Simultaneous Learning of Contact and Continuous Dynamics
Authors: Bibit Bianchini
Mathew Halm
Michael Posa
Venue: CoRL 2023 Poster (2023)
Keywords: system identification
dynamics learning
contact-rich manipulation

Abstract: Robotic manipulation can greatly benefit from the data efficiency, robustness, and predictability of model-based methods if robots can quickly generate models of novel objects they encounter. This is especially difficult when effects like complex joint friction lack clear first-principles models and are usually ignored by physics simulators. Further, numerically-stiff contact dynamics can make common model-building approaches struggle. We propose a method to simultaneously learn contact and continuous dynamics of a novel, possibly multi-link object by observing its motion through contact-rich trajectories. We formulate a system identification process with a loss that infers unmeasured contact forces, penalizing their violation of physical constraints and laws of motion given current model parameters. Our loss is unlike prediction-based losses used in differentiable simulation. Using a new dataset of real articulated object trajectories and an existing cube toss dataset, our method outperforms differentiable simulation and end-to-end alternatives with more data efficiency. See our project page for code, datasets, and media: https://sites.google.com/view/continuous-contact-nets/home

Simultaneous Learning of Contact and Continuous Dynamics
Bibit Bianchini, Mathew Halm, and Michael Posa GRASP Laboratory, University of Pennsylvania (bibit, mhalm, posa)@seas upenn. edu
Abstract: Robotic manipulation can greatly benefit from the data efficiency, ro- bustness, and predictability of model-based methods robots can quickly gen- erate models of novel objects they encounter. This is especially difficult when effects like complex joint friction lack clear first-principles models and are usu- ally ignored by physics simulators. Further, numerically-stii contact dynamics can make common model-building approaches struggle. We propose method to simultaneously learn contact and continuous dynamics a novel, possibly multi- link object by observing its motion through contact-rich trajectories. We formulate system identification process with a loss that infers unmeasured contact forces, penalizing their violation of physical constraints and laws of motion given current model parameters. Our loss is unlike prediction rredeetion-based losses used in differen- tiable simulation. Using new dataset of real articulated object trajectories and an existing cube toss dataset, our method outperforms differentiable simulation and end-to-end alternatives with more data efficiency. See our project page for code, datasets, and media: https::/sitts, http://siitssggglleeeee wtw.//////wwwwwwoooooooooo htte///ontinoous-coottttt-t wotes-oo-ottttttooooooone
Keywords: system identification, dynamics learning, contact-rich manipulation
d313
weights
Pauiddual
predidioo
currentivett pars
Contact solver
R
latkketk OI
Residual network
Viclation reulltiic
Simalator parameterss
Simulutor
dysamiia
contact
Inference (Shmuistionn
Tomn trajectorien
backprop
learning
Training
optimization
Our method for learning dynamics of an unknown object. Left: Franka Panda automates data col- lection by tossing an object onto table as the object's configu fiiuuratiion is recorded. Middle: Our violation-har hased implicit loss without explicit simulation trains simulator parameters and residual 8 that augments the learned continuous acceleration, cncouraging the residual to learn smooth accelerations characteristic of continuous dy- namics, while contact-related parameters implicitly define stiffer contact dynamics. Right: trained model can be used with any simulator (contact solver) during inference for performing dynamics predictions.
Figure 1:
Introduction
In the future of robotic manipulation off the assembly line, robots will encounter new objects in their environment and be expected to perform useful tasks with them, such cooking with kitchen uten- sils, using tools, opening doors, and packing items. Model- based control methods work increasingly well in contact-rich scenarios [1, 2]. but rely on models of the manipulated objects. Unlike factory settings where everything can be precisely modeled, or locomotion where the robot itself is typically the only dynamic agent, challenge of manipulation the wild lies in the unknown properties of the objects to be manipulated. Model-free methods are viable, though potentially require prohibitive amounts of data [3]. Building models the fly could enable model-based control and result in more generalizable and robust performance, but is only realistic if model- model-building building is fast.
Manipulation is fundamentally contact-rich, and the resulting discontinuous dynamics can make model construction particularly challenging [4], Standard system identification methods work well
7th Conference Robot Learning (CoRL. 2023), Atlanta, USA.

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for identifying smooth continuous dynamics parameters even in the presence of stiff contact [5, 6], though assuming contact-related parameters are known. Pfrommer et al. [7] developed a physics- based method which circumvented numerical difficulties directly by leveraging the physical struc- ture to derive a smooth, violation-basee loss, though assuming continuous dynamics are known. the aim of this work learn both continuous and contact dynamics simultaneously.
The challenge of jointly learning continuous and contact dynamics is that the overall dynamics in- herit the stiffness of contact, whose impacts can overpower the smaller, smooth, albeit important continuous accelerations. Thus, separating continuous dynamics from contact events, while de- sirable, is not straightforward. We extend Pfrommer et al. [7] which handles the contact-related portions, then combine ral network (DNN) practices of encouraging smoothness to handle the continuous dynamics via residual physics, all while enjoying the data efficiency of an implicit model with suitable loss [9].
crnniizaatio-friinddl inertial parameterizations [8] with common deep neu-
1.1 Contributions and Outline
We make the following contributions in this work:
Present and make available dataset of over 500 real toss trajectories of an articulated object,
whose state-dependent continuous dynamics are more complicated than single rigid bodies. Extend prior work on learning contact dynamics [7] by simultaneously learning continuous dy- namics via combination of model-based parameterization and DNN residual physics.
Demonstrate effective performance of our method on two real datasets and two simulation sce- narios with imposed actual-to-men to-modeled continuous dynamics gaps. We provide comparisons with differentiable simulation and end-to and-to-end learning as alternatives.
We ground motivations and methods in $2 with related background. $3 details model represen- tations, followed by loss formulations in $4. With experimental setup in $5, we present and discuss the results in $6, followed by a conclusion in $ and discussion of limitations and future work in $8.
Background and Related Work
Challenges of contact-rich dynamics. Detecting contact events is extremely difficult in many practical scenarios. Many model building works solve simpler variations, e.g. utilizing contact detection oracle [10], assuming knowledge of contact distances [5, 6, 11], or operating simple geometries like spheres or 2D interactions [6]. Our work builds off [7]'s contact-related parameter learning that performs automatic segmentation of contact/non-contact effects, without access to an oracle to identify contact events. Our work extends this contact-implicit model building beyond con- tact dynamics, to building full dynamics models, without impractical contact detection assumptions.
Implicit representations for discontinuous functions. Recent works have employed implicit ap- proaches to represent sharp functions smoothly, whether those functions represent discontinuous control policies [12] or contact models [13]. Other works demonstrating differentiation through these implicit representations make them viable for use in learning [14, 15]. These techniques rely on smooth parameters to implicitly encode signals for discontinuous or extremely stiff events, which accurately characterizes contact dynamics. However, the implicit model representation can be data inefficient to optimize when combined with explicit losses [9]. Implicit model representations in combination with informative loss successfully learn contact parameters [7].
Differentiable simulation. Widely used for policy learning and control, differentiable simulators are also useful for system identification [5, 16, 17]. Differentiable simulators use governing dy- namics that can be explicitly differentiated, and often compare simulated predictions with observed motion, using the difference to supervise model training. However because they use prediction- based losses, differentiable simulators notoriously can have difficult optimize loss landscapes when identifying centact-relatdd parameters [18]. Differentiable simulation can be combined with artificially soft contact models improve optimization [19], the cost of model accuracy [4].

