A General Framework for Open-loop Pivoting
Anne Holladay and Robert Paolini and Matthew T. Mason The Robotics Institute — Carnegie Mellon University
{ahollday, rpaolini}@cmu.edu, {matt.mason}@cs.cmu.edu
Abstract— Pivoting is the rotation of an object between two fingers using gravity and inertial forces to impart angular momentum. We present an analysis of the mechanics of piv- oting and a framework for planning and execution. Extrinsic dexterity was defined by Chavan-Dafle et al. [1] as the use of external forces, such as gravity and inertial forces in post grasp manipulation. We analyze one such regrasp termed “pivoting” by Rao et al. [2]. We find a grasp and arm trajectory which can rotate an object between stable poses, if any. We demonstrate an implementation of pivoting with an ABB industrial arm and a two fingered gripper.
I. INTRODUCTION
Humans have a huge repertoire of regrasps. Some regrasps employ coordinated motions of many hand freedoms, dubbed ‘intrinsic motions’ of the hand. However humans also use the environment, like gravity or momentum, as an additional resource. For example, we find it quite natural to roll an object from our fingertips to our palm or to reorient chop- sticks in our hand by pressing them against the table. Chavan- Dafle referred to these actions as “extrinsic dexterity”. Much robotics research has focused on how to manipulate an object with the hand, using only the hand: intrinsic dexterity. But robots, lacking the dexterity of humans, should use the strategies provided by extrinsic dexterity, if anything, more often than humans. Chavan-Dafle describes several examples of extrinsic regrasps. This paper will explore, in detail, one of those regrasps: extrinsic pivoting. Pivoting is defined to be the rotation of an object about an axis determined by two contacts between the effector and object.
The most common approach to manipulation is the “pick- and-place” paradigm, where an object is rigidly grasped and placed in the goal position. Pick-and-place provides an alternative to regrasping with pivoting. However, pick- and-place regrasps take more time and space to execute. In practice, industrial work cells commonly try to minimize the free space the arm motions require. Pick-and-place requires much more joint rotation compared to pivoting. Additionally, we will show that pivoting is faster than pick-and-place regrasps.
Philosophically, the goal of manipulation is to understand the interactions between a robot and the world and use that understanding to accomplish tasks. Thoroughly understand- ing and exploiting the environment is long-range, very chal-
This work was supported by National Science Foundation [NSF-IIS- 0916557] and Army Research Laboratory [W911NF-10-2-0016]. This work does not necessarily reflect the position or the policy of the U.S. Government or ARL. No official endorsement should be inferred.
Fig. 1: Pivoting with a contact surface
lenging goal. Current practice largely proceeds without this capability. For example, manufacturing automation engineers the environment for the task. However, we can make progress on smaller, more manageable aspects of this challenge. In the case of pivoting, we gain a deeper understanding of how an object can move when it is not rigidly grasped.
Traditionally, to rigidly grasp an object, one must consider the form/force closure of the object by a certain grasp. To rotate the object, this consideration is no longer required. One can grasp objects with two fingers. By grasping with only two fingers, the grasp can not achieve form closure since the part can rotate about the contact axis. This is the exact freedom we will exploit. If the fingertips approximate point contacts with friction, we can rotate the object without slipping. With this motivation, we present a study of how environmental forces can be exploited through extrinsic dexterity to easily and effectively increase the dexterity of a multi-fingered hand.
II. RELATED WORK
This paper explores a type of extrinsic regrasping. In general in robotic manipulation, regrasping is avoided. This is particularly true in manufacturing where the gripper and workspace can be engineered for the task [3]. Pivoting is a simple and reliable way to increase the dexterity of a gripper without augmentation of the workspace.
The importance of manipulation beyond pick-and-place has been noted in robotics research in the past. The Instant
Insanity demonstration [4], [5] and the Handey project [6], [7] both recognize the limitations of the “pick-and-place” formulation. Here, pick-and-place was used to ‘regrasp’ ob- jects by simply performing several pick-and-place operations in a row.
