An Empirical Comparison Among the Effect of Different Supports in Sequential Robotic Manipulation Chao Cao, Weiwei Wan, Jia Pan, and Kensuke Harada Abstract— Pick-and-place regrasp extends the manipulation capability of a robot by using a sequence of regrasps to accomplish tasks that are not possible using a single grasp due to constraints such as kinematics or collisions between the robot and the environment. Previous work on pick-and-place only leveraged static passive devices for intermediate placements, and thus is limited in the flexibility and robustness to reorient an object. In this paper, we extend the reorientation capability of a pick-and-place regrasp by adding an actively actuated gripper fixed in the working cell, and using it as the intermediate location for regrasping. In particular, our method automatically computes the stable placements of an object being hold in the gripper support, finds a rich set of force-closure grasps, performs k-means based grasp clustering, generates a graph of regrasp actions, and searches for the optimal regrasp sequence. To compare the regrasping performance with typical passive supports, we evaluate the success rate while performing tasks on various models. Experiments on reorientation tasks validate the benefit of using an actively actuated gripper for regrasp placement. I. I NTRODUCTION Object reorientation performed by a robot manipulator plays an important role in industrial assembly lines [1], [2]. In many cases, the robot may not be able to reorient an object from its initial pose to a target pose within one round of pick-and-place. This is due to several constraints posed on the robot’s movement, e.g., the robot needs to avoid colliding with its surrounding environments, and must take its joint limits and singularity into account while moving. To overcome these difficulties and extend the robot’s reorientation capability, one typical solution is using a sequence of pick-and-place operations to change the object’s pose incrementally. In particular, after the object is picked up by the first grasp, it would be stably placed on an intermediate support and then picked up again using another grasp [3]. The design of the intermediate support is crucial for the flexibility and robustness of the pick-and-place regrasping. A desirable support should provide the object with many different ways of being placed on, and each placement should allow of many valid grasps. More formally, the flexibility in placements helps to increase the connectivity of the regrasp graph [4] and is important to the quality of the regasp sequence. There has been extensive work [5], [6] on pick-andplace regrasp since the 1980s, due to its importance for Chao Cao is with the Department of Computer Science, the University of Hong Kong. Weiwei Wan is with National Institute of AIST, Japan. Jia Pan is with the Department of Mechanical and Biomedical Engineering, the City University of Hong Kong. Kensuke Harada is with the Systems Innovation Department, Osaka University, Japan. jiapan@cityu.edu.hk object reorientation. Starting from early seminal work only considering supports in terms of a horizontal plane, many different types of supports have been investigated, including the tilted flat support [7], [4], the pin shape support [8], and surfaces with general geometry [9], [10], [11]. Leveraging these non-horizontal supports in the sequential regrasping can increase the number of valid placements and grasps, and thus improves the reorientation capability of a single robotic arm. However, due to physical factors such as gravity and friction, many placements and grasps associated with an object will still be invalidated during the grasping process. For instance, objects with round surfaces (like a screw) may not be able to be placed stably on a titled surface or a pin. This greatly limits the number of possible placements and thus also the connectivity of the resulting regrasp graph. To address this challenge, in this paper we propose a novel method which facilitates the pick-and-place operation of a robot manipulator by using an additional gripper fixed in the working cell as the support. In a single step of pickand-place, the robot manipulator first hands over the object to the gripper support and then picks it up again using a different handover. Thanks to the active grab of the gripper support, each of the gripper’s valid grasp will correspond to a valid placement of the object in the gripper support. In this way, we can have many more placements associated with the object than the case when plane or pin supports are used. In addition, these placements are only determined by the geometry of the object and the gripper support, and are not affected by physical issues such as gravity and frictions, which is beneficial for the robustness of the regrasp planning. Our method of regrasp planning with the gripper support can be viewed as a special case of the dual-arm manipulation problem, where a gripper mounted on a high-DOF arm is used as the support. We fix the supporting gripper in the working cell in order to benefit from the placement flexibility of a gripper, but avoid the complexity of determining the handover poses and solving the motion planning problem for the second manipulator. We perform statistical analysis on arbitrary mesh models with thousands of experiments to demonstrate the advantages of using a support gripper for regrasp. We also empirically compare the regrasping performance while using various types of supports, which is helpful to develop intuitions about how to select an appropriate support. Our algorithm first computes all the force-closure