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Grasping with Chopsticks: Combating Covariate Shift in Model-free Imitation Learning for Fine Manipulation

Liyiming Ke, Jingqiang Wang, Tapomayukh Bhattacharjee, Byron Boots, Siddhartha Srinivasa

arXiv:2011.06719v1cs.ROcs.LG

TL;DR

Model-free imitation learning for fine manipulation lacks reliable generalization because covariate shift compounds action errors into unseen states. The paper increases grasp-critical data support with an object-centric transform and generates synthetic corrective labels by injecting noise and reusing actions, combined with parametric and non-parametric methods. The agent achieves an 80% average success rate across three objects, compared with 12% for naive behavior cloning and 82% for expert human performance.

  • Problem

    Model-free imitation learning for fine manipulation lacks reliable generalization because covariate shift compounds action errors into unseen states.

    Source: §I · pp. 1–2

  • Method

    The paper increases grasp-critical data support with an object-centric transform and generates synthetic corrective labels by injecting noise and reusing actions, combined with parametric and non-parametric methods.

    Source: §I · p. 2, B. Noise: Generating Synthetic… · p. 3

  • Results

    The agent achieves an 80% average success rate across three objects, compared with 12% for naive behavior cloning and 82% for expert human performance.

    Source: §I · p. 2

  • Takeaways & Limitations

    The methods provide a non-interactive way to reduce covariate shift in fine-manipulation imitation learning without access to an expert policy or environment model.

    Source: §I · p. 2, §V · p. 6

    The approach assumes a critical region requiring increased data support and a direct state-action connection; the latter may not hold for torque-controlled robots.

    Source: §V · p. 6

Abstract

from arXiv · show

Billions of people use chopsticks, a simple yet versatile tool, for fine manipulation of everyday objects. The small, curved, and slippery tips of chopsticks pose a challenge for picking up small objects, making them a suitably complex test case. This paper leverages human demonstrations to develop an autonomous chopsticks-equipped robotic manipulator. Due to the lack of accurate models for fine manipulation, we explore model-free imitation learning, which traditionally suffers from the covariate shift phenomenon that causes poor generalization. We propose two approaches to reduce covariate shift, neither of which requires access to an interactive expert or a model, unlike previous approaches. First, we alleviate single-step prediction errors by applying an invariant operator to increase the data support at critical steps for grasping. Second, we generate synthetic corrective labels by adding bounded noise and combining parametric and non-parametric methods to prevent error accumulation. We demonstrate our methods on a real chopstick-equipped robot that we built, and observe the agent's success rate increase from 37.3% to 80%, which is comparable to the human expert performance of 82.6%.

I. INTRODUCTION

The paper studies covariate shift in model-free imitation learning for fine manipulation with chopsticks, where small, slippery tips and limited failure tolerance make grasping difficult. It proposes non-interactive methods that expand data support and generate corrective labels without an interactive expert or model.

  • The study uses a 6DOF arm with a 1DOF actuated chopstick to learn fine-manipulation strategies from human demonstrations.Source: §I · p. 1
  • Model-free imitation learning is challenged by covariate shift because compounding action errors lead agents into unseen states, especially near the few critical steps for fine manipulation.Source: §I · p. 1
  • The approach targets a non-interactive setting because online expert queries burden demonstrations, with DART increasing collection time by 43% in this task.Source: §I · p. 1
  • The proposed transform increases data support around grasp-critical regions by using an object-centric representation that preserves relative end-effector–object transformations.Source: §I · p. 2
  • Synthetic corrective labels reuse actions after injecting noise into collected states, implicitly encouraging smooth policies and recovery from deviated states.Source: §I · p. 2
  • The proposed approach achieves an 80% average success rate across all three tested objects, compared with 82% for expert human performance.For the most challenging small ball, it achieves 60% success versus 12% for naive behavior cloning.Source: §I · p. 2

A. Transform: Increasing Data Support

The paper addresses covariate shift through two complementary mechanisms: an object-centric transform that densifies demonstrations near grasp-critical regions and noise-based synthetic corrective labels that support recovery from deviations.