Regrasping, as it was originally formulated, relies on the application of continuous controlled forces to the object through the fingertips. A hand capable of this form of dexterity is often referred to as a dexterous hand [8], [9], [10]. Much work has been done along this vein, including rolling [11], sliding [12], and finger gaiting [13], [14], [15], [16], [17], [18].
However, this paper concerns regrasping using external resources. This form of regrasping was proposed by Chavan- Dafle et al. [1] as “extrinsic dexterity”. A general use of external forces was suggested by Lynch and Mason [19]. The external forces can be categorized as either quasi-static, passive dynamic, or active dynamic.
Quasi-static actions include motions like pushing or squeezing. Nilsson [20] implemented pushing and squeezing on Shakey the robot. Mason [21], [22] analyzed pushing an object under frictional contact with a flat surface. Brock and Salisbury [23] proposed using controlled slippage to regrasp object by identifying possible slipping motions and selecting a grasp force that would produce a desired slipping motion.
Using dynamics to manipulate an object allows actions such as throwing, catching, and juggling. In these cases, inertia is imparted to the object through the dynamic motions of the driving manipulator. Aboaf et al. [24], [25] and Burridge et. al [26] developed learning and control strategies for these types of actions. Lynch and Mason [27] introduced the concept of “dynamic dexterity”, referring to the con- trollability and planning of dynamic manipulation actions. Srinivasa et al. [28] proposed a technique for trajectory planning of dynamic contact manipulation which separated the path planning problem from the time-scaling needed to satisfy the dynamic constraints.
The work most closely related to this work uses passive dynamics by introducing an understanding of gravity. Several different approaches have studied the motion of an object lying on a flat surface, for example a movable tray or a robot palm which tilts. Erdmann and Mason [29] manipulated a planar object from an arbitrary location on a tray to a known final location through a series of tray tilts. Erdmann [30] later presented a framework for non-prehensile manipulation of an object which can slide and rotate using two palms. Bai [31] studied the tumbling of objects on the palm of a dexterous manipulator using the fingers to stop the object.
Sawasaki and Inoue [32] recognized the usefulness of grasps which do not hold an object firmly and need not support its whole weight. They presented a physical analysis of tumbling objects using a multi-fingered dexterous hand by calculating the forces necessary to push objects about an edge contacting the table. Aiyama et al. [33] continued this work on pivoting showing how heavy objects can be manipulated by only lifting part of its weight and rotating about a vertex or edge. Finally, Carlisle et al. [34] presented a method of
parts feeding to rotate an object about an arbitrary axis. Here a specialized gripper was designed to allow free rotation between the fingers using a bearing. Rao et al. [2] developed an automatic planner to identify stable poses of polyhedral objects and choose a grasp such that the object would stably rotate due to gravity into the desired goal position. This work expands on this by relaxing the requirements of stability and introducing dynamics.
III. PROBLEM FORMULATION
We will formulate the problem of manipulating an object by considering an idealized model of the manipulator. For a two-fingered hand, let the manipulator be a set of two point contacts p1, p2 in the workspace W ' R3, and let M =Wp1 ×Wp2 ' (R3)2 be the configuration space of the manipulator.
Let O ⊂ W be the object to manipulate. Let FP be the fixed reference frame. The object is endowed with a task frame FO which is rigidly attached to its center of mass. Let ρ = (ro, Ro) ∈ SE(3) be the configuration of O where ro is the position vector and Ro is the quaternion defining the rotation of the body-attached frame w.r.t. FP .
A grasp g specifies two points on the object, which are coincident with the two end effector points. The two end effector points describe a configuration of the manipulator that constrain the mobility of the object to rotation in SO(2) relative to the effector. This plane is defined by the normal ng = (p2 − p1)/||p2 − p1|| and the midpoint of the manipulator pg = (p1 + p2)/2. Let Rg ∈ SO(2) be the set of object configurations reachable under grasp g.
