Visual Repetition Sampling for Robot Manipulation Planning

En Yen Puang1, Peter Lehner1, Zoltan-Csaba Marton1, Maximilian Durner1

Rudolph Triebel1,2, Alin Albu-Schäffer1,2

Abstract— One of the main challenges in sampling-basedmotion planners is to find an efficient sampling strategy. Whilemethods such as Rapidly-exploring Random Tree (RRT) haveshown to be more reliable in complex environments thanoptimization-based methods, they often require longer planningtimes, which reduces their usability for real-time applications.Recently, biased sampling methods have shown to remedy thisissue. For example Gaussian Mixture Models (GMMs) havebeen used to sample more efficiently in feasible regions ofthe configuration space. Once the GMM is learned, however,this approach does not adapt its biases to individual planningscene during inference. Hence, we propose in this work a moreefficient sampling strategy to further bias the GMM based onvisual input upon query. We employ an autoencoder trainedentirely in simulation to extract features from depth imagesand use the latent representation to adjust the weights of eachGaussian components in the GMM. We show empirically thatthis improves the sampling efficiency of an RRT motion plannerin both real and simulated scenes.

I. INTRODUCTION

Mobile robotic manipulation systems are becoming moreand more important for industrial applications, because mod-ern production lines are becoming more customized, andthis requires flexible mobile robots that can adapt to newsituations. Consequently, planning efficient and collision-freepaths for the manipulator must be performed online and cannot be pre-processed. However, the time constraints of mostindustrial applications do not allow any intensive search inConfiguration-space (C-space), which limits the usability ofmost of the current path planning methods. For example,RRT belong to a recent family of Sampling-based MotionPlanner (SMP), but despite being relatively fast, in generalthey still exhibit an inefficient sampling strategy. This oftenleads to large areas in configuration space being exploredand consequently to long planning times.

Recent work has focused on reducing the computationtime by exploiting past experiences for efficient C-spacesampling. Repetition Sampling [1] in particular learns aprobability distribution to bias the search of SMP into thetask relevant regions of the C-space. The algorithm learnsthe probability distribution by combining the key informationof previous, similar queries in a GMM. The method showspromising results in computational efficiency, but is unawareif the current query actually reflects a previous experience.

In this work, we propose an efficient combination ofvisual scene recognition system and experience based motionplanner to recognize and exploit past experiences in solving

1Institute of Robotics and Mechatronics, German Aerospace Center(DLR), Germany. en.puang@dlr.de

2Department of Computer Science, Technical Univ. of Munich, Germany.

Fig. 1: Adapting GMM sampling biases (right) in RRTbased-on visual information deduced from planning sceneresulted in more efficient planning compared to vanillaRepetition Sampling (left).

new motion planning queries efficiently, as shown in Fig.1. We design and train an Autoencoder (AE) to extract keyinformation about the planning scene directly from depthimage. Based on the information encoded by the AE wethen learn sampling distributions for similar planning querieswith Repetition Sampling. During inference our methodsfurther bias the sampling distribution of Repetition Samplingto reflect the task relevant configuration space. The maincontributions here therefore involve two major areas:

• Improve efficiency of SMP for robot manipulation taskwith deep-learned scene-understanding vision module.

• Improve data efficiency of training AE with only sim-ulated data and adaptation-randomization methods forrobotics application.

We evaluate the complete pipeline on pick-and-place ex-periments in simulation as well as on our real mobile manip-ulator. The results show that visual workspace understandingof past experiences improve sampling efficiency and hencedecrease computation time during execution.

II. RELATED WORK

Boor et al. [2] proposed to only accept samples thatare close to obstacle while Yang et al. [3] proposed theopposite by biasing along the medial axis. The utility-guidedapproach [4], maximizes the information gain of the nextsample by predicting the sample utility with a probabilitydistribution. Informed path sampling [5] learns a probabilitydistribution to generate paths which are robust to obstacleuncertainties. These methods bias the sampling distributionof SMP but are not designed to include information from pre-vious experiences. Kernel Density Estimation (KDE)-basedsampling [6] and Repetition Sampling [1] utilize previous

experiences by estimating the probability distribution in C-space based on solutions of a set of similar tasks using KDEand GMM respectively. During inference, however, GMMneed not to select a kernel for samples drawing, which is acritical aspect for KDE-based biases.

