude changes, and gait oscillations propagate to the end effector.Continuous legged manipulation goes beyond repositioning the base to extend the arm’s workspace.Source: §I · p. 1
  • The planner must predict the policy-controlled base response to candidate commands, which varies with gait phase, contact, and payload.Assuming commanded velocity or posture is realized immediately can miss periodic height and attitude motion that propagates to the end effector.Source: §I · p. 1
  • A locomotion policy should be robust and predictable enough for a low-order model to forecast its response over a useful horizon.A consistent delay can be compensated by feedforward, whereas a variable delay cannot.Source: §I · p. 1
  • Response shaping makes command responses repeatable through reference tracking, phase repeatability, steady-state gain, and cross-domain consistency rewards.The resulting policy-aware MPC jointly plans locomotion commands and arm motion for continuous world-frame end-effector SE(3) tracking using an identified closed-loop response model with a gait-periodic component.Source: §I · pp. 1–2
  • 28.7% position RMSE and 27.4% orientation RMSE reductions relative to the best of five baselines for each metric accompany a 59.6% reduction in normalized prediction MSE.The full system also runs onboard.Source: §I · p. 2

II. RELATED WORK

Prior work coordinates legged manipulation through explicit models, learned controllers, or hybrid interfaces, but ReCo focuses on predicting the response of a learned locomotion policy. Its method shapes that response, identifies a closed-loop model, and uses it in MPC to plan locomotion and arm motion jointly.

A. Model-Based Legged Manipulation

  • Model-based legged manipulation coordinates base and arm motion through explicit models and constraints, while ReCo supplies a prediction of the learned policy’s command-to-motion response.Prior examples include ALMA and perceptive MPC.Source: A. Model-Based Legged Manipulation · p. 2

B. Learning-Based Locomotion and Manipulation

  • Learning-based work spans robust locomotion and learned whole-body manipulation, while ReCo adopts a command interface and shapes transient and periodic policy responses for predictive planning.Examples include Deep Whole-Body Control, RoboDuet, and UMI on Legs.Source: B. Learning-Based Locomotion and… · p. 2

C. Hybrid Control and Policy Response Modeling

  • Unlike Ma et al.’s interface, which lets locomotion anticipate arm-induced disturbances, ReCo’s response model predicts base motion under candidate commands; it also models gait-periodic height and attitude variations.RAMBO learns feedback corrections to model-based whole-body control, whereas ReCo fits its response model to the learned locomotion policy.Source: C. Hybrid Control and Policy Response… · p. 2

III. METHOD

  • ReCo trains a locomotion policy with a consistent command response, identifies its closed-loop response model, and uses that model in policy-aware MPC to jointly plan locomotion commands and arm motion.The overview also shows MPC integrating arm kinematics and state feedback.Source: §III · p. 2, Figure 2 · p. 2

A. Problem Formulation

The formulation tracks a time-indexed world-frame end-effector pose during locomotion, with MPC selecting locomotion commands and arm joint velocities. The training passages describe response shaping to encourage repeatable command transients and gait-dependent body motion across randomized dynamics.

A. Problem Formulation

  • MPC selects locomotion commands and arm joint velocities to track a time-indexed world-frame end-effector pose during locomotion.Frames W, B, and E denote the world, base, and end-effector; T_AB maps coordinates from B to A, and q denotes arm joint positions.Source: A. Problem Formulation · pp. 2–3
  • The gait-conditioned policy receives commands for planar velocity, yaw rate, height, and pitch, while gait timing conditions its leg control.Roll remains a predicted state, not a policy command, because it affects the end-effector pose.Source: A. Problem Formulation · pp. 2–3
  • The base prediction state includes position, orientation, heading-frame velocity, and body-frame yaw velocity, with gait phase included in the full state.The arm joint-velocity commands are part of the input, alongside the locomotion commands.Source: A. Problem Formulation · p. 3

B. Response-Consistent Locomotion Training

  • Response shaping trains for repeatable command transients and gait-phase-dependent body motion across randomized dynamics.The shaping terms act on planar velocity, yaw rate, height, and pitch; PPO and the gait-conditioned Walk These Ways interface provide the training setup.Source: B. Response-Consistent Locomotion… · p. 3
  • Each command channel uses a critically damped reference generator, with unsaturated zero-order-hold updates and rate-limited ramps under saturation.The height command uses the same nominal offset as body height.Source: B. Response-Consistent Locomotion… · p. 3
  • Training separates command transients from gait oscillations using a phase- and speed-dependent estimate, and disables reference tracking during disturbances and a recovery interval.This lets recovery take precedence over matching the target transient.Source: B. Response-Consistent Locomotion… · p. 3
  • Cross-domain consistency compares matched command sequences and gait phases across nominal and randomized environments, with masks excluding invalid or desynchronized comparisons.Randomizations include mass, payload, friction, and actuator strength; the response-shaping terms supplement locomotion rewards and regularization.Source: B. Response-Consistent Locomotion… · p. 3
  • Training progresses from establishing locomotion to adding reference tracking, consistency penalties, broader randomization, and stronger disturbances.Table I groups the reference reward in r+ and three nonnegative losses in r− with negative weights.Source: B. Response-Consistent Locomotion… · p. 3, Table I · p. 3