The pivoting grasp is similar to the definition of a caging grasp [35], [36] in that the object is not immobilized by a grasp. However, in this paper, the point fingers p1 and p2 contact the object and remain fixed with respect to the object throughout the manipulation task. A pivoting grasp provides partial closure. A pivoting grasp will not enforce full force-closure, specifically it can not resist torques in the direction of ng . The grasp wrench space (GWS) [37], [38], [39] defining the space of wrenches that can be applied to an object by a grasp can be found by approximating the contact normal force and friction cone at each contact point. Each force representing the boundary of the friction cone can be translated to the wrench space origin. The convex hull of the union of these boundary wenches defines the GWS. A grasp is in force closure when this convex hull contains the wrench space origin. By definition, a rotational grasp is not in force closure. The GWS will be a lower dimensional subspace of the full wrench space, and, therefore, the wrench space origin can never be enclosed in the convex hull.
This degree of freedom inherent in the grasp describesRg . An object can pivot around the axis ng with an origin at the midpoint of the manipulator pg . The direction of rotation will be the defined by the torque about ng . Let θ be the object orientation relative to the hand.
We will henceforth only consider rotations between stable poses of the object, although our framework may be extended in the future to accommodate arbitrary configurations in Rg
(a) (b) (c)
Fig. 2: (a) An example of a collision between the gripper and the table. If the gripper tried to grasp the object at the corner, there would be a collision with the table. (b) A collision between the object and gripper during rotation. As the object rotates, the corner would collide with the palm of the hand. (c) Infeasibility due to object and hand dimensions. The hand cannot open wide enough to grasp the object.
(see Section VIII). Assuming a flat work surface, a configu- ration is stable when the center of mass ocm lies above the face of the convex hull that is in contact with the support surface. The space Rg ∈ SO(2) can be represented by the unit sphere. We will partition Rg based on the “capture regions” of the faces of the object. Each face of the convex hull can be projected onto a unit sphere centered on ocm. These projected faces define the set of configurations which will converge to a representative stable configuration under quasi-static conditions. We will henceforth refer to the set of configurations within a capture region by their representative stable configuration, recognizing that the object will tumble due to gravity into the stable configuration.
Our goal is to find the rotation R : [ρs ⇒ ρf ] ∈ Rg where ρs and ρf are representative stable poses. We will find a pivot grasp and trajectory which will execute this rotation.
IV. QUASI-STATIC MANIPULATION
In some cases, the final configuration can be reached solely with gravitational torque. This means the object would rotate into the goal pose due to the grasp by simply lifting the object off the table. For a given object, there may be a grasp point, pg which could completely rotate the object into the goal, however this grasp is often not a feasible grasp. First, we will describe this ideal grasp, p∗. Then, we will define feasibility and a strategy for adjusting the initial grasp to meet the feasibility requirements.
From an arbitrary stable pose to any other, the rotation axis is not necessarily horizontal. However, rotations about the vertical axis can be trivially done by rotating the gripper. We are only concerned with which face of the convex hull contacts the table. In this case, the rotation axis is always horizontal, perpendicular to gravity. Let the moment arm pr = (ocm−pg) be the vector from the grasp midpoint to the center of mass ocm. The torque due to gravity is τ = pr×G where G denotes gravity. When the object is lifted, the torque due to gravity will cause the object to rotate such that pr is parallel with gravity. If it is already parallel with the gravity vector, as in the case where the ρs and ρf differ by a 180
rotation, dynamics will be necessary to complete the rotation.
To find the grasp, we proceed in this step as if a face between ρs and ρf is the goal face.
We must choose the moment arm pr such that it intersects the goal face of the convex hull. For uniformly distributed objects, the centroid of that face, oc, is stable (requires no tumbling into a stable pose). Any alternative point on that face would produce a valid grasp; we have chosen the centroid for simplicity. Therefore, we can choose pg to be the point along the line from oc to ocm where it intersects the boundary of the object. The grasp axis n should be parallel to the cross product of ρs and ρf where the configuration can be represented by a unit vector in that coordinate frame.