grasps for a Robotiq 2finger adaptive gripper given the mesh model and an object. In our experiment, the robotic manipulator end-effector and the fixed gripper support use the same type of gripper. As (a) mesh model (b) total grasps (c) clustered grasps (d) keep one grasp for each cluster (e) valid grasps associated with a placement (f) re-grasp graph (g) reorientation task Fig. 1: An overview of our sequential robotic manipulation using one gripper fixed in the working cell as the intermediate support. Given the mesh model of an object, our method automatically computes the stable placements of the object on the support gripper, finds force-closure grasps, performs grasp clustering, generates a graph of regrasp actions, and searches for regrasp sequences. a result, the grasps computed can be used as the handover grasps of the fixed gripper support, and each of them corresponds to a valid placement of the object on the gripper support. For each placement, we can use the computed forceclosure grasps to find the grasps associated with it. In this way, we can generate a large number of placements and associated grasps, and their explosive combinatorics result in a gigantic regrasp graph, which makes the regrasping process computationally expensive. Our solution is using k-means algorithm augmented with the triangular inequality [12] to cluster the force-closure grasps and thus simplify the regrasp graph, where the parameter k controls the complexity of the resulting simplified regrasp graph. Finally, the manipulation sequence for re-orientating the object can be found by searching through the regrasp graph for a shortest path connecting the initial and goal poses. We use the two-layer regrasp graph in [4] to decouple the search of pick-andplace sequence and the search of grasps, and delay expensive inverse kinematics and collision detection computations until necessary. We evaluate the success rates of reorientation tasks with different mesh models and regrasp graphs with different levels of complexity, by performing thousands of trials of pick-and-place tasks. Our results show that an added fixed gripper support is more beneficial for the reorientation task, comparing to the planar support and the pin support. We also find the regrasping success rate increases with the complexity of the regrasp graph but saturates quickly, which can help us to select an appropriately small value of k making a good balance between the success rate and the computational efficiency. II. R ELATED W ORK There is extensive work on the sequential robotic manipulation, which plans a coordinated sequence of motions involving picking and placing, as well as moving through the free space. Previous approaches can be classified into two categories according to whether a passive or active support is used for the intermediate placement. A. Passive Supports A passive support does not is actively actuated, and relies gravity and friction to provide object. Many different types of have a movable part that on passive forces such as a stable placement for an passive supports have been leveraged in previous work, including horizontal planes [5], [6], tilted planes [7], [4], pins [8], and surfaces with general geometry [9], [10], [11]. Most passive supports are either preassigned or pre-designed [7], [4], [8], or are selected online from a set of candidate supports either autonomously [13], [10], [11] or interactively [9]. Due to their simplicity, passive supports are widely used in previous regrasp planning research and also in industrial applications. However, a passive support may not be able to provide many valid placements because some placements may not satisfy the stability constraints posed by the gravity and friction. For instance, a screw is difficult to be placed stably on a tilted surface or on a pin. Another challenge of the passive support is its dependence on the unknown/uncertain physical constraints such as friction coefficient and the object’s mass distribution. As a result, a placement which is predicted to be valid in the regrasp planning may not support an object stably during the real execution (e.g., sliding on a tilted surface), and thus reduces the robustness of the sequential robotic manipulation [5]. A special case of the passive support is the fixture, which is an important tool used to hold an object firmly for manufacturing [14], [15]. The seminal work for 2D fixture layout design is by Brost and Goldberg [16], which is then extended to 3D objects in [17]. Similar to passive supports, a fixture immobilizes a given object using the point-based [18] or surface-based contacts [19] between the fixture’s locators and the object. A fixture is designed to provide a single stable placement for a given object, while a desirable passive support should have many placements to maximize the flexibility of sequential robotic manipulation. B. Active Supports An active support is an actively actuated mechanism which is able to hold an object firmly at different poses. Each pose corresponds to a valid placement of the object in the workspace. Thanks to the firm grab of the actuated mechanism, these placements are determined only by the geometry of the active support and the object, and is independent of the passive forces such as gravity and friction. This is beneficial for the consistency between the planned regrasp sequence and the actual execution sequence of the robot. The most general active support is a gripper mounted on a high-DOF robotic arm. The gripper-arm support is able to place objects at arbitrary positions and orientations within the reachability space of the robotic arm. When using the