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Reactive Humanoid Multi-Contact Using Learned Stability Models

Stephen McCrory, Beomyeong Park, Nicholas Kitchel, Nehar Poddar, Robert Griffin

arXiv:2610.00823v1cs.RO

TL;DR

Humanoid recovery methods are largely limited to feet contacts and quasi-flat terrain, leaving a need for hand bracing on arbitrary surfaces. This work uses learned post-impact CoP models to rapidly evaluate sampled hand contacts and plan bracing. In standing hardware tests, optimized placement reduced average recovery time relative to the stated baselines.

  • Problem

    Existing push-recovery approaches are largely restricted to quasi-flat terrain and feet contacts, while humanoids may need upper-body contacts and models for arbitrary surfaces.

    Source: §I · p. 1

  • Method

    The planner rolls out sampled contacts through pre-impact, impact, and post-impact centroidal dynamics, using learned CoP models to select a bracing surface and point.

    Source: §I · p. 1

  • Results

    Average recovery time decreased 57% for the optimized plan versus the closest reachable brace point in standing multi-surface tests, and 29% versus the baseline in standing single-surface tests.

    Source: C. Hardware · pp. 6–7

  • Takeaways & Limitations

    The planner targets reactive hand-contact recovery on arbitrary surfaces, including tilted or vertical ones, within ≤10 ms.

    Source: B. Contributions · p. 2

Abstract

from arXiv · show

We present a planning and control approach to reactively use hand contacts to stabilize a humanoid in low stability scenarios, where only using feet contacts may result in a fall. Candidate contacts are sampled within the robot's reachable workspace, and a preview is computed by rolling out the centroidal dynamics through pre-impact, impact and post-impact phases. Sampled points are scored based on the Center of Pressure (CoP) control authority at the post-impact phase. Central to our approach is a learned model of the robot's CoP region during post-impact, which enables rapid evaluation of candidate contact points compared to traditional optimization-based methods. The presented planner has two stages: the first selects an optimal bracing region and the second computes an optimal bracing point within the region. Our simulation results demonstrate an average increase in impulse resilience of 89% over recovery without hand contacts and 17% over a naive planning strategy (closest reachable region). We validate our framework on hardware, performing push tests while standing and walking. The standing trials show an average 43% reduction in stabilization time compared to naive hand placement and the walking trials demonstrate a 18% reduction compared to baseline recovery (without hand contacts).

I. INTRODUCTION

Existing humanoid push-recovery methods largely rely on feet contacts and quasi-flat terrain, while this work plans hand bracing for low-stability scenarios using learned post-impact CoP models. Its contributions include rapid planning for arbitrary surfaces, model predictions across hand-foot contact combinations, and simulation and hardware demonstrations.

I. INTRODUCTION

  • Existing push-recovery approaches are largely restricted to quasi-flat terrain and feet contacts, motivating upper-body contacts and models for arbitrary contact surfaces.Prior learning approaches include predicting capturability and hand loading, alongside learning to mimic optimization-based stability models.Source: §I · p. 1, A. Related Work · p. 2
  • Learned CoP models evaluate post-impact stability about 40× faster than optimization-based techniques and support a two-pass planner that selects a bracing surface, then a point within it.Candidate contacts are previewed through pre-impact, impact, and post-impact centroidal dynamics and scored by post-impact CoP control authority.Source: §I · p. 1

A. Related Work

  • Related approaches use reduced-order models and heuristics, optimization-based contact feasibility, or learned stability predictions for recovery planning.The paper builds on reactive hand-contact planning [15] and optimal region selection.Source: A. Related Work · pp. 1–2, B. Contributions · p. 2

B. Contributions

  • The contributions include a reactive planner targeting ≤10 ms for arbitrary surfaces and neural networks that predict feasible CoP placement across hand-foot contact combinations.The work also reports simulation comparisons using minimum unrecoverable impulse and hardware demonstrations of hand-contact recovery from high impulses.Source: B. Contributions · p. 2

II. BACKGROUND

The background frames robot stability as an optimization problem over unilateral, friction-constrained contacts. The stability model extends this framing to dynamic stability and uses feasible CoP regions to represent the control available from mixed hand and foot contacts.

II. BACKGROUND

  • The robot’s stability is modeled through an optimization problem over unilateral- and friction-constrained contacts, with the planner using a dynamic-stability formulation.The dynamic formulation sets a1 = 0 and a2 ≠ 0.Source: §II · p. 2

III. STABILITY MODELING

  • The nominal CoP region is the support-foot region, while the multi-contact CoP region represents feasible CoP placement with hand contacts.The robot can place the CoP within the red convex region shown for an example with two feet and two hand contacts.Source: §III · p. 2, Figure 2 · p. 2

A. Optimization-based stability model

  • An optimization problem evaluates centroidal force along a query direction, maps the optimal force to a CoP using an LIPM relationship, and traces the region’s vertices across directions.The example region is computed by successively solving Eq. (2) while varying the query direction.Source: A. Optimization-based stability model · pp. 2–3

B. Feasible CoP region neural networks

The section replaces costly optimization-based CoP-region evaluation with learned models, then applies those models to score sampled contacts during centroidal rollouts. The models encode additional CoP authority for mixed hand-and-foot contact configurations.