A given grasp can be infeasible for any of four reasons, described in the following paragraphs. In some cases, the grasp can be adjusted to satisfy a constraint. When it can not be adjusted, a pivot is not possible.
1) Collisions between the gripper and the environment: For example, it is common for the gripper to collide with the work surface, see Figure 2a. This happens when pg is on the face which is in contact with the table. This can also occur in an environment with clutter or a limited workspace. To account for these collisions, we move the grasp directly away until there is no collision. The contact normal of the collision provides the direction to move. So in the case of a collision with the table, if we move the grasp in the +z direction, we can avoid the collision.
2) Collisions between the gripper and the object during rotation: By definition pg will be within the object. We are specifically concerned with collisions other than the grasp contact points. This includes collisions caused by the rotation of the object, as shown in Figure 2b. These collisions can be detected using the model of the object and the depth of the hand (the distance from fingertips to palm). In general, we must sweep the volume of the object throughout its rotation and check for collisions with the gripper. For the wooden blocks in our test set, the problem can be solved using a planar projection. We only need to check whether the worst point on the object collides with the hand. The worst point is the point on the object farthest from the line pr in the direction of rotation. When these collisions occur, the grasp
Fig. 3: Diagram of Swaying Motion.
should be moved closer to this worst point. 3) Instability due to slippage: If the grasp is too close
the object’s edge, slippage could occur causing the gripper to prematurely drop the object. In fact, every initial grasp is at an object edge by definition, since it is found by intersecting the line through the goal face centroid and the center of mass with an edge. Therefore, the grasp must be adjusted by moving closer to the interior of the object along a line to the center of mass.
4) Object dimensions: Finally, the most restrictive con- straint comes from the shape of the object. The object must fit inside the gripper. If this is impossible, the grasp can not be adjusted to be usable. The object must have two parallel faces with a width smaller than the width of the hand. These faces must be perpendicular to n surrounding pg . Figure 2c shows an example where the object can not be rotated.
Once a grasp is determined, simply lifting the object straight up will cause a rotation. This motion can be done at any speed and does not require any minimum acceleration of the arm.
V. DYNAMICS
Rotation using quasi-static manipulation can reach some goal rotations. However, we can reach larger angles by intro- ducing dynamics. First, we must have a better understanding of the motion of the object. The object can be in one of two modes: swaying motion or pendulous motion.
A. Swaying Motion
When the object is being lifted off the table, part of the object is free to slide, with friction, along the surface of the table. We will consider the planar projection of this motion in the Y Z plane. Any motion in the direction of ng will not affect the rotation. Therefore, a point pA will represent the sliding edge in contact with the table. The grasp point pg can be moved in the Y Z plane by the arm.
Let position of pg be given by u(t) = (ux(t), uy(t)) T .
Then the motion of pA is given by AX = √ l2 − uy(t)2 +
ux(t) where l is the length of the support face. This ap- proximates pg at the edge of the block, which is actually infeasible. However, it is sufficient for this analysis. AY = 0 while uy(t) <= l. This condition insures contact with the table. This is shown in Figure 3.
Under the quasi-static assumption, u(t) will be slow enough that there is no angular momentum when pA loses contact. We will break this assumption and allow u(t) to have a non-zero acceleration. Let θ be the object orientation relative to the hand. Then the angle is given by
θ = cos−1( uy(t)
l )
From the object model, we know the initial θ and the θ where pA loses contact. We can discretize our angular velocity ω using waypoints of u(t) described in Section VI.
B. Pendulous Motion
When pA loses contact with the table, the object is now free to rotate about ng . There are many factors affecting the motion of the object which are difficult to model, especially the friction between the fingertips and the object. However, we can approximate this system as a simple pendulum. We will model the contact area as point contact with friction. This treats the object like an additional linkage attached to the hand with a rotational joint. The resulting inaccuracies of the model will be insignificant compared with the size of the capture regions in many cases. We can analyze the dynamics of this system, but we can not control it using strategies like those used on inverted pendulum or cart-pole problems since our system is open-loop.
