Distributional Depth-Based Estimation of Object Articulation Models
Anonymous Author(s)
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Abstract: We propose a method that efﬁciently learns distributions over articulation model parameters directly from depth images without the need to know articulation model categories a priori.
By contrast, existing methods that learn articulation models from raw observations typically only predict point estimates of themodel parameters, which are insufﬁcient to guarantee the safe manipulation of articulated objects.
Our core contributions include a novel representation for distributions over rigid body transformations and articulation model parameters basedon screw theory, von Mises-Fisher distributions, and Stiefel manifolds.
Combining these concepts allows for an efﬁcient, mathematically sound representation that implicitly satisﬁes the constraints that rigid body transformations and articu- lations must adhere to.
Leveraging this representation, we introduce a novel deeplearning based approach, DUST-net, that performs category-independent articulation model estimation while also providing model uncertainties.
We evaluate ourapproach on several benchmarking datasets and real-world objects and compareits performance with two current state-of-the-art methods.
Our results demonstrate that DUST-net can successfully learn distributions over articulation modelsfor novel objects across articulation model categories, which generate point estimates with better accuracy than state-of-the-art methods and effectively capturethe uncertainty over predicted model parameters due to noisy inputs.
Introduction
Articulated objects, such as drawers, staplers, refrigerators, and dishwashers, are ubiquitous in human environments.
These objects consist of multiple rigid bodies connected via mechanical jointssuch as hinge joints or slider joints.
Robots in human environments will need to interact with theseobjects often while assisting humans in performing day-to-day tasks.
To interact safely with suchobjects, a robot must reason about their articulation properties while manipulating them.
An idealmethod for learning such properties might estimate these parameters directly from raw observations,such as RGB-D images while requiring limited or no a priori information about the task.
The abilityto additionally provide a conﬁdence over the estimated properties, would allow such a method to beleveraged in the development of safe motion policies for articulated objects [1].
The majority of existing methods to learn articulation models for objects from visual data eitherneed ﬁducial markers to track motion between object parts [2–5] or require textured objects [6–10].
Recent deep-learning based methods address this by predicting articulation properties for objectsfrom raw observations, such as depth images [11–14] or PointCloud data [15, 16].
However, themajority of these methods [11, 12, 15, 16] require knowledge of the articulation model category forthe object (e.g., whether it has a revolute or prismatic joint) which may not be available in manyrealistic settings.
Alleviating this requirement, Jain et al.
[14] introduced ScrewNet, which uses auniﬁed representation based on screw transformations to represent different articulation types andperforms category-independent articulation model estimation directly from raw depth images.
However, ScrewNet [14] and related methods [11–13, 15, 16] only predict point estimates for an object’sarticulation model parameters.
Nonetheless, reasoning about the uncertainty in the estimated param- eters can provide signiﬁcant advantages for ensuring success in robot manipulation tasks, and allowsfor further advancements such as robust planning [1], active learning using human queries [17], andthe learning of behavior policies that provide safety assurances [18].
Motivated by these advantages,we propose a method for learning articulation models, which estimates the uncertainty over modelparameters using a novel distribution over the set of screw transformations based on the matrix von Mises-Fisher distribution over Stiefel manifolds [19].
We introduce DUST-net, D eep U ncertaintyestimation on S crew T ransforms- net work, a novel deep learning-based method that, in addition toproviding point estimates of the object’s articulation model parameters, leverages raw depth imagesto provide uncertainty estimates that can be used to guide the robot’s behavior without requiring toknowledge of the object’s articulation model category a priori.
DUST-net garners numerous beneﬁts over existing methods.
First, DUST-net estimates articulationproperties for objects with uncertainty estimates, unlike most current methods [11–16].
These uncertainty estimates, apart from helping robots to manipulate objects safely [1], could allow a robotto take information-gathering actions when it is not conﬁdent and enhance its chances of successin completing the task.