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Inertial parameterizations. The inertia of a rigid body is completely described by 10 parameters: the mass, center of mass (3), and moments/products of inertia (6). Learning these directly can be problematic since many members of R are physically infeasible inertia vectors. There are several previously developed mappings from Oinertia E IR= to physically feasible sets of inertial parameters [8. 20, 21], and thus learning mentia to indirectly yield inertial properties becomes well posed optimization problem. We use the Rucker and Wensing [8] parameterization in this work.
Residual physics. While model-based structures typically boast data efficiency compared to model-free approaches [3], they fundamentally suffer from inaccuracies of the model on which they are based. Residual physics [22, 23, 24, 25, 26] mitigates this by learning an expressive residual that fills a data efficient but possibly insufficient structured model's sim-to-real gap. We use a residual physics DNN in this work to specifically augment the continuous dynamics of our structured model.
Model Representations
We consider discrete dynamics model parameterized by a set of learnable parameters 0 that takes in some state z(k) and set of control inputs u(k) and performs a single simulation step.
x(k + 1) - f (x(kk) u(k)).
(1)
This makes assumptions about the structure of f or what the learned parameters 0 represent. In an unstructured case, f could be learned as DNN where 0 is the weights and biases of the network. In more structured case (e.g. rigid body dynamics). 0 represents physical parameters of the system. Numerical methods commonly simulate contact by introducing an optimization problem to search for contact impulses X(k) from a feasible set of contact impulses over the time step.
<okk + 1) = 9" (ar(k), ((x), A(k)),
(2a)
where
A(k) = arg min h (ar(k,, u(k), <Ah: 1), xEA
(2b)
where h measures violation of contact constraints. This generic formulation underpins many com- mon simulators, where the embedded optimization problem may be a linear complementarity prob- lem (LCP) [27, 28), coddnr cone program [29], or some more generic structure [30].
3.1 Measuring Violation of Rigid Body Contact Dynamics
Inspired by the LCP formulation from Stewart and Trinkle [28], we follow standard methods for conversion an equivalent optimization problem form in (2), introduced by Pfrommer al. [7]. First, we let A describe Coulomb friction cone,
<
|aaell S p.A., 1,....
(3)
for a system with contacts. Then we use penalty terms to describe violation of force complemen- tarity, energy dissipation, and geometric penetration for each contact i,
h (k)) (k, + 1),
(4a)
[M (k)) 1)1l (k) + +1
h diss. (k-) X7 (A:)
(4b)
h h (k)) min (0, di + 1))²
(4c)
where & is the set of signed distances, μ is set of friction coefficients, = [Jn; Jt] is the normal and tangential contact Jacobians, and x = [g: v] the state of system configuration and velocity. Thus, with relative weighting between the terms, h becomes
1 (kk)
Σ
Σ
w. (k).
(5)
1= jE (comp.dixs.pen)

