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Augmenting Physical Simulators with Stochastic Neural Networks: Case Study of Planar Pushing and Bouncing

Anurag Ajay, Jiajun Wu, Nima Fazeli, Maria Bauza, Leslie P. Kaelbling, Joshua B. Tenenbaum, Alberto Rodriguez

arXiv:1808.03246v1cs.ROcs.LG

TL;DR

Real-world contact can produce outcomes that parameter distributions in analytical simulators do not adequately capture. The paper augments analytical motion models with recurrent neural networks that learn residuals and represent uncertainty. It reports better performance than purely analytical and purely learned simulators across bouncing and planar-pushing evaluations.

  • Problem

    Analytical simulators can mismatch real-world contact, and distributions over contact parameters may not capture the full range of outcomes.

    Source: §I · p. 1

  • Method

    The framework augments an analytical simulator with a recurrent neural network that learns residual errors and provides distributions over possible outcomes.

    Source: §I · p. 1, C. Data-Augmented Residual Models · p. 3

  • Results

    The data-augmented model outperforms purely analytical and purely data-driven counterparts in bouncing-ball and planar-pushing experiments.

    Source: §I · p. 1

  • Takeaways & Limitations

    The framework is reported to generalize across shapes and materials while generating complex posterior distributions over future states.

    Source: §VI · p. 7

    The experimental setup assumes access to the noisy full state space; learning an observation model alongside the residual model is proposed as future work.

    Source: §VI · p. 8

Abstract

from arXiv · show

An efficient, generalizable physical simulator with universal uncertainty estimates has wide applications in robot state estimation, planning, and control. In this paper, we build such a simulator for two scenarios, planar pushing and ball bouncing, by augmenting an analytical rigid-body simulator with a neural network that learns to model uncertainty as residuals. Combining symbolic, deterministic simulators with learnable, stochastic neural nets provides us with expressiveness, efficiency, and generalizability simultaneously. Our model outperforms both purely analytical and purely learned simulators consistently on real, standard benchmarks. Compared with methods that model uncertainty using Gaussian processes, our model runs much faster, generalizes better to new object shapes, and is able to characterize the complex distribution of object trajectories.

I. INTRODUCTION

The paper augments analytical motion models with learned residuals to improve predictions and represent uncertainty. It applies this framework to bouncing and planar pushing, using an ellipsoidal limit-surface model for pushing.

I. INTRODUCTION

  • Real-world contact outcomes can differ from simulator predictions, and distributions over contact parameters may not capture the full range of outcomes.Contact involves local deformations and vibrations, and outcomes are sensitive to initial conditions,,.Source: §I · p. 1
  • The proposed framework learns residual errors with recurrent neural networks, correcting analytical predictions while providing distributions over possible outcomes.The framework is evaluated on a toy bouncing-ball problem and planar pushing with a single point pusher.Source: §I · p. 1
  • The framework outperforms purely analytical and purely data-driven models in bouncing-ball and planar-pushing experiments.The planar-pushing evaluation uses the empirical dataset from Yu et al..Source: §I · p. 1

A. Models for Planar Pushing

  • For planar pushing, the study uses Lynch et al.’s motion model, which predicts object motion from pusher motion using an ellipsoidal limit surface.The ellipsoidal approximation assumes uniform pressure, constant friction, and quasi-static motion,.Source: A. Models for Planar Pushing · p. 2

B. Learning Contact Dynamics

Prior contact-dynamics approaches either rely on analytical-model expressiveness or make single-step predictions. The paper motivates residual learning and stochastic recurrent prediction, then introduces a framework combining an analytical model with a learned residual.

B. Learning Contact Dynamics

  • Residual corrections can extend analytical predictions beyond their predictive range, while a stochastic recurrent network represents long-horizon outcomes as distributions.This contrasts with approaches that make only single-step predictions, which may be affected by compounding errors.Source: B. Learning Contact Dynamics · p. 2
  • Gaussian-process residual models improve analytical contact-model accuracy, but are slower than neural networks, limited to Gaussian predictive distributions, and were not evaluated for long-term predictions.The cited work focused on individual impact prediction accuracy.Source: B. Learning Contact Dynamics · p. 2

C. Uncertainty Modeling

  • Prior work used Gaussian processes to model planar-shape motion and propagate uncertainty as mixtures of Gaussians; the paper uses this approach as a benchmark.That work showed pushing can be multimodal [20].Source: C. Uncertainty Modeling · p. 2

III. FORMULATION

  • The proposed simulation framework combines an analytical model with a data-driven residual model to improve accuracy and maintain a belief over states.It first defines each component, then describes the residual model’s role.Source: §III · p. 2

A. Physics-Based Analytical Models

The section describes analytical and data-driven motion models, then combines them by learning residuals to analytical predictions. For long-horizon prediction, a recurrent residual model uses an initial state, action sequence, and physics-engine trajectory.