Second, similar to ScrewNet [14], DUST-net can estimate model parameters without the need to to know the articulation model category a priori, by leveraging the uniﬁedrepresentation for different articulation model types.
Third, this uniﬁed representation helps DUSTnet to be more computationally and data-efﬁcient than other state-of-the-art methods [11, 12], asit uses a single network to estimate model parameters for all common articulation models, unlikeother methods that require a separate network for each articulation model category [11, 12, 15, 16].
Empirically, DUST-net outperforms other methods even when trained using only half the trainingdata in comparison.
Fourth, the distributional learning setting yields more robustness to outliers andnoise.
Fifth, DUST-net is able to reliably estimate distributions over articulation model parametersfor objects in the robot’s camera frame.
By contrast, ScrewNet [14], the most closely related approach to ours, can only predict point estimates for articulation model parameters in the object’slocal frame.
We evaluate DUST-net through experiments on two benchmarking datasets: a simulated articulatedobjects dataset [11] and the PartNet-Mobility dataset [20–22], as well as three real-world objects: amicrowave, a drawer, and a toaster oven.
We compare DUST-net with two state-of-the-art methods,namely ScrewNet [14] and an MDN-based method proposed by Abbatematteo et al.
[11], as wellas two baseline methods.
The experiments demonstrate that the samples drawn from the distributions learned by DUST-net result in signiﬁcantly better estimates for articulation model parametersin comparison to the point estimates predicted by other methods.
Additionally, the experimentsshow that DUST-net can successfully and accurately capture the uncertainty over articulation modelparameters resulting from noisy inputs.
Related Work
Articulation model estimation from visual observations: A widely used approach for estimatingarticulation models is based on the probabilistic framework proposed by Sturm et al.
It usesthe time-series observations of 6D poses of different parts of an articulated object to learn the relationship between them [2, 5, 6, 10].
More recently, Abbatematteo et al.
[11] and Li et al.
[12]proposed methods to learn articulation properties for objects from raw depth images given articulation model category.
In a related body of work on object parts mobility estimation, Wang et al.[15] and Yan et al.
[16] proposed approaches to segment different parts of the object in an inputpoint cloud and estimate their mobility relationships, given a known articulation model category.
Alleviating the requirement of having a known articulation model category, Jain et al.
[14] recentlyproposed ScrewNet that performs category-independent articulation model estimation from depthimages.
However, these methods only predict point estimates for the articulation model parameters,while DUST-net predicts a distribution over their values.
Rigid Body Pose Estimation : Our contributions are related to existing work on estimating distributions describing the orientation of rigid bodies.
Gilitschenski et al.
[23], Arun Srivatsan et al.
Srivatsan et al.
[25] and Rosen et al.
[26] propose strategies that can be used to estimate the rigidbody transformation of an object using a combination of Bingham and Gaussian distributions, andthe von Mises-Fisher distribution, respectively.
The mathematical model used by our approach isinspired by these works, but 1) extends them to also represent uncertainty over the conﬁguration ofarticulated object components about screw axes, and 2) integrates them into a deep learning modelthat is capable of learning these conﬁgurations from raw depth images.
In addition, while theseapproaches use distributions over orientations and rigid body transformations to produce estimates,
DUST-net directly outputs a distribution that can be used to facilitate further applications such asuncertainty-aware behavior planning.
Interactive perception (IP) : Katz and Brock [3] introduced IP as a method to leverage a robot’sinteraction with objects to generate a rich perceptual signal for articulation model estimation forplanar objects, and extended it to learn 3D articulation models for objects [4].
Mart´ın-Mart´ın et al.[8] used hierarchical recursive Bayesian ﬁlters to make estimation more robust and developed onlinemethods for articulation model estimation from RGB images [7–9].
A comprehensive survey on
IP methods in robotics was presented by Bohg et al.
While IP presents a powerful tool forestimating articulation properties for objects, a wide majority of existing IP methods require texturedobjects, unlike DUST-net, which learns these properties using depth images.