gripper-arm support, a single-arm regrasp planning problem is equivalent to the dual-arm regrasp planning, which is challenging due to the high-dimensional configuration space composed of two arms and the exploded number of combinatorics between the two grasps during handovers. This difficulty was first discussed by Koga et al. for the 2D case [20] and 3D case [21] respectively. Some approaches formalized the regrasp planning as an optimization problem minimizing an objective function with respect to the regrasp position and object orientation. The objective function can be the wrist motions and approaching angles of two hands [22], time needed to move the two hands to the estimated positions [23], or manipulability [24]. In order to reduce the dual-arm combinatorics, recent work pre-filtered dual-arm grasps using different criteria, including manipulability & approachability [25] and synergy analysis [26]. The gripper support used in this paper is also an active support, and is a simplified version of the gripper-arm support mentioned above, where the arm is of zero degreeof-freedom. In this way, we sacrifice part of the flexibility provided by the dual-arm setting, but achieve a significant acceleration in the performance of the regrasp planning while also share the robustness advantage of the active support, i.e., it is insensitive to the unknown/uncertain of the physical parameters such as friction coefficients and the mass distribution of the objects. [28]. To solve this difficulty, given an object containing curved surfaces, we first decompose it into low curvature areas and high curvature areas. For low curvature areas, we use the method mentioned above to compute the grasps. For high curvature areas, we approximate them using primitive geometries like cylinders and spheres. For each primitive, we per-determine a set of grasps, and then by combining the grasps of each primitive part, we can obtain the grasps for the high curvature areas. For instance, for the screw object in Figure 2(i), we decompose it into two parts: the hexagon head and the cylinder shank. The hexagon head is of low curvature and its grasps (Figure 3(a)) are computed using methods in [8], [4]. The cylinder shank is of high curvature and its grasps are pre-determined as shown in Figure 3(b), which can be categorized into three groups: The first group of grasps have approaching vectors pointing orthogonally toward and sampled around the central axis of the cylinder; the second group of grasps are approaching the screw from the two ends of the cylinder; and the last group of grasps have two finger pads touching each end of the cylinder, given that the cylinder’s height is lower than the maximum distance between the fingers. We combine these pre-determined grasps with the grasps for the hexagon part, and then perform collision checking test for these grasps. Figure 3(c) show the resulting grasps that pass through the collision checking test. III. R EGRASP USING A F IXED G RIPPER S UPPORT In this section, we discuss the details about our pickand-place regrasp leveraging a gripper fixed in the working cell as the temporary support. Our method mainly consists of three parts: 1) computing all possible stable placements with collision-free grasps associated; 2) building a regrasp graph whose connectivity reflects the number of common grasps associated with each pair of different placements; 3) searching in the regrasp graph for a shortest path between the initial and goal placements, in order to generate a possible pick-and-place grasp sequence. A. Grasp Computation Given an object, a single grasp gi of a parallel gripper can be determined by the gripper’s position (xi , yi , zi ) and orientation (αi , βi , γi ) relative to the object and the distance df inger between two parallel fingers. We compute all the possible force-closure grasps of an object using a method similar to [8] and [4]. In particular, all the parallel face pairs of the mesh model are first checked, and then rotation directions are sampled around the normal of candidate parallel faces, where the number of rotation directions is related to the grasp density. However, this method is not applicable to objects containing curved surfaces. This is because in order to achieve an accurate approximation to high curvature areas, these objects would have a large number of small facets, which are challenging for efficient grasp computation [27], Fig. 2: All objects used in our experiments. (a) (b) (c) Fig. 3: Grasps of the screw object. (a) shows the grasps associated with the hexagon part. (b) shows the grasps associated with the cylinder part. Since the height of the cylinder is greater than the finger distance, there are only two kinds of grasps remained for the cylinder and they are shown in red and blue colors respectively. (c) The grasps for the object passing through the collision checking test. B. Grasp Clustering and Placement Computation A placement pgripper on the fixed gripper is determined by i the pose at which an object is grabbed by the fixed gripper support. Mathematically, a placement is a transformation matrix transforming the object from its own frame to the frame of the fixed gripper. After the transformation, we perform collision checking for all the grasps associated with the object to avoid collisions between the robotic manipulator and the gripper support, as well as the collisions between the robotic manipulator and the table. The collision-free grasps are then associated with the placement and they are denoted as pgripper , Gi , where pi is the placement on the fixed gripper i i and G = gpi , gqi , ... is the valid grasp set for