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Behavior--Realization Separation for Constrained Physical Human--Robot Interaction

Yongyan Cao

arXiv:2609.00669v1cs.ROeess.SY

TL;DR

Physical human–robot interaction software must distinguish desired interaction behavior from constrained robot realization, because the two operate on different variables and responsibilities. The paper implements this separation through a desired-acceleration interface and a receding-horizon quadratic-program runtime, then validates it with planar behavior reassignment and FR3 constraint experiments. Under sustained pushing, predictive realization limits workspace overshoot relative to reactive clipping, while horizon-wide torque enforcement avoids infeasible future plans in the frozen model.

  • Problem

    Robot-control software often couples desired interaction behavior with constrained realization, although behavior and physical feasibility depend on different variables and responsibilities.

  • Method

    The paper separates a behavior layer that outputs desired contact-port acceleration from a realization layer that converts it into constrained robot commands through a receding-horizon quadratic program.

  • Results

    4.4 cm and 4.7 cm reactive overshoots for impedance and admittance were reduced to predictive displacement within 0.0601 m under the sustained push.

  • Takeaways & Limitations

    The studies support behavior–realization separation across two plants, online behavior-layer replacement, explicit realization-error auditing, and horizon-wide constraint enforcement within the tested scope.

  • Takeaways & Limitations

    The evaluation covers only impedance and admittance under a sustained push, without delay, sensor-noise, mass-mismatch sweeps or collision constraints, and does not establish terminal invariance or soft-constraint risk.

Abstract

from arXiv · show

Physical human--robot interaction software often couples desired-behavior specification with constrained realization; we treat these as separate layers. A \emph{behavior layer} supplies a desired contact-port acceleration $a_k^{\mathrm{id}}=f_θ(e_k,\dot e_k,F_{h,k})$. A \emph{realization layer} converts it into constrained robot commands and reports total desired-versus-realized acceleration error instead of hiding it in saturation. A same-objective unconstrained counterfactual separates regularization from constraint intervention, while plant data expose model error. This paper implements a receding-horizon quadratic program realizing memoryless affine behaviors. Changing the behavior modifies objective coefficients through $(C_θ,G_θ)$ while the robot-command variable and feasible set remain unchanged. A planar study instantiates impedance and admittance; the same running layer accepts an impedance--admittance--impedance reassignment without reconstruction, under its existing rate limit. On a torque-controlled 7-DOF Franka FR3 in MuJoCo, the runtime freezes task-space dynamics per solve and enforces torque feasibility across its horizon. Under a sustained 20~N push, it holds a slack-relaxed workspace boundary to within approximately 0.1--0.2~mm, versus 4.4~cm (impedance) and 4.7~cm (admittance) overshoot from instantaneous clipping. A derated actuator budget then activates the torque constraint: horizon-wide enforcement keeps its frozen-model plan feasible to $2.1\times10^{-4}$~N$\cdot$m, whereas a first-step-only ablation plans up to 11.329~N$\cdot$m beyond budget; on the executed nonlinear plant, where both share the same local-model error, the gap is smaller but still favors horizon-wide enforcement (0.161 vs.\ 0.380~N$\cdot$m). These results are a focused proof of behavior--realization separation.

I. INTRODUCTION

The paper separates desired interaction behavior from constrained robot realization through an explicit acceleration-level interface. It evaluates one reusable predictive runtime across behavior generators while exposing realization error and constraint intervention.

  • I. INTRODUCTION: Desired interaction behavior and physical feasibility are assigned to separate software layers because they use different variables and constraints.Behavior concerns interaction-state quantities, whereas realization concerns robot-command feasibility such as torque, joint, and workspace limits.
  • I. INTRODUCTION: The interface supplies desired contact-port acceleration, while the realization layer converts it into feasible commands and reports total residual error.A same-objective constrained/unconstrained audit distinguishes constraint intervention from secondary-objective and model effects.
  • I. INTRODUCTION: One predictive realization runtime retains its robot-command variable and feasible set across memoryless affine impedance and admittance behaviors.Behavior changes enter through objective coefficients, enabling generator substitution without rebuilding the runtime state.
  • I. INTRODUCTION: The executable evidence consists of planar and FR3 simulations covering behavior-layer replacement, anticipatory state-constraint handling, and command- and torque-limited realization.The study is presented as a focused validation rather than a complete manipulator evaluation.
  • I. INTRODUCTION: The paper’s narrower contribution is the combination of an interaction-law contract, reusable realization runtime, residual audit, and live generator substitution.The authors explicitly distinguish this combination from prior architectural separation, impedance MPC, and constrained interaction-control work.