Further approaches : Articulation motion models can be viewed as geometric constraints imposedon multiple rigid bodies.
Such constraints can be learned from human demonstrations by leveragingdifferent sensing modalities [13, 28–31].
Recently, Daniele et al.
[30] proposed a multimodal learning framework that incorporates both vision and natural language information for articulation modelestimation.
However, these approaches predict point estimates for the articulation model parameters,unlike DUST-net, which predicts a distribution over the articulation model parameters.
Problem Formulation
Given a sequence of n depth images I 1: n of motion between two parts of an articulated object, weestimate the parameters of a probability distribution p (  |I 1: n ) representing uncertainty over the parameters  of the articulation model M governing the motion between the two parts.
Following Jain et al.
[14], we deﬁne the model parameters  as the parameters of the screw axis of motion, S =
( l , m ) , where both l and m are elements of R 3 .
This uniﬁed parameterization can be used in articulation models with at most one degree-of-freedom (DoF), namely rigid, revolute, prismatic, andhelical [14].
Additionally, we estimate the parameters of a distribution p ( q 1: n  1 |I 1: n ) representing 122 uncertainty over the conﬁgurations q 1: n  1 identifying the rigid body transformations between the 123 two parts in the given sequence of images I 1: n under model M with parameters  .
Conﬁgurations 124 q i , i 2 { 1 ...n  1 } correspond to a set of tuples, q i =
( ✓ i , d i ) , deﬁning a rotation around and adisplacement along the screw axis S 1 .
We assume that the relative motion between the two objectparts is determined by a single articulation model.
[-F ( X | m, F ) = 
-]
[-It can be shown that 0 F 1 ( m 2 , 14 F T F ) = 
-]
Approach
Given a sequence of depth images I 1: n of motion between two parts of an articulated object, DUSTnet estimates parameters of the joint probability distribution p (  , q 1: n  1 |I 1: n ) representing uncer- 130 tainty over the articulation model parameters  governing the motion between the two parts andthe observed conﬁgurations q 1: n  1 .
When deciding how to learn this distribution, two goals arise.
While some parameters, such as the translation of an object part along a screw axis, are deﬁnedon Euclidean space, the set of valid screw axes exhibits constraints that prevent standard distributions deﬁned on R 6 from being applied without complicating the learning process.
For example, astandard representation for distributions over screw axes can be the product of a Bingham distribution over the line’s orientation and a multivariate normal distribution over its position in space [32].
However, this representation produces non-unique estimation targets.
A rotation of ✓ about thescrew axis with orientation l results in the same transformation as a rotation of  ✓ about the screwaxis with orientation  l .
Similarly, a displacement d along l results in the same transformation asa displacement  d along  l .
This leads to ambiguities in the targets in the estimation problem andcan hinder the performance of the trained estimator.
By selecting a representation that accounts forthese symmetries, these non-unique estimation targets are removed.
Second, once a suitable parameterization is chosen, we seek a parametric form for the joint distribution which can be learned by adeep network.
First, we consider the problem of parameterizing the set of screw axes.
As noted earlier, we deﬁnethe model parameter  as the parameters of the screw axis of motion S =
( l , m ) .
However, thisparameterization requires that l has unit norm, and that l and m are orthogonal.
To eliminate theseconstraints, we rewrite the moment vector of a screw axis as m = k m k ˆ m , where k m k and ˆ m represent its magnitude and a unit vector along it respectively, and the Pl¨ucker coordinates for the screwaxis as S
= ( l , ˆ m , k m k ) .
The Pl¨ucker coordinates can then be seen as an unconstrained point in thespace S :
= V 2 , 3 ⇥ R + , where ( l , ˆ m ) 2 V 2 , 3 with V 2 , 3 denoting the Stiefel manifold of 2-frames in
R 3 and k m k 2 R + with R + denoting the set of positive real numbers.
