Constraint-Decomposed Impedance Control from Generative Policy for Articulated Object Manipulation

Kyungseo Park; Byeongdo Lim; Jungbin Lim; Minseok Choi; Frank C. Park

cs.ROOct 12, 2026

Constraint-Decomposed Impedance Control from Generative Policy for Articulated Object Manipulation

Authors: Kyungseo Park, Byeongdo Lim, Jungbin Lim, Minseok Choi, Frank C. Park

Organizations: Seoul National University · Department of Mechanical Engineering, KAIST

Abstract

Articulated object manipulation tasks such as opening doors, tightening bolts, and pulling drawers impose kinematic constraints on a robot end-effector's motion that neural policies may fail to satisfy. Unlike hybrid force-position control that strictly separates force and position control into orthogonal subspaces, impedance control modulates a mechanical impedance system in the form of a virtual inertia, damping, and stiffness. However, selecting task-appropriate impedance gains remains challenging for robot policies. In this paper, we address this problem for the case of manipulating articulated objects. Our constraint-decomposed impedance control method uses the sampling diversity of a generative policy to estimate the feasible motion directions in twist space. The key idea is to infer the feasible and constrained subspaces of twists from an ensemble of trajectories generated by the policy from the same observation. Principal component analysis (PCA) of the end-effector twists determines the feasible twist subspace, which is then used to form 6x6 impedance gain matrices. For many common articulated objects, the feasible twist subspace is independent of the object configuration, so the subspace and resulting gains are estimated once and held fixed during manipulation, minimizing computational overhead. For less common cases where this independence does not hold, we instead estimate a configuration-independent twist subspace of higher dimension that contains the local feasible subspaces, allowing the same fixed-gain strategy to be used. Experiments across simulated and real-world single- and multi-DoF objects show that the proposed method consistently reduces constraint-violating contact loads relative to isotropic impedance control while maintaining task execution.

Figures & tables

Figure 1: Overview of the proposed constraint-decomposed impedance control. Top: (1) At grasp closure, the generative policy $\pi_{\theta}(a|O;z)$ samples multiple trajectories from the same observation $O$ . (2) The trajectories are converted to end-effector body twists and stacked into a data matrix $W\in\mathbb{R}^{6\times NH}$ . (3) A weighted PCA recovers the feasible twist subspace $U_{\parallel}$ and its complementary constrained subspace $U_{\perp}$ , (4) which define the constraint-decomposed impedance gains $K_{v},D_{v}$ that are stiff along $U_{\parallel}$ and compliant along $U_{\perp}$ . Bottom: the articulated objects used in our real-world experiments, spanning revolute, prismatic, helical, cylindrical, and crank mechanisms.

Figure 2: Articulated object examples. Visualization of the body frame and feasible body twist $V_{b}=(\omega,v)$ , with joint axes (yellow dashed). (a) For a laptop with a revolute joint, $\omega$ always aligns with $+x$ and $v$ with $+y$ (configuration-independent). (b) For a coffee-grinder crank, $v$ aligns with $-y$ in solid case, but with $+x$ in translucent case (configuration-dependent).

Figure 3: Simulated articulated objects. Revolute, cylindrical, planar, and universal joints in Isaac Sim, manipulated by a flying gripper.

Task	SR (%)	SE (°)	ICF (N $\cdot$ s)	PCF (N)	ICM (N $\cdot$ m $\cdot$ s)	PCM (N $\cdot$ m)
Revolute	0 99 / 0 99 / 0 99	1.64	7.18 / 2.62 / 2.13	3.38 / 1.56 / 1.48	.29 / .22 / .22	.19 / .18 / .17
Cylindrical	0 99 / 100 / 100	1.73	5.31 / 0.83 / 0.53	1.96 / 0.36 / 0.31	.32 / .22 / .21	.16 / .14 / .14
Planar	0 99 / 0 99 / 0 99	2.78	15.3 / 1.93 / 2.20	4.03 / 1.18 / 1.16	.74 / .48 / .34	.29 / .23 / .21
Universal	100 / 100 / 100	4.36	2.18 / 0.46 / 0.34	1.25 / 0.23 / 0.19	– / – / –	– / – / –

Table 1: Simulation results. Entries are Iso / Ours / Oracle; SE reports Ours only, and boldface marks the better of Iso and Ours. Dashes indicate structurally empty complement components.