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With the contact dynamics described by h in (5) and the constraint in (3), the function g is a dis- cretized version of Newton's third law to update system velocities, and an implicit Fuler step to update the configuration. This g is a function of the implicit variable X, and can be written as
(A + 1) = =(k) + Acontimoous At - M J"
(6a)
< + 1) = ((k) L'vk + 1)
(6b)
where Occotimuuus is the acceleration of the system due to continuous dynamics, and maps velocity- space to configuration-spaee (e.g. mapping angular velocity to the time-derivative an orientation quaternion). See Appendix A.I for the selection of the introduced hyperparameter weights in h?.
3.2 Learnable Parameters
With the above model structure, the learnable parameters include the following. Geometry deter- mines J and Φ, both functions of the system configuration, i.e. [((k)), ((((k)). We parameterize and & by a set of vertices whose 3D locations are learnable. Friction, via μ4, determines the permissible set of contact impulses per contact point. In this work, the friction is parameterized by single scalar p.. Inertia affects the model's forward predictions in (6), where M and Ocontinoous appear. With articulation, M is function of the system configuration, i.e. (g(k)), and Ocontimous of the full state, ( (z)). We map learnable parameters in IR to a physically feasible set of 10 inertia parameters, per Rucker and Wensing [8]. Under autonomous dynamics, the mass of system is unobservable if contact forces are not measured [6]. Thus, we keep the total system mass fixed, then learn the remaining moments and products proportionally as well as the center of mass.
3.3 Residual Network
residual physics DNN compensate for inaccuracies in the model structure in (2). Since rigid body contact solvers like [28] work reasonably well to capture real inelastic contact dynamics [31], we encourage the residual to fill gaps in the continuous dynamics. We add components to the continuous acceleration the system,
In this work,
Açontinuous (I(k:) Acontinuous, model (I(k)) + 8 (x(+:)
(7)
where 5 E Rhd is the output of residual network whose input is the state of the system. See Appendix A.2 for network architecture details.
Adding costs on the norm of the network's output and on its weights encourages the residual to be small and smooth, respectively, as continuous dynamics are in comparison to contact dynamics. For end-to-end alternatives which aim to capture both continuous and contact dynamics in one network, weight regularization is no longer beneficial since it leads to unrealistically soft contact dynamics. To capture the stiffness of contact, the result is an end-to-end network with extreme input sensitivity. In contrast, incorporating our residual into the continuous acceleration allows the inherent stiffness of contact to be implicitly learned via geometric and frictional properties, leaving the residual in a smooth domain better suited for standard DNN approaches [4].
Loss Formulation
Our specific model structure alone does not affect the generalization capabilities of a model. and the choice of loss function is also of vital importance for stiff function classes [9]. Fig. 2 diagrammat- ically illustrates the differences between the losses presented in this section and how they relate to explicit versus implicit model usage for simulation.
4.1 Prediction Loss
Standard approaches in model-buulding system identification [32, 17, 23] use prediction-based loss that penalizes the error in candidate model's predictions.
pprddiction = || + 1) fd (x(()), (x<()),
(8)

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state, controls
controls
physical parameters
Learning
Contact
Learning
solver
next
Explicit Predictions
implich Dynamics Predictions
start,
stale,
physical parameters
physical
Learning
backprop
Contact solver
Learning
Optimiztlann
Learning
next state
predicted
predicted
backprop
best exp laiiiing contect forces
backprap
loso prediction error
loss prediction enrrr
true next
true next state
Realuum Measures
viclation
state
realistic contact dynamtcs
End-to-end Learning
Learning via Differentialee Simulation
Learning via Violation Implicit Loss (Ours)
Using an explicit model (left) versus an implicit model (right) for performing dynamics predictions. Explicit models aim to predict next states directly from current states and inputs. Implicit models instead parameterize and leverage contact solvers, which produce next states result of optimization problem. Bottom row: common way train explicit model via prediction-baset loss (left). Implicit models can also trained through the contact solver. Our approach trains an implicit model with a violation- loss (right), avoiding simulation during training time and producing smoother, more informative gradients.
Figure 2: Top row:
a prediction- -ased loss (middle), requiring performing and differentiating
Differentiable simulators typically employ the implicit optimization problem as in (2) solve for contact impulses, so the loss becomes (equivalently)
Eprediction ||a((k 1) (x(k,, (()) such that ((k) = arg min h (a:(k), u (k), =( 1), A).
(9a)
(9b)
Both explicit approaches (8) and implicit approaches (9) functionally result in simulating a candidate model and penalizing the difference between its prediction and the true dynamics observation.
4.2 Violation-Barn Based Implicit Loss
Despite the increasing prevalence of implicit approaches, prediction-bann based losses inhibit the gener- alization benefits implicit models [9]. A violation- based implicit loss of the form
|| [A + 1) 9d (o(k), uk:), 1)]l + h (x:(k, u (k), (t + 1).1)]. (10)
Lviolation = min xEA
uses h soft constraint and, result, boasts greater data efficiency [9]. This loss itself is an optimization problem that solves for the set of contact impulses À that balances 1) explaining the observed motion and 2) matching the learned contact dynamics model. Thus minimizing this loss function through the training process is bilevel optimization problem. For full details, see [9, 7J. This loss performs inference over contact mode, a key enabling technique for contact-implicit planning and control [1, 33].
The exact form of the prediction error term |a(k + 1) 9 (a<k)), ukk) a)]l employed herein pe- nalizes errors in velocity space, since configurations are an affine function velocity predictions (6b). natural way to combine mixed linear and angular terms is to convert all into energy units via
.pred. energy (k) (.MAA(())))) J X|I
(11)
where An(k) cok + 1) + v(k) Geontinurus Al.
(12)
Experimental Setup
For all experiments, we consider system autonomously falling under gravity and colliding with flat plane. In addition the cube toss dataset contributed by Pfrommer al. [7], we contribute one freedom new real dataset and two simulated scenarios. We used Franka Emika Panda 7 degree-of-frreedm
robotic arm to automate the toss data collection of two-link articulated object. Pose information
5

