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Keeping Contact: Task-Adaptive Friction Margins for Bimanual Non-Prehensile Manipulation

Qian Ying Lee, Lin Yang, Domenico Campolo

arXiv:2610.36961v1cs.RO

TL;DR

Nominal friction-cone feasibility does not indicate how much margin a planned contact force has against slip, or how that margin should vary with task demand. The paper plans bimanual tilting forces with task-adaptive signed friction-distance margins. In the tested conditions, task-adaptive trials succeeded, while fixed margins failed under model mismatch and the no-margin ablation led to contact loss and task failure.

  • Problem

    Nominal feasibility accepts forces near the slip boundary as well as forces well inside it, leaving open how much contact-wise margin to maintain and how it should vary with task demand.

    Source: §I · p. 1

  • Method

    The planner lower-bounds each planned contact force’s signed distance from the nominal friction boundary using a task-adaptive margin derived from pivot moment deviations.

    Source: §I · p. 1, §VI · p. 7

  • Results

    All task-adaptive trials completed successfully under tested conditions, while fixed margin failed under model mismatch and no margin produced a larger violation fraction leading to contact loss and task failure.

    Source: §VI · p. 8

  • Takeaways & Limitations

    The tested results support configuration-dependent margin allocation to accommodate model uncertainty in bimanual tilting.

    Source: §VI · p. 8

Abstract

from arXiv · show

Maintaining contact in non-prehensile manipulation requires more than nominal friction cone feasibility: a force barely inside the cone and one well inside it are both feasible, but they provide different margins against slip and contact loss. This paper uses signed friction distance to measure friction margin in force space and derives a task-adaptive margin from the force correction needed to balance pivot moment deviations in bimanual tilting. The resulting contact margins are embedded in a sequence of second-order cone programs (SOCPs), each giving a globally optimal contact force solution at a tilt angle. The optimizer balances the object about an environmental pivot while keeping robot and pivot contact forces away from the nominal friction boundary. Optimizer-level results show interpretable force redistribution and adaptation to object property changes. Real-world experiments demonstrate successful execution under object property variations and model mismatch, while fixed margin and no-margin comparisons illustrate the importance of adapting the margin to task demand. These results support signed friction distance margins as a force planning mechanism for maintaining contact in bimanual non-prehensile manipulation. Project page: https://keeping-contact.github.io/

I. INTRODUCTION

Nominal friction-cone feasibility does not specify how much margin a contact force has against slip, or how that margin should vary with task demand. The paper proposes task-adaptive, force-space margins for planned contacts in bimanual tilting.

I. INTRODUCTION

  • A force barely inside the friction cone and one well inside it are both nominally feasible, but only the latter has meaningful margin against deviations.The margin should vary with task demand rather than be treated as uniform.Source: §I · p. 1

B. Contact Force Optimization and Friction Margins

  • The paper uses signed friction distance and a task-adaptive lower bound based on task force demand in a convex force planner.The planar bimanual tilting task uses non-opposing robot contacts and an environmental pivot; maintaining both robot contacts is central because slip or contact loss can lead to task failure.Source: §I · pp. 1–2

A. Non-Prehensile Manipulation with Force Planning

III. METHOD

The method measures contact-force margin as signed distance from the nominal friction boundary and imposes a lower bound on that distance. This converts the margin requirement into a second-order cone constraint for force planning.

A. Signed Friction Distance as a Force Space Margin

  • Signed friction distance is positive inside the nominal cone, zero at the slip boundary, and negative outside it.It measures the signed distance from the contact force to the slip boundary in the local force plane.Source: A. Signed Friction Distance as a Force… · p. 2
  • A lower bound ρ on signed friction distance makes the planned force tolerate force deviations up to ρ before reaching the nominal slip boundary.The margin is measured in force units and the constraint is equivalent to a second-order cone constraint.Source: A. Signed Friction Distance as a Force… · p. 3
  • A positive margin also induces a minimum compressive normal force when tangential force is zero and can certify tolerance to friction-coefficient overestimation.A conservatively reduced friction coefficient can encode a friction uncertainty bound, while ρ sets clearance from that reduced boundary in force units.Source: A. Signed Friction Distance as a Force… · p. 3

B. Pivot-Centered Model for Bimanual Tilting

The model treats bimanual tilting as quasi-static rotation about a known environmental pivot, with prescribed motion and sticking robot contacts. The robot forces are planned to balance moments about the pivot; force balance determines the passive pivot reaction.

