Using Manifolds for Dextrous Hand Control€¦ · Fuentes and Nelson [3] learn a mapping fromperceptual goals consisting of targeted object position/orientation and applied nger forces

J.Steffen, R.Haschke, H.Ritter (Neuroinformatics Group, Bielefeld University, Germany)Title: ”Using Manifolds for Dextrous Hand Control”

[Preprint] – page 1

Using Manifolds for Dextrous Hand ControlBlind Submission. Paper-ID #4

Abstract— In dextrous hand control, the implementation ofmanipulation movements still is a complex and intricate un-dertaking. Often, a lot of object physics and modelling ef-fort has to be incorporated into a controller working onlyfor a very restricted task specification and performing quiteartificially looking movements. In this paper, starting fromour representation for dextrous grasping, namely the GraspManifold, we motivate and present adaptations which enablethe new manifold – the Manipulation Manifold – to robustlyrepresent manipulation movements which have been recordedfrom human demonstration. It facilitates later application andpromotes natural motion. We use manifolds of hand posturesembedded in the finger joint angle space which are constructedsuch that manipulation parameters including the advance in timeare represented by distinct manifold dimensions. This allowsfor purposive navigation within such manifolds. We present themanifold construction using the Unsupervised Kernel Regression(UKR) and our first results of representing the turning movementof a bottle cap.

I. I NTRODUCTION

During the last decades, researchers and engineers havemade huge advances in constructing and building anthropo-morphic robot hands which have become more and moresophisticated as one can see for example in the SalisburyHand [8], the Utah/MIT Hand [5], the DLR II Hand [2]and the Shadow Dextrous Hand [22]. Together with thesedevelopments, researchers are facing the question of howto dexterously control such complex robots with up to 20degrees of freedom in up to five fingers and a wrist. It quicklybecame clear that implementing fixed grasp and manipulationprograms does not lead to satisfying results as it is verytime consuming on the one hand and not robust against orgeneralisable to differences in the grasping or manipulationsituation. Thus, several sophisticated approaches have beenpresented to realise more robustness and generalisability.

In the domain of dextrousgrasping, most of the publishedapproaches focus on one of the two most obvious aspectsof the grasping task - either the object geometry or thetactile impressions during the grasp. Concerning the geometryaspect, several approaches have been presented to incorporateexplicit object geometry models to calculate (optimal) contactpoints and plan grasp postures to realise them [1, 11, 14].On the other side, the grasping approaches involving tactileinformation do not plan beforehand, but close the fingersaround the object solely based on the tactile feedback of thehand until stable object contact is detected [13, 21, 17].

When it comes to dextrousmanipulation, the task is morecomplex and the fundamental ideas of the approaches be-come more distinct and diverse. Michelman and Allen [10]implemented simple object translations and rotations with theUtah/MIT Hand and combined them to more complex tasks.

In this manner, they achieved to remove a child-proof bottletop with two fingers exploiting a decomposition into subtasksand explicit force and position control schemes. Zhang etal. [25] define a graph of vertices representingcanonicalgrasps consisting of topological hand/object feature pairshaving contact when the associated grasp is achieved. Directededges between two grasps represent possible transitions whichhave to be designed as lower-level control laws. Manipulationplanning then is implemented as path planning in the graphbetween defined start and end vertices. Fuentes and Nelson[3] learn a mapping fromperceptual goals– consisting oftargeted object position/orientation and applied finger forces– onto robot commands realising these goals using an evo-lution strategy. Afterwards, manipulation can be performedby defining the task-specific perceptual goal and applyingthe learned mapping. Han et al. [4] propose a pure contactwrench analysis approach. They use a planner to generate apath in the space offeasible configurations of the manipulationsystemrespecting hand/object constraints. A controller thenincorporates sensor readings and system kinematics and staticsto properly actuate the planned path. Platt et al. [15] addressdextrous manipulation by sequencing concurrent combinationsof hierarchical organised closed-loop controllers each derivedfrom potential functions and realising force-related objectives.By dint of operating subordinated controllers in the nullspaceof superiors, higher-level conditions like wrench closure canbe prioritised and thus sustained.