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Figure 3: Our experimental systems. Left: real two-link articulated object, each link as Sem by 5em by 10cm. Left middle: real cube width 10cm, whose dataset was contributed by [7]. Right: simulated 6-vertex asymmetric object from two views. The volume of the asymmetric is similar to the volume of one of the articulated object links.
of each link tracked using TagSLAM [34]. These two body poses are combined into minimal coordinates via optimization problem that minimizes pose offset of both links. While keep the system mass fixed, our model can freely decide the mass distribution across the two links.
We add a vortex simulation of an asymmetric object example, simulating dynamics with a spatially-varying force field pulling towards and swirling around a fixed vertical line. The initial- ized model is unaware of this continuous dynamics augmentation. We test this scenario with an asymmetric object with 6 vertices. Lastly, include gravity simulation of the articulated object. This scenario features simulated dynamics of the articulated object from our new dataset with typical gravitational acceleration of 9.81 9.81m/s². We test at a fixed training set size of 256 tosses from poor initial guesses, at some fraction E [0, 2] of this simulated gravity. All simulation data was generated using Drake [35] and features a significant gap between the model's 's believed and the simulator's ' actual dynamics. See Fig. for visuals of these systems.
Parameter Initializations. All experiments parameter initialization using process described in Appendix A.4. Shaded regions in the results plots indicate 5%/95% normal t-score confidence intervals.
minimum of 9 times each with random
Comparisons and Evaluation Metrics. See Table for the five approaches we tested. An- itescu dynamics [36] were selected as a reasonable differentiable simulation baseline, as it forms the basis of many widely-used, modern simulators, notably including MuJoCo [30] and Drake [35]. We present prediction errors for all approaches and parameter errors for the structured approaches. Prediction errors the average norm error of all bodies' position orientation over the course of trajectory. Defining V as the set of points inside body's geometry and I = [m. Pay Py: Pæ, Izz; Lwy. Less Awy. Læz, Lys] as the set of body inertial parameters, parameter er- rors for quantifying the geometry, friction, and inertial properties for system with n bodies are
Vol ((Vi,actual Vileamned) U (eeeeaded Vi
Cvolume
Σ
(13a)
Vol (Vi.acuat)
1=1
Efriction
= [11....
Amn [M1.... f Jasuaalllll
(13b)
Cincrtia
[s II..... In]leamed - [s II,..., In) nemalll
(13c)
The vector is akin to a "characteristic length" that is effectively normalized by the inertia of the true object. See more details on the volume and inertia metrics in Appendices B.1 and B.2, respectively.
Name
Parameterization
Loss
Residual
CCN (ours)
Structured Structured
Violation implicit Violation implicit
CCN-R (ours)
DiffSim
Structured
Prediction error
DiffSim-R
Structured
Prediction error
End-to-end
DNN
Prediction error
N/A
Table 1: Tested approaches. CCN stands for our extension of Continuous dynamics learning plus the contact dynamics learning in ContactNets [7]. DiffSim is Differentiable Simulation using differentiable contact dy- namies defined in Anitescu [36]. The -R modifier indicates residual physies included. DiffSim ablates our violation implicit loss function, and the End-to-end baseline ablates the physical structure imposed by the rigid body model-based parameterization. See Appendix A.3 for End-to-end network details.

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Artinuiated Object with heal Data
Cube with Real Data
Asymmetric Vortex Sim
Articulated Oxject Gravity Sim
Trajectory rotetione (deg)
CCN-R (ours)
DiffSim
DiffSim--
End-to-End
Training tosses
Training tasses
Training tossas
Modaled Accaleration [ous"]
Figure 4: Results from the four experiments. Shaded regions indicate normal I-score 95% confidence inter- real articulated object featured rotations that were difficult for any of the methods to capture over long time horizon (middle), yet our CCN approaches outperforms DiftSim on geometry er- ror (bottom) and all alternatives on positional eтror (top). Left middle column: For every metric on the real cube experiments, CCN approaches outperform DiffSim and End-to-end. Right middle column: While every method achieved low geometry error the asymmetric object in simulated vortex dynamics, approaches performed the best rotational error, and only our approach with residual (CCN-R) was able to achieve low positional error. Right column: The x-axis for the gravity experiments swept over an initial mod- eled gravitational acceleration. Despite poor model discrepancy. only our approach with residual CCN-R is able maintain good performance across all metrics different model discrepancies.
vals. Left column:
CCN
Articulated On Gravity
Gravity
(ours)
CCN-R (ours)
DiffSim
mntta paramatte WTTCF
Friction GrTer
DiffSim-R
End-to-EEnd
Training
Modeled Gravity Acceleration [mssP]
un
Training
Modeled Gravity [mns?]
un
Figure 5: Friction (Left, Left middle) and inertia (Right middle, Right) parameter errors for the vortex and gravity simulated experiments.
Results
We test the methods across challenging datasets featuring collisions through contact-rich trajecto- ries. While the contact dynamics are prominent all the example trajectories, we built the artic- ulated system in particular for its continuous dynamics: non-trivial due to state-dependent Coriolis and centrifugal effects and unmodeled joint friction, damping, backlash.

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Observations. Both real experiments (articulated object and cube in left and left middle columns in Fig. 4, respectively) show separation between CCN, Dif and End-to-end methods, with CCN matching or outperforming alternatives along all metrics, especially with more data. On the cube dataset, CCN and CCN-R consistently converge to <10% volume error while DiftSim struggles to improve even with more data. The residual does not significantly help with real data but does in simulated examples, where CCN-R in the vortex scenario (right middle column in Fig. 4) improves its positional trajectory enror significantly, achieving consistently 5x better performance than other methods at the largest dataset size. On the same metric, DiffSim-R sees no improvement beyond DiftSim. Fig. 5 shows CCN and CCN-R nearly always outperforms DiftSim and DiffSim-R, ex- cept for the vortex scenario where all methods perform well. In the gravity scenario (right column in Fig. 4), the residual helps CCN-R maintain good performance achieved at the correct gravita- tional accelcration, across all initial models. In contrast, DiffSim-R outperforms DiffSim at every initial gravitational acceleration model. Since this gravity scenario swept over different modeled gravitational accelerations, End-to-end is unaffected since its representation is unstructured, and its consistent performance over the x-axis of these plots are included for reference against CCN and DiftSim. Parameter errors in Fig. 5 indicate DiftSim and DiftSim-R struggled to capture both the friction and inertial terms in the gravity scenario to levels attained by CCN and CCN-R.
Implications. The residual's lack of effect on real data in alignment with prior works that found the rigid body model already performs well contact-rich scenarios with simple systems [31]. The residual shows the most merit in the more extreme simulation examples, though its effect isn't realized until larger dataset sizes unsurprising for DNN. The residual helps DiffSim to much lesser extent because our method better separates continuous and contact dynamics and allows the residual to identify the smooth nature of the unmodeled vortex dynamics. Relatedly, there is better performance for DiffSim and DiffSim-R at overestimated gravitational accelerations rather than underestimated, where contact less often predicted. Without contact, prediction losses experience a lack of informative parameter gradients, in which case DiffSim-R outperforms DiffSim.
Conclusion
We demonstrate with real experiments that our violation implicit loss trains models that outperform prediction loss-based structured and unstructured models. Our approach leverages the structure of contact versus continuous dynamics to learn both simultancously, with physically meaningful parameters driving separate contact and continuous dynamics with DNN residual to augment.
8 Limitations and Future Work.
The articulated object is the most challenging system presented herein for dynamics learning. While our methods outperformed alternatives in all other metrics, there is still a significant gap between ground truth and our models' trajectory predictions, and the rotational error showed lackluster per- formance from all methods. Further closing this gap remains for future exploration, and we are open-soureing our articulated object dataset for the community contribute their own methods. The scalability of the method in this paper has not yet been demonstrated on large-scale systems (e.g. robotic arm) in multi-object settings. It remains be seen whether the advantages demonstrated here will extend scope increases. While we tested one version of differentiable simulation using Anitescu [36] dynamics, future studies will compare alternatives against each other and our viola- tion implicit loss performing system identification. Our approach encouraged the residual to fill gaps in continuous dynamics while relying on a rigid body contact dynamics model to handle con- tact. Other works have demonstrated improved prediction capability by learning the contact model [37], though integrating this with system identification remains future work. While other works have learned articulated structures from scratch [38, 39, 40], we assumed access to kinematic structure in this paper, leaving joint kinematics/dynamie learning for future studies. Lastly, we relied on AprilTags to estimate poses, which are more challenging to obtain via perception [41, 42, 43].
8