Thus, our system has three degrees of freedom, x, y, and φ, where x is the horizontal position ux(t) of the hand, and y is the vertical position uy(t), and φ denotes the counter- clockwise angle between the moment arm, pr = (ocm−pg), and the vertical. lcm denotes the length from pg to ocm. The position of the point mass ocm is given by
ocm =
) (1)
T = 1
1
The Lagrangian yields the equations of motion:
(mh+mo)x+molcmφ cos(φ)−molcmφ 2 sin(φ) = fx (4)
(mh+mo)y+molcmφ sin(φ)+molcmφ 2 cos(φ)−mg = fy
(5) molcmx cos(φ) +molcmy sin(φ)
+mol 2 cmφ+moglcm sin(φ) = −bφ (6)
where mo is the mass of the object, mc is the mass of the hand, g is gravity, b is a constant for friction at the fingertips, and fx and fy are the forces applied by the hand in x and y respectively.
VI. PLANNING
We can now formulate our problem: given a model of an object and its center of mass and a goal orientation, find the pivoting action which will rotate the object from the current orientation. We will use the vision system described
by Paolini [40] to detect the object’s current pose, plan an open-loop trajectory for the arm, and execute this trajectory. Our algorithm consists of three steps:
1) Choosing a feasible grasp: We will choose a grasp as described above, finding the initial, ideal grasp and adjusting it until it is feasible.
2) Initialize an arm trajectory: Let ξk be our trajectory at iteration k. The trajectory is parameterized by a series of waypoints ξk = (xk1 , ..., x
k n). Each waypoint is a 2D point,
thus the space of possible trajectories T ∈ R2n . Let ~x = (x1, ...xn) be our waypoints. Then a trajectory is expressed as ξk~x ∈ T .
We will initialize our trajectory as a quasi-static motion. This means the waypoints will simply trace a straight line in the +z direction with zero acceleration.
3) Optimize the arm trajectory: We model the cost of a trajectory using three terms: the δφξ error of the object’s final pose, the final angular velocity ωξ of the object, and the sum of the euclidean distances between the waypoints dξ. Our objective can be written
U(ξ) = αδφξ + β|ωξ|+ γdξ (7) where α, β, γ are weights. This cost function minimizes the final error in φ. This determines the success of the rotation. We would also like to minimize the final angular velocity for two reasons: to minimize the object “banging” on the table when the velocity is into the table, and to stop over-swinging in the opposite case. Finally we would like to minimize the overall distance the hand must travel.
To optimize, we want to minimize our cost with respect to the waypoints ~x.
ξk+1 = argmin ~x∈R2n
U(ξk~x) (8)
We first used gradient descent. Next we perform a line search in that direction to find the maxima and iterate until convergence.
VII. IMPLEMENTATION
Fig. 5: Square prism. (Top) Pick-and-place. (Bottom) Pivot- ing.
We have implemented this framework on a 6-DOF indus- trial manipulator (ABB IRB140) with a maximum speed of 2.5 m/sec and maximum acceleration of 20 m/sec2 (∼ 2g). Attached to this manipulator, we used a two-fingered parallel jaw industrial gripper (Robotiq) with modified fingertips. Attached to the end of the fingertips were acorn nuts (see Figure 2) which would contact the object with minimal surface area. Conforming with the current capabilities of our vision system, we used wooden polyhedral blocks as our objects.
We found it easiest to interface to ABB’s RAPID language if we used only five waypoints, on average. This was due to the way the arm interpolates velocities between points, by stopping or slowing at each point. ABB interpolates between the waypoints using parabolic interpolation. We found the use of five waypoints had several advantages. Firstly, the computation time to find the gradient of the trajectory was extremely quick. Secondly, the trajectories
Fig. 6: Rectangular prism. (Top) Pick-and-place. (Bottom) Pivoting
TABLE I: Execution Times (sec)
Pick & Place Pivoting Mean Stand. Dev. Mean Stand. Dev.
