Sensorless Pose Determination using Randomized Action Sequences
Pragna Mannam, Alexander Volkov Jr., Robert Paolini, Gregory Chirikjian, Matthew T. Mason
SSensorless Pose Determination usingRandomized Action Sequences
Pragna Mannam , Alexander Volkov Jr. Robert Paolini ,Gregory Chirikjian , and Matthew T. Mason The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213, USA Department Of Mechanical Engineering, Johns Hopkins University,Baltimore, MD 21218, USA [email protected], [email protected], [email protected],[email protected], [email protected]
Abstract.
This paper is a study of 2D manipulation without sensingand planning, by exploring the effects of unplanned randomized actionsequences on 2D object pose uncertainty. Our approach follows the workof Erdmann and Mason’s sensorless reorienting of an object into a com-pletely determined pose, regardless of its initial pose. While Erdmannand Mason proposed a method using Newtonian mechanics, this papershows that under some circumstances, a long enough sequence of randomactions will also converge toward a determined final pose of the object.This is verified through several simulation and real robot experimentswhere randomized action sequences are shown to reduce entropy of theobject pose distribution. The effects of varying object shapes, action se-quences, and surface friction are also explored.
Keywords: manipulation, probabilistic reasoning, automation, manu-facturing and logistics
Robots are envisioned to manipulate and interact with objects in unscripted en-vironments and accomplish a diverse set of tasks. Towards this, reducing objectpose uncertainty is necessary for successful task execution. There are naturalways to reduce pose uncertainty including the addition of physical constraints,relative positioning to a known object’s pose, and actively sensing the desired ob-ject’s pose. In this paper, we explore a novel pose uncertainty reduction techniquebased on executing randomized sequence of actions. We evaluate our proposedpose uncertainty reduction technique on parts orienting, an industrial automa-tion task.Reducing task state uncertainty in parts orienting systems is an importantpart of factory automation, especially product assembly. The problem is to takeparts in a disorganized jumble and to present them one at a time in a predictablepose. Most industrial solutions involve a part-specific mechanical design. One a r X i v : . [ c s . R O ] D ec Pragna Mannam et al.
Fig. 1: Experimental setup (top). An industrial robot tilts an allen key, withApril Tag attached, in an aluminum tray. The overhead camera records the poseof the allen key after each tilt. Each trial (1), (2), . . . (500) performs the samerandom sequence of actions with a different initial position. The pose beforethe sequence, mid-sequence after 25 tilts, and after the sequence of 50 tilts areshown per trial, as well as the entropy of object pose distribution over 500 totalrepeated trials (bottom).goal of parts-orienting research is to avoid part-specific mechanical designs, re-ducing the time required to develop the automation for a new or redesignedproduct.Tray-tilting is one kind of part-agnostic object reorientation system. Theoriginal tray-tilting work was an early entry in a research approach termed “min-imalism.” Minimalism refers to “the art of doing X without Y,” or “finding theminimal configuration of resources to solve a task” [5]. The purpose of the ap-proach is not just to conserve resources, but to yield insights into the structureof tasks and the nature of perception, planning, and action. ensorless Pose Determination using Randomized Action Sequences 3
The role of sensing in the sense-plan-act structure was examined by the tray-tilting work of Erdmann and Mason [9], which eliminated all uncertainty in thetask state without sensing. Rather than sensing, the discrete set of feasible taskstates could sometimes be reduced to a singleton through judicious choice ofactions. So in some tasks, even allowing for the noisy mechanics of frictionalcontact, task state uncertainty can be eliminated without sensing.While the original paper by Erdmann and Mason [9] examined the role ofsensing, this paper is an extension exploring similar minimalism in planning. Wereplace Erdmann and Mason’s [9] planned sequence of actions with a random-ized sequence of actions and evaluate the reduction in object pose uncertainty.Using tray-tilting random actions, instead of planning, can provide simple part-agnostic designs in factory automation. Our experiments stay close to the origi-nal work to focus on the role of planning. We test the limits of minimalism withrespect to system complexity and hope to pursue its practical applications infuture work. For this reason, we adopt the same task domain: planar sliding ofa laminar object in a rectangular tray. The robot can tilt the tray as desired,and the goal is to move the object to a single final pose, irrespective of its initialpose. If independent actions do not scramble the task state too much, then oc-casionally some action maps two initial task states to the same final task state.Furthermore, we expect the set of feasible task states to approach a singleton,for sufficiently long sequences, as seen in Figure 1. The phenomenon, while alsoreminiscent of contraction mapping, is similar to an interesting card trick calledthe Kruskal Count [1], so we have dubbed the phenomenon as “Kruskal effect.”The goal of this paper is to better understand the role of planning by observ-ing the effects of using only randomized actions. For proof of concept, we exper-imented with various triangular objects. We note that orienting a symmetricalor concave shape with this approach might be more difficult. For objects similarto allen keys, relatively low tray friction noise, and a long enough sequence ofrandom actions, we show that the Kruskal effect applies. We also observe thatit does not apply as well to cases with high tray friction noise, and explorationinto more cases is left for future work. The insights we gain from our explorationof the limits of Kruskal effect can lay the foundations for compartmentalizedtray-tilting of a kit of parts in factory automation or 3D pose determination infuture work.