pgripper . We i also denote the placements while using the planar support and the pin support as pplanar and ppin respectively. Fig. 4: Examples of placements for the screw object. as nodes and connecting their shared identical grasps. For more details about the graph construction, please refer to [4], [8]. Given the re-grasp graph, the manipulation sequence could be found by searching through the re-grasp graph for a shortest path connecting the initial and goal placements. The path may include intermediates nodes where the robot put the object temporarily in the fixed gripper and do regrasp. It may also include only the initial and goal placements so that the robot can directly do reorientation. A demo re-orientation task of the screw object is shown in our attached video. IV. E XPERIMENTS AND A NALYSIS The resulting number of placements would be huge if every single grasp is converted to a corresponding placement. This would result in a large number of nodes in the regrasp graph, and will increase the time cost while building and searching in the graph. In addition, large number of similar grasps also increase the overhead for collision checking. We solve this problem by clustering similar grasps and only keeping one representative grasp for each cluster. We use the k-means algorithm to cluster grasps into k clusters according to a similarity measure among grasps. As mentioned above, a grasp can be defined by a 6-tuple gi = (xi , yi , zi , αi , βi , γi ) if we neglect the difference in finger distance, where (xi , yi , zi ) represents the position of the gripper center, and (αi , βi , γi ) represents the orientation of the gripper. To measure the similarity between two grasps, we use the scaled Euclidean distance [29] as the distance metric, which is defined as:  12  X X Qij (k)2 , Pij (k)2 + (1 − s) d(gi , gj ) = s k=x,y,z k=α,β,γ (1) where Pij (k) = |gi (k) − gj (k)|, k ∈ (x, y, z) and Qij (k) = n|gi (k) − gj (k)|, k ∈ (α, β, γ), and n is the normalization factor. s is a parameter adjusts the relative weights of P and Q in the distance metric. In particular, we choose 1−s > s so that distance between orientations are weighed more heavily. In addition, we use the scale of the object to normalize the orientation part, which is inspired by [29]. The grasps are then clustered using the k-means algorithm augmented with the triangular inequality [12]. After clustering, one grasp from each cluster that is the nearest to the cluster center is chosen as the representative grasp. For the sake of keeping the cover range of the grasps, we set the parameter k to be 24 at the beginning. Figure 1 shows the clustered grasps associated with the lmodel, where each face is at least be covered by one grasp. The selection of k would affect the cover range of the clustered grasps thus affect the success rate of the pick-and-place tasks. The relation between the success rate of the tasks and parameter k would be evaluated in the experiment session. From the clustered grasps, we can obtain a set of placements providing as much support as possible but in a rather small size. C. Graph Searching and Planning After generating a number of grasps, we construct the regrasp graph by taking the placements P gripper = p1 , p2 , ... In this section, we demonstrate the advantage of using an added gripper fixed in the working cell for intermediate placement in the pick-and-place regrasp. In particular, we perform a large number of reorientation tasks in a simulated environment. We compare the success rates in the presence of three different placement settings: one only using the flat plane, one using an added support pin, and the third using the a gripper fixed in the working cell. In addition, we compare the computational costs (split into the regrasp graph construction cost and the regrasp graph online search cost) among the regrasp planning algorithms using the three types of placements. Meanwhile, for the gripper support, we also investigate the effects of grasp clustering against the success rates and the graph complexity of the resulting regrasp graph. A. Experiment Settings We use an ABB IRB140 robot manipulator with a 2-finger Robotiq gripper 85 mounted as the end-effector to repeatedly perform reorientation tasks for different objects as illustrated in Figure 2. The object 1t1p ( Figure 2(h)) is of a pot lid shape that is challenging for the planar support. It has a large body and a small handle and all its stable placements could be roughly categorized into two types: handle-down and body-down. Using only using the planar support, most bodydown placements are not valid due to collision, which results in a sparse regrasp graph. The object screw ( Figure 2(i)) has a cylinder body which is difficult to be placed stably on a pin support. We will show that the gripper support is able to provide high quality placements for all these objects. The working space is evenly divided into a 20 by 15 grid of 4 by 4 cm grid squares. At the corner of each grid square, 10 trials of pick-and-place tasks are performed by the robot. The initial and the goal positions of the objects are at the same corner while the orientations and placements are randomized in each trial. The object’s initial and goal placements are also randomly chosen from pplanar , i.e., the beginning and end of the manipulation are always placements on the flat surface. Several examples for the experimental settings are shown in Figure 1 and Figure 5. B. Comparison of Placements and Grasps We first compare three different types of supports in terms of placements and associated graphs. In Figure 6 we show the regrasp graphs for the model 1t1p using