To a certain extent, all these approaches require the manualdesign of (lower-level) controllers from scratch. In [18], Schaalargues that learning without incorporating prior knowledgeis a mostly artificial approach rarely taken by humans andanalyses the benefit of learning from demonstration. He appliesreinforcement learning on balancing a pole with an anthro-pomorphic robot arm to find an optimal policy and solvesthe problem based on data from a 30 second demonstration.Nevertheless, he concludes from his experiments that not everylearning problem can profit from prior knowledge in the samethe way.

Although these approaches all realise robust dextrous grasp-ing or manipulations to a certain degree, their implementationsrequire considerable effort in problem modelling on the levelof task definition and object characteristics. In addition, to ourknowledge, none of the mentioned grasping approaches couldbe generalised to the manipulation task, nor vise versa.

In this paper, starting with a review of our previous approachof representing grasp postures as manifolds in the hand jointangle space [20, 19], we propose a modification of thisapproach to represent manipulation movements as well. Themain idea is to construct manifolds – again embedded in the

Final version in: Proc. RSS ’08 Workshop on Robot Manipulation: Intelligence in Human Environments



finger joint angle space – which represent the subspace of handpostures associated with a specific manipulation movement.Instead of learning these representations in a purely unsuper-vised manner yielding unpredictable, ”undirected” manifolds,we want to construct them such that specific movementparameters – and especially the advance in time – are explicitlyrepresented by specific and distinct manifold dimensions.For our initial experiments, we focus on the manipulationmovement of turning a bottle cap incorporating the advancein time and the cap radius as manipulation parameters.

The paper is organised as follows: In Section II, we reviewthe basic principle of our manifold representation for dextrousgrasping. Section III addresses the differences in the repre-sentational requirements for grasp postures and manipulationmovements, Section IV concerns the computational meansthat we chose for the implementation, namely theUnsuper-vised Kernel Regression. In Section V we describe our first,constructional approach to fulfilling the stated requirementsfollowed by the results in Section VI. Finally, we end up witha conclusion and an outlook on future work in Section VII.

II. T HE GRASPMANIFOLD

In our previous work [20, 19], we presented a new approachto dextrous robot grasping that combines the advantagesof geometry-based and tactile-driven grasping employing animplicit representation of grasping experience using a self-organising map (SOM, cf. [20, 16]). The SOM lattice is trainedwith previously recorded hand postures which led to successfulgrasps. In this manner, it forms a discrete approximation of asmoothGrasp Manifoldrepresenting the subspace of the handjoint angle space described by the training data and thus bythe set of known grasp postures. Using tactile information toinfer implicit knowledge about the object position and shape,the algorithm dynamically exploits the SOM to adapt thegrasping motion to the actual situation. According to observedfinger contacts, the most suitable hand posture is selected fromthe grasp manifold represented by the SOM nodes’ referencevectors. Fig. 1 visualises a 10x10 SOM-based Grasp Manifold.Each hand picture represents one of the adapted referencevectors of the SOM and thus one point on the Grasp Manifold.Notice that this representation ofgrasp posturesconsists onlyof hand postures in the final grasp positions in which the handis in contact with the object.For further details, please refer to [20, 19].

III. F ROM GRASPING TO MANIPULATION

Grasping and manipulation are related in the sense thatboth actions aim at using a hand to establish contacts withthe targeted object and then realise a specific goal with it.Nevertheless, these goals usually are quite different: in thecase of grasping, we want to fixate the object, whilst whenthinking of manipulation, we rather aim at performing a certainmovement with it, or a change of its position and orientationrespectively. In terms of our manifold representation, this canbe formulated as follows:

Fig. 1. A two-dimensional 10x10 SOM-baseddiscrete Grasp Manifoldtrained with 4220 cylinder grasp postures. Each hand picture represents areference vector of a single SOM-node and a point on the Grasp Manifoldrespectively. Represented are only hand postures in the final grasp position.