Tri. 90 7.23 0.24 5.31 0.97 Tri. 315 12.79 0.47 5.46 0.05 Squ. 90 8.45 0.86 5.94 0.15 Squ. ∗180 17.37 0.47 4.50 0.43 Rect. 90 7.75 0.16 6.13 0.91 Rect. ∗180 14.66 0.53 4.43 0.90 Rect. ∗180 17.33 0.56 5.48 0.52
were extremely simple, making them robust to noise and different objects. Finally, these simple trajectories were in fact 100% successful in our trials, implying an arbitrarily more complex trajectory is unnecessary.
We tested our system on three types of wooden blocks: a right triangular prism, a rectangular prism, and a square prism. With each of these blocks we found a grasp and trajec- tory for several possible rotations between two given sides, without specifying the object position. For the rectangular and square prism, we implemented a 90 rotation from the longest side to the adjacent smaller side. This pivot with the rectangular prism can be seen in Figure 6. The pivot did not require dynamics. The trajectory was simply lifting the grasp point straight up. In fact, dynamics caused a failure where the block would over rotate and tip over when released. Therefore, the arm had to move slowly enough to not violate the quasi-static assumption. These relatively slow times can be seen in Table I. We also pivoted the rectangular and square prisms 180 degrees from the longer faces to the opposite longer faces. These pivots required dynamics: the grasp point should be lifted quickly then jerked backwards and down. Finally, we implemented a pivot between the symmetric sides of the triangular prism, requiring no dynamics, and the hypotenuse and leg sides, requiring dynamics.
As a baseline, we compared the pivot actions to a pick-and-place sequence accomplishing the same rotation. These sequences were hand coded. Several examples of the pivot and pick-and-place trajectories can be seen in Figures 4, 5, and 6. To test repeatability, we implemented each pivot action 25 times. Additionally, we timed the pivot and pick-and-place actions. Although these actions are open- loop, small variations in the time occurred due to system stochasticity. These times and the variation can be seen in Table I.
Several things should be noted about these times. Namely, the pick-and-place actions are remarkably slow. Several factors explain this. The Robotiq gripper is in fact quite slow relative to many industrial grippers. On average, to open and then close the hand fully takes 4.84 seconds with 0.05 variation. In several pick-and-place operations, two pick-and- places were required (denoted by ∗ in Table I). Additionally, these actions are, by nature, rotations. This industrial arm can translate its end effector quite quickly, but rotating the wrist is much slower. The pivot actions required no wrist rotation and are extremely fast (almost all of the time accounted for
with the gripper). However, the pick-and-place operations required the wrist to rotate 90 or 180 which is quite slow. Also, such large rotations are quite clumsy and require a lot of free space around the object for the arm to move in.
Additionally many of the pick and place operations were quite difficult to accomplish without causing the wrist of the robot arm to collide with the table. A simple solution is to use a fixture in the workspace to lift smaller objects, like these blocks, off the table. A fixture was required for the triangular prism 315 rotation.
Several examples showing pick-and-place actions com- pared to pivoting actions are shown on our website1 and in the accompanying video.
VIII. FUTURE WORK
We would like to incorporate sensor feedback correspond- ing to the location of the object throughout the motion.This could be visual feedback of the position of the block. This would give us more accuracy in the final location of the object and allow us to more thoroughly take advantage of the pendulum model. Through feedback control, we could pivot the block to an arbitrary rotation if we can close the gripper with enough accuracy. We could detect slippaged with haptic feedback from the fingertips allowing us to modulate the gripping force of the fingertips.
Further, we would like to continue to explore fingertip material and shape and how it affects the rotation process. Soft or hard fingertips and objects have a large effect on the success of a pivot. The shape and regularity of the object need not be limited to objects with parallel faces. We would like to explore a more general class of pivotable objects.