The problem of presenting a single object from disorganization has interestedrobotics researchers as far back as Grossman and Blasgen’s work in 1975 [11].Grossman and Blasgen introduced a fixed tilted tray that used vibration to elim-inate the effects of friction. An irregular part in the tray would settle into oneof a small number of stable poses, and the robot used a touch probe to disam-biguate the pose. V´arkonyi [17] includes additional details on approaches to theproblem by using simulation to systematically evaluate various pose estimators.Erdmann and Mason [9] substituted a fixed tray with an active tilting tray,and showed that for some parts, a sequence of tilts would reduce the possible
Pragna Mannam et al. poses to a singleton, completely orienting the part without a touch probe or anyother sensor.While the tray is not part-specific, the Erdmann and Mason [9] approachuses part-specific motions. In this paper, we substitute the motions with a ran-dom sequence of tilts, which is not part-specific. If we can identify an interestingclass of parts that are oriented by a random sequence, then we have what issometimes termed a “universal” parts orienting system. B¨ohringer et al. [5] in-cludes an overview of universal parts orienting research, detailing the design andimplementation of planar force vector fields that will orient asymmetric laminarparts.Sanderson [16] introduced parts entropy in the context of automated manu-facturing. We use probability density functions in the configuration space, SE (2)for planar motion of rigid parts, and we use entropy to measure and comparedistributions. Our calculation of entropy is based on Chirikjian’s work on com-puting the discrete entropy of histograms [7].Pose uncertainty has previously been addressed with the use of action, ratherthan sensing, in manipulation. Brost [6] uses squeeze-grasp actions to intrinsi-cally reduce uncertainty of the object’s position. Goldberg [10] planned sequencesof pushes and squeezes to orient planar polygons up to symmetry. Zhou et al.[18] plans similar sequences based on an efficient simulation of planar pushing.Berretty et al. [4] proposed an approach of executing pulling actions using over-head fingers for object reorientation. Akella and Mason [2] applied a similarapproach to parts with uncertain shape. Unlike these previous works, we use arandom sequence of actions to reduce the uncertainty associated with the pose ofan object. A random sequence of actions is a part-agnostic plan that minimizessoftware complexity and hardware changes for new parts. First, Section 2 will discuss how we calculate pose uncertainty after every actionin the sequences. Then, experimental setup and results are presented in Sec-tions 3 and 4, respectively. Finally, we discuss our observations in Section 5 andconclude with directions for future research in Sections 6 and 7.