Grasping corresponds to ”pulling” the current hand postureonto the manifold such that the resulting posture isone pointon it which causes a stable immobilisation of the object.Hence, the goal is one specific final hand posture.

Manipulation in contrast is not the search for only onespecificpoint onthe manifold, but rather for a wholetrajectorythroughan adequate manifold. Thus, the goal is a sequence ofseveral intermediate hand postures which result in the targetedmanipulation when actuated sequentially. Notice, that in theinitial phase, the hand posture needs to be pulled onto themanifold similar to the grasping process, but the resultingposture causes not necessarily an object immobilisation or noteven object contacts.

The Grasp Manifold is a good starting point for the con-struction of theManipulation Manifolds, but the conditionswhich have to be fulfilled need to be adapted to the new task.The basic ideas of theGrasp Manifoldrealised in [20] are:

a) every point on the manifold is agrasp posturebeinga hand posture that realises a grasp in combination with thecorresponding object in the corresponding position.

b) the manifold spans over the whole targeted workspaceor over all targeted grasping contexts, respectively. Obviously,the grasp algorithm would not be able to perform well in alltargeted contexts otherwise.

c) the manifold representation net to support theassociativecompletionmechanism [20, 23] which enables the projectionof partially specified data points onto the manifold resultingin the completed hand postures lying on the manifold. Thisallows for a dynamic incorporation of the tactile information.

d) the sample resolution in the represented manifold re-




alised by prototypes or reference vectors need to be highenough. Nevertheless, a continuous manifold representation isnot necessary because a generic closing algorithm is able toterminate the grasp starting from a hand posture near a finalgrasp posture.

In the case ofManipulation Manifolds, we have modifythese conditions in the following way in order to fit to themodified task:

a) To represent the pure manipulation phases – thus onlythose moments in which the hand is in direct interactionthrough contacts with the object – it is again necessary thatevery point corresponds to a contact situation. However, inour approach, we aim at representing whole manipulationmovements possibly containing non-contact phases. Hence, wecan soften the previous requirement to: the resulting manifoldconsists only of points corresponding to hand postures gener-ated by the manipulation movement to be represented. Noticethat thegrasppostures demanded by theGrasp Manifoldcon-ditions are comprised herein. Additionally, remark that onlyhand postures representing contact situations (not necessarilygrasp postures) implicitly inhere object information and thus,only these postures can be used later on to infer object-specificparametrisation of the manipulation movement.

b) For manipulation, it is still necessary to represent thewhole subspace of the aimed manipulation movement toenable an algorithm to reproduce it.

c) In the grasping case, the associative completion is used to”pull” the current hand posture onto the manifold. Basically,this is not needed to perform the manipulation movement bynavigating through the manifold. Nevertheless, to find a goodstarting point, it is a good approach to perform an initial”pulling” onto the manifold similar to grasping. Hence, weaim at manifold representations again allowing for associativecompletion.

d) As we do not target only one specific point but needto navigate through the manifold following a trajectory whereevery intermediate hand posture lies on the manifold, a discreteapproximation like the SOM lacks the necessary precision.Instead, we use a continuous manifold representation, namelythe Unsupervised Kernel Regressionbriefly reviewed in thenext section.

Notice that – if we guarantee condition c) and speciallymark the regions of the manifold described by hand posturesin the training data that effect object contacts – theGraspManifold is a subset of theManipulation Manifold and wecan combine grasping and the reproduction of manipulationmovements in one simple representation. In this combination,the initial grasping can be seen as object-specific parametrisa-tion of the subsequent manipulation movement.