A. Transform: Increasing Data Support

B. Noise: Generating Synthetic Corrective Labels

  • Noise-based corrective labels perturb demonstration states and reuse the collected action, providing recovery examples without an interactive expert or accurate model.Source: B. Noise: Generating Synthetic… · p. 2
  • The method uses small additive Gaussian noise, scaled to data variance, because larger perturbations could pair states with detrimental actions.Source: B. Noise: Generating Synthetic… · p. 3
  • Reusing actions is justified because state and action both contain end-effector pose, while the assumed state-action smoothness supports returning toward the demonstrated trajectory.Source: B. Noise: Generating Synthetic… · p. 3

C. Ensemble: Following the Expert Advice

The ensemble combines behavior cloning with k-nearest neighbors to use scalable neural predictions near training data and constrained corrective actions when queries deviate substantially.

C. Ensemble: Following the Expert Advice

A. Experimental Setup

The study evaluates a 6-DOF chopstick-equipped robot on small-object grasping and compares baseline, object-centric, noise-injected, and ensemble agents against expert and replay conditions.

A. Experimental Setup

  • The robot uses a 6-DOF arm with chopsticks to grasp a 1 cm cube and balls measuring 2 cm and 1.4 cm in diameter.Hardware inaccuracies produce 1–6 mm end-effector position errors, comparable to the objects’ radii.Source: A. Experimental Setup · p. 3
  • Each object has 500 expert teleoperation trajectories, while success requires grasping, lifting above the workstation, and holding the object for 1 s.Performance is measured over 25 trials with objects placed across a 5 × 5 workspace grid.Source: A. Experimental Setup · pp. 3–4

B. Experimental Procedure

  • The evaluation compares learned agents with human teleoperation and replayed successful demonstrations to assess expert performance and hardware repeatability.Replay uses the same object locations as data collection.Source: B. Experimental Procedure · p. 4
  • Robot-centric behavior cloning and k-nearest-neighbor agents serve as baselines, while object-centric, noise-injected, and decision-tree ensemble variants test the proposed methods.The ensemble combines BC+ObjC+Noise with k-NN+ObjC.Source: B. Experimental Procedure · p. 4

IV. RESULTS

The results show that object-centric data support, synthetic noise-based corrections, and their ensemble improve chopstick grasping across challenging object placements.

A. Success Rates for Fine Manipulation

  • BC+RobotC struggles with objects farther from the robot because long approaches lead it toward incorrect locations.This behavior highlights covariate shift in the robot-centric baseline.Source: A. Success Rates for Fine Manipulation · p. 4
  • k-NN+RobotC produces poses resembling demonstrations but can move jerkily or stop on the object without completing the grasp.Its failures reflect sensitivity to the distance function and direct imitation of paused or slowed demonstration motions.Source: A. Success Rates for Fine Manipulation · p. 4
  • 20% and 6.7%: transforming to the object-centric frame improves k-NN and BC success rates, respectively.The denser object-centered data reduce jerky k-NN motions and make BC more likely to reach the object despite residual covariate shift.Source: A. Success Rates for Fine Manipulation · p. 4
  • 28%: injecting noise into BC+ObjC increases its success rate, with nearly 100% success for objects close to the robot.For distant objects, failures sometimes consist of rotating the chopsticks without grasping.Source: A. Success Rates for Fine Manipulation · p. 4
  • Fig. 5 compares rollout states with demonstrations as a covariate-shift proxy, where farther green states indicate greater shift than yellow states.The visual provides distributional context for the success-rate comparisons.Source: Figure 5 · p. 5
  • The Ensemble combining BC+ObjC+Noise and k-NN+ObjC achieves the highest performance and near-expert behavior across object placements.It uses k-NN when the query state is farther from training neighbors and occasionally misses the grasping point by sub-millimeter error.Source: A. Success Rates for Fine Manipulation · p. 5

B. Covariate Shift Across Methods

State-distribution analysis links improved action matching and noise injection with reduced covariate shift, while simulated validation finds statistically significant average gains from noise injection.