REFERENCES
[1] N. Chavan-Dafle, A. Rodriguez, R. Paolini, B. Tang, S. Srinivasa, M. Erdmann, M. T. Mason, I. Lundberg, H. Staab, and T. Fuhlbrigge, “Extrinsic dexterity: In-hand manipulation with external forces,” in IEEE International Conference on Robotics and Automation (ICRA), May 2014.
[2] A. Rao, D. Kriegman, and K. Goldberg, “Complete algorithms for feeding polyhedral parts using pivot grasps,” Robotics and Automation, IEEE Transactions on, vol. 12, no. 2, pp. 331–342, Apr 1996.
[3] G. Monkman, S. Hesse, and R. Steinmann, Robot grippers. John Wiley and Sons, 2007.
[4] R. Paul, K. Pingle, J. Feldman, and A. Kay, “Instant insanity,” film, 1971.
[5] J. Feldman, G. Feldman, G. Falk, G. Grape, J. Pearlman, I. Sobel, and J. Tenenbaum, “The Stanford hand-eye project,” in Proceedings of the First International Joint Conference on Artificial Intelligence. Citeseer, 1969, pp. 521–526.
[6] P. Tournassoud, T. Lozano-Perez, and E. Mazer, “Regrasping,” in IEEE International Conference on Robotics and Automation, vol. 4, 1987, pp. 1924–1928.
[7] T. Lozano-Perez, J. Jones, E. Mazer, P. O’Donnell, W. Grimson, P. Tournassoud, and A. Lanusse, “Handey: A robot system that recognizes, plans, and manipulates,” in Robotics and Automation. Proceedings. 1987 IEEE International Conference on, vol. 4, mar 1987, pp. 843 – 849.
[8] J. K. Salisbury Jr., “Kinematic and Force Analysis of Articulated Hands,” PhD Dissertation, Stanford University, 1982.
[9] M. T. Mason and J. K. Salisbury, Jr., Robot Hands and the Mechanics of Manipulation. The MIT Press, 1985.
[10] J. Salisbury and J. Craig, “Articulated hands: Force control and kinematic issues,” The International Journal of Robotics Research, vol. 1, no. 1, pp. 4–17, 1982.
[11] A. Bicchi and R. Sorrentino, “Dexterous manipulation through rolling,” in IEEE Int. Conf. on Robotics and Automation, 1995, pp. 452–457.
[12] M. Cherif and K. Gupta, “Planning quasi-static fingertip manipulations for reconfiguring objects,” in IEEE Transactions on Robotics and Automation, vol. 15, 1999, pp. 837–848.
[13] R. Fearing, “Simplified grasping and manipulation with dextrous robot hands,” IEEE Journal of Robotics and Automation, vol. 2, no. 4, pp. 188–195, 1986.
[14] J. Hong, G. Lafferiere, B. Mishra, and X. Tan, “Fine manipulation with multifinger hands,” in ICRA, Cincinnati, OH, 1990, pp. 1568–1573.
[15] T. Omata and K. Nagata, “Planning reorientation of an object with a multifingered hand,” in Proceedings of the IEEE International Conference on Robotics and Automation, 1994, pp. 3104–3110.
[16] L. Han and J. Trinkle, “Dextrous manipulation by rolling and finger gaiting,” in Proceedings of the IEEE International Conference on Robotics and Automation, 1998, pp. 730–735.
[17] D. Rus, “In-hand manipulation of piecewise-smooth 3d objects,” in International Journal of Robotics Research, vol. 18, no. 4, 1997, pp. 355–381.
[18] T. Schlegl and M. Buss, “Hybrid closed-loop control of robotic hand regrasping,” in Proceedings of the IEEE International Conference on Robotics and Automation, 1998, pp. 3026–3031.
[19] K. M. Lynch and M. T. Mason, “Stable pushing: Mechanics, con- trollability, and planning,” in The First Workshop on the Algorithmic Foundations of Robotics (WAFR). A. K. Peters, Boston, MA, 1994, pp. 239–262.