IV. U NSUPERVISEDKERNEL REGRESSION

Unsupervised Kernel Regression(UKR) is a recent approachfor learning continuous manifold representations. It has beenintroduced as an unsupervised formulation of the Nadaraya-Watson kernel regression estimator by Meinecke, Klanke etal. in [9] and further developed by Klanke in [7, 6]. It

uses the Nadaraya-Watson estimator [12, 24] to find a lower-dimensional (latent) representation of the original data and asmooth mapping from that latent space back to the originaldata space at the same time. The original Nadaraya-Watsonestimator defines a mapping

~y = f(~x) =∑

i

~yiK(~x− ~xi)∑j K(~x− ~xj)

(1)

which realises a smooth, continuous generalisation of thefunctional relationship between~x and ~y described by givendata samples(~xi; ~yi). Here, K(·) is a density kernel. UKRnow treats Eq. (1) as a mapping from a lower dimensionallatent spaceX to the original data spaceY which is describedby a set of observed dataY = {~yi}. Here, the correspondingX = {~xi} play the role oflatent parametersof the regressionfunction:

~y = f(~x;X) =∑

i

~yiK(~x− ~xi)∑j K(~x− ~xj)

. (2)

The training of the UKR manifold thus can be realised bygradient-based minimisation of the reconstruction error

R(X) =1N

∑m

‖ ~ym − f(~xm;X) ‖2 . (3)

As special benefit, the UKR can very efficiently performLeave-K-Out Cross-Validation by using a modifiedf(~xm;X)in Eq. (3):

fm(~x;X) =∑

i 6∈Nm

~yiK(~x− ~xi)∑

j 6∈NmK(~x− ~xj)

(4)

whereNm is the set of neighbours excluded for the recon-struction of~ym.

For further details, please refer to [9, 7, 6].

V. M ANIFOLD CONSTRUCTION

The problem using unsupervised manifold learning methodsoften is that there are usually only limited means of incorporat-ing partial task knowledge or of controlling the way of how”the manifold is laid into the underlying data” respectively.On the other side, we can not provide completely specifiedtraining data that enable us to perform a purely supervisedapproach. Thus, our goal was to develop a mechanism thatrenders us possible to learn a manifold representation of thedata in a partly unsupervised manner and additionally imprintspecific meanings into the directions within the manifold. Interms of our scenario, the representation shall provide thatevery point on the manifold corresponds to one moment intime of a motion trajectory and additionally that the directionswithin the manifold, and especially its single dimensions,inhere the meaning of one specific motion parameter. Thus,in the example of turning a bottle cap, the goal is to realisea manifold in which one dimension controls the progress intime of the turning movement and another dimension specifiesthe radius of the cap. Then, performing the movement reducesto modifying the time component of the latent parameter.




(a) Equidistant initialisation of the latent pa-rameters (blue) respecting the order of the handposture samples in the movement trajectory(red). The black circles in latent space depictpossible displacements of the latent parametersdue to the UKR optimisation.

(b) Procedure of incrementally adding newsequences by projecting new samples into thelatent space of the previously trained manifold.The new manifold consisting of the combina-tion of old and new data samples and latentparameters gets retrained afterwards.

(c) Synchronising different radiirk andr(k+1) by projecting new samples correspond-ing to r(k+1) into the latent spaceXrk,.

corresponding tork. The projections then areused as initialisation ofXr(k+1),1 for thesubsequent training ofMr(k+1),1.

Fig. 2. Schematic description of different steps in the manifold construction process.

A simple but - as presented in the following - effectiveapproach to achieving this is to construct the final manifoldout of several sub-manifolds each realising a manipulationmovement of one motion parameter set.

In this first approach, we incorporate two parameters - theprogress in time of the movement and the radius of the cap.As training data, we recorded sequences of hand posturesduring cap turning movements for five different cap radii(r = 1.5cm, 2.0cm, 2.5cm, 3.0cm and 3.5cm). For eachradius, we produced five sequences each of about 30 to 45hand postures. Each hand posture consists of a vector of the24 joint angles corresponding to our anthropomorphic roboticShadow Dextrous Hand[22].

The construction of the final manifold is performed itera-tively starting with training sequences corresponding to theminimal cap radius successively increasing the radius of thesubsequent sequences.