The Stiefel manifold V k,mis the space whose points are sets of k orthonormal vectors in R m , called k -frames in R m ( k  m ) 1[19].
Consequently, because of the one-to-one mapping from elements of V 2 , 3 ⇥ R + to screw axes,the non-unique estimation targets described above are eliminated.
Based on this parametrization ofscrew axes, we deﬁne the set of valid conﬁguration parameters as follows.
We restrict the range ofvalues for the rotation about the screw axis to be ✓ 2 [0 , 2 ⇡ ) and restrict the displacement alongthe axis to be d 2 R + .
Note that these constraints do not reduce the representational power of thescrew transform ( l , m , ✓ , d ) to denote a general rigid body transform, but merely ensure a uniquerepresentation.
Having described the parameterization of the set of screw axes and conﬁgurations, we now considerthe task of deﬁning a joint probability distribution over their values.
We propose to represent thedistribution over predicted screw axis parameters, p ( S | I 1: n ) with S 2 S , as a product of a matrix 164 von Mises-Fisher distribution F ( ·| 3 , F ) deﬁned on the Stiefel manifold V 2 , 3 1 and a truncated normal 165 distribution N + ( ·| µ,  ) with truncation interval [0 , + 1 ) over R + .
Formally,
[Equation]
where F is a 3 ⇥ 2 matrix representing the parameters of the matrix von Mises-Fisher distribution over
V 2 , 3 , and µ m and  m denote the mean and standard deviation of the truncated normal distribution.
Given the sequence of n images, we also wish to estimate the posterior over conﬁgurations q 1: n  1 ={ ✓ 1: n  1 , d 1: n  1 } corresponding to the rotations about and displacements along the screw axis S .
We 170 deﬁne the joint posterior representing the uncertainty over the screw axis S and the conﬁgurations{ ✓ 1: n  1 , d 1: n  1 } about it as a product of the aforementioned distribution and a set of distributions 172 deﬁned over the conﬁguration parameters,
[Equation]
where  = { F , µ m ,  2 m , ,  } is the set of parameters for the distribution and and ⌥ represent theset of distributions having parameters and  over the conﬁgurations ✓ 1: n  1 and d 1: n  1 , respec- 175 tively.
For the sake of brevity, we present further details on modeling assumptions in the supplementary material (see Appendix B).
In this work, we consider and ⌥ to be products of truncatednormal distributions such that
[Equation]
with
M ✓ = { µ 1 ✓ , ..., µ n  1 ✓ } , M d = { µ 1 d , ..., µ n  1 d } ,  ✓ , and  d denoting the set of means and the standarddeviations of the set of truncated normal distributions over the conﬁgurations ✓ 1: n  1 and d 1: n  1 , 180 respectively.
Distribution parameter matrix F: The parameter matrix for the matrix von Mises-Fisher distribution over V 3 , 2 is a 3 ⇥ 2 matrix, F .
This presents two possible parameterizations of the matrix: ﬁrst,to estimate each of the 6 elements of the 3 ⇥ 2 matrix F and second, to estimate the matrices  , ⇤ ,and ⌦ deﬁning the SVD of F , given by F = ⇤⌦ T .
The second parameterization decouples thetwo objectives of distribution mode alignment with the ground truth labels and uncertainty representation; the mode of the distribution is given by M = ⌦ T , and the concentration matrix for thedistribution is given by K = ⌦⇤⌦ T .
This decoupling allows the network to independently optimizeboth objectives, whereas in the ﬁrst parameterization, changes in the elements of F causes changesin both components.
By deﬁnition, ⇤ is a 2 ⇥ 2 diagonal matrix with two independent parameters, and ⌦ 2 O (2) is arotation matrix in two dimensions with one independent parameter, the rotation angle ! .
