Learning to Leverage Compliance: A Policy-Admittance Learning Framework for Robotic Insertion

Chongren Wang; Minghe Li; Honghua Dai; Zhicheng Lin; Shiyang Wei; Xiaokui Yue

cs.ROSep 25, 2026

Learning to Leverage Compliance: A Policy-Admittance Learning Framework for Robotic Insertion

Authors: Chongren Wang, Minghe Li, Honghua Dai, Zhicheng Lin, Shiyang Wei, Xiaokui Yue

Organizations: School of Astronautics and the National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University

Abstract

Policy learning and compliant control offer a promising route to reliable autonomous assembly under pose errors and contact uncertainty. However, combining them does not ensure coordination: the policy may continue pushing against contact while the controller yields, producing sustained loading with limited progress. To address this problem, we propose LeCo (Leverage Compliance), a policy-admittance learning framework that guides a visual policy through execution-time interaction under fixed admittance. A multirate feedback mechanism aggregates high-rate contact-interaction records into policy-transition rewards. An integrated conflict cost then characterizes sustained policy-loading/controller-unloading opposition, while a directional high-force tail cost captures continued-loading events within a transition. Together with task completion, these costs encourage the policy to leverage compliance with less unproductive loading. We evaluate LeCo on four real connector-assembly tasks, obtaining an aggregate success rate of 94%. Across tasks, mean successful-trial resultant-force and torque peaks decrease by approximately 30% and 64% relative to the comparison baseline. Reward ablation further shows that adding conflict shaping reduces median successful-trial contact-conditioned conflict density by approximately 53%. These results support learning to leverage fixed compliance by turning multirate policy-admittance interaction into complementary reward signals for effective, lower-load insertion.

Figures & tables

Fig. 1: Motivation for learning to leverage compliance. (a) Task-driven execution can complete insertion while sustaining substantial contact loads. (b) LeCo coordinates task motion with admittance unloading to reduce contact loading while preserving task completion.

Fig. 2: LeCo architecture: a 10-Hz visual policy and fixed 100-Hz admittance execute task motion; recorded wrench and separate commands supply conflict-integral and directional-tail rewards to SAC/RLPD replay. In the timing schematic, $\mathcal{W}_{m}=[b_{m},b_{m+1})$ is a recording window; $b_{m}$ and $b_{m+1}$ are the timestamps of its starting and ending controller-buffer snapshots, respectively. Rates are nominal; 0 denotes a zero policy reference while admittance continues. The command decomposition precedes limiting.

Fig. 3: Temporal aggregation of interaction rewards. (a) Integrating shared command power preserves conflict duration. (b) The maximum of gated loading retains brief peaks attenuated by averaging. Curves illustrate one policy window.

Fig. 4: Four real connector-assembly tasks: (a) aviation-connector insertion; (b) Anderson-head insertion; (c) Anderson-side interlocking; (d) ATX 20+4-pin connector housing assembly.

	$x$	$y$	$z$	$r_{x}$	$r_{y}$	$r_{z}$
$M$	40	40	100	0.375	0.375	0.75
$D$	800	800	2000	7.5	7.5	15
Deadband	0.5	0.5	1.0	0.03	0.03	0.03
Limit	0.010	0.010	0.020	0.20	0.20	0.10

TABLE I: Fixed admittance parameters in axis order

x,y,z,r_{x},r_{y},r_{z}

. Translational/rotational units:

M

, kg / N m s 2 /rad;

D

, N s/m / N m s/rad; Deadband, N / N m; Limit, m/s / rad/s (residual-twist bounds).

Fig. 5: Online learning on four tasks. Rows show episode-wise XY-force peaks in the recorded frame, intervention ratios, and autonomous success. Force curves are medians of up to ten recent episode peaks. Online time excludes ConRFT offline training.

Task	Method	Success	Steps	$F_{xy}$ peak (N)	Force peak (N)	Torque peak (N m)
MAF36A-17TK	HIL-SERL	14/20	90	$9.809\pm 1.239$	$11.950\pm 0.965$	$2.304\pm 0.252$
	ConRFT	17/20	46	$6.658\pm 1.833$	$10.701\pm 1.693$	$1.569\pm 0.433$
	LeCo	19/20	33	$\mathbf{3.121\pm 0.669}$	$\mathbf{7.760\pm 0.807}$	$\mathbf{0.722\pm 0.147}$
Anderson head	HIL-SERL	26/30	58.5	$6.147\pm 1.056$	$7.856\pm 1.119$	$1.701\pm 0.242$
	ConRFT	30/30	45	$5.702\pm 0.862$	$7.293\pm 1.409$	$1.563\pm 0.249$
	LeCo	30/30	49	$\mathbf{2.236\pm 0.654}$	$\mathbf{6.188\pm 1.309}$	$\mathbf{0.596\pm 0.172}$

TABLE II: Autonomous evaluation: successful-trial median steps and mean

\pm

sample SD of trialwise peaks. Resultant force/torque use three-axis norms. Bold: highest success or lowest mean/steps per task, including ties.

	$\lambda_{c}$	$\eta_{F}$	Success	Steps
A0	0	0	15/20	43.0
A1	0.025	0	12/20	88.5
A2	0	0.1	18/20	46.0
LeCo	0.025	0.1	19/20	33.0

TABLE III: Reward-component ablation. Steps are medians over successful trials.