Phillips et al. [7] proposed a biased roadmap planner by in-troducing cost on every edges in the graph. The graph is builtusing a solutions collection and a discrete planner is used tocompute path with minimal cost when queried. Zucker etal. [8] extract features from a discretized workspace using adiscrete planner and then apply reinforcement learning to up-date the workspace bias distributions using shorter planningtime as reward. Berenson et al. [9] propose a framework thatcollects solutions in a sparse roadmap and exploits it via aretrieve-repair module. These methods discretize the C-spacein contrast to Repetition Sampling which learns a probabilitydistribution in continuous C-space without using workspacefeature. Utilizing Repetition Sampling, our work appends theability to adapt biases according to situations.

Ellekilde et al. [10] blend several segments of solutionretrieved from database into a smooth one. Jetchev et al. [11]proposed to penalize differences from the retrieved solutionsin its inverse kinematic. In contrast our methods do not usethe retrieved solutions directly in generating new solution.In further work the same authors proposed a planning scenedescriptor using voxel grid and principal component analy-sis [12]. Scene similarity computed with a function whoseweights are optimized by minimizing the required effort toadapt retrieved solutions to query scene. Our work doesnot require hand-crafting features to represent the planningscene. Ichter et al. [13] proposed to reconstruct solutionsusing Variational AE, conditioned on planning scene newsamples are generated by sampling on latent distributionand forwarded to the decoder. This method offers promisingalgorithm but did not address cases in which the planningscenes are in high dimension i.e. image.

Sharif et al. [14] shows the competitiveness of Con-volutional Neural Network (CNN) compared to classicalmethods in multiple visual tasks. Recent work used pre-trained networks for feature extraction in image retrievaltask [15], [16]. General purpose pre-trained networks arenormally huge and offer limited architecture flexibility. Ourmethod trains a significantly smaller network from scratchwith reduced computation cost. Using variants of AE Sunder-meyer et al. [17] proposed object pose estimation; Kendall etal. [18] proposed scene semantic segmentation; and Nguyenet al. [19] proposed tabletop affordance detection. Guptaet al. [20] proposed hand-crafted features for depth image(HHA). Our work uses a variant of AE, but without HHAencoding for faster data pre-processing.

Recent works fine-tune feature extraction networks end-to-end so that the resulted descriptors yield high similarityscore for correctly paired input [21], [22]. These methodsrequire paired data with a defined relationship which isnot applicable in general database similarity search. Ourmethods employ self-supervise training to circumvent theneed of paired images and hence achieve high data effi-

ciency. Li et al. [23] proposed to predict similarity scoresdirectly. Besides requiring paired data, this method doesnot transform images into smaller representations and hencerequires repeated network’s forward-passes for each query.Mohedano et al. [15] proposed a Bag-of-Words methodfor visual retrieval which involve CNN features, K-Meansclustering and histogram descriptors. These method has goodaccuracy but lacks the runtime efficiency required in roboticapplications. Our method uses entirely CNN that computesthe latent representation in a single encoder’s forward-pass.

III. REPETITION SAMPLING

Repetition Sampling improves the efficiency of SMP bybiasing the sampling towards specific regions in C-space. Itstarts by building a database D consisting of n robot motionpaths P that are generated in a particular task domain usingstandard RRT. Important milestones or key-configurationsq ∈ C are then extracted Ψ : P → {q} from each paths inthe database and form Q with a total N key-configurations

D ={Pi

}ni=1

(1)

Q =n⋃

i=1

Ψ(Pi) . (2)

Next, Q is clustered using GMM to obtain a parametricapproximation of the density distribution in C-space. Meanµj , covariance Σj and weight wj of each mixture compo-nents j where j = 1, . . . , G and G is the total number ofmixture components are then estimated using Expectation-Maximization (EM). Concretely, the E-step computes theassignment probabilities pi ∈ [0, 1]G s.t.

