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Adaptive Compliance Policy: Learning Approximate Compliance for Diffusion Guided Control

Yifan Hou, Zeyi Liu, Cheng Chi, Eric Cousineau, Naveen Kuppuswamy, Siyuan Feng, Benjamin Burchfiel, Shuran Song

arXiv:2410.09309v2cs.RO

TL;DR

Human demonstrations do not directly determine full compliance parameters, and many visuomotor policies use uniform constant stiffness. ACP learns approximate, spatially and temporally varying compliance from demonstrations; the paper reports over 50% higher performance than state-of-the-art visuomotor policy methods on two contact-rich manipulation tasks.

  • Problem

    Human demonstrations do not directly determine full compliance parameters, and prior approaches may depend on pre-selected parameters or uniform constant stiffness.

    Source: §I · p. 1

  • Method

    ACP learns spatially and temporally varying compliance from human demonstrations using approximate profiles designed to avoid large internal forces while encouraging precise tracking.

    Source: §I · pp. 1–2

  • Results

    Over 50% increase in performance versus state-of-the-art visuomotor policy methods on real-world object flipping and vase wiping tasks.

    Source: §I · p. 2

  • Takeaways & Limitations

    ACP adjusts compliance based on visual and force feedback to maintain desired contact modes despite uncertainties and disturbances.

    Source: §I · p. 2

    Estimating compliance parameters from a single human demonstration is ill-conditioned because demonstrations may lack sufficient force-motion variation.

    Source: C. Estimating Compliance from… · p. 3

Abstract

from arXiv · show

Compliance plays a crucial role in manipulation, as it balances between the concurrent control of position and force under uncertainties. Yet compliance is often overlooked by today's visuomotor policies that solely focus on position control. This paper introduces Adaptive Compliance Policy (ACP), a novel framework that learns to dynamically adjust system compliance both spatially and temporally for given manipulation tasks from human demonstrations, improving upon previous approaches that rely on pre-selected compliance parameters or assume uniform constant stiffness. However, computing full compliance parameters from human demonstrations is an ill-defined problem. Instead, we estimate an approximate compliance profile with two useful properties: avoiding large contact forces and encouraging accurate tracking. Our approach enables robots to handle complex contact-rich manipulation tasks and achieves over 50\% performance improvement compared to state-of-the-art visuomotor policy methods. For result videos, see https://adaptive-compliance.github.io/

I. INTRODUCTION

Manipulation requires balancing position accuracy and response to external forces, but human demonstrations do not directly determine full compliance parameters. ACP learns spatially and temporally varying compliance from demonstrations using approximate profiles designed to avoid large internal forces while encouraging precise tracking, and improves performance by over 50% on two contact-rich tasks.

I. INTRODUCTION

  • Human demonstrations do not directly determine full compliance parameters, while prior methods require known dynamics, repeated identical-task demonstrations, pre-selected parameters, or uniform constant stiffness.Such approaches cannot handle new scene configurations or unexpected perturbations.Source: §I · p. 1
  • ACP learns to adjust compliance spatially and temporally for a manipulation task from human demonstrations.It represents compliance using an additional stiffness value and a virtual target; the target difference encodes spatial stiffness distribution, and a low-level compliance controller executes the predictions.Source: §I · pp. 1–2
  • Approximate compliance profiles are derived to avoid large internal forces while encouraging precise tracking, under mild task assumptions.The rule can approximate varying stiffness across demonstration episodes with different object variations and scene configurations.Source: §I · p. 2
  • Over 50% increase in performance versus state-of-the-art visuomotor policy methods on object flipping and vase wiping.The paper identifies these as two real-world contact-rich manipulation tasks.Source: §I · p. 2
  • A kinesthetic teaching system supports demonstrations with varying compliance profiles, and the method computes spatially and temporally varying compliance labels from human demonstrations.ACP is formulated to adjust compliance to maintain desired contact modes despite uncertainties and disturbances.Source: §I · p. 2

II. RELATED WORK

Prior work computes compliance through physical modeling, reinforcement learning, repeated demonstrations, or manually specified stiffness, but these approaches have scaling or generalization constraints. Visuomotor policies using force feedback often still predict position with uniform constant compliance.

II. RELATED WORK

  • Model-based compliance methods can compute robust stiffness from contact geometry and friction, but typically require careful modeling work to set up.The paper contrasts these with its model-free approach, which it describes as easier to scale.Source: §II · p. 2
  • Reinforcement-learning compliance policies need retraining for scene variations, while most use fixed-parameter low-level controllers that lack robustness against disturbances.Stiffness estimation from repeated motions does not fit demonstrations that differ, and a single-demonstration estimator requires perfect knowledge of human mass and damping.Source: §II · p. 2
  • Despite force input, most visuomotor policies predict robot position with uniform constant compliance, which does not capture spatial and temporal compliance variation.Prior work encodes force/torque temporal relations using causal convolution, TCN, LSTM, VAE, and self-attention.Source: §II · p. 2

III. METHOD

The method models robot compliance and contact interaction as foundations for ACP. Its setup uses a low-level compliance controller and assumes contact forces dominate other forces in the manipulation model.