The matrix 2 ˜V 3 , 2 can be constructed from a rotation matrix R 2 O (3) by keeping only the ﬁrst two columnsof R. Hence, the matrix  can be deﬁned by three independent Euler angles, ( ↵ ,  ,  ) denotingrotation according to the ZY X convention in the rotating frame.
Euler angles can suffer from theproblem of gimble lock [32], which we resolve by restricting the Euler angles to be in the ranges↵ 2 [0 , 2 ⇡ ) ,  2 [0 , ⇡ ) , and  2 [0 , 2 ⇡ ) .
Normalization factor: One of the main challenges of using the matrix von Mises-Fisher distributionis the calculation of its normalization factor 0 F 1 ( m 2 , 14 ⇤ 2 ) , which is a hypergeometric function ofmatrix argument [19].
In this work, we approximate this hypergeometric function using a truncatedseries in terms of zonal polynomials, which are multivariate symmetric homogeneous polynomialsand form a basis of the space of symmetric polynomials [19].
Through our preliminary experiments,we found that this truncated series is a good approximation of 0 F 1 as it converges to a ﬁnite value,if the singular values of the F , i.e.  1 and  2 are less than  max = 50 .
Architecture: DUST-net sequentially connects a ResNet-18 CNN [33] and a 2-layer MLP.
ResNet18 extracts task-relevant features from the input images, which are used by the MLP to predict aset of parameters  for the distribution p ( S , ✓ 1: n  1 , d 1: n  1 | I 1: n ,  ) .
The network is trained end- 207 to-end, with ReLU activations for the hidden fully-connected layers.
The ﬁrst four output (out of40) of the last linear layer of MLP, corresponding to the parameters ( ↵ ,  ,  ) and ! representing thematrices  and ⌦ respectively, are fed through a ReLU-6 layer to ensure that the predictions map totheir respective ranges.
Remaining output is fed through a Softplus layer for non-negative output.
Detailed network architecture is presented in the appendix (Fig. 7).
Training:
The training data for the model consists of sequences of depth images of objects parts moving relative to each other and the corresponding screw transforms y =( l, ˆ m , k m k , ✓ 1: n  1 , d 1: n  1 ) .
The objects and depth images are rendered in Mujoco [34].
We train 215 DUST-net by maximizing the log-probability of the labels y under the distribution p ( y | I 1: n ,  ) :
L ( y ,  ) =
log p ( y |  ) .
We assume that the observed conﬁgurations in I 1: n share the same vari- 217 ance.
We use the precision parameters rather than the standard deviations,  m ,  ✓ and  d to representthe distribution during training for better numerical stability.
Following the discussion on training
MDNs by Makansi et al.
[35], we separate the training in three stages.
In the ﬁrst stage, we assumethe dispersion of the matrix von Mises-Fisher distribution to be ﬁxed with ⇤ = diag(  0 ,  0 ) ,  0 =
1and learn parameters corresponding to  and ⌦ matrices.
In the second stage, we ﬁx the ⇤ matrixand learn the rest of the parameters in the set  .
Finally, we train to predict the complete set  .
Experiments
In this section, we evaluate DUST-net on its ability to learn articulation model parameters and uncertainty estimates.
We conducted three sets of experiments evaluating DUST-net’s performanceunder different criteria: (1) how accurate point estimates of the articulation model parameters drawnfrom DUST-net’s estimated distribution are in comparison to the existing methods, (2) how effectively DUST-net captures the uncertainty over parameters arising from noisy input, and (3) howeffectively DUST-net transfers from simulation to a real-world setting.
We evaluated DUST-net’sperformance on two simulated benchmarking datasets: the objects dataset provided by Abbatematteo et al.
[11], and the PartNet-Mobility dataset [20–22], as well as a set of three real-world objects.
From the simulated articulated object dataset [11], we considered the cabinet, microwave,and toaster oven for revolute articulations and the drawer object class for prismatic articulations.
