Abstract
This paper proposes an algorithm for the scrollic (synchronously closing with rolling constraints) gripper based on active sensing about the displacement of its joints, in order to control the trajectory of objects grasped outside the workspace. The gripper has fingers composed of two cylinders in parallel, the translation and rotation of which are independently driven. This characteristic gives a dynamic decoupled behavior to the gripper, and makes it compliant to open during a close motion, or to rotate against the actuated direction, when forced by the inwards movement of the object. The algorithm presents a high level of tolerance concerning uncertainties about the object's position, weight and shape. The kinematics, design concept and control algorithm of the gripper are discussed in detail.
Dexterous manipulation; active sensing; robot hand; control algortithms
An Active Sensing-based Control Algorithm for the Scrollic Gripper
Paulo Fernando F. Rosa
Computer Science Dept.- IM UFF
24210-130 - Niterói RJ BRAZIL
Tokuji Okada
Inf. Eng. Dept.- Niigata University
2-8050 - Niigata 950-21 JAPAN
okada@info.eng.niigata-u.ac.jp
Abstract This paper proposes an algorithm for the scrollic (synchronously closing with rolling constraints) gripper based on active sensing about the displacement of its joints, in order to control the trajectory of objects grasped outside the workspace. The gripper has fingers composed of two cylinders in parallel, the translation and rotation of which are independently driven. This characteristic gives a dynamic decoupled behavior to the gripper, and makes it compliant to open during a close motion, or to rotate against the actuated direction, when forced by the inwards movement of the object. The algorithm presents a high level of tolerance concerning uncertainties about the object's position, weight and shape. The kinematics, design concept and control algorithm of the gripper are discussed in detail.
Keywords: Dexterous manipulation, active sensing, robot hand, control algortithms.
1 Introduction
Usually, articulated multi-fingered hands are able to execute fine manipulations, in order to reposition, reorientate, or grasp an unknown or partially known object. Non-articulated end-effectors, such as a parallel-jaw, lack dexterity and sometimes fail to execute programmed manipulations. However they are capable of robust grasping tasks. Consequently, it is desirable to conceive a tool gathering some dexterous functions of an articulated gripper with the simple design of a parallel-jaw. The scrollic gripper is an improvement of a conventional parallel-jaw with an additional DOF capable of object manipulation in the presence of uncertainty. The gripper has rolling fingertips(rollers), the translation and rotation of which are independently generated by backdrivable actuators. This characteristic implies in active compliance to the gripper and enables the fingertips to move against the actuated direction when forced by wrenches resulting from the dynamic behavior of the grasp. This paper proposes an algorithm for automatic grasping of convex three dimensional(3D) objects based on sensory information collected utilizing the compliance of the fingers, in order to control the trajectory of grasped objects towards the center of the gripper with flexibility. The algorithm presents a high level of tolerance concerning uncertainties about the object's position, weight and shape; also, permitting the gripper to manipulate objects whose bodies are mostly outside the gripper's workspace.
Many researchers have proposed the use of active or passive compliance to overcome uncertainties and simplify control tasks during fine manipulations. By compliance, we mean the property of a robot to respond to forces and torques arising from its interaction with the environment. Under the gripper's viewpoint, compliance is passive when generated internally by passive devices, i.e., mechanical elements such as springs and dumpers. Active compliance, on the other hand, requires an external energy source. Whitney [9] has analyzed the geometric and force equilibrium conditions for mating compliantly supported rigid parts, and explained the influence of the location of the remote compliance center (rcc) in reducing mating forces. In a compliance center, forces cause pure translation, and torques cause pure rotations about the center. Hanafusa and Asada [2] have proposed a grasp stability condition based on a potential function criterium for a gripper with elastic fingers. The gripper is composed of three fingers driven by a motor through linear springs, such that two-dimensional arbitrary grips can be adaptively configured. Previously, Okada [6] has shown a trajectory of contacts on a planar object when the object is manipulated by two multijointed spherical fingertips.