∑Gj=1 pij = 1 for

each key-configurations in Q where i = 1 . . . N

pij =wj N (qi |µj ,Σj)∑Gl=1 wlN (qi |µl,Σl)

. (3a)

Thus, pij represents the probability that key-configuration qicorresponds to mixture component j. Then, in the M-step themixtures’ parameters are updated

µj =1

nj

N∑i

pij qi (3b)

Σj =1

nj

N∑i

pij (qi − µj)(qi − µj)T (3c)

wj =njN

, nj =

N∑i

pij . (3d)

After convergence of EM, Repetition Sampling randomlyselects a Gaussian component (µj ,Σj) proportional to itsweight wj , to generate samples used by RRT for expandingthe search tree. However, as mentioned above, this approachcannot adapt to individual new query scene because it doesnot involve information obtained from perception. Therefore,we propose an alternative method in the following section.

IV. BIASED REPETITION SAMPLING

Our main idea is to modify the weights of mixture compo-nents according to the information deduced from individualquery scene using a vision component. More concretely,we extend our model by incorporating a depth image ofthe initial planning scene into biasing the vanilla RepetitionSampling using two methods, namely Weight Aggregation(WA) and Weight Prediction (WP).

A. Weight Aggregation

As shown in Fig. 2 we first populate the database insimulation with paired depth image I of the initial planningscene and all queries Φ in the scene. Each query φ containsa target pose tφ (end-effector’s 6 Degrees of Freedom (DoF)rigid transformation) and is solved as described in Sec. III

D ={(Ii, Φi

)}ni=1

. (4)

To be able to reuse existing solution in the database duringinference, we employ an AE to facilitate retrieval based-onthe associated planning scenes. This AE learns to representthe planning scene in the form of depth image I ∈ Rw×hwith a latent-encoding z ∈ R` where `� w×h. Concretely,we treat the encoding as key and the queries associated tothe scene as value for key‖value retrieval in the database

Ti =

tT1...

tT|Φi|

Pi = {p ∈ Ψ(P1)}...{

p ∈ Ψ(P|Φi|)} (5a)

D ={(

zi ‖Ti, Pi)}n

i=1. (5b)

When a real planning task (Iq, tq) is queried duringinference, retrieving the right information from the databaserequires a metric that reflects both the visual similaritybetween scenes and the geometric similarity between targetposes. The first stage of the retrieval uses σs to retrieves theK Nearest Neighbors (KNN) from the database in term ofthe top K [·]K cosine similarities between queried encodingzq and all keys in the database

σs(zq) =

[{zTqzi

‖zq‖ ‖zi‖

∣∣∣∣ zi ∈ D}]

K

. (6)

The second stage uses σt to compute task similarity betweenqueried target pose tq and those in the KNN. L2-Norm isused to compute the differences between target poses and αtis the hyper-parameter used to tune the sensitivity of σt

σt(tq, ti) =1

2cos

(min

(π, αt ‖tq − ti‖2

))+

1

2. (7)

The proposed new set of weights w′ is then a weightedaverage of assignment probabilities of all key-configurationscontained in the KNN. Pkφlj = p(kφl),j is the assign-ment probability for j-th mixture component of l-th key-configuration in φ-th query in scene k in the database, and

TrainingAutoencoder

FittingGMM

ExtractingKey-Config

Database Creation

Solving Simulated Tasks

Repetition Sampling

Vision Modules

Query

Depth Scene Biases

Target Pose(x, y, z, R, P, Y)

Weight Prediction Planning

RRT + GMM

W

(a) Training

(b) Inference

WA KNN

Search

WP Direct

Prediction

Fig. 2: Training phase first accumulates planning scenespaired with generated paths before fitting a GMM usingextracted key-configurations. AEs are then trained for theirrespective biasing methods using data from the database.During inference both WA and WP produce a new set ofweights to bias the GMM used in Repetition Sampling.

w′ =∑G

j w′j is the normalizing factor for all j

w′j =1

w′

K∑k

|Φk|∑φ

|Pkφ|∑l

σs(zq)k σt(tq, Tkφ) Pkφlj (8)

w∗j = αw supS w′j + (1− αw supS)wj . (9)

By calculating the final weight w∗, the supremum of thesimilarity score supS is used to adaptively scale the updatefactor αw, reducing updates when no good match can befound. A high update factor favor visual biasing over thestatical estimations from the database, while the oppositeattenuates adaptive biasing.