A. Physics-Based Analytical Models

  • Analytical models work well near their assumptions and in structured environments, but their performance degrades outside nominal conditions.Finding tractable models for complex tasks can also require substantial domain-specific expertise.Source: A. Physics-Based Analytical Models · p. 3

B. Data-Driven Models

  • Data-driven models learn from real-world state-action-state data without hand-engineering, but without domain knowledge they may require many examples.The model parameters are obtained through an optimization problem with regularization.Source: B. Data-Driven Models · p. 3

C. Data-Augmented Residual Models

  • A data-augmented residual model takes the physics engine’s prediction, state, and action as input, then learns the discrepancy from real-world data.The residual model refines the physics engine’s guess.Source: C. Data-Augmented Residual Models · p. 3

D. Recurrent Data-Augmented Residual Models

  • Because recursive predictions can create a training–simulation distribution mismatch, the recurrent residual model predicts a trajectory from an initial state and action sequence.The physics engine supplies an initial trajectory; the recurrent residual model uses it to predict the next state.Source: D. Recurrent Data-Augmented Residual… · p. 3

E. Stochastic Recurrent Data-Augmented Residual Models

The paper motivates stochastic prediction because future states are uncertain and that uncertainty matters for planning and control. It formulates a stochastic recurrent residual model and states that it is differentiable and trainable by minimization.

E. Stochastic Recurrent Data-Augmented Residual Models

IV. METHODS

The methods combine an analytical pushing model with recurrent stochastic neural networks that learn residual errors and represent distributions over outcomes. The paper describes the VRNN components used to build this stochastic residual model.

A. The Analytical Push Motion Model

  • The analytical pushing model classifies contact as sticking or sliding from the motion cone, then predicts object motion using that classification and the ellipsoidal limit surface.Observed prediction discrepancies also reflect friction variation, micro-interactions, and potentially anisotropic friction that are difficult to model analytically.Source: A. The Analytical Push Motion Model · p. 4

B. Stochastic Neural Networks

  • A GRU residual model is deterministic, while a simple Gaussian output limits its ability to represent complex real-world distributions.The paper introduces conditional VRNNs as a richer stochastic alternative.Source: B. Stochastic Neural Networks · p. 4

1) Variational Recurrent Neural Networks:

  • A VRNN uses an encoder to infer latent variables, a decoder to reconstruct trajectories, and a learned prior to model latent distributions over time.The encoder samples latent variables by reparameterization, and the trained prior can generate trajectories.Source: 1) Variational Recurrent Neural Networks · p. 4
  • The VRNN is trained by minimizing an objective that includes a latent-distribution term and trajectory reconstruction likelihood, with parameter regularization.The supplied training passages specify Gaussian noise, a regularization constant, and model parameters.Source: 1) Variational Recurrent Neural Networks · p. 4

2) Conditional VRNNs:

Conditional VRNNs incorporate control inputs into latent inference and the prior. The decoder can omit those inputs because the recurrent state can already contain information about the control sequence.

2) Conditional VRNNs:

  • The posterior for each latent variable is conditioned on both the trajectory state and the control input.The conditional prior is also defined with respect to the control input.Source: 2) Conditional VRNNs · p. 4
  • The decoder does not take the control sequence directly, because the recurrent state can contain information about that sequence.Source: 2) Conditional VRNNs · p. 4
  • Figure 3 lays out the conditional VRNN through separate prior, generation, recurrence, and inference components, plus an overall design.Source: Figure 3 · p. 5

3) Decoupled Conditional VRNNs:

Decoupled Conditional VRNNs approximate the conditional VRNN by separating its recurrent components, addressing slower training and evaluation on long trajectories. The model is then used as a stochastic data-augmented residual model alongside the physics engine.

3) Decoupled Conditional VRNNs:

  • For trajectories of length 100 to 1000, the authors propose Decoupled Conditional VRNNs as an approximation because conditional VRNN training and evaluation become slower.Source: 3) Decoupled Conditional VRNNs · p. 5
  • The encoder, decoder, and prior are separated into three recurrent networks because they are not interdependent.The loss function remains unchanged.Source: 3) Decoupled Conditional VRNNs · p. 5
  • The DCVRNN residual model uses the current state as its trajectory input and supplies the initial state, action, and physics-engine prediction as conditioning inputs.The physics engine predicts the next state from the previous predicted state and action.Source: 3) Decoupled Conditional VRNNs · p. 5

V. EXPERIMENTS

The experiments use synthetic ball-bouncing data as an illustrative case and planar-pushing data to evaluate performance against baselines and generalization across shapes and materials.