Recently, some authors addressed the task of improving the manipulability of a parallel-jaw. Brost [1] has proposed an algorithm for automatic grasps with a parallel-jaw in the presence of uncertainties in the object's position. He qualitatively demonstrated the insufficiency of pure squeezing in dealing with uncertainty, and implemented a couple of procedures, called offset-grasp and push-grasp in order to make grips of polygonal objects. Rao and Goldberg [7] implemented a controlled degree-of-freedom(DOF) to a parallel-jaw in order to orientate polygonal parts. The gripper has a controlled DOF in addition to the open-and-close motion. Also, many authors have reported on the kinematics of two-fingered - as well as multi-fingered - hands manipulating arbitrary workpieces with rolling or sliding contacts. For instance, Montana [4] developed generalized formulas for the contact configurations between two bodies in contact, and presented algorithms for curvature recovering and contour following tasks of unknown objects using a two-finger gripper. Assuming point contact with no slippage, Montana used the geometry of the contact to derive the kinematics of the grasp, and extended its application for fine manipulation tasks, such as: rolling a sphere between two arbitrary fingers, fine grip adjustment and twirling a baton.
Figure 1. An object outside the workspace (a), is pulled towards the center of the gripper (b), to be firmly grasped.
For the first version of the scrollic gripper [8], a single servomotor generates the torques required for the translation and rotation of the rollers of both fingers. This gripper is feasible for grasping objects the volume of which are mostly inside the gripper workspace, sometimes failing to manipulate objects located mostly outside. Hereafter, we focus on developing a gripper capable of drawing 3D objects toward its center and confining them in a firm grasp. The next section presents the theoretical background to support the design and functioning of the scrollic gripper. Grasping and manipulation with the gripper is also discussed. Then, we present our active sensing control strategy, showing the algorithm flowchart and its computational implementation. Finally, the gripper mechanism and the experimental setup is presented and discussed in detail.
2 The Active Sensing Control
2.1 The Control Strategy
The compliance of the rollers is actively generated by backdrivable motors on the gripper's joints. When the motors are actuated, the resultant wrench [f
]
at the object's geometric center can induce a motion to the rollers due to their compliance. The rollers' motion is dependent upon the applied torques, the local geometry of the object, and physical properties such as friction, damping and inertia of both gripper and object. In order to control the trajectory of the object, (a) these parameters must be closely monitored, (b) each finger must have enough joints to induce a general mobility of the object, and (c) a suitable control system must be applied. The modalities of sensing for this task - force/torque and tactile sensing - can make the system bulky, due to the wide sensitive area required for the finger, and make it necessary to compute a large amount of data parallelly in real time. Furthermore, a very fine strategy might be asserted to account for uncertainties in the model of the grasping process.
When grasping objects from the outside of its workspace, the scrollic gripper has a well defined trajectory planning, i.e., to bring the object inside the gripper. Consequently, an observer should verify that while the object makes the motion towards the center of the gripper, the rollers open or open-and-close, and rotate inwardly. Any deviation from this pattern means a trajectory error, and actions might be done, such as to change the applied torques, in order to give the appropriate balance to the resultant wrench at the object. Angular position sensors attached to the motors' shaft can gather information about their direction of motion. The applied torques should guarantee that the object is unable to drop or pop out of the gripper during all the manipulating task. Thus, the torques might be monitored. The scrollic gripper uses current-to-voltage sensors for this purpose. So, these informations are given as a feedback to the control system.
Figure 2. Flowchart of the sensing control strategy.