Parts entropy describes the probability distribution of an object’s pose overrepeated tasks [16]. We measure object pose uncertainty using parts entropythroughout our randomized action sequences over many trials. Using parts en-tropy from Sanderson [16] and notation from Lee et al. [13], we define an object’spose in a tray of size a × b with the tuple ( x, y, θ ) where each coordinate is dis-cretized with uniform spacing such that x ∈ { x j : j = 1 , . . . , α } on [0 , a ] (1) y ∈ { y k : k = 1 , . . . , β } on [0 , b ] (2) θ ∈ { θ m : m = 1 , . . . , γ } on [0 , π ] (3) ensorless Pose Determination using Randomized Action Sequences 5 The number of discretized intervals are α = a(cid:15) p , β = b(cid:15) p , γ = 2 π(cid:15) r (4)where (cid:15) p and (cid:15) r are the positional and rotational resolutions, respectively. Weselected resolutions (cid:15) p and (cid:15) r such that α , β , and γ are integers. Object posescan only change through a set of tray tilting actions A . Tilting directions werechosen to make a sequence composed of N actions. S = { a , a , ..., a N } , a i ∈ A where A is the set of tilting actions in the cardinal directions. We execute asequence S consisting of N random samples from A with replacement, and trackthe resulting sequence of object poses. We repeat the same sequence M timesto obtain an estimated pose probability distribution after each action a i , f i ( x, y, θ ) = 1 M V ix,y,θ (5)where V ix,y,θ is the number of object poses that occupy the 3-dimensional intervalin space, or voxel, ( x, y, θ ) after executing action a i .Given the pose probability distributions, we can compute the system entropy H i following action a i . H i = − (cid:88) x ∈X (cid:88) y ∈Y (cid:88) θ ∈ Θ f i ( x, y, θ ) log f i ( x, y, θ ) (6) H can be interpreted as the number of additional information bits required tospecify the object pose. If the pose distribution is uniform prior to the firsttilt, then the entropy would be close to the logarithm of the number of voxels, H = log ( α × β × γ ). Ideally, the sequence converges to a fully determined pose,and the entropy drops to zero, H N = 0. In terms of object pose uncertainty, highentropy corresponds to more uncertainty while low entropy corresponds to lowuncertainty.The main experimental challenge is the number of experiments required toreliably estimate the probability distribution of the poses. Lane [12] suggeststhat the number of trials M should satisfy α × β × γ = 2 M / (7)where α × β × γ is the number of voxels. The implication is that a large numberof trials is required for even a very modest number of voxels. For our physicalexperiments (Section 4) we selected a 3 × × M = 2 , N = 50 tilts, resulting in a totalof M × N = 123 ,
000 tilts.Unfortunately, the object and tray wear down after hundreds of tilts, chang-ing the frictional properties of the system. We therefore settle with M = 500 Pragna Mannam et al.
Fig. 2: Randomly generated object shapes used in simulation experiments. Den-sity of objects set to be the same as that of the simulated L-shape allen key.trials and a total of 25 ,
000 tilts. As discussed in Section 5, the number of oc-cupied voxels significantly decreases after the first couple of actions. In effect,we have a much smaller number of occupied voxels, which leads us to believethat the smaller number of trials are sufficient for our experiments. To conductexperiments on a large scale without the real world challenges such as wear andtear, we look towards simulation.For analyzing simulation data, we selected a 4 × × M ≈ ,
000 trials for high quality estimates of the probability distribution ofthe poses, according to Equation 7. Our three simulation experiments in Sections3.1,3.2, and 3.3 tested a total of 78 sequences ( M = 10 ,
000 trials per entropytrend for the first two experiments and M = 1 ,
000 trials for the third). Thisresults in almost 78 × , ≈ , ,
000 trials in total if we were to occupy all4 × × ,
000 trials with sequences consisting of 50 actions resulting in 30 , , Executing the experiment first in simulation enables us to generate the neces-sary number of trials required to estimate the object pose distribution with asufficient pose resolution, across different action sequences, object shapes, andfriction noise levels. For a realistic simulation we used the multibody contactfriction model library in MATLAB Simscape. The tray used in the tray-tiltingexperiments was modeled as a box with no lid. The actions were 30-degree traytilts in any of the eight cardinal directions. We started with an L-shaped object, ensorless Pose Determination using Randomized Action Sequences 7
Fig. 3: Kruskal effect for the allen key: M = 10 ,
000 trials of N = 50 actionswere repeated across 43 distinct random sequences. The mean (bold red linethat converges by the 20 th tilt) is bounded by the interquartile range (in blueshaded region). The thin black lines show individual sequences’ entropy trends,some of which approach zero by 50 actions. The shortest converging sequence isshown in green reaching zero entropy by the 8 th tilt.mimicking the allen key used by Erdmann and Mason [9]. In the rest of thepaper, we will use the terms actions and tilts interchangeably.We simulate the contact model as a linear spring damped normal force withparameters selected to match experimentally observed metal-on-metal interac-tions. In Section 3.2, we used a few other polygonal shapes, as shown in Figure2. All object interactions were modeled similarly, even for varied object shapes.The friction model is stick-slip with a velocity threshold [14]. To simulate noiseduring sliding for the tray friction noise in Section 3.3, the coeffecient of frictionis varied spatially with an amplitude that we can vary to explore the effect ofdifferent friction noise levels.The initial object pose in each trial was sampled from a uniform distributionin the objects configuration space (CSpace). Samples where the object was incollision with the wall were rejected. To compute entropy throughout the se-quence of actions as described in Section 2, we discretized the CSpace ( x, y, θ )into 4 × × x, y, θ ) voxels.We conducted three sets of experiments in simulation. Section 3.1 testswhether the Kruskal effect could be observed for the L-shaped object. Section3.2 tested other triangular shapes to confirm that the effect is not specific to L-shaped objects. Finally, Section 3.3 introduced friction noise in our simulation, Pragna Mannam et al.