III. METHOD

  • The method introduces a pipeline covering physical concepts, kinesthetic teaching, compliance-label annotation, and ACP design.These are presented as the stages from collecting human demonstrations to designing the policy.Source: §III · p. 2

A. Preliminaries: Modeling

  • Robot compliance models the elastic relation between force and motion using position, force, and a spring-mass-damper representation.The model's inertia, stiffness, and damping matrices, along with a reference position, describe the compliant behavior.Source: A. Preliminaries: Modeling · p. 3
  • The paper uses admittance control to convert force feedback into position targets for its high-accuracy position-controlled robot.It notes that robots with force-control interfaces may instead use impedance control or hybrid force-motion schemes.Source: A. Preliminaries: Modeling · p. 3
  • The manipulation model assumes contact force dominates inertia, friction, and gravity; the setup avoids fast motion and uses lightweight objects to support this assumption.Contact forces are represented by normal-force vector λ, and the contact Jacobian maps them into generalized force space.Source: A. Preliminaries: Modeling · p. 3

B. Demonstration Collection

Demonstrations are collected through kinesthetic teaching with direct haptic feedback, enabling operators to demonstrate variable compliance. The teaching setup uses low compliance to let the operator move the robot freely.

B. Demonstration Collection

  • Kinesthetic teaching is selected to let operators demonstrate variable compliance under direct haptic feedback.The setup includes a robot manipulator for accurate position feedback, an RGB camera, and a force-torque sensor near the hand.Source: B. Demonstration Collection · p. 3, Figure 3 · p. 3
  • During demonstrations, the robot uses low stiffness, damping, and virtual mass so the operator can move it freely.Low damping and mass are feasible during teaching because the human hand provides natural external stabilization; during testing, damping and virtual mass are increased to maintain admittance-controller stability.Source: B. Demonstration Collection · p. 3

C. Estimating Compliance from Demonstrations

The paper estimates an approximate stiffness profile rather than recovering true human compliance, which is ill-conditioned from a single demonstration. It uses low stiffness along the feedback-force direction and high stiffness elsewhere to balance avoiding internal forces with accurate tracking.

C. Estimating Compliance from Demonstrations

  • Estimating true stiffness from a single human demonstration is ill-conditioned because demonstrations may lack variation and kinesthetic teaching changes effective damping and mass.Prior stiffness estimation assumes known damping and virtual mass plus sufficient force-motion variation, conditions the authors say kinesthetic teaching does not meet.Source: C. Estimating Compliance from… · p. 3
  • The target stiffness profile instead seeks to avoid huge internal forces and encourage accurate tracking, using pre-selected mass and damping values.Source: C. Estimating Compliance from… · p. 3
  • The analysis assumes nonzero contact forces and no pinching contacts, with the latter restricting the contact-normal cone to lie within its dual cone.The authors say nonzero forces can be encouraged by making contacts clearly in demonstrations, and that the no-pinching condition means contacts are not too restrictive.Source: C. Estimating Compliance from… · pp. 3–4, Figure 4 · p. 4
  • Low stiffness along the feedback-force direction and high stiffness elsewhere lets the policy avoid constraint violations while improving position tracking in other directions.The theorem states that contact constraints can be satisfied when velocity is not controlled in the feedback-force direction; the method uses that direction for low stiffness.Source: C. Estimating Compliance from… · pp. 3–4
  • The low-stiffness value decreases continuously with force magnitude because its direction is estimated from noisy force signals; high stiffness supports tracking and is set empirically.When force magnitude is small, the policy uses high stiffness in all directions; hardware determines the magnitude parameters.Source: C. Estimating Compliance from… · p. 4

D. Adaptive Compliance Policy

Adaptive Compliance Policy represents reference actions and target stiffness as a diffusion process, predicting action trajectories from recent observations in a receding-horizon loop.

D. Adaptive Compliance Policy

1) Inputs and Encoding:

The policy encodes force/torque history and recent images, then combines image and force representations with recent end-effector poses for its diffusion-policy condition.

1) Inputs and Encoding:

  • Force/torque inputs use either causal convolution over the past 32 timesteps or FFT spectrograms encoded by a ResNet-18.The causal-convolution encoder has five layers and outputs a 768-dimensional vector; the spectrograms are 6×30×17.Source: 1) Inputs and Encoding · p. 4
  • Images from the past two timesteps are resized and randomly cropped, then encoded with a CLIP-pretrained ViT-B/16.Source: 1) Inputs and Encoding · p. 4
  • A transformer layer uses self-attention to learn adaptive visual-force representations, which are concatenated with end-effector poses from the past three timesteps as the diffusion-policy condition.Source: 1) Inputs and Encoding · p. 4

2) Outputs and decoding:

Each arm's policy output encodes reference and virtual target poses plus low-direction stiffness magnitude. Training derives stiffness and virtual targets from filtered wrench demonstrations, while inference reconstructs the stiffness matrix and sends it with the target to the compliance controller.