2.2 The Control Algorithm
For the control algorithm, we have used the notation: 
is the gripper width of opening;
and 
represent the applied torque and the angular motion of the rollers, respectively (subscript 
assumes denominations such as s (squeezing), 
(right) and 
(left); 
and 
indicate the initial value and variation of parameter 
, as well as, 
and 
mean the increase and decrease operation for this parameter, respectively. In order to simplify the control algorithm, all torques involved increase or decrease by a pre-specified amount 
. As the initial condition, we assume that the hand is wide open (
)and the rollers are free to move 
, i.e., no torques are applied. The objects are convex, rigid and light in weight. The initial position and orientation of the objects are unknown, although in the reach of the rollers. Initially, a squeezing torque
is appliepd to the rollers. Consequently, the rollers close with constant velocity. (Note: The torque 
is the torque to overcome the gripper's inertia and impart a small velocity to the rollers. Consequently, large displacements of the object due to the collision with the rollers are avoided). Due to uncertainties on the object's position, orientation and shape, it is most likely that both rollers do not collide with the object simultaneously. Thus, whenever one of the rollers collides with na object, the reaction force at the contact induces the roller to rotate inwardly 
or outwardly 
, reflecting the fact that the object is located inside or outside the gripper, respectively. The sign of 
is determined concerning a pre-assigned roller, since a couple of rollers in either left or right side are mechanically connected. When both left and right side rollers finally contact the object, the existence of a grasp can be determined through the measurement of the gripper opening width 
For instance, if the gripper stops closing 
before travelling all the gripper opening width 
it is likely to have the condition of the rollers grasping an object. If the grasp is confirmed, it can be classified into two different types: the case (a) squeezing grasp: when the object is located mostly inside the gripper's workspace, and case (b) acquisitive grasp: otherwise. This classification facilitates the application of a control policy based on active sensing.
Figure 3. All possible grasp configurations during the manipulation task for a squeezing grasp and an acquisitive grasp, and the respective control policy for the next step. Actual conditions of fingers on close and open are expressed by notations 
and 
respectively. Also, control commands to increase and to decrease the torques applied by the rollers are expressed by notations 
and 
respectively.
2.3 Squeezing Grasp Condition
In the case of a squeezing grasp, the initial inwards rotation torques 
and 
are applied to the right and left side fingers, respectively. Again, all these torques are slightly higher than the necessary to overcome the inertia of the rollers, such that they rotate (when unloaded) with a small and constant angular velocity. Meanwhile 
increases by . Then, the motion of the joints are monitored.Since the object's shape and orientation are unkown during the squeezing grasp, the gripper is allowed to open 
, to close 
, or to remain in a halt condition
.
When the gripper opens, the rotating torques are kept constant, and the squeezing torque must decrease (despite the direction of rotation for the rollers) to allow further motions of the object, since it is manipulated inside the gripper and accomodates in a stable condition. (see Figure 3). Note that the situation in which the gripper opens without rotating the rollers is not available. The directions of the arrows regarding 
and 
stand for the increase or decrease on the respective torques' values. For instance, 
means the increase of the squeezing torque. When the gripper closes, the squeezing torque increases and the rotation torques decrease if the rollers have an inwards motion, or only the squeeze torque increases, otherwise. Note that for this case, the situation where both left and right side rollers simultaneously rotate either clockwise or counterclockwisely is unavailable, since that means slippage of the contact point which is assumed not to ocurr during the manipulation. When the gripper stops, if there is a rotation of the rollers, the squeezing torque must increase. Otherwise, the support torques must be applied(to avoid the object from popping out of the hand) and the control algorithm stops. This condition means that the grasp has reached a force or form closure, i.e., a firm grasp configuration.
2.4 Acquisitive Grasp Condition
In the case of an acquisitive grasp, in addition to the initial inwards torques 
and applied to the rollers, the algorithm recognizes the condition that the gripper might open in order to make the object come inside
. Then the rollers' motion are monitored. If they have no rotation, the torques are rearranged such that 
decreases, and 
and 
increase, with an infinitesimal and constant value . This process repeats until some rotation is allowed to any of the rollers. Similarly to the squeezing grasp, due to the unkown nature of the object, during the manipulation task the gripper is allowed to open, to close , or to remain in a halt condition 
.
Figure 5. Overview of the mechanical system for the scrollic gripper with dd motors giving compliance to the fingers and angular sensors actively detecting the motion of the rollers.
Figure 6. The actual experimental setup for the scrollic gripper mounted and a sample of several arbitrary shaped objects used for the manipulation tasks.