From the PartNet-Mobility dataset [20–22], we considered ﬁve object classes: the dishwasher, oven,and microwave object classes for the revolute articulation model category, and the storage furnitureobject class consisting of either a single column of drawers or multiple columns of drawers, for theprismatic articulation model category.
Among the three sets of experiments, we conducted the ﬁrsttwo sets of experiments on the simulated datasets, while the last set of experiments were conductedon the real-world object dataset.
In all the experiments, we assumed that the input depth images aresemantically segmented and contain non-zero pixels corresponding only to the two objects betweenwhich we wish to estimate the articulation model.
We compared DUST-net’s performance in estimating point estimates for articulation model parameters with two state-of-the-art methods, ScrewNet [14] and an MDN-based approach proposed by Abbatematteo et al.
ScrewNet estimates the object’s articulation model parameters in a local framelocated at the center of the object, whereas DUST-net does so directly in the camera frame.
We compare our method with ScrewNet predicting parameters both in the object local frame and the cameraframe.
Additionally, we propose two baseline methods that estimate distributions over articulationmodel parameters and compare to them DUST-net.
The ﬁrst baseline method (vm-SoftOrtho) canbe viewed as an extension of ScrewNet to a distributional setting.
It represents the uncertainty overthe screw axis orientation vector l and the direction of moment vector ˆ m using two independent von
Mises-Fisher distributions and imposes a soft orthogonality constraint over the modes of the two distributions.
The distributions over the moment vector magnitude k m k and conﬁgurations q 1: n  1 are 253 considered to be normal distributions.
This method suffers from the same drawback as ScrewNet,i.e., the use of a soft orthogonality constraint during training, and therefore cannot predict a validset of screw axis parameters directly, unlike DUST-net.
The second baseline method (Direct F )uses the same probability distribution as DUST-net to represent the uncertainty over the articulationmodel parameters, but estimates the individual elements of the F matrix directly.
As a result, it failsto capture the uncertainty over model parameters accurately.
5.1 Accuracy of Point Estimates
The ﬁrst set of experiments evaluated DUST-net’s accuracy in predicting point estimates for articulation model parameters.
We use the mode of the estimated distribution as the point estimate formodel parameters.
We used two metrics to evaluate accuracy: Mean Absolute (Angular) Deviation (MAAD) and Screw Loss (Metric proposed in ScrewNet [14]).
MAAD metric indicates howclose the individual screw parameters are to targets, whereas the Screw Loss indicates how close thecomplete predicted screw transforms is to the target transforms.
The MAAD metric calculates theangular distance between the orientation of the predicted and ground-truth axis orientation vectorsl and the orientation vectors of the screw axis moment vectors ˆ m .
For the remaining parameters( k m k , ✓ 1: n  1 , d 1: n  1 ), it calculates the mean absolute deviation between the predicted and ground- 269 truth values.
The screw loss reports the angular distance between the predicted and ground-truthscrew axis orientation vectors l as orientation error and the length of the shortest perpendicular be- tween the predicted and ground-truth screw axes as the distance between them.
Conﬁguration errors✓ 1: n  1 are reported as the difference between the predicted rotation about the predicted screw axisand the true rotation, whereas errors over d 1: n  1 are calculated as the Euclidean distance betweenthe points displaced by the predicted and true displacements along respective axes.
Results for the synthetic articulated objects dataset and the PartNet-Mobility dataset are shown in
Figures 2 and 3, respectively.
Results demonstrate that under both metrics, the estimates obtainedfrom DUST-net are typically more accurate than those obtained from the state-of-the-art methods.
The ﬁrst baseline, vm-SoftOrtho, performs comparably with DUST-net on both datasets when only MAAD estimates are considered.
However, Figures 2 and 3 show that it produces a very highdistance ( ⇡ 1 m) between the predicted and ground-truth screw axes.
This error arises due to the softorthogonality constraint used by vm-SoftOrtho, as DUST-net and the second baseline method, bothof which handle the constraint implicitly, do not report high errors on that metric.