B. Covariate Shift Across Methods

  • BC exhibits more covariate shift than k-NN, while noise-injected BC and the BC–k-NN Ensemble show less shift than their respective alternatives.The analysis uses 25 rollouts per agent and PCA-reduced visited-state distributions.Source: B. Covariate Shift Across Methods · p. 5

C. Noise Injection: Validation through MuJoCo Environments

  • p < 0.05: paired t-tests across all MuJoCo environments provide evidence that noise injection improves imitation-learner performance on average.Five baseline and five noise-injected agents are trained using consecutive random seeds.Source: C. Noise Injection: Validation through… · p. 5, Figure 6 · p. 5
  • The simulated gains are less significant in some environments than on the real robot, possibly because simulations use synthetic RL demonstrations rather than human data.The authors note that further inquiry is needed to determine whether noise injection especially benefits multimodal demonstrations.Source: C. Noise Injection: Validation through… · p. 5

V. DISCUSSION

The proposals target non-interactive covariate-shift correction without requiring an accurate model or interactive expert. Their applicability depends on assumptions about critical regions and the relationship between action and state distributions.

  • The approach assumes a critical region requires increased data support and that better action-distribution matching produces better state-distribution matching.The latter assumption is supported when state and action representations are directly connected.Source: §V · p. 6
  • Torque-controlled systems violate the action-state connection assumption, so generating synthetic corrective labels for them requires further exploration.Source: §V · p. 6
  • The proposals generate synthetic corrective labels without model or interactive-expert access, making them more applicable to fine-manipulation tasks.They can also transfer directly to interactive settings.Source: §V · p. 6
  • The current work is an initial step toward general-purpose fine manipulation, with future work combining model-free and model-based methods for more diverse hard-to-grasp objects.The paper notes that accurate models for fine manipulation are rare.Source: §V · p. 6

APPENDIX

The appendix describes the robot state and control interface, calibration improvements, and the human demonstration dataset used for evaluation. Calibration substantially improved replay success, while demonstrations were collected at the test frequency and filtered for success.

A. Experimental Setup

  • The robot state uses an 8D end-effector pose, while target poses are sent at 100Hz and joints are controlled through inverse kinematics and PID at 500Hz.Source: A. Experimental Setup · p. 6
  • Calibration reduced average end-effector position error from 10 mm to 4 mm, while custom PID tuning raised cube and small-ball replay success to 100% and 80%.Source: A. Experimental Setup · p. 6
  • Demonstrations were collected at 100Hz, averaged 600 state-action pairs per trajectory, and retained 500 successful trajectories after filtering failures.One expert collected trajectories from randomized object locations around a fixed home configuration.Source: A. Experimental Setup · p. 6

B. Implementation Details

The implementation compares a neural behavior-cloning agent with k-NN, noise-augmented training, and a thresholded ensemble. The ensemble switches to k-NN when neighbor distances indicate that the state is insufficiently supported by the behavior-cloning policy.

B. Implementation Details

  • Behavior cloning uses a two-layer 64 × 32 ReLU network that predicts an 8D target end-effector pose with weighted component-wise losses.Source: B. Implementation Details · p. 6
  • The k-NN agent uses the last three end-effector poses and current object location, with a distance function modeled on the behavior-cloning loss.Source: B. Implementation Details · p. 6
  • Noise training replaces 20% of batch states with x′_i = x_i + ϵ, where ϵ follows a zero-mean Gaussian with diagonal covariance scaled by state variance.A fixed noise magnitude η is used across state dimensions.Source: B. Implementation Details · p. 6
  • The ensemble follows behavior cloning when the normalized nearest-neighbor distance is below threshold α and otherwise invokes k-NN.Source: B. Implementation Details · p. 6

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