Fig. 4: Varying the object shape: M = 10 ,
000 trials of N = 50 actions wererepeated using the same random sequence (green line from Figure 3) across 15various object shapes. The mean (bold red line) is bounded by the interquartilerange (in blue shaded region). The thin black lines represent distinct objectposes, most of which converge by 50 actions.to observe its effect on convergence rate. Each set of experiments is describedbelow. The first set of simulation experiments used a single object, the L-shaped modelof the allen key. We generated 43 distinct random action sequences S , each oflength N = 50. Each sequence was repeated M = 10 ,
000 times, starting frominitial poses uniformly sampled from the CSpace as described above.Figure 3 shows the entropy for each sequence, the mean across all sequences,and the inter-quartile range. In this instance, the Kruskal effect is readily ob-served. While the entropy is not monotonically decreasing, there is a clear trend.Of the 43 sequences tested, 29 converged to zero entropy, with all poses landingin a single voxel. The majority of data (25% −
75% or the interquartile range)is within the blue shaded region in Figure 3. On average, the entropy convergesto a value close to zero by the 20 th tilt. The best randomly-generated sequenceconverges in eight actions (shown as the green line in Figure 3), whereas theErdmann and Mason plan converges in five. While not conclusive, the resultssuggest that converging plans are common, but optimal plans are rare. This isexpected since the actions were randomly chosen instead of being planned. ensorless Pose Determination using Randomized Action Sequences 9 x [m] y [ m ] F l oo r F r i c t i on M odu l a t i on x [m] y [ m ] x [m] y [ m ] Fig. 5: Spatially varying floor friction with low (left), medium (middle), and high(right) variation
During the second set of experiments, we tested the effect of varying objectshape. We used 15 different triangular object shapes (see Figure 2) and appliedthe fastest converging sequence we found for the allen key (shown as the greenline in Figure 3). We conducted M = 10 ,
000 repetitions for each object, startingat a randomly sampled initial object configuration.The results are shown in Figure 4. Of the 15 objects tested, 10 converged tozero entropy. The majority of the data shown by the interquartile range (blueshaded region in Figure 4) oriented the test object into a single final determinedpose. On average, the entropy converges to a value close to zero by the 27 th tilt.The best sequence generated for the allen key does not perform as well on theother shapes, although it still tends to converge in most cases. One interpretationis that some objects are harder to orient than others, which is not surprising.In the context of pushing, this has already been proven [3]. It is also likelythat we have used a part-specific plan, by generating several part-agnostic plansand then selecting the best for the L-shaped object. We have only restrictedto triangular shapes as an initial exploratory experiment, and studying otherconvex and concave object shapes is left for future work. The third set of experiments explored the effect of friction noise with the same30-degree tray tilts and L-shaped object randomly initialized in the CSpace.We apply a simple noise model in which we let the coefficient of friction varyrandomly with respect to position within the tray as our real experiments ex-hibited spatially-varying friction due to wear. Figure 5 shows the low, medium,and high amplitudes of variation. We randomly generated 20 distinct frictionmaps, which were grouped by their mean friction to generate 13 low-noise maps,3 medium-noise maps, and 4 high-noise maps. We used the allen key, and thebest-performing action sequence found for the allen key in the first set of experi-ments, which is shown as the green line in Figure 3. The chosen action sequencethat converges by eight tilts allows for observable medium and high friction noise
Fig. 6: Varying the friction noise: M = 1 ,
000 trials of N = 50 actions repeatedusing the same random sequence (green line from Figure 3) with 20 distinct floorfriction noise amplitudes. The mean (bold red line) is bounded by the interquar-tile range for each category of friction floor noise illustrated in Figure 5—low,medium and high.convergence behavior, as low friction noise should converge close to eight tilts.We performed M = 1 ,
000 repetitions for each friction map, which is sufficientto observe the effect on the probability distribution of pose between maps.The results are shown in Figure 6. For the low noise maps, 10 of the 13entropy trends converged to zero entropy. On average, entropy converges to avalue close to zero by the 9 th tilt.Figure 6 also shows the results for medium and high noise. None of themedium- or high-noise maps converged to zero entropy. In both cases, the Kruskaleffect is observable in that the general trend of entropy is decreasing, althoughthey tend to not converge to zero entropy within 50 actions. These results showthat lower friction noise positively affects the probability distribution of objectposes towards convergence. It is also likely that better-performing sequencesexist for higher friction noise levels. Longer sequences are necessary to drawconclusions as to whether entropy for medium and high friction noise will leveloff or converge after more than 50 tilts. The simulation results suggests that the Kruskal effect can be observed for 2Dobjects, with significant entropy reduction for a variety of triangular objects and ensorless Pose Determination using Randomized Action Sequences 11