Meanwhile, thesecond baseline, Direct F , performs comparably with DUST-net on both metrics for both datasets,but fails to capture the uncertainty over parameters with the required accuracy.
5.2 Uncertainty Estimation
The second set of experiments evaluated howeffectively DUST-net’s predicted distributioncaptures epistemic uncertainty over the predicted articulation parameters.
We evaluate thisby adding artiﬁcial noise to the training labelsfrom the two simulated datasets while training DUST-net.
As more noise is added, we expectthe conﬁdence estimates produces by DUSTnet to decrease as well.
We add noise to thelabels by sampling perturbations from a matrix von Mises-Fisher distribution with varying singular values  1 and  2 of the distribution parameter matrix F and the truncated normal distributions with varying precision parameters  j , j 2 { k m k , ✓ , d } .
Figure 4 show the 301 variation of the mean of the singular values ofthe predicted distribution concentration matrices over screw axes by DUST-net with injectednoise.
In the noiseless case, the singular valuesof the matrix von Mises-Fisher distribution increases until they reach their maximum allowedvalue at  max = 50 .
When label noise is added,our results show that DUST-net’s conﬁdence over its predicted parameters decreases monotonicallyas more noise is added to the labels, supporting our hypothesis.
[Figure] 5.3 Sim to Real Transfer
Lastly, we evaluated how effectively DUST-net transfers from simulation to a real-world setting.
DUST-net was trained solely on the simulated articulated object dataset [11].
Afterward, we usedit to infer the articulation model parameters for three real-world objects.
Results (Fig. 5(a)) reportthat DUST-net outperforms the current state-of-the-art method, ScrewNet, in estimating the modelparameters for real-world objects. However, the estimated parameters using DUST-net are not yetaccurate enough to be used directly for manipulating these objects.
This sub-par performance stemsfrom the signiﬁcant differences between the training (clean and information-rich simulation data)and test datasets, which consists of noisy depth images acquired with a Kinect sensor and containhigh salt-and-pepper noise, spurious features, and incomplete objects.
Better performances couldbe achieved by either ﬁne-tuning the network on real-world data or retraining it using a larger realworld dataset.
A noteworthy insight from the results is that DUST-net also reports low conﬁdenceover the predicted parameters for real-world objects, compared to when tested on the simulateddata (Fig. 5(b)).
This clearly delineates why it is beneﬁcial to estimate a distribution over the articulation model parameters instead of point estimates.
Given only point estimates of articulationmodel parameters, a robot has no way to determine if the estimates are reliable for manipulating theobject safely or not. In contrast, DUST-net’s reported conﬁdence over the predictions could allowthe robot to develop safe motion policies for articulated objects [1, 18] or use active learning basedmethods [17] to reduce uncertainty over the articulation parameters.
Conclusion
We introduced DUST-net, which utilizes a novel distribution over screw transforms on a Stiefel manifold to perform category-independent articulation model estimation with uncertainty estimates.
Weevaluated our approach on two benchmarking datasets and three real-world objects and comparedits performance with two current state-of-the-art methods [11, 14].
Results show that DUST-net canestimate articulation models, their parameters, and model uncertainty estimates for novel objectsacross articulation model categories successfully with better accuracy than the state-of-the-art methods.
At present, DUST-net can only predict parameters for 1-DOF articulation models directly.
Formulti-DoF objects, an additional image segmentation step is required to mask out all non-relevantobject parts.
This procedure can be repeated iteratively for all object part pairs to estimate relativemodels between object parts that can be combined later to construct a complete kinematic model forthe object [10].
An interesting extension of DUST-net could estimate parameters for multi-DoF objects directly by learning a segmentation network along with it.
Another exciting direction of futurework is to use DUST-net in an active learning setting where, if the robot is not conﬁdent enoughabout the estimates of the articulation model parameters, it can actively take information-gatheringactions to reduce uncertainty.