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Acknowledgments
We thank our anonymous reviewers, who provided thorough and fair feedback. This work was supported by a National Defense Science and Engineering Graduate Fellowship, NSF Graduate Research Fellowship under Grant No. DGE-1845298, and an NSF CAREER Award under Grant No. FRR-2238480.
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[24] Abbeel, M. Quigley, and A. Y. Ng. Using inaccurate models reinforcement learning. In Proceedings of the 23rd international conference on Machine learning, pages 1-8, 2006.
[25] A. Ajay, Wu, N. Fazeli, M. Bauza, P. Kaelbling, J. B. Tenenbaum, and A. Rodriguez. Augmenting physical simulators with stochastic neural networks: Case study planar pushing and bouncing. In 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 3066-3073. IEEE, 2018.
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[27] M. Anitescu and A. Potra. Formulating dynamic multi-rigid-body contact problems with friction as solvable linear complementarity problems. Nonlinear Dynamics, 14(3):2312247, 1997.
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[37] K. R. Allen, L. Guevara, Y. Rubanova, Stachenfeld, Sanchez-Gonzalez, P. Battaglia, and T. Pfaff. Graph network simulators can learn discontinuous, rigid contact dynamics. In Conference Robot Learning, pages 1157-1167. PMLR, 2023.
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A Learning Details
Hyperparameter
CCN, real
CCN, sim
DifTSsm, real
DiftSim, sim
Wcomp
0.001
0.001
N/A
N/A
0.1
0.1
N/A
N/A
pen
100
100
N/A
N/A
res
1
0.001
1000
Wres,
0.1
Table 2: Tuned hyperparameters. Rows for residual norm (Wes) and weight (Wess, regularization only apply for variations. Real versus simulated experiments performed best with different residual regularization weights since the simulations featured larger model-to-actual dynamics gaps.
A.1
Model-Based Parameter Learning
For our CCN and CCN-R method, we performed a hyperparameter search to determine the most effective set of weights for balancing the loss terms in (5). See Table for these sets of weights.
A.2 Residual Network Architecture and Regularization
The residual network featured in both CCN-R and DiftSim-R has the same architecture. The first layer takes in the full state of the system and converts the quaternion orientation representation into a 9-vector the elements of the corresponding rotation matrix, letting the remaining state positions and velocities pass through to layer Beyond the first layer, the network a fully- cully-connected multi- layer perceptron (MLP) with two hidden layers of size 128. The last layer outputs values in the acceleration space of the system. All activations are ReLU.
We regularized the residual via both output norm regularization and weight regularization, with as- sociated weight hyperparameters Wres and Wres, w. respectively. See Table 2 for the optimal values. Since the simulation examples were specifically designed to test the capabilities the residual net- work, we found the optimal weights the residual terms were much lower for simulated examples than for the real data. We also note that the optimal residual weights were much higher for DiffSim than for CCN. This is direct result from the DiffSim residual's attempts to explain some of the contact dynamics, whose accelerations are orders of magnitude larger than the continuous accelera- tions. Our CCN method avoids this by better containing its residual in the continuous domain, and thus could use lower residual regularization weights.
A.3 End-to-End Network Architecture
The best performing network for the End-to-end baseline an MLP with hidden layers each of size 256 with Tanh activation. Its input the full state of the system, and its output the next velocity. The next configuration is obtained from predicted next velocity with Euler step (6b).
A.4 Parameter Initializations
All learned parameters are randomly initialized within pre-specified ranges. Geometric parameters are initialized between 0.5 and 1.5 times their true lengths, and friction coefficients between 0.5 and 1.5 times their approximate true values. Inertial parameters are initialized to set of physically feasible values via the following procedure for each link in the body:
1. A virtual link is sized via random set of three length scales I,, 1y,, 12. chosen between 0.5 and 1.5 times the link's true dimensions.
2. The center of mass of the link is initialized to be somewhere within the inner half of this virtual link's s geometry.
3. A random mass mand is selected from the range between 0.5m and 1 1.5m
12