B. Feasible CoP region neural networks

  • Neural networks model the multi-contact CoP region to reduce the computational overhead of optimization-based evaluation, which requires inverse kinematics, contact-Jacobian SVD, and repeated solves.The optimization-based region is parameterized by whole-body configuration and computed over multiple query directions.Source: B. Feasible CoP region neural networks · p. 3
  • Each network predicts additional CoP control authority beyond the nominal region as distances along 18 equally spaced directions from the mid-feet.The models cover five unmirrored mixed hand-and-foot contact configurations, with a distinct network for each.Source: B. Feasible CoP region neural networks · p. 3
  • Network inputs include hand-contact positions and normals, CoM position, and stance-foot geometry, expressed in a local mid-feet frame.Separate models are trained per contact configuration using sampled robot configurations and optimization-based reference regions.Source: B. Feasible CoP region neural networks · p. 3

IV. CONTACT PLANNING

  • The planner applies the stability networks in a sampling-based hand-contact planner that scores sampled contacts using a centroidal rollout.The rollout propagates the predicted capture point through impact, uses the feasible multi-contact CoP region to compute a post-impact CoP, and scores post-impact control authority.Source: §IV · pp. 3–4, Figure 5 · p. 4

A. Planar Region Mapping

The framework maps planar bracing surfaces and previews contact using capture-point dynamics across pre-impact, impact, and post-impact phases. Post-impact CoP authority provides a score for estimating recovery potential.

A. Planar Region Mapping

  • Depth images are converted into convex planar bracing regions at 30 Hz, which are shrunk by 7 cm to avoid edge contacts.The head-mounted camera supplies the robot’s map of bracing surfaces.Source: A. Planar Region Mapping · p. 4

B. Centroidal Dynamics Rollout

  • Rollouts plan each hand separately and omit step adjustment, upper-body angular momentum, and nominal-region CoP feedback, although the controller uses those strategies.The simplifications target reflexive planning within 10 ms.Source: B. Centroidal Dynamics Rollout · p. 4
  • Pre-impact rollout integrates capture-point dynamics until hand contact, initializing from the current capture point and estimating impact time from maximum hand acceleration.The nominal CoP without feedback can be mid-foot when standing.Source: B. Centroidal Dynamics Rollout · p. 4
  • Impact is modeled as a fixed impulse along the bracing-surface normal; simulations use 4 Ns, corresponding to a 1.6 cm capture-point displacement for Alex.Source: B. Centroidal Dynamics Rollout · p. 4
  • At post-impact, the planner scores a snapshot of CoP control authority using the predicted capture-point error and a CoP projected to the multi-contact boundary.The score approximates post-impact recovery time; the network is queried for the predicted contact state.Source: B. Centroidal Dynamics Rollout · pp. 4–5

C. Select Optimal Region (1 sample per region per side)

Planning triggers on capture-point tracking error and a minimum interval between plans. For each hand, the planner scores the closest reachable point on each reachable region and chooses the highest-scoring region.

C. Select Optimal Region (1 sample per region per side)

D. Contact Placement (n samples per side)

After selecting a bracing surface, the planner samples contact points around its closest reachable point and uses a fitted score gradient in a quadratic program to choose placement.

D. Contact Placement (n samples per side)

  • The planner samples six points radially at 12 cm around the closest reachable point, shifting the sample center inward when that point is near the workspace boundary.Source: D. Contact Placement (n samples per… · p. 5
  • A least-squares-fitted linear score gradient informs a quadratic program that balances score with proximity to the closest reachable point within the reachable region.The placement is adjusted to increase post-impact CoP control authority.Source: D. Contact Placement (n samples per… · p. 5

V. BRACING CONTROL

Bracing control separates pre-impact and post-impact phases. Before contact, the hand follows a world-frame cubic trajectory toward the planned contact point, with touchdown conditions expressed in the bracing-plane frame.

V. BRACING CONTROL

  • Bracing control is divided into pre-impact and post-impact phases.Source: §V · p. 5

A. Pre-Impact Bracing Control

  • During pre-contact, a world-frame cubic trajectory matches the hand’s current position and velocity and ends at the planned contact point.Source: A. Pre-Impact Bracing Control · p. 5
  • The trajectory uses a fixed 0.9 m/s touchdown velocity and 9 m/s^2 maximum hand acceleration; touchdown conditions are expressed in the planar-region frame.The touchdown bounds account for plane and robot-position estimation error, with zmax = 4 cm and vz,max = 30 cm/s.Source: A. Pre-Impact Bracing Control · pp. 5–6

B. Post-Impact Bracing Control

After impact, the controller uses the current contact conditions to place the desired CoP at the most recovery-favorable feasible position. Its planar control objective depends on the desired arm load, and contact is released under specified conditions.