III. BEHAVIOR–REALIZATION FORMULATION

The formulation defines behavior as a desired acceleration rather than a robot command, then realizes it through a constrained predictive optimization and diagnoses the resulting residual.

  • A. Behavior–Realization Interface: The manipulator maps joint states and torques to task acceleration through task-space kinematics and an affine acceleration relation.The task coordinate satisfies ẏ = J(q) q̇ and ÿ = J(q)q̈ + J̇(q,q̇)q̇ before substitution of joint dynamics.
  • A. Behavior–Realization Interface: The behavior layer is a causal map whose output is desired contact-port acceleration, not a robot command.Its general form may include internal behavior state and parameters, but the paper evaluates only the memoryless affine specialization.
  • A. Behavior–Realization Interface: The realization layer selects robot torque so physical acceleration approaches the requested acceleration while satisfying robot constraints.The predictive quadratic program is one implementation of this realization layer, while the planar study isolates the interface with an exactly discretized point-mass specialization.
  • A. Behavior–Realization Interface: The planar formulation provides an exactly discretized specialization for isolating behavior–realization separation without kinematic or inverse-dynamics confounds.Its affine runtime instance is a strictly convex quadratic program when the assembled Hessian is positive definite, including the common case λu > 0.
  • A. Behavior–Realization Interface: The total realization residual measures the gap between behavior-specified acceleration and robot-delivered acceleration.Zero residual means exact realization at that sample, but nonzero residual alone does not establish constraint causation.
  • A. Behavior–Realization Interface: A same-objective unconstrained counterfactual separates regularization compromise from constraint intervention, while plant measurements expose model and acceleration-measurement error.The empirical decomposition closes using model accelerations and plant-derived acceleration, with rmod equal to zero for the exact planar model.
  • A. Behavior–Realization Interface: The residual components retain physical acceleration units and serve as logging and causal-diagnostic signals rather than normalized cross-generator scores.The decomposition does not identify the contribution of any individual active constraint without additional multiplier or leave-one-constraint-out analysis.
  • A. Behavior–Realization Interface: The interface tracks desired behavioral acceleration directly rather than deviation from a nominal impedance force or prior controller output.This distinction compares two physical accelerations and is demonstrated for impedance and admittance generators.

B. Implemented Behavior Layers

The runtime implements impedance and force-guided admittance behaviors through a shared acceleration interface, with behavior differences encoded in the requested dynamics.

  • The impedance generator requests a desired impedance through the shared QP template.
  • The impedance parameters M_d, D_d, and K_d describe requested behavior rather than optimization decision variables.
  • The admittance generator requests a force-dependent velocity and omits a position-restoring term.
  • After force release, admittance velocity decays while the displaced position is retained.

C. Predictive Realization Runtime

The predictive runtime optimizes robot command sequences against desired behavioral acceleration while preserving a fixed command interface and feasible set across behavior changes.

  • The affine generator supplies C_θ and G_θ, producing one condensed-QP template whose numerical cost coefficients vary with the generator.
  • The controller carries the previously applied command into the first rate penalty and constraint, while holding measured force constant across the horizon.
  • The optimizer tracks the difference between realized and desired acceleration rather than a desired position or velocity trajectory.
  • Switching from impedance to admittance changes C_θ and G_θ, not the robot-command variable or QP constraints.

IV. PROPERTIES OF THE AFFINE RUNTIME INSTANCE

For affine behaviors, the realization problem is a convex QP with a generator-invariant decision structure, exact unconstrained realization under stronger conditions, and explicit limits on recursive-feasibility guarantees.

  • Template invariance: Theorem 1 fixes the QP decision variable, feasible set, and constraint structure while varying only cost coefficients with the affine generator.
  • Template invariance: A nonlinear generator falls outside the fixed template unless linearization restores an affine dependence on the command sequence.
  • Convexity: The runtime is a convex quadratic program when W ⪰ 0 and the command and command-rate regularization weights are nonnegative.
  • Exact realization: Under W ≻ 0, no active constraints, and lexicographic or zero-weight secondary objectives, every optimal primary solution realizes the reference dynamics exactly.
  • Constraint guarantees: Finite secondary weights can leave predictive realization residual nonzero during unconstrained intervals, unlike the reactive comparator’s numerical-tolerance residual.
  • Constraint guarantees: One-step constraint inheritance holds under exact model and force assumptions with feasibility, but recursive feasibility is not guaranteed.