Task	SE (°)	ICF (N $\cdot$ s)	PCF (N)	ICM (N $\cdot$ m $\cdot$ s)	PCM (N $\cdot$ m)
Revolute	13.01	46.6 / 25.2 (0.54)	8.54 / 3.62 (0.42)	5.00 / 3.34 (0.67)	0.93 / 0.37 (0.40)
Prismatic	0 4.74	12.3 / 8.79 (0.72)	4.63 / 3.51 (0.76)	1.84 / 1.46 (0.80) †	0.61 / 0.55 (0.90) †
Helical	0 2.89	6.96 / 6.50 (0.93)	4.56 / 4.40 (0.96)	1.82 / 0.60 (0.33)	1.08 / 0.45 (0.41)
Cylindrical	0 5.76	8.35 / 4.42 (0.53)	3.37 / 2.20 (0.65)	1.09 / 0.82 (0.75)	0.45 / 0.37 (0.81)
Crank	0 5.70	20.8 / 23.6 (1.14)	4.62 / 4.28 (0.93)	4.99 / 4.15 (0.83)	1.12 / 0.82 (0.74)

Table 2: Real-world results. Entries are Iso / Ours (Ours/Iso); SE reports Ours only, and boldface marks the better of Iso and Ours. Daggers mark full moments, as prismatic has no feasible rotation.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Primitive	DoF	Generators	Structure
Revolute (R)	$1$	$(\hat{n};\,-\hat{n}\times p)$	Abelian
Prismatic (P)	$1$	$(0;\,\hat{d})$	Abelian (any dim)
Helical (H)	$1$	$(\hat{n};\,h\hat{n}-\hat{n}\times p)$	Abelian
Cylindrical (C)	$2$	$(\hat{n};\,-\hat{n}\times p),\ (0;\,\hat{n})$	Abelian
Spherical (S)	$3$	$(\hat{e}_{i};\,-\hat{e}_{i}\times p)_{i=1,2,3}$	$\mathrm{so}(3)$
Planar (E)	$3$	$(\hat{n};\,0),\ (0;\,\hat{t}_{1}),\ (0;\,\hat{t}_{2})$	$\mathrm{se}(2)$

Appendix

Table 3: Configuration-independent primitives and their Lie-subalgebra verification. Body screws

B=(\omega;v)

in the home frame: unit axes

\hat{n},\hat{d}

, axis point

p

, helical pitch

h

, in-plane unit vectors

\hat{t}_{1},\hat{t}_{2}\perp\hat{n}

. Every generator bracket lies in the span, so each is a Lie subalgebra and, by Proposition B.1 , configuration-independent on its regular set.

Mechanism	$B_{2}$	$B_{1}(q_{2})$	$\mathcal{S}_{\rm env}$	$\dim\mathcal{S}_{\rm env}$	Excitation for full $\mathcal{S}_{\rm env}$
U-joint (intersecting 2R)	$(\hat{e}_{x};0)$	$(R_{x}(-q_{2})\hat{e}_{y};\,0)$	$\operatorname{span}\{\omega_{x},\omega_{y},\omega_{z}\}$	$3$	$B_{2}$ excited, $\geq 2$ phases
Parallel-offset crank (parallel 2R)	$(\hat{e}_{z};0)$	$(\hat{e}_{z};\,-L\sin q_{2}\,\hat{e}_{x}-L\cos q_{2}\,\hat{e}_{y})$	$\operatorname{span}\{\omega_{z},v_{x},v_{y}\}$	$3$	$\geq 3$ $B_{1}$ phases ( $B_{2}$ redundant)
Door hinge $+$ lever (off-axis orthogonal 2R)	$(\hat{e}_{x};0)$	$(R_{x}(-q_{2})\hat{e}_{z};\,-L\,\hat{e}_{x})$	$\operatorname{span}\{\omega_{x},\omega_{y},\omega_{z},v_{x}\}$	$4$	$B_{2}$ excited, $\geq 3$ phases

Appendix

Table 4: Global envelope for the three nondegenerate configuration-dependent

2

R examples. Screws are expressed in the distal frame

\{c\}

with origin on the distal joint axis, so

B_{2}

is constant and

B_{1}(q_{2})=\mathrm{Ad}_{e^{-B_{2}^{\wedge}q_{2}}}B_{1}

. At every fixed

q

the local feasible subspace has

\dim\mathcal{S}(q)=2

; sweeping

q_{2}

over an interval with nonempty interior enlarges the envelope to the listed dimension. Shorthand:

\omega_{i}=(\hat{e}_{i};0)

v_{i}=(0;\hat{e}_{i})