[20] N. J. Nilsson, “Shakey the robot,” SRI International, Tech. Rep. 323, 1984.
[21] M. T. Mason, “Manipulator grasping and pushing operations,” Ph.D. dissertation, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1982.
[22] ——, “Mechanics and planning of manipulator pushing operations,” IJRR, vol. 5, no. 3, pp. 53–71, Fall 1986.
[23] D. L. Brock, “Enhancing the dexterity of a robot hand using controlled slip,” Master’s thesis, MIT, 1987.
[24] E. W. Aboaf, S. M. Drucker, and C. G. Atkeson, “Task-level robot learning: Juggling a tennis ball more accurately,” in ICRA, Scottsdale, AZ, 1989, pp. 1290–1295.
[25] E. W. Aboaf, C. G. Atkeson, and D. J. Reinkensmeyer, “Task-level robot learning: Ball throwing,” MIT,” AI Memo 1006, 1987.
[26] R. R. Burridge, A. A. Rizzi, and D. E. Koditschek, “Toward a dynamical pick and place,” in IROS, 1995, pp. 2: 292–297.
[27] K. M. Lynch and M. T. Mason, “Dynamic nonprehensile manipulation: Controllability, planning and experiments,” International Journal of Robotics Research, vol. 18, no. 1, pp. 64–92, January 1999.
[28] S. Srinivasa, M. Erdmann, and M. Mason, “Control synthesis for dynamic contact manipulation,” in IEEE International Conference on Robotics and Automation. IEEE, April 2005.
[29] M. Erdmann and M. Mason, “An exploration of sensorless manipu- lation,” IEEE Journal of Robotics and Automation, vol. 4, no. 4, pp. 369–379, 1988.
[30] M. A. Erdmann, “An exploration of nonprehensile two-palm manipu- lation: Planning and execution,” in ISRR, 1995.
[31] Y. Bai and C. K. Liu, “Dexterous manipulation using both palm and fingers,” in IEEE international conference on robotics and automation, 2014.
[32] N. Sawasaki, M. Inaba, and H. Inoue, “Tumbling objects using a multi- fingered robot,” in Proceedings of the 20th International Symposium on Industrial Robots and Robot Exhibition, 1989, pp. 609–616.
[33] Y. Aiyama, M. Inaba, and H. Inoue, “Pivoting: A new method of gras- pless manipulation of object by robot fingers,” in IEEE International Conference on Intelligent Robots and Systems (IROS), Yokohama, Japan, 1993, pp. 136–143.
[34] B. Carlisle, K. Goldberg, A. Rao, and J. Wiegley, “A pivoting gripper for feeding industrial parts,” in IEEE Int. Conf. on Robotics and Automation, 1994.
[35] A. Rodriguez, M. T. Mason, and S. Ferry, “From caging to grasping,” The International Journal of Robotics Research, vol. 31, no. 7, pp. 886–900, 2012.
[36] R. Diankov, S. Srinivasa, D. Ferguson, and J. Kuffner, “Manipulation planning with caging grasps,” in IEEE International Conference on Humanoid Robots, 2008.
[37] M. A. Erdmann, “A configuration space friction cone,” in IROS, Osaka, Japan, 1991, pp. 455–460.
[38] B. Mishra, J. T. Schwartz, and M. Sharir, “On the existence and synthesis of multifinger positive grips,” Algorithmica, vol. 2, no. 4, pp. 541–558, 1987.
[39] A. Miller and P. Allen, “Graspit! A versatile simulator for robotic grasping,” Robotics & Automation Magazine, IEEE, vol. 11, no. 4, pp. 110–122, 2004.
[40] R. Paolini, A. Holladay, A. Rodriguez, S. Srinivasa, and M. Mason, “Robust and accurate object pose estimation for robotic manipulation using colorless point clouds,” 2015, submitted to IEEE International
Conference on Robotics and Automation (ICRA).
INTRODUCTION
Collisions between the gripper and the object during rotation
Instability due to slippage