For the first sequence of hand posturesY r1,1 = {~y r1,1i }

corresponding to the minimal cap radiusr1 , we manually dis-tribute the latent parameters of a 1D-UKR manifold equidis-tantly in a predefined interval of the latent space accordingto the intra-sequence order of the hand postures and performthe UKR training to optimise the latent parametersXr1,1 ={~x r1,1

i } afterwards (cf. Fig.2a). We denote the resulting UKRmanifold asMr1,1. The incorporation of the second sequence(representing another example of a movement for the sameradius) is performed in an iterative manner: the hand posturevectorsY r1,2 of this sequence are projected pointwise intothe latent space of the previously trained 1D-manifoldMr1,1

resulting inXr1,2 (cf. Fig.2b). By dint of this projection, weapproximate a synchronisation of the temporal advance of thetwo movements. In the next step, we combine those data to anew UKR manifoldMr1,{1,2} with observed dataY r1,{1,2} =Y r1,1∪Y r1,2 and latent parametersXr1,{1,2} = Xr1,1∪Xr1,2.

A subsequent UKR training ofMr1,{1,2} optimises the latentparameters subject to the whole combined data set.

By performing this procedure for all sequences of handpostures corresponding to similar cap turning movements forone specific cap radius, a 1D–UKR is trained representing ageneralised radius-specific movement. Thus, by applying thismethod to all sets of radius-specific sequences, we generateone 1D–UKR per radius. To promote the synchronisationof the temporal advances also between the different radius-specific manifolds, we only initialise the first manifoldMr1,1

with equidistant latent parameters as describes above. Whenproceeding with sequencesY r(k+1),1 of a new radiusr(k+1),we project the sequence onto the previously trained manifoldMrk,{1,..,n} (as with sequences for the same radius) and utilisethe resulting latent parameters as initialisationXr(k+1),1 ofthe new manifoldMr(k+1),1 instead of combining them to amanifoldMrk,{1,..,n+1} (cf. Fig.2c). The training then contin-ues as described above. Notice that each first sequence usedto initially train a new 1D-manifold plays a special role anddetermines the relevant subspace in the hand posture space.Therefore, it is important that these first sequences representcomplete movements rather than only specific phases.

The subsequent combination of all 1D-manifoldsMri,· toone 2D-manifoldM representing the complete cap turningmovements for all radiiri covered by the training data thenis performed manually and without the usage of the UKRtraining. M then consists of all incorporated training data{Y ri,j}i,j together with the corresponding latent parameters{Xri,j}i,j and represents the whole manipulation movementdescribed by the training data. Therefore, we denote it asManipulation Manifold. The extension to two dimensions isrealised by expanding each latent parameter~xi by a seconddimension denoting the appropriate radius corresponding tothe associated training sequence.




VI. RESULTS

We applied the method described in Section V to allrecorded training sequences starting with the set of sequencescorresponding to the minimal radiusr1 = 1.5cm and succes-sively incorporating sequences of greater radii. After havingtrained one 1D-manifold for each of the training radiir =1.5cm, 2.0cm, 2.5cm, 3.0cm and 3.5cm in the describedsynchronised manner, we added the corresponding radius val-ues as second dimension to the latent parameters (by manuallyextending each latent parameter by an extra dimension). Thedistribution of the latent parameters in the new latent spaceis depicted in Fig. 3. As constructed, the horizontal (first)dimension represents the temporal advance within the capturning movement and the vertical (second) dimension denotesthe associated cap radius. As no further UKR training isperformed, the latent parameters only lie on the previouslyset discrete radius values.