; “

\geq k

phases” means

k

distinct distal angles

q_{2}

Group	Symbol	Value
Estimation	Ensemble size $N$	$128$ (simulation); $32$ (real)
	Trajectory horizon $H$	$24$
	Absolute threshold $v_{\rm abs}$	$5$ mm/s (simulation); $3$ mm/s (real).
	Relative threshold $\kappa_{\rm rel}$	$4$ (simulation); $10$ for revolute, prismatic, helical, and cylindrical objects and $4$ for the crank (real).
	Sampler at grasp closure	DDIM, $10$ steps (simulation); DDPM, $100$ steps (real).
	Characteristic-length clip $[\alpha_{\min},\alpha_{\max}]$	$[0.03,\,0.5]$

Appendix

Table 5: Common configuration. Estimation and control hyperparameters shared across all simulated and real-world mechanisms. The reduction ratio

r

and damping ratio

\zeta

define the complement gains via Appendix G.2 ; per-platform numerical gain values are in Table 6 .

Figure 4: Stiffness-gain matrices over the real FR3 $\alpha$ sweep. Each panel shows the decomposed stiffness matrix $K_{v}=\bar{\Lambda}(k_{\parallel}P_{\parallel}^{\bar{\Lambda}}+k_{\perp}P_{\perp}^{\bar{\Lambda}})$ in body-twist order $(\omega_{x},\omega_{y},\omega_{z},v_{x},v_{y},v_{z})$ . Rows correspond to real tasks, one rollout each (the one with the median SE), and columns to $\alpha/\alpha_{0}\in\{0.25,0.5,1,2,4\}$ , with $\alpha_{0}$ the clipped estimate of Eq. ( 34 ). Printed numbers are the physical matrix entries; cell color encodes the signed, per-task-normalized value (blue $<0$ , red $>0$ ). All five tasks vary little across the sweep.

Platform	$\bar{m}$	$\bar{I}$	$\ell_{\Lambda}$	$k_{0}$	$r$	$\zeta$	$k_{\parallel}$	$k_{\perp}$	$d_{\parallel}$	$d_{\perp}$
Flying gripper (sim)	$0.586$	$0.00622$	$0.103$	$250$	$0.10$	$0.766$	$250$	$25$	$24.21$	$7.66$
FR3 (real)	$7.70$	$0.724$	$0.307$	$400$	$0.10$	$2.775$	$400$	$40$	$111$	$35.1$

Appendix

Table 6: Numerical inertia and gain values. Per-platform inertia-metric parameters and the decomposed scalar gains under the construction of Appendix G.2 . The inertia columns use kg, kg

\cdot

m 2 , and m for

\bar{m}

\bar{I}

, and

\ell_{\Lambda}

, respectively. The scalar gains

k_{\parallel},k_{\perp}

and

d_{\parallel},d_{\perp}

are normalized modal gains with units s -2 and s -1 ; physical wrench-level stiffness and damping units arise only after forming

K_{v}

and

D_{v}

with the normalized metric of Appendix A.2 . The damping ratio

\zeta=\sqrt{\bar{m}/m_{\rm ref}}

of this normalized design model makes every mode critically damped for the physical surrogate inertia; it is not a measured damping ratio of the robot–object system. Iso uses

r=1

Setting	Value
Backbone	Diffusion Policy [ 21 ]
Observation history	$1$ step
Predicted / executed action horizon	$24$ / $16$ steps
Policy sampling period	$0.1$ s ( $10$ Hz)
Observation	$224\times 224$ wrist RGB, end-effector pose (position $+$ $6$ -D rotation), and gripper opening ( $\mathbb{R}^{10}$ )
Action	Per-step $\mathbb{R}^{10}$ relative pose chunk in the current EE frame: pose ( $9$ ) and gripper command ( $1$ )

Appendix

Table 7: Diffusion Policy training configuration. Common policy interface and training recipe used for the per-object checkpoints and the simulated multi-task checkpoint.

Item	Value
Demonstrations	$400$ scripted rollouts per object
Object placement	Uniform $x\in[-0.15,0.15]$ , $y\in[-0.20,0.20]$ , $z\in[-0.10,0.10]$ m, yaw $\in[-15^{\circ},15^{\circ}]$
Gripper start	Fixed at $(-0.1,0,0.5)$ m before approach and grasp
Waypoint generation	Object progress mapped to handle poses by analytic forward kinematics, interpolated on $\mathrm{SE}(3)$

Appendix

Table 8: Simulation policy data. Demonstration collection details for the four simulated objects (interface as in Table 7 ). Stored actions are absolute end-effector poses, converted to relative pose chunks for training. Placement is in the simulator world frame relative to the object origin