B. Weight Prediction

Using the same database structure in (5), a weights pre-dictor W(w′ | z, t) is built on top of the same AE as anadditional softmax output head to predict the weights ofthe mixture components w′ ∈ [0, 1]G directly using theencoding z and target pose t.

LW = αW[DKL(w

′ |w)]

K

= αW

K∑j

wj logwjw′j

(10)

LW is a Kullback–Leibler (KL) divergence loss designedto minimize differences in probability distribution betweenprediction w′ and target w. This target distribution is theassignment probability p ∈ Piφ, paired with zi and itscorresponding tφ ∈ Ti. p are summed component-wise andre-normalized if |Piφ| > 1.

Operator [·]K includes only the K largest components’losses out of G. Due to the peaked distributions in p, thetop K of KL divergence consist of those that undershoot

Robot base boundary

Robot

Tabletop

Taskboundary

Background

Fig. 3: Simulated workspace. Perlin noise [25] is used ingenerating uneven surfaces for background and SLC load.

wj/w′j > 1 and a lot of those with wj = 0. Those that

overshoot wj/w′j < 1 are then indirectly excluded. Sincethe network has the tendency to bias itself into learning theempirical weight distribution of the entire dataset, penalizingonly the undershoots has the implication of learning scenespecific knowledge while preserving the background infor-mation. We therefore set K to be half of G for LW.

w∗j = αwW(zq, tq)j + (1− αw)wj (11)

During inference the weights predictor is fed with a pairedlatent code zq and target pose tq of a query scene. With theupdate factor αw, the final weight w∗ is computed withoutadaptive scaling as in (9).

V. IMPLEMENTATION

A. Database Creation

For evaluation we use tabletop pick-and-place sceneswhich involve a robot with a manipulator on a mobileplatform [24] manipulating Small Load Carrier (SLC). Therobot perceives the workspace with a stereo camera systemmounted on a vision mast. The robot is able to move its basealong the x-axis (1 DoF) and arm (7 DoF) while reaching forempty nullspace pre-grasp/release target pose. The arm hasa fixed start configuration while the base is randomly placedalong the table edge at the beginning shown in Fig. 3. Theonly kinematic constraint requires the end effector to be up-right all the time. Each scene contains 1-2 pick-tasks and 0-3place-tasks depending on the random obstacle arrangementon the tabletop.

In Cartesian-space, we specify the DoF of the end effectorfor obstacle avoidance and require the rest of DoF to besimple if not fixed by kinematic constraints. For the tabletopscenario the z-axis of the end effector is assigned for obstacleavoidance. Straight line curve fittings are therefore appliedon the xy Cartesian paths of the end effector. By thresholdingthe goodness-of-fit between actual and regressed straight linewe populate the database only with low variance solutions.

For the extraction of key-configurations, we use the dis-crepancies between actual and straight line path to indicatethe likelihood of useful configuration. Given a low variancepath, a group of corresponding straight lines is constructed by

Fig. 4: Synthetic depth image augmentations involve distancecrop, normalization, invert, baseline shift, depth shadow andrandom homogeneous dropout on objects and table.

using the DoF of the end effector in Cartesian-space. Ψ(P)uses local extremal detectors to determine the time-stepswhere the amount of deviations exceed certain threshold.

B. Autoencoder

DenseNet [26] with Weight-BatchNorm-Activation archi-tecture is the backbone of this AE. It is different from theoriginal BatchNorm-Activation-Weight combination. SinceBatchNorm-Activation make no difference when placed be-fore or after a feature concatenation, our proposed combi-nation prevents unnecessary computations by concatenatingactivated features directly. Dilated convolution [27] is appliedin every dense-layer and the amount of dilation goes in thecycle of 1 to 3 until the end of each dense-block.

Given a depth image, the decoder uses the latent codegenerated by the encoder to predict a clean input reconstruc-tion xrec, semantic segmentation xsec and object boundaryxbou shown in Fig. 5. The loss functions are smooth L1,multi-class and binary cross-entropy respectively. On-linebootstrapping [28] is implemented in all 3 losses, and onlypixels with the highest loss per image are back-propagated.