B. Post-Impact Bracing Control

  • After impact, the controller sets acceleration normal to the planar region to zero and uses planar PD feedback or zero acceleration depending on desired arm load.Planar control uses zero acceleration to eliminate drift when the hand is lightly loaded.Source: B. Post-Impact Bracing Control · p. 6
  • At each control tick, the controller uses the network for the current contact conditions to place the desired CoP at the maximal feasible recovery position.This placement is conditioned on the robot’s current state.Source: B. Post-Impact Bracing Control · p. 6
  • Contact is released and the arm returns to its nominal position if the hand deviates 9 cm from touchdown or nears the reachable-workspace edge.Source: B. Post-Impact Bracing Control · p. 6

VI. RESULTS

The results section evaluates neural-network prediction error and tests impulse resilience in standing and walking simulations. In the sideways-walking case, contact placement yields a 16% improvement in impulse resilience.

A. Neural network evaluation

  • The network’s RMSE was evaluated against optimization-computed example data on a dataset distinct from training, and nonzero error was expected because the network receives partial information.The ground-truth value is characterized by the robot’s whole-body configuration; erroneous negative predictions are ignored at runtime because the multicontact CoP region cannot under-approximate the nominal region by design.Source: A. Neural network evaluation · p. 6
  • Table I presents RMSE errors for the neural-network evaluation.Source: Table I · p. 6, A. Neural network evaluation · p. 6

B. Simulation

  • 16% improvement in impulse resilience was reported for sideways walking, where contact placement adjusted the contact by 14.9 cm.The simulation compared no bracing, closest-reachable-point bracing, and the presented planner across standing, sideways walking, and backwards walking.Source: B. Simulation · p. 6, Figure 8 · p. 6
  • Impulse resilience was tested by applying a pelvis impulse and using binary search to find the maximum sustainable impulse before a fall.The three scenarios were standing, sideways walking, and backwards walking; comparisons were against no bracing and closest-reachable-point bracing.Source: B. Simulation · p. 6, Figure 8 · p. 6

C. Hardware

Hardware push tests show shorter recovery times with optimized hand bracing across standing and walking conditions. The conclusion reports a 15–20% improvement over naive bracing and notes reliance on reduced-order models.

C. Hardware

  • 57% decrease in average recovery time was observed when the standing multi-surface planner chose the wall rather than the closest reachable tilted surface.The wall choice also produced larger tracking error, partly because time to contact was longer.Source: C. Hardware · p. 6, Figure 9 · p. 7
  • 29% decrease in average post-impact recovery time followed an approximately 12 cm upward contact adjustment in single-surface standing tests.The experiment ignored the right hand; the authors associate the decrease with higher CoP control authority.Source: C. Hardware · p. 7
  • 18% reduction in recovery time was observed during walking with hand bracing versus baseline trials without hand contacts.High stability was achieved on average 316 ms after push detection with bracing, versus 384 ms in baseline trials.Source: C. Hardware · p. 7
  • Walking contact release left average capture-point error near 3 cm until about 750 ms, attributed partly to arm momentum absent from the nominal centroidal plan.Contact lasted about 55 ms; the authors attribute this partly to contact-detection latency and propose testing higher push forces.Source: C. Hardware · p. 7

VII. CONCLUSION

  • The approach achieves significant 15–20% improvement compared with naive bracing, with ≈50× faster computation and ≈10 ms total reaction time.The conclusion reports substantial stability improvement over baseline walking in simulation and hardware.Source: §VII · p. 7
  • The approach still relies heavily on reduced-order models, and the authors identify impact-map scoring as a direction for future work.They report that the impact phase often accounted for most recovery, rather than the post-impact phase.Source: §VII · p. 8

APPENDIX

The appendix constrains candidate bracing regions to the robot’s reachable workspace and describes capture-point error dynamics for estimating recovery time. Its scoring function is related to that estimate but avoids cases where the logarithm’s argument is negative.

A. Reachability Model

  • Reachable bracing regions use a shoulder-centered spherical workspace with 32–72 cm reach, cropped along the sagittal plane to prevent arm collisions.The cropped workspace is encoded as linear constraints when bracing regions are cropped.Source: A. Reachability Model · p. 8

B. Capture point error dynamics

  • Capture-point error dynamics are linear because the feed-forward trajectories are designed to satisfy the LIPM relationship.Source: B. Capture point error dynamics · p. 8
  • Recovery time is estimated under a fixed CoP feedback offset set to kξ_err(T), yielding a scalar dynamic relationship along the initial capture-point error direction.Source: B. Capture point error dynamics · p. 8
  • High scores correlate with low recovery times, but the planner avoids scoring directly by recovery time when the logarithm argument is negative.That case may occur when the robot is capturable using both hands but not one.Source: B. Capture point error dynamics · p. 8
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