To get a more distinct impression of the movements repre-sented by the manifold and its generalisation abilities, Fig.4 depicts a matrix of hand postures corresponding to thepositions in a regular grid covering the latent space of themanifold. Again, the temporal advance is depicted in thehorizontal and the different radii in the vertical direction. Tofacilitate the comparison, a bottle cap with radius(r = 1.5cm)is depicted in each sub-figure. As shown in Fig. 3, onlythe radii r = 1.5cm, 2.0cm, 2.5cm, 3.0cm and 3.5cmare directly supported by training data. Thus, the depictedintermediate radiir = 1.75cm, 2.25cm, 2.75cm and3.25cmin Fig. 4 visualise the generalisation ability of the constructedmanifold to new cap radii. The corresponding movementsfor the intermediate radii are clearly similar to the trainingsequences. Secondly, it illustrates the effect of the temporalsynchronisation between the different 1D-manifolds by pro-jecting new sequences into the latent space of the previouslytrained manifolds before newly training as described in SectionV. The most distinct picture of this synchronisation can beseen in columns3 − 5 (t = 20% − 40%) where the fingersare shown in the moments (virtually) contacting the cap (orin the video referenced in Fig.4). Additionally, those columnsgive an impression of the smoothness in the2nd manifolddimension. Remark the smooth finger opening with increasingcap radius in the column direction. In the row direction, allrows depict smooth transitions from left to right indicating asmooth manifold also in the row direction.

One effect of the presented training method is not directlyobvious in Fig. 4. When reaching the manifold border in thetemporal dimension while performing the turning movement,the temporal position has to be reset to the beginning (go backfrom 100% to 0%) to restart the turning movement. As by now,there is no regulation for border synchronisation incorporatedin the training, the 100%- and 0%-postures usually signifi-cantly differ from each other yielding an abrupt non-smoothhand movement when jumping back to the 0%-posture. As thebeginning and the end of the movement are the phases wherethe fingers are the farthest away from the cap, the motion

0 1 2 3 4 5 6 7 8 9 101.5

2

2.5

3

3.5

1st latent dim: advance within movement

2nd

late

nt d

im: r

adiu

s

Distribution of latent parameters

Fig. 3. Distribution of the latent parameters ofM. The1st dimension rep-resents the advance within the movement. As constructed, the2nd dimensionrepresents the defined cap radii.

artifact resulting from the missing border synchronisation doesnot effect the cap turning and thus is not of particular relevancefor the success of the cap turning manipulation. Nevertheless,we will address this issue in future work to optimise the naturalimpression of the manipulation.

VII. C ONCLUSION

We presented the first steps towards a new approach indextrous manipulation that uses sequences of hand posturesrecorded from human demonstration to learn and constructManipulation Manifoldsin which distinct dimensions repre-sent distinct parameters of the associated manipulation. Withthe example of turning a bottle cap, we provided a proof ofconcept by incorporating two parameters in a manifold – thecap radius and the temporal advance within the movement.

From our experiments, we conclude several subjects andaims for our future work. The most important for us willbe to change the learning and construction mechanism suchthat it works in a more unsupervised fashion with the goalof completely replacing the manual construction part by anunsupervised learning. For this, we have several ideas in mindof how to modify the UKR learning to better fit to the problemof chronologically ordered data sequences. Other importantobjectives are to explicitly incorporate contact conditions andto remove artifacts due to the missing border synchronisation.

While following our goals, we want to sustain our mainprinciple of this work of constructing manifolds in which dis-tinct dimensions have imprinted distinct and specific meaningslike the radius of a bottle cap and the temporal advance withinthe manipulation movement.

REFERENCES

[1] C. Borst, M. Fischer, and G. Hirzinger. Calculating hand configurationsfor precision and pinch grasps. InProc. IROS, 2002.

[2] J. Butterfass, M. Grebenstein, H. Liu, and G. Hirzinger. DLR-Hand II:next generation of a dextrous robot hand. InProc. ICRA, 1986.

[3] O. Fuentes and R. Nelson. Learning Dextrous Manipulation Strategiesfor Multifingered Robot Hands Using the Evolution Strategy.MachineLearning, 31, 1998.

[4] L. Han, Z. Li, J. Trinkle, Z. Qin, and S. Jiang. The planning and controlof robot dextrous manipulation. InProc. ICRA, 2000.

[5] S. Jacobsen, E. Iversen, D. Knutti, R. Johnson, and K. Biggers. Designof the Utah/M.I.T. Dextrous Hand. InProc. ICRA, 1986.