Fig. 7: Experimental setup. An industrial robot tilts an allen key, with April Tagattached, in an aluminum tray. The overhead camera records the pose of theallen key after each tilt.friction noise levels. However, physical rigid body interactions can be complex tosimulate accurately. The goal of the physical experiments is to test the validity ofthe simulations. We tested one of the randomly generated sequences consistingof 50 actions. We used a 6-DOF ABB IRB 120 robotic arm tilting a 200 mmsquare aluminum tray. The object is a 77.5 × × × H . A uniform distribution over 27 voxels would yield an entropy of about 4 . .
72. Themeasured entropy of our initial distribution is around 3 .
9, for a difference ofjust under one bit. We attribute the difference to the fact that some of ourCSpace volume
X × Y × Θ is infeasible due to collisions with walls, and to smalllimitations in our vigorous shaking motion.Entropy is calculated in the same way as Section 3, discretizing the trayvolume into 3 × × x, y, θ ) voxels. Corresponding results are shownin Figure 8. The entropy line is quite noisy which makes it difficult to drawconfident conclusions, but the general trend is downwards and indicative of the E n t r op y Fig. 8: Robot Entropy Data: M = 500 trials of N = 50 actions repeated on therobot using the same sequence that was used in simulation experiments 3.2 and3.3.Kruskal effect. In future work, real world issues like wear and tear should beaddressed to obtain more trials and finer resolution for more concrete inferences. In this section, we will discuss the results presented in Sections 3 and 4, drawconclusions and discuss insights for future exploration.From the planner proposed by Erdmann and Mason [9], we know that plannedactions can orient an allen key to a final determined pose. Although their pro-posed sequence efficiently oriented the object, we wanted to explore how randomsequences would perform at the same task. Towards this end, Section 3.1 testsvarious random sequences on the same test object. Almost all sufficiently longsequences significantly reduce the entropy, and most sequences result in zeroentropy. We show that the Kruskal effect applies for any random sequence tomostly or completely reduce object pose uncertainty.Given an object, it would be possible to produce an object-specific planby searching random sequences and selecting the best. However, we consideraction sequences that are not object-specific which is beneficial when introducingnew objects. We show this in Section 3.2, where we selected the best allen keysequence, and repeated it for other triangular shapes. Figure 4 shows that thesequence reduced entropy to a few poses within 30 tilts. On average, the sequencesucceeds at decreasing entropy for all tested objects, perhaps because the objects ensorless Pose Determination using Randomized Action Sequences 13 are all somewhat similar to the L-shaped object. Even a part-specific sequenceserves as part-agnostic sequence, although a less efficient one. Testing shapeswith more edges, especially with a rectangular tray, could affect the amount ofuncertainty in object pose. A possible extension of this work is to identify suchobjects and environments.In Section 3.3, we explore the significance of non-deterministic actions, byintroducing a noise model. While the entropy did generally decrease over thetilting sequence regardless of noise, the higher the noise, the slower the objectposes seemed to converge. The Kruskal effect can be observed in less than idealconditions such as high noise, but lower friction noises are more efficient atlowering pose uncertainty. Future work might extend the sequences to see if theentropy levels off at some value depending on the friction noise level or determinewhether different sequences perform better at different noise levels.In Section 4, we show that our theory can be applied to the real world. Evenwith the noise arising from variations in setup and execution, the object posesstill converge to a relatively low entropy. In the future we are interested in furtherexploring the limits of tray tilting actions reducing object pose uncertainty inthe real world and the effects of wear on physical systems through exploitationof material interactions.Simulation provided large amounts of data and easily varied parameters toconfirm the decrease in entropy provided by randomized action sequences. Thelargest entropy decrease among simulation and robot experiments was after thefirst move. At first, random initialization causes the object to be anywhere in thetray and subsequently, only