C. Data Augmentation

To bridge the reality-gap, our applied synthetic trainingdata generation takes the hardware properties of targetedapplication into account. Hence, artifacts in the depth imagesacquired by a passive stereo camera system are artificiallyintroduced (see Fig. 4):

• Baseline Shift induced blind region at vertical imageboundary is implemented by nullifying left-most pixels.

• Depth Shadow caused by occlusion is added accordingto the magnitude of horizontal image gradient.

• Homogeneous Dropout simulates failed depth estima-tion using distance to nearest image edge and [25] mask.

Unlike [29] we use the entire mini-batch, randomizedaugmentation strength and adversarial example generation(Fast Gradient Sign Method (FGSM), iterative FGSM andleast-likely FGSM) for the regression and classification tasksto further avoid synthetic features from over-fitting.

Dense-Layer

. . .

Conv 1x1

AvgPool 2x2

BtachNorm

ELU

Conv 1x1

BatchNorm

Dropout

Encoder Decoder

UpSample 2x

Dropout ELU

Conv 1x1

BatchNorm

ELU

Conv 3x3

BatchNorm

ELU

Concat

(a) (b)

Dense-Layer. . .

Dense Layer Transition LayerConv / ConvT 8x8 Transition Layer w/o pooling/upsamplingBatchNorm + ELU Conv 3x3Latent Code Input / OutputFully Connected Task

64

64

1 4180

120

8064

80 120

8041

40

4 5G G

xrec

xseg

xbouz

x

w’

(c)

Fig. 5: (a) Dense-layer with bottleneck; (b) Transition-layer in encoder and decoder. (c) Autoencoder with weight predictionhead. The number of trainable network parameters is 1.9M, which split equally (0.95M) among encoder and decoder.

TABLE I: Combinations of multi-tasked decoders (left) andrandomized adversarial augmentation strengths � (right).

rec seg bou S3

X 0.7540X X 0.7533X X 0.7900X X X 0.7929

ε S3

0 0.78910.1 0.79180.3 0.79290.5 0.7914

TABLE II: Number of nearest neighbors required to retrievethe correct scene in real test-set. K← 5 in all other WA.

KNN 1 2 3 5 10 20

Retrieval (%) 62 83 88 91 97 100

VI. EVALUATION

A. Scene Retrieval Accuracy

In total 14000 scenes are generated. The first half of themcontains all training labels i.e. image-path pairs; The secondhalf contains only images. With the full information, theformer half forms the database D with 7000 scenes, and isable to train the entire network. Whereas the latter, which wasacquired relatively easier and with faster pace, is excludedfrom updating weights prediction head.

To evaluate the image retrieval, semantic segmentationlabels of query q and K retrieved scenes S are used fordirect comparison in Semantic Scene Similarity (S3). xsi,j isthe semantic label of the ith image at jth pixel location.

S3 =1

|t|1

K1

w × h

|t|∑i=1

K∑k=1

w×h∑`=1

{1 if xsqi,` ∧ x

sSk,`

0 otherwise(12)

is averaged across |t| = 500 test scenes, their respectiveK = 5 nearest neighbors and the number of pixels per output.

As shown in Table I, we evaluate the effects of multi-tasking the decoder on S3 by using various combinationsof input reconstruction rec, semantic segmentation seg andboundary prediction bou. We furthermore show the effects ofaugmenting training data on S3 by applying the randomizedadversarial example with varying strength ε.

Fig. 6: Examples of simulated scene retrieval for real queries.∗ indicates the corresponding identically rendered scene.

The additional semantic segmentation and boundary pre-diction tasks force the latent code to be more informativewithout increasing the code length. This resulted in a moreefficient database search as well as better robustness to noise.

In order to draw conclusions about the generalizability ofour method, we investigate the ability of applying knowledgelearned in simulated environment onto the real world. There-fore, 100 real planning scenes with ground truth poses werecollected and their identically rendered scene in simulation isadded to the existing database. Table II shows the amount ofnearest neighbors required to retrieve the correct renderedscene given the corresponding real query scene. Fig. 6depicts some examples of planning scenes retrieval.