C. Closed-Loop Response Model

The closed-loop response model combines command-response dynamics with gait-periodic base motion. Its parameters are identified offline for each frozen policy, and the model does not explicitly represent arm-induced wrenches.

C. Closed-Loop Response Model

  • Velocity channels use one response state each, with response gain and time constant parameterizing the closed-loop command response.The second-order training reference sets a target transient but does not impose the realized closed-loop order.Source: C. Closed-Loop Response Model · p. 3
  • A speed-dependent harmonic series models gait-periodic base height, pitch, and roll variations.The model uses stride and half-stride components; roll has no command input, while the height command corresponds to c_z.Source: C. Closed-Loop Response Model · p. 3
  • The periodic component is identified offline for prediction, with the model accounting for phase and speed variation in the gait oscillations.The lag acts on the state after subtracting the periodic component, and its time derivative accounts for phase and speed changes.Source: C. Closed-Loop Response Model · p. 4
  • The model captures empirical closed-loop response without explicitly modeling arm-induced wrenches.Source: C. Closed-Loop Response Model · p. 4
  • Parameters are identified offline for each frozen policy by bounded nonlinear least squares on multi-step open-loop prediction errors.Step, ramp, and chirp commands excite the response across randomized domains, using data separate from prediction and tracking runs.Source: C. Closed-Loop Response Model · p. 4

D. Policy-Aware Model Predictive Control

ReCo’s MPC combines the identified response model with arm kinematics to predict end-effector motion and jointly coordinate locomotion commands and arm movement. Its optimization penalizes pose error while accounting for command, joint, and self-collision constraints.

D. Policy-Aware Model Predictive Control

IV. EXPERIMENTS

The experiments compare ReCo with alternative control architectures, then examine response shaping, model identification, prediction accuracy, repeatability, gait-periodic response, and hardware execution.

IV. EXPERIMENTS

  • The experiments first compare ReCo with alternative control architectures.Source: §IV · p. 4
  • Further experiments isolate response shaping and model identification, and assess how shaping affects prediction and repeatability.Source: §IV · p. 4
  • Additional experiments evaluate the gait-periodic component of the response model and onboard hardware execution.Source: §IV · p. 4

A. Experimental Setup

The evaluation uses a Go2 with an X5 arm on diverse world-frame end-effector trajectories, comparing hybrid, model-based, and learned whole-body controllers under nominal and push conditions.

A. Experimental Setup

  • The MuJoCo benchmark uses a Go2 with a six-DoF X5 arm and 50 world-frame end-effector trajectories, including targets outside the arm workspace at a fixed base pose.Source: A. Experimental Setup · p. 4
  • Each controller runs every trajectory nominally and with an 80 N world-+X force applied at the base center of mass for 0.1 s, yielding 100 runs per controller.Source: A. Experimental Setup · p. 4
  • Baselines represent RL+MPC, pure model-based MPC, and learned whole-body control, with the related hybrid baseline reimplemented using the same OCS2 infrastructure, horizon, and arm model.Source: A. Experimental Setup · p. 4
  • RoboDuet and Visual WBC are paired with a pure-pursuit base tracker because their evaluated low-level controllers do not generate base commands directly from world-frame end-effector trajectories.Source: A. Experimental Setup · p. 4
  • Success requires at least 97% progress without a fall or early termination, endpoint errors within 0.15 m and 40° held for 0.5 s, and at least 40% of samples within both tolerances.Source: A. Experimental Setup · p. 5

B. Trajectory Tracking Performance

ReCo achieves the lowest benchmark tracking errors and greater completion than the baselines, including under the tested push disturbance. Results also show limitations in baseline generalization and distinguish performance on one selected trajectory.