(0.5,0,0.5)

Figure 5: From trajectory ensemble to constraint-decomposed impedance on the real FR3. Each row is one real task, ordered by the estimated feasible dimension $\hat{m}$ (revolute/prismatic/helical $\hat{m}{=}1$ , cylindrical $\hat{m}{=}2$ , crank $\hat{m}{=}3$ ); all matrices are in the gripper body frame at the grasp pose. The columns trace the pipeline of Algorithm 1 : (1) the grasp-closure ensemble ( $N=32$ ) recentered on the grasp point and colored by sample index, with the selected tracking trajectory highlighted and the body frame $(x_{b},y_{b},z_{b})$ drawn as the red/green/blue triad; (2) the singular-value ratio $\widetilde{\sigma}_{k}^{2}/\widetilde{\sigma}_{6}^{2}$ $=\lambda_{k}/\lambda_{6}$ and the dimension gate $\kappa_{\rm rel}^{2}$ (dashed) selecting $\hat{m}$ ; (3) the retained PCA-scaled basis $\widetilde{U}_{\parallel}=L_{\alpha}U_{\parallel}$ , rows ordered $(\omega_{x},\omega_{y},\omega_{z},v_{x},v_{y},v_{z})$ ; (4) the projector building block $\bar{\Lambda}P_{\parallel}^{\bar{\Lambda}}$ (Appendix E.1 ); and (5) the resulting stiffness $K_{v}=k_{\perp}\bar{\Lambda}+(k_{\parallel}-k_{\perp})\bar{\Lambda}P_{\parallel}^{\bar{\Lambda}}$ , with the damping entries $D_{v}$ in parentheses. Printed numbers are the physical entries; cell color encodes the signed, per-task-normalized value (blue $<0$ , red $>0$ ; as in Fig. 4 ).

Single-task policies
Task	$n_{c}$	$\lambda_{f}$	$\lambda_{m}$	$\beta_{f}$	$\beta_{m}$
Revolute	0 99	.26 / .12 / .10	.245 / .177 / .181	.75 / .92 / .95	.86 / .96 / .96
Cylindrical	0 99	.15 / .03 / .02	.122 / .086 / .084	.85 / .98 / .98	.94 / .98 / .98
Planar	0 99	.68 / .21 / .24	.114 / .077 / .057	.32 / .81 / .78	.90 / .95 / .98
Universal	100	.31 / .14 / .11	.000 / .000 / .000	.69 / .87 / .91	1.00 / 1.00 / 1.00
Multi-task policy

Appendix

Table 9: Simulation rollout diagnostics (auxiliary to Table 1 and Table 10 ). Entries are Iso / Ours / Oracle.

n_{c}

is the three-controller common-success count for wrench metrics.

\lambda_{f},\lambda_{m}

are the force/moment complement load fractions,

\beta_{f},\beta_{m}

the force/moment-side feedback feasible fractions (Appendix H.3 ;

\beta_{m}{\equiv}1

for the universal joint, whose angular complement is empty).

Task	SR (%)	SE (°)	ICF (N $\cdot$ s)	PCF (N)	ICM (N $\cdot$ m $\cdot$ s)	PCM (N $\cdot$ m)
Revolute	0 99 / 0 99 / 0 99	1.71	7.75 / 2.87 / 2.55	3.55 / 1.76 / 1.81	.31 / .26 / .26	.21 / .22 / .22
Cylindrical	0 96 / 0 97 / 0 96	2.39	4.61 / 1.36 / 0.64	1.74 / 0.67 / 0.51	.31 / .20 / .21	.15 / .13 / .15
Planar	100 / 100 / 100	2.76	14.4 / 2.02 / 2.21	3.85 / 1.13 / 1.13	.73 / .49 / .34	.29 / .24 / .22
Universal	0 99 / 100 / 100	3.83	1.98 / 0.45 / 0.33	1.17 / 0.23 / 0.19	– / – / –	– / – / –

Appendix

Table 10: Simulation results with one multi-task policy. Entries are Iso / Ours / Oracle. In Table 1 and here, SR counts all trials, and the other entries are means over the trials in which all three controllers succeed; SE reports Ours only, and boldface marks the better of Iso and Ours.

$N$	SE, 95th percentile (°)	Correct dimension (%)
$1$	$78.95$	$64.7$
$2$	$23.15$	$84.2$
$4$	$8.59$	$92.8$
$8$	$7.23$	$97.7$
$16$	$6.92$	$99.4$
$32$	$6.79$	$99.8$

Appendix

Table 11: Ensemble-size sweep in simulation. 95th-percentile SE with the dimension fixed to its true value, and the fraction of trials in which the dimension rule selects the true dimension, pooled over the four objects.