along the edges of the tray after the first tilt. Testingacross different triangular object shapes demonstrated some of the generality inshapes that the system can tolerate. Simulation using different noise parameters,showed that entropy reduction works under stochastic conditions.In some of our sequences, the object pose did not converge completely to 0after 50 iterations. We think this is because for some objects, a certain mini-sequence of actions must be executed consecutively for distinct poses to convergeto one pose. When randomly selecting actions, it may sometimes require a verylong sequence for this mini-sequence to appear. Additionally, for our experi-ments, small increases in entropy occur due to small changes between similarposes that map to distinct voxels. Later, these poses will converge again butmay take some time to find the rights actions to realign. Informally, it is possi-ble to make a few observations about the tray tilting process. The main order-producing phenomenon is when we drive the object pose to the boundary of theCSpace, i.e. a contact between object and tray wall. Ideally, this is a projectionof the feasible poses to the boundary, and reduces the dimension of the feasibleCSpace. For example, if each dimension of SE (2) is quantized into N bins, thenat the beginning the pose is spread across N bins, and after one action it hasbeen projected to a surface spanned by N bins.In the simplest case, shown in Figure 9 using squeezing actions of a disk,this projection would be a normal projection onto a line. These actions wouldbe analogous to tilting a tray back and forth. For a second action to combine Fig. 9: The effect of orthogonal actions on object pose. Long blocks representa manipulator’s two fingers with which we can execute horizontal and verticalsqueeze grasps. Translucent disks indicate possible initial poses, and opaquedisks indicate the resulting final poses after executing the action. Starting fromrandom initial poses of the disk, the pose uncertainty in (x,y) goes to 0 if thesqueeze grasps are orthogonal.most effectively with the first, the second line would be orthogonal to the first,and the final disk position would then be uniquely determined.In general, the CSpace surfaces that correspond to kinematic constraintscannot be modeled as linear, nor are the projections linear, but still the toyexample may provide some useful insights. The more closely two actions can bemodeled as orthogonal projections, the better.The main disorder-producing phenomenon might be sliding across the trayfloor, where minor variations in friction can cause rotation of the object. Thevagaries of sliding friction can also make it impossible to say whether an objectwill stick or slide along a tray wall.There are also disorder-amplifying phenomena. For example, if the partstrikes the wall sharply it will rebound, and the small variations in initial posewill be integrated over time to produce large variations. It is this effect we reliedupon to randomize the object pose prior to testing a sequence of actions in ourphysical experiments.The effectiveness of a sequence depends on how common and how effectivethe order-producing actions are, how frequently combinations occur, and howeffectively they combine, versus the frequency and degree of disorder producedby the other actions. One goal of future work will be to explore this underlyingstructure more precisely, as a way of characterizing tasks.
Examining the traditional approach of sense-plan-act, we observe the effects of analternative approach of executing random sequences of actions without sensing. ensorless Pose Determination using Randomized Action Sequences 15
We show that a sufficiently long random sequence of actions can move an objectfrom an unknown initial pose to a determined final pose, regardless of initialpose of the object, varying object shapes, and stochasticity in the environment.This effect is explored in greater detail through simulation using millions of tiltsand observing the entropy trends over action sequences. We learned how someparameters affect our system: longer sequences lower object uncertainty, andstochasticity in the environment as well as some variation in triangular objectshapes does not disturb the system. We also illustrated the same effect on areal robot and saw a decreasing trend in entropy. However, the final entropy isnot as low as suggested by simulation results, due to real world challenges andcomplications such as wear and tear.This is a different paradigm than the sense-plan-act approach where the finalpose and the action sequence to achieve that pose are planned; exploring thisalternative paradigm and its limitations could be fruitful. We offer insights intothe idea of randomized action sequences instead of planning. The advantage inour setup is that random tray-tilting actions are not part-specific and reducesystem complexity for new objects. For example, orienting a kit of parts is ahard planning problem, but compartmentalized trays executing random tiltingactions is a part-agnostic way to make progress in solving that problem.