B. Trajectory Tracking Performance

  • 28.7% lower position RMSE than Pure MPC and 27.4% lower orientation RMSE than Ma et al. make ReCo the lowest-error controller on both benchmark metrics.Source: B. Trajectory Tracking Performance · p. 5
  • ReCo succeeds in 75/100 runs versus 42/100 for RoboDuet+PP, the strongest baseline by success count, while its mean progress is 11.4 percentage points above the next-best controller.Source: B. Trajectory Tracking Performance · p. 5
  • RoboDuet+PP and Visual WBC+PP complete at most 65.7% of the reference on average, with position RMSE 5.0 and 10.8 times ReCo’s, respectively.The comparison is consistent with a benefit from jointly planning base displacement and arm motion, but does not isolate planning from underlying controller differences.Source: B. Trajectory Tracking Performance · p. 5
  • UMI on Legs reaches 0.035 m position and 4.7° orientation RMSE on in-distribution trajectories but falls in 80/100 benchmark runs.Source: B. Trajectory Tracking Performance · p. 5
  • Under the applied push, ReCo’s mean position RMSE rises from 0.1326 m to 0.1371 m (3.4%), versus a 6.4% increase for Ma et al.The tested impulse covers one direction, duration, and application schedule.Source: B. Trajectory Tracking Performance · p. 5
  • On the selected 3.43 m trajectory, ReCo achieves 0.0695 m position and 8.20° orientation RMSE, less than half the error of either Pure MPC or Ma et al. on both metrics.Pure MPC reaches the endpoint but does not satisfy the hold requirement; ReCo and Ma et al. succeed.Source: B. Trajectory Tracking Performance · p. 5

C. Response Shaping and Model Identification

Response shaping improves prediction and repeatability, while model identification further lowers position error but can trade off orientation accuracy. Height residuals do not show the same repeatability improvement.

C. Response Shaping and Model Identification

  • 35.4%: shaping alone reduces position RMSE from 0.257 to 0.166 m; identification then lowers shaped-policy error to 0.135 m (18.7%).The factorial ablation compares response shaping and model identification; without identification, MPC assumes instantaneous command execution.Source: C. Response Shaping and Model… · p. 5, Table III · p. 6
  • Model identification raises orientation RMSE from 21.7° to 24.3° for the unshaped policy and from 21.5° to 23.8° for the shaped policy.The authors suggest omitted attitude dynamics and translation–rotation coupling may explain this trade-off.Source: C. Response Shaping and Model… · p. 5

D. Response Prediction and Repeatability

E. Gait-Periodic Prediction

The gait-periodic response component improves height prediction and closed-loop tracking, while shifted phase degrades prediction. The reported height gains use causal phase extrapolation.

E. Gait-Periodic Prediction

  • A deliberately shifted phase degrades height prediction, supporting the importance of phase alignment.Forecasts use causal phase extrapolation.Source: E. Gait-Periodic Prediction · p. 7, Figure 7 · p. 7
  • In closed-loop comparison, adding the gait-periodic component reduces position RMSE by 5.5%, orientation RMSE by 6.9%, and vertical tracking-error RMS in the 1.5–8 Hz band by 6.5%.Source: E. Gait-Periodic Prediction · p. 7
  • 44.8%: adding the gait-periodic component lowers height RMSE from 6.49 to 3.58 mm across 36 trajectories at 0.10, 0.25, and 0.34 s.The aggregate averages squared errors across trajectories and horizons before taking the square root.Source: E. Gait-Periodic Prediction · pp. 6–7, Figure 7 · p. 7

F. Hardware Experiments

ReCo demonstrates onboard manipulation during locomotion, with tracking evaluated using motion capture and estimated world-frame poses. The conclusion reports benchmark gains while noting orientation and height-repeatability trade-offs.

F. Hardware Experiments

  • The Go2–X5 control stack runs entirely onboard, averaging 75% CPU and 43% RAM.Source: F. Hardware Experiments · p. 7
  • With motion-capture state feedback and EE ground truth on eight trajectories, mean RMSEs are 0.0760 m and 9.93°; shaping lowers them by 29.1% and 7.4%.Source: F. Hardware Experiments · p. 7, Figure 8 · p. 8
  • ReCo completes object organization, cabinet-door opening, and pick-and-place during locomotion, with mean RMSEs of 0.153 m and 24.9° over three runs per task.These metrics use onboard odometry and arm forward kinematics, without an independent measure of odometry drift.Source: F. Hardware Experiments · pp. 7–8

V. CONCLUSION

  • 28.7% and 27.4%: ReCo reduces position and orientation RMSE versus the best baseline for each metric, succeeding in 75 of 100 runs versus 42 for the strongest baseline.Source: §V · p. 8
  • The conclusion identifies increased orientation error after model identification and unchanged height repeatability under shaping as open issues for future response-model improvements.Source: §V · p. 8
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