V. PLANAR ARCHITECTURE VALIDATION

The planar validation compares predictive realization with reactive clipping for impedance and admittance under identical command and rate limits.

  • The planar experiment compares predictive realization against a reactive comparator under identical command and rate limits.
  • Reactive clipping tracks the requested behavior but ignores dotted state limits, whereas predictive realization departs from the behavior near the bound.

A. Reproducible Setup

The planar setup uses a 2.5 kg point mass with bounded force and force-rate commands, comparing predictive realization against a reactive comparator without predictive state-constraint handling.

  • The simulation uses a 2.5 kg planar point mass, a 0.02 s timestep, and a 20-step, 0.4 s prediction horizon.
  • The smooth 12 N force acts along +y from 1 s to 3 s.
  • Behavior generators: The impedance generator uses Md = 2.0 kg, Dd = 18 Ns/m, and Kd = 45 N/m.
  • Behavior generators: The admittance generator uses Ta = 0.25 s and Y = 0.025 m/(Ns).
  • Comparator: The reactive comparator applies the same 18 N force and 180 N/s slew limits but does not predict position or speed constraints.

B. Results

The studies validate a shared behavior–realization runtime across planar and nonlinear manipulator settings, including online behavior replacement and horizon-wide constraint handling. The runtime exposes realization error and supports constrained behavior modification without changing the behavior interface.

  • Planar and manipulator validation: The planar impedance and admittance studies used the same constrained predictive implementation while separating constraint intervention from small regularization effects through an unconstrained counterfactual.The reported residual decomposition treats predictive realization error as total behavior error rather than hiding deviation in saturation.
  • Online behavior reassignment: One controller instance accepted impedance–admittance–impedance reassignment at t = 2 s and t = 4 s under the existing 3.6 N per-tick rate limit.The largest switch jump was 3.02 N, or 84% of that limit, while position and speed remained within 0.067 m and 0.083 m of the origin.
  • Torque-controlled FR3: The manipulator realization map changed through the command-force choice, while the generator interface remained unchanged across the torque-controlled implementation.Projected auxiliary torques and task-kinematic terms were retained in the local task-space dynamics used by the QP.
  • Torque-controlled FR3: Gain selection reduced configuration deviation below 0.29 rad and removed the tested joint-limit violation when using gains 40/8.With gains 10/2, configuration deviation reached 1.32–1.85 rad and reactive impedance exceeded a joint limit by about 1.6 N·m.
  • Torque-controlled FR3: The FR3 realization layer froze task-space dynamics per solve, held the local model across the horizon, and enforced the total torque constraint at every predicted step.Executed torque was recomputed and monitored at 1 kHz because the frozen QP model is only a local predictor of nonlinear MuJoCo dynamics.
  • Planar and manipulator validation: 0.077 mm and 0.027 mm peak position slack were observed for impedance and admittance, respectively, while peak speed slack stayed below 10^-6 m/s.These are frozen-model QP slack values; executed nonlinear-plant violations were approximately 0.0001 m for both conditions.

B. Benchmark Scenario

The benchmark applies a sustained physical 20 N end-effector push toward workspace and speed limits, comparing predictive realization with a reactive command/rate-limited controller. The six-second setup uses identical command/rate bounds and zero-order-hold forecasts for both controllers.

  • Force and reference conditions: The benchmark holds a fixed nominal end-effector pose and orientation while pushing toward workspace and speed boundaries.Predictive realization is compared against command/rate-limited reactive control with no predictive workspace handling under identical command/rate boxes.
  • Force and reference conditions: 20 N force was applied physically along −z with a raised-cosine ramp, a 2 s hold, and symmetric ramp-down.The force ramp runs from 1.0 to 1.25 s, holds to 3.25 s, and ramps down to 3.5 s.
  • Controller and constraint settings: The six-second conditions use impedance parameters Md = 2.0 kg, Dd = 28 Ns/m, Kd = 200 N/m and admittance parameters Ta = 0.3 s, Y = 0.01 m/(Ns).The QP horizon is 15 steps at Δt = 0.02 s, with FR3 per-joint torque limits of ±87 N·m for joints 1–4 and ±12 N·m for joints 5–7.

C. Results

The FR3 benchmark evaluates predictive realization at a workspace boundary without torque intervention, then audits residual sources and computational timing. Predictive realization tracks the boundary, while reactive clipping overshoots it for both impedance and admittance.