---

4. Principal axis moments of inertia are computed using the assumption of uniform density throughout the randomly-sized virtual link, via e.g. for Tx=
Lyw principal axis
Myand
(9) (2).
(14)
12
5. Rotate the inertia matrix from its principal axis definition by random rotation in SO(3). The link's initialized moments and products of inertia are derived from this rotated version.
B Evaluation Metric Details
B.1 Volume Evaluation Metric
The volume error metric defined in Equation (13a) is computed as the fraction of volume that the learned geometry incorrectly included or incorrectly excluded. To compute this, we used the identity
(ol(A B) = Vol(A) N
(15)
The numerator of (13a) can therefore be computed as
Vol(Va.acuaa) + Vol(Ve,eemmed) 2Vol(V O Vi.lcumed)
(16)
Veaamed Vatuull and their intersection are all convex hulls of finite number of vertices. Therefore, the interaction operation as well as volume calculation can be conducted with standard convex hull or halfspace intersection library, such as qhull.
B.2 Inertia Evaluation Metric
A body's set of inertial parameters is I [m, Pz. Pys Psy Luz; Lzy Since in- ertia parameter vectors feature values wildly different scales, the vector is selected normalize I to more equally evaluate all inertial parameter errors. For example, the true inertial parameters for the simulated asymmetric object used in the vortex example are
Tusmm 00.55, 0, O, O, 0.00081, 0.00081, 0.00081, 0, 0, 0].
(17)
Choosing 3.5cm reasonable center of mass location distance, the associated Sayy normalizer is
1
Snsym
0.25 0.035
0.035'
0.035
0.00081 0.00081
0.00081
0.00081
0.00081
0.00081
(18)
13