Statistic	Selection	$k{=}2$	$4$	$8$	$16$	$32$	$64$	$128$
Mean of per-object	DTW-max	$5.91$	$3.32$	$2.74$	$2.61$	$2.48$	$2.49$	$2.34$
median SE (°)	DTW-min	$19.73$	$9.93$	$4.45$	$3.43$	$2.58$	$2.43$	$2.34$
Grasps with	DTW-max	$16.0$	$8.8$	$2.8$	$2.3$	$1.8$	$1.0$	$1.0$
SE $>10^{\circ}$ (%)	DTW-min	$40.5$	$28.0$	$13.8$	$9.5$	$1.5$	$1.5$	$1.0$

Appendix

Table 12: Sample-diversity study in simulation. Subspaces re-estimated from the

k

most (DTW-max) or least (DTW-min) diverse samples of each

128

-sample ensemble; the last column uses all

128

samples.

Noise	Direct	Trained	Ratio
None	$2.14$	$2.02$	–
Position $5$ mm	$11.97$	$3.10$	$0.26$
Orientation $5^{\circ}$	$16.05$	$10.59$	$0.66$

Appendix

Table 13: Robustness to noise in simulation. Pooled median SE (°) over the four objects at

N{=}128

. (a) Noise of the same amplitude added directly to the sampled trajectories or to the demonstrations before training. (b) Image perturbations of the observation: Gaussian noise (

\sigma{=}32/255

), Gaussian blur (

\sigma{=}2

px), and random shift (

\sigma{=}4

px). (c) Number of DDIM steps at inference.

Task	$\lambda_{f}$	$\lambda_{m}$	$\beta_{f}$	$\beta_{m}$
Revolute	.766 / .672 (.88)	.734 / .522 (.71)	.738 / .843 (1.14)	.717 / .848 (1.18)
Prismatic	.362 / .321 (.89)	1.000 / 1.000 (1.00)	.848 / .918 (1.08)	.000 / .000 (–)
Helical	.412 / .424 (1.03)	.724 / .569 (.79)	.187 / .332 (1.78)	.751 / .890 (1.18)
Cylindrical	.244 / .126 (.52)	.536 / .421 (.79)	.708 / .894 (1.26)	.572 / .680 (1.19)
Crank	.425 / .469 (1.10)	.926 / .850 (.92)	.841 / .892 (1.06)	.261 / .550 (2.11)

Appendix

Table 14: Real-world auxiliary diagnostics. Entries are Iso / Ours (Ours/Iso) arithmetic means over the same

10

rollouts per task as Table 2 .

\lambda_{f},\lambda_{m}

are the measured force/moment load fractions and

\beta_{f},\beta_{m}

the feedback feasible fractions of Appendix H.3 . The rotational block of prismatic is structurally complementary (

\lambda_{m}{=}1

\beta_{m}{=}0

Impedance Control

Impedance control lets robots adjust their stiffness and damping to manage forces during contact with people and objects.

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Manifold Generative Annealing for Contact Constraint-aware Impedance Control with Reinforcement Learning Prior

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Carnegie Mellon University · Institute of Automation, Chinese Academy of Sciences

Contact-Rich Robotic Manipulation Impedance Control Trajectory Optimization Model-Based RL

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Contact-rich robotic tasks require coordinated motion and impedance under uncertain interaction dynamics and physical constraints. While recent methods on learned policies provide useful interaction strategies, they may fail when contact conditions differ from those encountered during training. Model-based generative methods show promising receding-horizon trajectories optimization results, but often lack structured behavioral guidance and refinement that jointly accounts for constraint geometry and actual contact responses. To this end, we propose Manifold Generative Annealing (MGA), a joint model-free and model-based generative framework for motion--impedance optimization. MGA first organizes pretrained reinforcement learning policies into structured sequence proposals, retaining task-specific interaction strategies without committing to their execution. It then evaluates these proposals alongside exploratory samples through model-based rollouts for refinement or separate execution selection. Crucially, realization-aware manifold refinement aligns updates from the refinement bank with both task constraints and locally achievable physical responses, allowing learned experience to guide online adaptation under changing contact conditions. Experiments cover surface scanning, peg insertion, and humanoid pushing, with improved safety success rate of impedance control under nominal and sensing-shift conditions.

Abstract

Impedance Control

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