2) Outputs and decoding:

  • Each arm outputs a 19-dimensional vector encoding position target, stiffness matrix, and reference force.Source: 2) Outputs and decoding · p. 4
  • The output includes a 9D reference pose, a 9D virtual target pose, and a scalar low-stiffness magnitude.The virtual target is computed so that reaching the reference pose while tracking it with the specified stiffness produces the reference force; it converts a force target into a position target.Source: 2) Outputs and decoding · p. 4
  • During training, a one-second moving average filters episode wrench data before stiffness is computed and the virtual target is derived using a 3D mechanical spring.The filtering smooths virtual targets and gives action labels hindsight information about impending contacts for smoother contact engagement.Source: 2) Outputs and decoding · p. 4
  • At inference, the full stiffness matrix is reconstructed using the direction from reference pose to virtual target, and both matrix and target go to the low-level compliance controller.Source: 2) Outputs and decoding · p. 4

IV. EXPERIMENTS

The experiments evaluate ACP and three comparison policies on two real-world, contact-rich manipulation tasks. The policies use common training data and epochs, with different force inputs and compliance settings.

IV. EXPERIMENTS

  • The evaluation uses a UR5e, a GoPro RGB camera streaming at 60 Hz, and an ATI mini-45 force-torque sensor streaming at up to 7000 Hz.The robot receives Cartesian pose commands and provides pose feedback at 500 Hz.Source: §IV · p. 5
  • Four policies are compared after training on the same dataset for the same number of epochs: ACP, ACP without FFT, a stiff diffusion policy, and a compliant policy.The stiff policy outputs target positions; the compliant policy uses uniform stiffness k = 500 N/m.Source: §IV · p. 5
  • All policies use two RGB frames and three end-effector pose frames, while ACP variants use 3D translational compliance.ACP without FFT uses 32 wrench frames sampled at 250 Hz; the other policies use one second of wrench data at 7000 Hz.Source: §IV · p. 5

A. Task I: Item Flipping

The flipping task tests whether policies can pivot varied items against a fixture while maintaining contact without making the fixture slide. ACP variants maintain contact across position uncertainty, unlike the stiff and compliant baselines in less favorable conditions.

A. Task I: Item Flipping

  • The task requires consistent contact across changes in item shape, weight, and fixture location, while excessive force can slide the fixture.Training used 230 demonstration episodes from 15 items for 300 epochs.Source: A. Task I: Item Flipping · p. 5
  • Testing covers five scenarios: training items, unseen items, pushing an item 5 cm toward the fixture, two fixture poses, and an unstable lighter fixture.There are 20 tests per scenario, or 100 tests per algorithm; Fig. 5 depicts geometry, configuration, and fixture-movement variations.Source: A. Task I: Item Flipping · p. 5
  • Success means rotating the item more than 70 degrees, and typical failures include falling off the finger, getting stuck, or triggering a robot force violation.Table I presents flipping-up success rates.Source: A. Task I: Item Flipping · p. 5, Table I · p. 5
  • Both ACP variants tolerate a large range of position uncertainties while maintaining needed contacts; the stiff and compliant baselines fail when rigid items or unfavorable uncertainty break contact.The baselines have some successes when they can exploit passive compliance with deformable items.Source: A. Task I: Item Flipping · p. 5
  • ACP scores 96/100 and ACP without FFT scores 95/100, with the two variants performing similarly on flipping.The passage attributes this similarity to the force signal having little high-frequency content in this task.Source: A. Task I: Item Flipping · p. 5

B. Task II: Vase Wiping

Vase wiping tests compare ACP with stiff and compliant policies across varied marks and contact perturbations. ACP safely maintained contact and tracked the wiping motion, while the alternatives showed tool damage or friction-related tracking loss.

B. Task II: Vase Wiping

  • The wiping task used 200 demonstrations with varied vase poses, marking shapes, and colors; each demonstration contained one to five wipes.A bimanual robot used its left arm to hold the vase and its right arm to wipe.Source: B. Task II: Vase Wiping · p. 5
  • Success required cleaning the mark within three wipes, with remaining marks contained within 1cm×1cm.The experiment included small and large marks, plus vase perturbations before and after contact.Source: B. Task II: Vase Wiping · pp. 5–6
  • The stiff policy’s contact force varied with position-action accuracy, and the robot broke its tool during the fourth test.ACP safely engaged and maintained contact during wiping.Source: B. Task II: Vase Wiping · p. 6
  • The compliant policy deviated from its position target under vase friction, producing insufficient sliding for a high-quality wipe.The comparison in Tab. II excludes the stiff policy because it frequently broke the tool.Source: B. Task II: Vase Wiping · p. 6
  • ACP maintained safe contact and accurate wiping motion, while the stiff and compliant policies respectively risked tool damage and lost tracking accuracy.Fig. 8 contrasts ACP’s contact and trajectory behavior with the stiff policy’s tool breakage and the compliant policy’s friction-limited wiping.Source: Figure 8 · p. 6, B. Task II: Vase Wiping · p. 6

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