V. EXPERIMENTS

  • Synthetic ball-bouncing data illustrate the model, while the MIT Push dataset is used for comparisons with baselines and state-of-the-art motion models.Source: §V · p. 5
  • The experiments also analyze how well the model generalizes across shapes and materials.Source: §V · p. 5

A. Experiments with Bouncing Balls

Across synthetic bouncing and real planar-pushing experiments, the Hybrid model outperformed physics and neural baselines; on planar pushing, it also required less data and performed consistently across materials.

A. Experiments with Bouncing Balls

  • Ball trajectories varied drop height from [4m, 5m] and restitution from N(0.5, 0.1), while the analytical engine fixed restitution at 0.65.The experiment recorded ball height and vertical velocity for 400 time steps at 60 Hz.Source: A. Experiments with Bouncing Balls · p. 5

B. Experiments on Planar Pushing

  • Neural test errors were 2.81 versus Hybrid’s 2.04 for position and 2.48 versus Hybrid’s 2.03 for rotation on MIT Push.Table I reports Hybrid as best in position and rotation estimation for rect1 compared with physics-engine and neural methods.Source: Table I · p. 6, B. Experiments on Planar Pushing · p. 6

A. Experiments with Bouncing Balls

B. Experiments on Planar Pushing

  • The MIT Push uncertainty experiment used 2,000 repeated straight-line pushes of a rectangle at 20 mm/s with 15 cm total pusher displacement.The push contact was perpendicular to the edge and halfway between the block’s center and edge.Source: B. Experiments on Planar Pushing · p. 6
  • Hybrid outperformed baselines for rectangles made of plywood and delrin, extending the reported result across materials.Table III presents results for those two materials.Source: Table III · p. 6, B. Experiments on Planar Pushing · p. 6
  • Hybrid reached comparable performance with 2,500 training examples, while data-driven models remained behind with 6,500.Fig. 5 compares prediction errors against training-set size.Source: Figure 5 · p. 7, B. Experiments on Planar Pushing · p. 7
  • Hybrid achieved lower Chamfer distance than GP-SUM when matching the one-second object-position distribution from repeated pushes.The comparison used 2,000 samples from each model and ground-truth data from repeated pushes.Source: B. Experiments on Planar Pushing · p. 7

C. Generalization Power

The Hybrid model generalizes across tested materials and a new object shape, with lower position and rotation errors than the baselines. The authors hypothesize that residual errors transfer across regimes, but note that this depends on the quality of the physics model.

C. Generalization Power

  • The Hybrid model has lower generalization error than baselines for both position and rotation across tested materials and the new rect2 shape.The comparison is summarized in Fig. 7.Source: C. Generalization Power · p. 7
  • The authors hypothesize that generalization improves because physics-model residuals are similar across shapes and materials.This assumption depends critically on the quality of the physics model; generalization may be limited when it no longer holds.Source: C. Generalization Power · p. 7
  • The Hybrid model achieves lower Chamfer-distance error than GP-SUM when capturing the distribution of possible push outcomes.Fig. 6 presents this comparison.Source: Figure 6 · p. 7

VI. DISCUSSION AND CONCLUSION

The discussion presents residual learning as a way to adapt analytical motion models to real-world pushing while retaining uncertainty over outcomes. The authors report generalization across shapes and materials, while noting that predictions can violate physical principles and that their experiments assume noisy full-state access.

VI. DISCUSSION AND CONCLUSION

  • Residual learning adapts analytical motion models to real-world scenarios with little need for domain-specific knowledge or hand-crafting.The authors attribute improved accuracy potentially to learned frictional interactions, including variation in friction coefficients and possibly anisotropic friction.Source: §VI · p. 7
  • Compared with learning the full motion model from scratch, the residual model has less to learn and generalizes better to other shapes and materials.The full data-driven approach is described as more data-hungry.Source: §VI · pp. 7–8
  • The Hybrid model achieves lower generalization error for position and rotation than baselines across materials and a new shape.Fig. 7 summarizes the comparisons.Source: Figure 7 · p. 8
  • Reasoning about possible outcomes can help planning and control; for planar pushing, a planner can exploit predictable pushes.The authors give predictable pushes as an example of a property a planner can use.Source: §VI · p. 8
  • Because no output-level mechanism enforces basic physics, the residual model can predict physically impossible outcomes, though the authors expect sufficient training to prevent implausible outcomes in practice.Energy conservation is given as an example of a principle not enforced at the output level.Source: §VI · p. 8
  • The experiments assume access to noisy full-state data; learning an observation model alongside residuals is proposed as an extension for joint state estimation and prediction.The framework requires only a coarse domain-specific analytical motion model for application to other robotic tasks.Source: §VI · p. 8
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