different (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) Fig. 5: Experiment settings for the sequential robotic manipulation while using the horizontal plane, the pin, and the fixed gripper as the support. The regrasp sequences for the planar support, the pin support and the fixed gripper support are illustrated in the first, second and third row respectively. For each support type, the robot is manipulating an object which benefits the most from it, i.e., 3t2s for the planar support, 1t1p for the pin support, and the screw for the gripper support. supports. As we discussed above, the 1t1p’s lip pot shape is challenging for the planar support, which only provides five placements for the object and the resulting regrasp graph is very sparse. The pin support is able to provide many more interconnected placements and the resulting regrasp graph is denser. The gripper support can provide the largest number of placements and result in a dense regrasp graph, which is helpful to generate high quality regrasp sequences. 1 0.9 success rate (a) support does not outperform the pin support significantly. For the object 3t2s, the gripper support’s success rate is even slightly lower. This is probably because the gripper’s larger geometric shape than the pin, which may limit the way the manipulator approaching the gripper support and thus results in fewer placements on the gripper support for choosing. Nonetheless, the gripper support is able to provide excellent regrasping success rate on all objects, while the planar support and the pin support behaves poorly on 1t1p and screw respectively. From the success rate results, we can also find that 1t1p is the most difficult one for the gripper support, because the gripper can only grab it at the brim and at the handle. For objects 3t, 3ts and 3t2s, which are intentionally decided to be a morphing sequence increasing the volume while decreasing the possible directions of grasps, the success rates decrease in the order of 3t > 3ts > 3t2s no matter which support is used. 0.8 0.7 0.6 0.5 without pin with pin with gripper l el 3t 3ts 3t2s object name cross tmodel 1t1p screw Fig. 7: Comparison of the average success rates of the reorientation task, while using three different types of support for the temporary placement. The red bars are the results only using the planar surface for support, the red bars are the results using one added pin for placement, and the green bars are the results using the gripper fixed in the working cell as the support. The comparison among the computational costs of three different supports are shown in Table I. We can observe that the sequential manipulation using the gripper support is slower than while using the planar and pin support. However, thanks to the acceleration due to grasp clustering, the gripper support still provides fast online performance. D. Grasp Clustering (a) (b) (c) Fig. 6: The regrasp graphs of the 1t1p object when using the horizontal plane (a), the pin (b), and the gripper fixed in the working cell (c) as the supports. C. Comparison of Success Rates and Computational Costs We then compare the reorientation task’s success rates while using three different types of support settings for temporary placement. From the result shown in Figure 7, we can observe that for most objects the fixed gripper will provide the highest success rate and for some of them the success rate is almost 100%. For objects el and 1t1p, the gripper We first show the complexity of the regrasp graph before and after the grasp clustering in Table II to demonstrate how the clustering algorithm effectively simplifies the structure of the regrasp graph while using the gripper support. Next, we vary the parameter k, i.e., the number of clusters in the k-means algorithm, to investigate the how the success rates change along with the parameter k. We observe that the reorientation success rate increases with the parameter k for all objects, but after k = 8, the success rate increases slowly. V. C ONCLUSION In this paper, we improve the pick-and-place regrasp planning by using a gripper fixed in the working cell for intermediate placements. We demonstrate that by using the support type average time(s) plane build graph time search graph time 41.1284 0.0735 pin build graph time search graph time 84.4023 0.2248 gripper build graph time search graph time 359.6374 0.3794 TABLE I: Comparison among the timing cost of the orientation task, while using three different placement settings. The timing cost is split into two parts: for the offline regrasp graph construction and for the online graph search, respectively. For the gripper support, we use k = 24 for the k-means based grasp clustering. support type post-processing average graph complexity(k = 24) gripper before clustering before clustering after clustering after clustering # Nodes # Edges # Nodes # Edges 169.7 29974.2 25.2 582.7 TABLE II: Average graph complexity of the regrasp graphs while using the gripper support. gripper placements, we can improve the connectivity of the regrasp graph, and eventually increase the success rate of the reorientation task for almost all objects, especially for objects with the screw shape which is ubiquitous in industrial applications. We perform a large number of experiments to empirically investigate how the performance of the reorientation task is influenced by a variety of factors, including the object’s shape and the grasp density. For the future work, we are interested in implementing the entire framework on real industrial robots for challenging manufacturing tasks such as 3C assembly. 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