Reviews:
[{"review_id": "u32vX3kOyd", "reviewer": "Reviewer_TJk2", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "The paper proposes an extension to \"ContactNets\" proposed in [1]. \n\nContactNets assume that the smooth \"non-contact\" impulses and the system's inertia matrix governing the system's dynamics are known. [1] proposed that one can directly learn the parameters of the signed distance function and its partial derivative using a \"violation-based loss function\". In this loss an implicit function is included explicitly imposing structure onto the contact forces. As pointed out in [2], such a loss compares favorable to the loss of a \"naive implicit model\".\n\nThe authors contributions are:\n\n1) While ContactNets assume that the \"non-contact\" dynamics are known, the authors learn these dynamics using residual physics. That is, the \"non-contact\" dynamics are modeled analytically where in particular the learnable parameters of the inertia matrix are constrained as done in [3] and the analytical model's residuals are learned with an MLP.\n2) A data set of a two-link articulated object is provided.", "summary_of_recommendation": "While the paper has some notable strengths, I lean toward a marginal accept. The research topic is relevant and the methodology is generally sound, although the experimental result section requires further refinement. The findings offer modest contributions to the field but may lack strong impact considering the already extensive literature on learning \"non-contact\" dynamics with residual physics. The writing is clear, but the writing style uses at times ambiguous wording and is not on point. The weakest point of this paper are the chosen model baselines which have been insufficiently been discussed and do not form the state-of-the-art. Overall, this submission has potential and warrants further discussion, but would clearly benefit from a minor revision to strengthen its impact.", "technical_quality": "Good: Generally convincing, but some additional experiments or analyses needed.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Limitations are addressed clearly", "questions_for_rebuttal": "The following issues need to be addressed:\n\n1) Add a short paragraph detailing more critically the limitations of this work.\n2) Polish / Replace Figure 2.\n3) Add more convincing model baselines, e.g. ResNet and RNN with additional sign activation function.\n4) Add a sentence to the related work mentioning the workshop paper \"Simultaneously Learning Contact and Continuous Dynamics\".\n5) In the related work section detail more explicitly how the proposed work relates to the mentioned prior work.\n\n", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper proposes an interesting extension to ContactNets. The work appears to be novel and is clearly relevant to the field.\nBelow I list of major comments and minor comments to the proposed work.\n\nC1: Quite simple dynamical systems and limited experiment scope.\nThe chosen dynamical systems in the absence of contacts are really simple. The first system are two rigid-bodies that are connected by a revolute joint and the second system is a single rigid body that is pulled by a force field. In the absence of contacts it would be trivial to learn these dynamics with a purely data-driven or physics-informed model. As the violation-based loss as in [1] and [2] handles the discontiniuous nature of contacts, it is not really surprising that learning some residuals of very simple dynamics is possible. Moreover, most of the proposed paper focuses on the questions \"Does it work?\". However, it would be more insightful to look at when such a residual physics approach does not work. For example... How large can the error in the inertia parameters or initial signed distance functions be until the parameters do not converge? Can CCN-R learn the dynamics of a soft contact surface? What are the limitations of this approach?\n\nC2: Model baselines\nIt is not stated why DiffSim has been chosen as a baseline of comparison. I would be interested to know the reasons for choosing DiffSim being an approach from 2006 while a lot has happened in contact dynamics identification in the last 17 years. Moreover, that the end-to-end model is chosen as a four layer MLP is a bit surprising. I found that ResNets and RNNs significantly outperform MLPs when learning dynamics. When benchmarking CCN to the state-of-the-art, the authors should consider adding a sign activation to the network's first layer to give it a realistic chance of learning discontinuous contact dynamics. After all, a network using smooth activation functions such as Tanh and Softplus might require substantial amounts of data to learn discontinuities.\n\nC3: Figure 2\nIt took me some time to decipher what the authors want to convey with Figure 2. I guess that the figure shall visualize the model structure proposed in [2] using a \"violation-based loss\" in comparison to an explicit model / \"naive implicit model\". However, the terms \"contact solver\", \"learning\", and \"optimization\" depending on the context may be used interchangeably while the term \"realism measure\" is not introduced in the text. In addition, even if the figure would be clear it only shows the model structure as proposed in [1] and discussed in detail in [2]. I would  prefer that the authors use the page space to illustrate their own contributions.\n\nC4: The published workshop paper \"Simultaneously Learning Contact and Continuous Dynamics\" \nhttps://neural-implicit-workshop.stanford.edu/assets/pdf/bianchini.pdf\nhas not been cited even though it contains the same figure. I kindly ask the authors to cite this work and emphasize in the related work section how the proposed work forms a significant extension to this prior publication.\n\nMC1: Writing style\n\nPaper structure:\n- The model baselines are introduced in the description of Table 1. I would prefer a brief paragraph detailing the models instead. \n\nVerbose writing:\n- Table 1: \"End-to-end baseline ABLATES the physical structure imposed by the rigid body model-based parameterization\" - While you indeed do an ablation study, I would simply say that you use an MLP for the end-to-end approach.\n- Why mention \"Newton’s third law\" in line 106? Instead you could just say that the function g is obtained by \"forward integration of the systems dynamics and adding the contact impulse transfer\". Ideally, after pointing to the \"system dynamics\" you also write the number of the equation that you are referring to.\n\nImprecise wording:\n- Page 6 - \"Featuring actual dynamics\" - what does \"actual\" mean in this context?\n- Line 162 to Line 164: \"... penalizes errors in velocity space, since configurations are an affine function of velocity predictions (6b).\" - The loss is on $x$ being the concatenation of position and velocity variables. So of course it penalizes velocity errors. How does this relate to (6b) describing position through a forward euler discretization aka \"affine function of velocity predictions\"?\n\nMC2: Some paragraphs of the related work section to not detail how the proposed work relates to the mentioned prior work. For example, it would help if the authors add a sentence on how previous developed mappings to the inertia parameters relate to the particular mapping used in this work.\n\nMC3: The title of citation number 7 in the proposed work includes an \"of\" that is not part of the paper's actual title.\n\nMC4: Some Figures depict confidence intervals, but I could not find a statement detailing the number of training runs and what exactly has been random in these runs.\n\nMC5: The code was not accessible during review time. I would have liked to check the code and data set. Especially, as the data set forms a contribution of this work.\n\nRemark 1: Equation 11 seems related to \"Gauss Principle of least constraint\". Gauss postulated that nature chooses the implicit constraint forces $Q=J^T \\lambda'$ such that a functional $G(q) = Q(q, \\dot q)^T M(q)^{-1}Q(q, \\dot q)$ is minimized. If one minimizes this functional by introducing a Lagrange multiplier vector (the implicit constraint forces aka contact normal force) then one arrives at the standard EOM of an implicitly-constrained system.\n\n[1] \"Contactnets: Learning discontinuous contact dynamics with smooth, implicit representations\", Pfrommer et al., CORL 2020\n[2] \"Generalization Bounded Implicit Learning of Nearly Discontinuous Functions\", Bianchini et al., L4DC 2022\n[3] \"Smooth parameterization of rigid-body inertia\", Rucker and Wensing, RA-L 2022", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed."}, "extra_text": {}}, {"review_id": "rdTBT-Bhe-i", "reviewer": "Reviewer_XnXf", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "The main idea and contributions of the paper are the following points: \n* The authors developed a system identification method using a violation-based implicit loss and residual physics to learn continuous and contact dynamics simultaneously.\n* The authors demonstrated that the proposed method could learn the continuous and contact dynamics more accurately than differentiable simulation and end-to-end learning methods.\n", "summary_of_recommendation": "The contribution of the paper is not sufficient: weakness in both quality and originality of the paper. The effectiveness of a part of the proposed method has not been adequately demonstrated.", "technical_quality": "Good: Generally convincing, but some additional experiments or analyses needed.", "clarity_of_presentation": "Very Good:  Well organized and clear.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Limitations are addressed clearly", "questions_for_rebuttal": "* I would like to know on what kind of data of a real experiment the residual physics will be effective.\n* Why was the differentiable simulation using Anitescu [34] chosen for comparison?\n* I would like to know why Equation (4b) represents energy dissipation.\n* I would like to know the specific calculation procedure for Equation (13a).\n", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Strengths:\n* The paper is well organized and seems to provide sufficient information to the reader. Therefore, the clarity of the paper is high.\n\nWeaknesses:\n* The experimental settings for the real experiments are not appropriate since the effectiveness of the residual physics cannot be not demonstrated. Moreover, it is unclear why the differentiable simulation using Anitescu [34] was chosen for comparison. Thus, the quality of the paper is not high.