Fig. 6: Autonomous success in the reward ablation. Curves are ten-episode moving means; markers indicate the first window reaching 80% autonomous success.

Fig. 7: Reward ablation: (a) success with 95% Wilson intervals; (b) successful-trial steps; (c,d) all-attempt lateral-force exposure/conflict (log axes). Points/crosses denote successes/failures; black segments are medians.

Fig. 8: Successful-trial 100-Hz records: (a,b) contact conflict/cancellation; (c) contact duration; (d,e) lateral/rotational conflict density averaged within 20 equal-duration contact bins; (f) cumulative contact conflict. The horizontal axis in (d)–(f) is cumulative above-threshold contact time normalized per trial. Boxes/shading: interquartile ranges; lines: medians.

	Instantaneous peaks			Accumulated interaction
	$F_{xy}$ (N)	$\|F_{z}\|$ (N)	$\tau$ (N m)	$J_{xy}$ (N s)	$J_{\tau}$ (N m s)	$C_{c}^{\rm ep}$
A0	3.389 / 4.453	8.487 / 9.563	0.827 / 1.115	5.216 / 41.904	1.216 / 16.332	5.007 / 92.552
A1	3.028 / 3.871	8.761 / 10.088	0.756 / 0.981	8.815 / 17.800	1.951 / 4.040	6.320 / 15.340
A2	3.414 / 4.304	7.915 / 8.571	0.827 / 0.988	6.170 / 8.804	1.378 / 2.049	5.027 / 9.077
LeCo	3.298 / 4.008	7.997 / 8.890	0.776 / 0.938	3.637 / 6.943	0.808 / 1.521	1.379 / 2.606

TABLE IV: Contact statistics across all attempts (

n=20

per method, including failures). Entries are median / P90 across episodes. Bold indicates the lowest median and P90 in each column.

Robotic Insertion

Robotic insertion studies how robots place objects through openings or into tissue despite tight tolerances, uncertain alignment, and contact forces.

See all 46 papers

InsertAnything: Generalizable Contact-Rich Precision Insertion from Simulation to Reality
Sep 21, 2026Zhenghua Ma, Xinpan Meng, Zeyu Liu +4RL for Robotics Contact-Rich Robotic Manipulation
School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China, and the State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China · PaXini AI Technology (Beijing) Co., Ltd., Beijing 100080, China
PHASE: Compliance-Enabled Tactile Phase Retrieval for Few-Shot Insertion Learning
Sep 25, 2026Jeremy Siburian, Cristian C. Beltran-Hernandez, Tatsuya Matsushima +3Contact-Rich Robotic Manipulation Robot Imitation Learning
OMRON SINIC X Corporation, 5-24-5 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan · The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8654, Japan
TDC: Sim-to-Real Transferable Directional Compliance for Contact-Rich Manipulation
Feb 15, 2026Yifei Yang, Anzhe Chen, Zhenjie Zhu +6Contact-Rich Robotic Manipulation Sim-to-Real Transfer
Zhejiang University · Zhejiang Humanoid Robot Innovation Center

Sep 21, 2026J/K move · Enter open · S save

InsertAnything: Generalizable Contact-Rich Precision Insertion from Simulation to Reality

Zhenghua Ma, Xinpan Meng, Zeyu Liu, Muyuan Ma+3

School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China, and the State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China · PaXini AI Technology (Beijing) Co., Ltd., Beijing 100080, China

RL for Robotics Contact-Rich Robotic Manipulation Sim-to-Real Transfer Generalization in Robotic Manipulation Robotic Insertion

Open paper AskPDF arXiv

Contact-rich precision insertion is a key manipulation skill in robotic assembly. Tight clearances make insertion more sensitive to alignment errors and prone to collisions and jamming, while variations in geometry and clearance across parts further complicate policy reuse. We present a reinforcement learning framework that trains insertion policies entirely in simulation for direct deployment without real-world demonstrations or policy fine-tuning. By combining target poses with compact three-dimensional fingertip force feedback, the policy learns to search for alignment and correct its motion despite errors in the estimated hole position. A decoupled gated reward coordinates alignment and insertion. Force-signal smoothing and state-independent standard deviations stabilize the learning process. The resulting policies perform real-world insertion across multiple hole geometries with a minimum nominal clearance of 0.02 mm and improve success while reducing peak contact forces under hole-position errors. Cross-clearance and cross-geometry evaluations further confirm policy generalization. The system achieved the first perfect score of 20/20 on ManipulationNet's peg-in-hole benchmark under its Human-in-the-Loop protocol, with fully autonomous insertion motions. A single policy trained only on a simulated hexagonal insertion task achieved an overall success rate of 95.0% across eight unseen real-world insertion tasks. These results show that learning entirely in simulation can yield precision insertion skills that can be deployed directly and reused across real-world tasks. The project website (https://mzhsoul.github.io/InsertAnything/) provides open-source simulation and real-robot experiment scripts, assets, and trained checkpoints.

Abstract

Robotic Insertion

Explore similar work

InsertAnything: Generalizable Contact-Rich Precision Insertion from Simulation to Reality

PHASE: Compliance-Enabled Tactile Phase Retrieval for Few-Shot Insertion Learning

TDC: Sim-to-Real Transferable Directional Compliance for Contact-Rich Manipulation