B. Biased Sampling Efficiency

The test-set t for this evaluation consists of 200 sceneswith a total of 528 pick-and-place tasks. For the final pathoptimization RRTs are given 300ms. The vision modulesin WA and WP take about 10ms for image encoding andweights generation.

We propose performance metric AUCf which representsthe normalized area under curve of cumulative frequencyof planning time histogram with 100ms resolution over therange of 5s, which is the threshold for failed attempt bytimeout. Normalized by timeout threshold and the size of the

TABLE III: Left: Hyper-parameters search. αt involves parameters for xy translation and z euler angle of end effector.Right: Motion planner benchmark with 528 planning instances in pick-and-place scenes.

αt αW αw∆AUCf (%)

15G 30G 45G

(7.0, 2.5) -0.50 6.5 6.4 4.5

WA 0.75 6.5 6.8 4.51.00 6.7 6.7 4.5

-1.5

1.006.1 7.0 7.8

WP 3.0 7.2 7.0 7.24.0 6.9 7.0 6.9

RRTKOMO

U GMM15G 30G 45G WA WP

Failure 26 6 4 5 4 1 26Median (s) 0.357 0.356 0.357 0.359 0.365 0.365 0.140

Min (s) 0.339 0.338 0.339 0.341 0.348 0.348 0.080AUCf 0.856 0.914 0.915 0.917 0.924 0.934 0.933

test-set AUCf ’s output ranges from 0 meaning the plannerfailed the entire test-set, to 1 meaning the planner solvedevery query within 100ms.

We apply both methods with RRT planner and evaluatethe effects of hyper-parameters by comparing their AUCfwith uniform samplings. The best performing combinationsare then used in the benchmarking among vanilla repetitionsampling and KOMO [30] the optimization-based planner.KOMO has squared accelerations and sum of squared poseerrors as costs, and inequality constraints for collision andjoint limits. Its trajectories have 1 phase and 20 time slicesin 5s. Additional criteria for failed attempts involve limitingcollision constraint and task cost at 0.01 and 1.0 respectively.

The deterioration of WA’s performance with large numberof components as depicted in Table III (left) seems to bethe result of the inability to represent highly non-linearsimilarity scores by the cosine similarity and task proximityfunction. WP in contrast is able to utilize the detailed densityestimation provided by the larger number of components.Table III (right) shows where WP achieves the highestsuccess rate and maintained high overall planning efficiency.

Altering failure definitions do change the landscape ofcomparison between sampling-based and optimization-basedplanner. The point here is to show their pros and cons asthey cover different area in AUCf depicted in Fig. 8.

Using the same 100 real and identically rendered planningscenes in the full pipeline evaluation, we show that ourmethods achieve high data efficiency by only using syntheticdata in the entire training and yet are able to perform in bothreal and simulated input domain. Fig. 9 depicts the negligibledifferences in AUCf using the best performing WP.

VII. CONCLUSION

This work introduces vision assisted biasing for adaptiveC-space biased sampling in RRT, an extension for RepetitionSampling that only offers fixed biases in GMM. The end-to-end method (WP) that predicts weights directly performsbetter than the modular method (WA) which contains sim-ilarity measures and solutions aggregation modules. Themodularity however allows the method to work even withother sets of GMMs (with on-line assignment probabilityadaptation), which would requires re-training for end-to-endmethod. Both methods nevertheless enhance the performanceof vanilla Repetition Sampling and show competitiveness

Fig. 7: Comparison between difference sampling strategies.

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00Planning time (s)

0

100

200

300

400

Freq

uenc

y

WPKOMO

350

400

450

500

550

Cum

ulat

ive

Freq

uenc

y

Fig. 8: Comparison between WP and KOMO in AUCf.

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00Planning time (s)

0

20

40

60

80

100

Freq

uenc

y

RealSimulated

0

25

50

75

100

125

150

Cum

ulat

ive

Freq

uenc

y

Fig. 9: Comparison between real and simulated scene usingWP. Both yielded ∼0.93 AUCf in the real test-set.

with optimization-based counterpart without introducing sig-nificant overhead during inference. Furthermore, a successfuland data-efficient sim2real is achieved by using multipleadaptation-randomization methods when training the AE.

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