\n* Since the validity of the residual physics is not fully demonstrated, the paper seems to be a minor update of ContactNets [7]. Thus, the originality of the paper seems week.\n* Although the proposed method outperformed the differentiable simulation and end-to-end learning methods, from the accompanying media, there still seems to have a large prediction error. Therefore, it is difficult to assess the significance of the paper.\n", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed."}, "extra_text": {}}, {"review_id": "f57QufxhS1", "reviewer": "Reviewer_h2vE", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "This paper proposes a framework for simultaneously learning smooth motion and contacts. This is done by starting with an implicit method for resolving contacts by solving appropriate convex optimization problems, and parameterizing it using a dynamics model. Rather than differentiating through the contact events directly, the authors use a violation-based implicit loss to balance contact events with parameter learning through a bilevel optimization problem. The authors create and release a dataset of tosses of a two-link rigid object, and evaluate their ideas using this dataset.", "summary_of_recommendation": "My view is that this paper is borderline, and contains both good reasons to accept such as the dataset made available, and good reasons to reject such as confusing presentation. In general, I think this paper would be significantly improved if the authors edit it and submit a revised version to a future conference on basis of feedback obtained via reviewing. However, I am not very confident because it is not completely clear to me what is new and what is not, and I am very curious to see other reviewers' opinions, and could therefore probably be persuaded by other reviewers to change my mind if there are good reasons for this.", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Fair: Major revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Highly relevant to robotics but no hardware experiments", "quality_of_limitations": "Limitations are addressed clearly", "questions_for_rebuttal": "What precisely are the original ideas presented in this paper, as opposed to prior works?\n\nAt the end of the day, is it correct that you're just doing timestepping using symplectic Euler, but with this extra \\lambda-term added in to handle contacts, and using a convex optimization problem to find \\lambda?\n\nHow do you handle noise? Is this just kept small enough that it plays little role? If so, that's fine, but it should be stated much more bluntly upfront to make clear to readers. For example, how do you ensure the residual network does not learn discontinuous contact events?\n\nWhy does Pfrommer* et al. have a star?\n\nQuestions regarding vague text:\n* The intro paragraph positions the Pfrommer et al. paper as a predecessor of this work, but from the description of the sentence I have little to no idea of what that paper actually did. Could you please provide a more specific description?\n* What's an \"implicit approach\"? I figured this out by reading the paper further - you should make it clear upfront that this refers to optimization-problem-based simulation of contacts.\n* \"Stiffness\" is described as a problem, but it is not clear in what sense this is meant or why it is a problem.\n* Why do implicit models have generalization benefits? Why do prediction-based losses inhibit those? This is just stated as if it's truth - is there a concrete description of the evidence this rests on?\n* What is a normal t-score 95% confidence interval? I am very confused about what the authors might even mean by this, why are we even thinking about t-tests and confidence intervals in the context of a figure, rather than of a hypothesis test? What's wrong with simply presenting mean, and 5%/95% quantiles?\n\n\nTypos:\n* L53: \"with experimental setup in #5\" -> \"with the experimental setup in #5\"", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Strengths\n* **Important topic.** Figuring out how to simultaneously model systems with smooth behavior and contacts is a critically important direction for robotics, and I entirely agree with the authors desire to study this.\n* **Non-trivial problem.** Simultaneous modeling of smooth dynamics and contacts is known to be hard, so the authors approach - and indeed any approach which performs well even on simple problems - is very respectable.\n* **Two-link articulated object experiment** is particularly non-trivial compared to a pure rigid object compared to a plastic cube, because one needs to simultaneously understand how the object rotates and how it moves due to contacts.\n* **Dataset contribution.** The authors make available a dataset of simulated trajectories, which is very good because it allows others who may not have the same hardware access to also work on similar problems. From the pictures, I have reasonable confidence that the dataset collected is of reasonable quality and does not have so much noise, etc in, and is a good contribution.\n\nWeaknesses\n* **Misleading, overly general title.** Simultaneous learning of contact and continuous dynamics has already been studied in many prior works. This paper is proposing a very specific way to learn both components together. Even for a review paper, the present title would have been inappropriate without the addition of the word \"review\" \n* **In too many places, the writing is vague and not specific enough.** See \"questions regarding vagueness\" in the questions section.\n* **Not clear what is from prior work and what are the authors' original ideas**. Prediction-based losses are definitely not new, but the authors cite papers for their violation-based loss too. Is this new? If this is a paper that brings together a bunch of existing ideas to do a fancy experiment, that's totally fine, but it needs to be made clear that this is what is happening.\n* **No explicit consideration of noise - a key issue - in the formalism** in simultaneous modeling of smooth and contact dynamics. One of the key difficulties working in this area in my experience is that simultaneous noise and contacts introduce a fundamental ambiguity: one can explain discontinuous motion due to contacts, or due to noise, and in the absence of some kind of signal it need not be possible, even for a human, to distinguish one from the other. This is written about in some detail by Hochlehnert et al (2021), \"Learning Contact Dynamics using Physically Structured Neural Networks\".\n* **Blurry figures, hard to view.** Figures 1, 2, and others are not vector graphics and should be converted to those to ensure the text is large and sharp enough to be accessible.", "extra_scores": {"impact": "4: The work contains interesting new ideas that will potentially have major impact in robotics or machine learning."}, "extra_text": {}}, {"review_id": "QcBBatnPeA", "reviewer": "Reviewer_w1Bc", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "The authors introduce a method for learning the continuous dynamics of articulated rigid body dynamics in conjunction with the contact dynamics from real-world object motions. The system identification method extends the ContactNets method to introduce a violation-based loss function that constraints the violation of physical constraints and laws of motion for multi-body systems. In addition, this work introduces a new dataset of real-world tosses of an articulated object onto a table. In addition to the real-world cube tossing dataset and simulated scenarios, the proposed method is compared against explicit simulation-based and end-to-end dynamics learning approaches.", "summary_of_recommendation": "Although the technical contributions are quite incremental, the execution of the paper is well done with a detailed analysis of the proposed system ID method against common baselines. The release of the multi-body tossing dataset is a welcome addition to the field of learning continuous and contact dynamics, hence I recommend acceptance of this work.", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Very Good:  Well organized and clear.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Limitations are addressed clearly", "questions_for_rebuttal": "The simulated scenario of the articulated object in gravity sim appears to exhibit no contact dynamics - how can the differences in performance between the prediction loss and violation-based implicit loss be explained? Since there are no contact impulses to be resolved, the only differences must be in the violation terms from Eqs. (4)?\n\nGiven that the initialization of the dynamics parameters typically matters a lot in system identification, how far were the initial parameters from the true parameters? What method was used to optimize the proposed loss functions? Have multiple initial parameter settings been used to analyze the convergence and avoid getting stuck in poor local minima?", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "## Strengths\n\nThe approach to formulate the dynamics violation as a soft constraint inside the system identification loss is promising and the results clearly show the benefit of this technique.\n\nThe proposed violation-based loss can be easily adapted by other system identification works to improve upon the commonly used prediction loss.\n\nThe authors promise to release the dataset of tossing articulated objects which would be very valuable to this area of research.\n\n## Weaknesses\n\nThe technical contributions appear quite incremental where the ContactNets approach is extended via a new violation-based implicit loss function to learn continuous dynamics parameters for articulated rigid-body systems.\n\nThe system ID approach assumed that the articulation is known upfront, i.e. the joint connectivity and number of rigid bodies.", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed."}, "extra_text": {}}]

Author rebuttal:

Meta-review: All reviewers agreed that the paper containes a interesting contribution for a very challenging problem, learning contact and continuous dynamics. Moreover, the paper offers an interesting dataset that will be useful for the community. Initial  concerns regarding clarity of the paper and novelty have been addressed well by the authors. All reviewers vote for acceptance of the paper. I agree with this judgement.
Decision: Accept (Poster)