Extensions of this work to various polygons or approximations of non-convexobjects and tray-tilting alternatives like pushing would further explore the effectsof randomized action sequences. The sustainability of our approach can be testedthrough longer sequences in simulation and on physical systems, as well as moretrials for higher quality estimates of entropy. We are also interested in waysto capture the order of the system in a data-efficient way. A future goal is tomove towards a tray with a lid that can offer a 3D exploration of part-agnostictray-tilting to determine 3D object pose.To identify action sequences that are efficient at orienting a given object, wecould learn a policy like Christiansen et al. [8], but with finer discretized trayregions for more accurate object poses. Another future direction would be toexplore potential applications of the proposed approach in simplifying a poseestimation problem for a manipulation task.
References (12), 1147–1170 (2000). DOI 10.1177/02783640022068002. URL https://doi.org/10.1177/027836400220680023. Berretty, R.P., Goldberg, K., Overmars, M.H., van der Stappen, A.F.: On fencedesign and the complexity of push plans for orienting parts. In: Proceedings of6 Pragna Mannam et al.the Thirteenth Annual Symposium on Computational Geometry, SCG ’97, pp.21–29. ACM, New York, NY, USA (1997). DOI 10.1145/262839.262853. URLhttp://doi.acm.org/10.1145/262839.2628534. Berretty, R.P., Goldberg, K., Overmars, M.H., van der Stappen, A.F.: Orientingparts by inside-out pulling , 1053–1058 vol.2 (2001). DOI 10.1109/ROBOT.2001.9327335. B¨ohringer, K., Brown, R., Donald, B., Jennings, J., Rus, D.: Distributed roboticmanipulation: Experiments in minimalism. In: O. Khatib, J. Salisbury (eds.) Ex-perimental Robotics IV, Lecture Notes in Control and Information Sciences, vol.223, pp. 11–25. Springer Berlin / Heidelberg (1997). 10.1007/BFb00351936. Brost, R.C.: Automatic Grasp Planning in the Presence of Uncertainty. TheInternational Journal of Robotics Research (1), 3–17 (1988). DOI 10.1177/0278364988007001017. Chirikjian, G.S.: Stochastic Models, Information Theory, and Lie Groups, Volume1: Classical Results and Geometric Methods, vol. 1. Springer Science & BusinessMedia (2009)8. Christiansen, A.D., Mason, M.T., Mitchell, T.M.: Learning reliable manipula-tion strategies without initial physical models. Proceedings., IEEE InternationalConference on Robotics and Automation pp. 1224–1230 vol.2 (1990). DOI10.1109/ROBOT.1990.1261659. Erdmann, M.A., Mason, M.T.: An exploration of sensorless manipulation. IEEEJournal on Robotics and Automation (4), 369–379 (1988). DOI 10.1109/56.80010. Goldberg, K.Y.: Orienting polygonal parts without sensors. Algorithmica (2),201–225 (1993). DOI 10.1007/BF01891840. URL https://doi.org/10.1007/BF0189184011. Grossman, D.D., Blasgen, M.W.: Orienting mechanical parts by computer-controlled manipulator. IEEE Transactions on Systems, Man, and Cybernetics SMC-5 (5), 561–565 (1975). DOI 10.1109/TSMC.1975.540838112. Lane, D.M.: Online Statistics Education. Rice University. URL http://onlinestatbook.com/13. Lee, K., Moses, M., Chirikjian, G.S.: Robotic Self-replication in Structured En-vironments: Physical Demonstrations and Complexity Measures. The Interna-tional Journal of Robotics Research ,600–608 (1984). DOI 10.1109/ROBOT.1984.108715517. V´arkonyi, P.L.: Estimating part pose statistics with application to industrial partsfeeding and shape design: New metrics, algorithms, simulation experiments anddatasets. IEEE Transactions on Automation Science and Engineering (3), 658–667 (2014). DOI 10.1109/TASE.2014.231883118. Zhou, J., Paolini, R., Johnson, A.M., Bagnell, J.A., Mason, M.T.: A probabilisticplanning framework for planar grasping under uncertainty. IEEE Robotics andAutomation Letters2