B. Pivot-Centered Model for Bimanual Tilting

  • The object rotates quasi-statically about an environmental pivot at a known vertex, along prescribed motion with robot contacts sticking at fixed object-frame locations.The planned forces are expressed using contact positions and the nominal center of mass in the object frame.Source: B. Pivot-Centered Model for Bimanual… · p. 3
  • The environmental pivot is passive, so its reaction is determined by force balance rather than optimized as a decision variable.The planned force vector contains only the two robot contact forces.Source: B. Pivot-Centered Model for Bimanual… · p. 3
  • Taking moments about the pivot removes its reaction from the task balance, leaving robot-contact moment contributions to balance the gravitational moment.Each robot force contributes according to its moment arm about the pivot.Source: B. Pivot-Centered Model for Bimanual… · p. 3

C. Task-Adaptive Margin

The task-adaptive margin is derived from the force correction needed to balance pivot-moment deviations and is shaped by task demand. The resulting margin is allocated across robot contacts, with the pivot margin defined heuristically.

C. Task-Adaptive Margin

  • The task force demand is the minimum-norm robot contact force vector needed to balance the pivot moment.The scalar demand measures pivot-moment demand after mapping it through the minimum-norm contact-force map, before margin or objective-dependent force redistribution.Source: C. Task-Adaptive Margin · p. 3
  • The minimum-norm task force assumes the robot contacts have nonzero moment-generating capability about the pivot.The section also gives a conservative parameter choice when property-deviation bounds are identified.Source: C. Task-Adaptive Margin · pp. 3–4
  • A first-order force-correction derivation for mass and CoM deviations supplies the task-level basis for margin allocation.The derivation considers bounded mass and CoM deviations and combines the resulting relations into a sufficient task-level margin.Source: C. Task-Adaptive Margin · p. 4
  • The force-deviation derivation motivates an affine task-adaptive margin whose configuration-dependent structure follows from the model.The model-based force-deviation derivation determines the structure of the task-adaptive margin in Eq. (23).Source: C. Task-Adaptive Margin · p. 4
  • The minimum-norm correction allocates margin to each robot contact, while the passive pivot reaction receives a heuristic margin.The correction derivation applies to robot contacts and does not directly bound the pivot reaction.Source: C. Task-Adaptive Margin · p. 4

D. Contact Force Planning

At each tilt angle, the planner computes robot contact forces that balance the pivot moment while satisfying signed friction-distance margins. With fixed margins at that angle, the problem is an SOCP, and shifting the lower bounds preserves convexity.

D. Contact Force Planning

  • At each tilt angle, the optimizer computes robot contact forces satisfying pivot-moment balance and signed friction-distance margin constraints.Robot and pivot contacts use contact-specific margins and their corresponding friction coefficients.Source: D. Contact Force Planning · p. 4
  • For a fixed tilt angle, the moment constraint is linear in the forces and each friction-margin constraint has second-order-cone form.The angle-specific margins are fixed parameters, so the force-planning problem is an SOCP solvable with interior-point methods.Source: D. Contact Force Planning · p. 4
  • Task-adaptive margins shift lower bounds within the same friction constraints, preserving convexity.Source: D. Contact Force Planning · p. 4

E. Robot Execution

The optimized robot contact forces are executed through impedance control by converting each desired force into an equilibrium point. The command uses object-pose frame transformations and a defined translational stiffness, while end-effector orientation follows the object tilt.

E. Robot Execution

  • Impedance control executes optimized robot contact forces by converting each desired force into an equilibrium point.Source: E. Robot Execution · p. 4
  • The object pose q is used for frame transformations, with tilde quantities expressed in each robot's base frame.Source: E. Robot Execution · p. 4
  • The robot translational stiffness matrix is K_i, and end-effector orientation follows object tilt with a fixed object-frame offset.Source: E. Robot Execution · p. 4

IV. EXPERIMENTS

The experiments use two instrumented Kinova arms to tilt a box, with a nominal centered-CoM model and fixed margin parameters selected from that setup. Evaluation varies object mass, CoM, and assumed model properties, with success defined by completing the tilt while maintaining both robot contacts.

A. Setup

  • Two 7-DoF Kinova Gen3 arms tilt a 0.3 × 0.2 × 0.2 m box with a base mass of 1.7 kg.The nominal condition adds a centered 200 g weight, for 1.9 kg total; measured friction coefficients are 0.75 at robot contacts and 0.5 at the environment contact.Source: A. Setup · p. 4
  • The margin parameters λ_m = 0.25 and λ_CoM = 0.5 N are selected once from the nominal setup and held fixed across conditions.The experiments assess resulting contact behavior rather than identifying tight physical deviation bounds.Source: A. Setup · p. 4

B. Evaluation Conditions

  • Evaluation varies mass and CoM while retaining the same contact-specific margin law; the no-margin ablation uses nominal properties with ρ_i = 0.The light condition removes the calibration weight, the heavy condition uses a centered 500 g weight, and CoM conditions displace the 200 g weight by 60 mm from center.Source: B. Evaluation Conditions · p. 4, Table I · p. 5
  • Three independent model mismatches assume mass 10% below nominal, CoM shifted toward the pivot by 10% of the half-width, or friction coefficients 10% above measured values.Source: B. Evaluation Conditions · p. 5
  • Five leftward-tilt trials are run per condition, and success requires completing the tilt while maintaining both robot contacts.Severe slip, contact loss, or an object drop preventing completion counts as failure.Source: B. Evaluation Conditions · p. 5

V. RESULTS

The results show that the task-adaptive margins and optimized force profiles respond to changes in mass and center of mass (CoM), while maintaining contact in all tested object-property conditions. In the nominal case, the margins vary with task demand and contact leverage, and adding them leaves solve times comparable to the no-margin formulation.