  • No condition violates a per-joint torque limit, no solve is infeasible, and torque utilization stays below 38% in the primary benchmark.The benchmark therefore evaluates workspace-boundary behavior realization rather than torque intervention.
  • Workspace-boundary behavior: 0.0601 m displacement: predictive impedance realization holds the 0.06 m workspace bound, versus 4.4 cm overshoot from reactive clipping.The unconstrained impedance equilibrium is 0.10 m under the sustained 20 N force.
  • Workspace-boundary behavior: 0.1066 m peak displacement: reactive admittance overshoots the bound by 4.7 cm and never recovers after the force is released.Admittance has no position-restoring term, so its displacement accumulates during the hold.
  • Residual audit: Constraint intervention is the largest residual component for both generators, but finite regularization and plant/model terms are also material.For admittance, vector cancellation makes the empirical total smaller than individual component RMSE values.
  • Runtime: The deployed variable change reduces the condensed Hessian condition number from 4.3×10^9 to 4.34×10^3 for impedance.The transformation preserves the physical objective and feasible set and is verified by a unit test.
  • Runtime: 3.45 ms mean and 6.89 ms 99th-percentile solve time: impedance meets the 20 ms manager period in all 3000 warm-started solves.Admittance measures 3.68 ms mean and 7.28 ms at the 99th percentile; these measurements apply to the tested development machine.

D. Torque-Active Runtime Intervention

The torque-active experiment deliberately derates one actuator budget while leaving the behavior layer unchanged. Horizon-wide enforcement avoids infeasible future plans, whereas the first-step-only ablation plans beyond the budget; the study remains a focused architecture validation.

  • Torque-active intervention: 31.5 N·m: joint 4’s budget is derated from the nominal 87 N·m to activate realization-layer torque intervention.The behavior, force profile, horizon, weights, workspace/speed bounds, and solve rate remain unchanged.
  • Architectural responsibility: The experiment tests whether the realization runtime changes commands and exposes behavioral deviation when a fixed behavior conflicts with an actuator budget.The behavior layer itself is unchanged, so this is not presented as another controller comparison.
  • Scope: The evaluation covers only impedance and admittance in a sustained-push scenario, without sweeps over delay, sensor noise, or mass mismatch, and without collision constraints.The reactive controller is a mechanism ablation rather than a survey-complete baseline.
  • Torque-active intervention: Horizon-wide enforcement keeps the plan feasible across the ramp, while first-step-only enforcement satisfies only i = 0 and plans an infeasible future.The blue horizon-wide trajectory remains within the derated budget; the orange ablation does not.
  • Scope: Planar online behavior-layer switching is demonstrated, but an FR3 counterpart remains future work.Human-participant and hardware validation, matched predictive baselines, hardware timing, and stale-solution handling also remain future work.

VII. WHY BEHAVIOR–REALIZATION SEPARATION?

Behavior–realization separation assigns interaction semantics to a replaceable behavior layer and physical feasibility to a stable realization layer. The paper tests this boundary through substitution, constraint intervention, and explicit limitations.

  • Architectural rationale: The architecture makes desired interaction behavior independently testable and replaceable while assigning physical feasibility to a stable downstream contract.The separation is useful rather than universally dominant: fully coupled optimization may be better when behavior parameters are task decisions.
  • Architectural rationale: The runtime receives a predicted-state interaction law and desired acceleration, rather than generating a trajectory or modifying a reference for a separate controller.MPC is the current realization mechanism; the architectural interface is the central choice.
  • Architectural rationale: The realization layer itself optimizes robot commands, while reporting desired-versus-realized discrepancy and distinguishing constraint intervention from other residual terms.This makes feasibility intervention observable instead of conflating it with behavior specification.
  • Evidence for separation: The same realization object and carried state support impedance–admittance substitution, while actuator-budget changes preserve the behavior layer.These are complementary tests: behavior semantics change without rebuilding feasibility logic, and feasibility intervenes without rewriting behavior parameters.
  • Scope and limitations: The study is a reproducible proof of concept rather than a complete framework, with evidence limited to two plants and the implemented memoryless affine behavior class.Future stateful or learned behaviors would require augmented prediction and explicit model-uncertainty treatment.
  • Scope and limitations: The residual remains coordinate-dependent, and the FR3 study exercises translation only; raw RMSE across differently scaled generators is not a direct performance ranking.Empirical and frozen-model residuals can differ materially, indicating model-adequacy and estimation gaps rather than contradicting the formal result.
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