[6] S. Klanke. Learning Manifolds with the Parametrized Self-OrganizingMap and Unsupervised Kernel Regression. PhD thesis, BielefeldUniversity, 2007.




r[cm]

\t 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

3.50

3.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

Fig. 4. Generalisation results of the UKR training/construction. The depicted hand postures correspond to the positions of a regular grid covering the latentspace of the manifold. The horizontal direction is associated with the1st (temporal) latent dimension and the vertical direction with the2nd (radius) latentdimension. The size of the depicted bottle cap in all pictures is the same (r = 1.5) as a comparison aid. The radiir = 1.5, 2.0, 2.5, 3.0 and3.5 correspondto radii covered by the training data, the radiir = 1.75, 2.25, 2.75 and3.25 demonstrate the generalisation capability of the approach. A more sophisticatedimpression of the manifold can be received by means of a movie available underhttp://www.techfak.uni-bielefeld.de/˜jsteffen/mov/ .

[7] S. Klanke and H. Ritter. A Leave-K-Out Cross-Validation Scheme forUnsupervised Kernel Regression. InICANN 2006, volume 4132 ofLCNS. Springer, 2006.

[8] M. Mason and J. K. Salisbury.Robot Hands and the Mechanics ofManipulation. MIT Press, 1985.

[9] P. Meinicke, S. Klanke, R. Memisevic, and H. Ritter. Principal Surfacesfrom Unsupervised Kernel Regression.IEEE Trans. on Pattern Analysisand Machine Intelligence, 27(9), 2005.

[10] P. Michelman and P. Allen. Forming Complex Dextrous Manipulationsfrom Task Primitives. InProc. ICRA, 1994.

[11] A. Miller, S. Knoop, P. Allen, and H. Christensen. Automatic graspplanning using shape primitives. InProc. ICRA, 2003.

[12] E. A. Nadaraya. On Estimating Regression.Theory of Probability andIts Application, Vol.9, 1964.

[13] L. Natale and E. Torres-Jara. A sensitive approach to grasping. In6thIntl. Conf. on Epigenetic Robotics, Paris, France, 2006.

[14] R. Pelossof, A. Miller, P. Allen, and T. Jebara. An SVM LearningApproach to Robotic Grasping. InProc. ICRA, 2004.

[15] R. Platt Jr., A. Fagg, and R. Grupen. Manipulation gaits: sequences ofgrasp control tasks. InProc. ICRA, 2004.

[16] H. Ritter, T. Martinetz, and K. Schulten.Neural Computation and Self-Organizing Maps. Addison-Wesley, 1992.

[17] F. Rothling, R. Haschke, J. J. Steil, and H. Ritter. Platform PortableAnthropomorphic Grasping with the Bielefeld 20-DOF Shadow and 9-DOF TUM Hand, 2007. accepted for IROS 2007.

[18] S. Schaal. Learning from Demonstration. InAdvances in NeuralInformation Processing Systems, volume 9. MIT Press, 1997.

[19] J. Steffen, R. Haschke, and H. Ritter. Experience-based and Tactile-driven Dynamic Grasp Control. InProc. IROS, 2007.

[20] J. Steffen, R. Haschke, and H. Ritter. SOM-based experience represen-tation for Dextrous Grasping. InProc. WSOM, 2007.

[21] J. Steil, F. Rothling, R. Haschke, and H. Ritter. Situated robot learningfor multi-modal instruction and imitation of grasping.Robotics andAutonomous Systems, Special Issue on ”Robot Learning by Demonstra-tion”(47), 2004.

[22] The Shadow Robot Company. Shadow Dexterous Hand.www.shadowrobot.com/hand, 2002.

[23] J. Walter. Rapid Learning in Robotics. PhD thesis, Faculty ofTechnology, Bielefeld University, 1996.

[24] G. S. Watson. Smooth Regression Analysis.Sankhya, Series A, 26,1964.

[25] H. Zhang, K. Tanie, and H. Maekawa. Dextrous manipulation planningby grasp transformation. InProc. ICRA, 1996.


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Using Manifolds for Dextrous Hand Control€¦ · Fuentes and Nelson [3] learn a mapping fromperceptual goals consisting of targeted object position/orientation and applied nger forces