A. Contact Force Profiles and Margin Effects

  • Both contact margins decreased near the tipping angle as task force demand fell, while the right contact margin remained larger because of its greater moment leverage about the pivot.The margin kept optimized normal forces above the no-margin solution near tipping, moving forces away from the nominal friction boundary at early tilt and retaining positive normal force near tipping.Source: A. Contact Force Profiles and Margin… · p. 5, Figure 5 · p. 5
  • Mean solve times were 8.99 ± 1.22 ms with the margin and 9.05 ± 1.45 ms without it, with both formulations preserving the same SOCP structure.The margin changes only the lower bound in the SOC friction constraint.Source: A. Contact Force Profiles and Margin… · p. 5

B. Adaptation to Object Property Variations

C. Robustness to Model Mismatch

All tested model-mismatch trials completed successfully, though violation rates exceeded those in model-matched trials. At matched average combined force magnitude, task-adaptive margins succeeded under CoM mismatch while fixed margins failed all trials; the margin schedule allocates protection differently across tilt configurations.

C. Robustness to Model Mismatch

  • All trials under the tested model-mismatch conditions completed successfully, although violation rates exceeded those in model-matched trials.Underestimating mass or shifting the assumed CoM toward the pivot can underestimate required forces.Source: C. Robustness to Model Mismatch · pp. 6–7
  • Under tested friction-coefficient overestimation, optimized forces remained inside the measured cone and all trials completed successfully.Increasing the margin moves its intersection with the measured cone farther from the cone apex, increasing tolerance to friction uncertainty.Source: C. Robustness to Model Mismatch · pp. 6–7

D. Fixed Margin Study

  • Under CoM mismatch, the task-adaptive formulation completed all trials, whereas the fixed-margin formulation failed all trials.Both formulations completed all nominal trials; the fixed-margin mismatch failures involved severe slip and contact loss.Source: D. Fixed Margin Study · p. 7, Figure 9 · p. 7
  • At matched average combined force magnitude, the fixed margin was lower than the task-adaptive margin at higher-demand tilt portions and higher near minimum demand.At θ = 10◦, the fixed-margin solution lay closer to the friction boundary; this provided less local tolerance for underestimated task demand, consistent with the observed failures.Source: D. Fixed Margin Study · p. 7, Figure 9 · p. 7

E. No Margin Ablation Study

In the no-margin ablation, nominal friction feasibility alone did not maintain contact in the tested setup: the no-margin condition failed all trials, while the margin condition completed all trials. The conclusion presents signed friction distance as a force-space margin and supports configuration-dependent allocation under model uncertainty.

E. No Margin Ablation Study

  • The with-margin nominal condition completed all trials with a 6.9% violation rate, whereas the no-margin ablation failed all trials and reached 90.7%.No-margin forces stayed near ηmax = 1, while the with-margin solution kept optimized forces farther from the friction boundary.Source: E. No Margin Ablation Study · p. 7
  • In the tested setup, enforcing a finite lower bound on signed friction distance helped maintain contact compared with nominal friction feasibility alone.Measured no-margin samples frequently lay outside the friction cone or below the normal-force threshold.Source: E. No Margin Ablation Study · p. 7

VI. CONCLUSION

  • For bimanual tilting, pivot-moment deviations yield an affine task-adaptive margin allocated to robot contacts by their moment contributions and combined with a heuristic pivot margin.At matched average combined force magnitude, fixed margins failed under model mismatch, while the no-margin ablation had a larger violation fraction and task failure.Source: §VI · pp. 7–8

APPENDIX GENERAL TASK-ADAPTIVE MARGIN

The appendix defines a general task-level margin from admissible wrench deviations and the minimum-norm contact-force corrections that balance them.

APPENDIX GENERAL TASK-ADAPTIVE MARGIN

  • For a quasi-static task, the formulation balances the external wrench with contact forces, then finds a minimum-norm contact-force correction for each admissible wrench deviation.It assumes all admissible deviations admit balancing corrections and that the maximum exists.Source: APPENDIX GENERAL TASK-ADAPTIVE MARGIN · p. 8
  • The task-level margin is the maximum norm of those minimum-norm force corrections over the admissible deviation set.The definition is ρ(q) = max over δw in D(q) of ∥∆F*(q, δw)∥.Source: APPENDIX GENERAL TASK-ADAPTIVE MARGIN · p. 8
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