If the gripper stops, the algorithm is based on increasing or decreasing the rotation torques, and/or the squeezing torque, in accordance with the direction of the roller's motion. If both rollers have an inwards motion
, then the left and right roller's torques 
and 
, as well as the squeezing torque, must decrease, as is shown in cell 3-a(Figure 3). If only the right roller, or only the left roller, rotates inwardly, the respective rotation torque might decrease. If there is no rotation at all, the rotation torques might increase and the squeezing torque must decrease. The remaining cases are not available for this condition. If the gripper opens, the algorithm recognizes the condition that the rollers are opening while forced to close 
, and the algorithm increases or not the rotation and/or the squeezing torques, in order to keep the inwards motion of the object. If the gripper is opening and the rollers are rotating inwardly (such that 
), the most likely situation is that the object is pulled towards the center of the gripper, as shown in cell 2 - a(Figure 3). Thus, there is no need to apply any control parameter, since this is the desired grasp behavior. When both rollers have the same rotation,
must increase if the rotation is clockwise, and 
must increase if the the rotation is counterclockwise. When one of the rollers have a clockwise motion while the other remains without rotation,
might increase. Similarly, when one of the rollers have a counterclockwise motion while the other remains without rotation, 
must increase. For an outwards motion of the rollers, the overall torques must increase. Note that the situation of the gripper opening with the rollers without rotation is not available, since we assume that the contact is kept through the manipulation task and the object is a rigid body. Figure 4 shows the pseudocodes of the control algorithm, that was implemented in the C language.
3 The Design Concept and Experimental Setup
We implemented the scrollic gripper with cylindrical fingers and provided three direct-drive motors for their rolling motion: one DD motor for the close-and-open motion, and another for the rotation of each pair of rollers. This configuration enables the gripper to have a decoupled stiffness, damping and frictional characteristic (see Figure 5). The mechanism to drive the linear motion of the rollers is equivalent to that of a conventional parallel-jaw, except for the backdrivability of the actuator. The direct-drive motor used (QT-0707B, Inland) has peak torque rating of 1.4N and a motor constant of 
. A reduction gear rating 0.3 is used to attach the shaft of the open-and-close motor to the shaft of a potentiometer. This potentiometer gathers information to measure the gripper's opening width 
, and to determine the direction of the roller's linear motion, i.e., open or close. The direction of the linear motion of the rollers is calculated in off state by sampling the potentiometer's output. Since we are using single-turn potentiometer, the reduction gear is adjusted such that the maximal gripper opening width
is traveled within a complete revolutional range of the potentiometer. Besides, the other end of the motor's shaft is attached to a pinion-and-rack gear, which converts the rotation of the motor's shaft into the desired linear motion of the fingers.
The gripper grasping several objects using the active sensing control algorithm. A sphere(a), a polyhedron of 12 surfaces(b) and a polyhedron of 16 surfaces(c).
From now, on we focus only in the left side finger to describe the gripper design, since it has a symmetrical mechanism and behavior. A pair of light roller guides with very low friction and negligible bending moment are tightly connected to the gripper support. One lateral of the moving part of the roller guide is attached to the rack of the pinion-and-rack gear. Furthermore, the finger base is fixed on the top of the roller guide. Each finger base supports a pair of rollers, a dd motor, a rotary encoder and a pair of spur gears. The rollers are disposed in parallel and are made of aluminum cylinders covered with thin rubber, in order to make the contact hard with friction. The rotation of the pair of rollers is generated by a single dd motor (QT-0717B, Inland) having a peak torque of 0.6N and a motor constant of 
. The torque is applied to the shaft of the lower roller, and the rotation is transmitted to the upper roller through a spur gear engagement of unitary ratio. This enables both rollers to have angular velocities of same magnitude and opposite directions. The rotation of the rollers is sensed by an encoder connected to the shaft of the upper roller. The encoder is of the optical miniaturized type with resolution of 
. Since the error margin (around 3%) of these encoders is high for our application, we modulated their analogical output into a digital signal, and used a pulse signal decoder of rate 4 (four) to obtain a 
resolution. Also, the counterclockwise and clockwise signals are given to different channels of a counter board interfaced with a personal computer (75MHz). Furthermore, the gripper opening width is roughly 
and, when closed, presents a clearance of 
between the rollers. The rollers are 
long and 
in diameter. The three dd motors are servoed by similar servomechanisms. The command voltage is given by the application program trough a D/A board to a servo amplifier used to control the power delivered by the motors. A voltage follower circuit is used as a current-to-voltage sensor for the motors. The output of this sensor is used as a feedback for the servo amplifier and as a torque sensor for the control algorithm. Since the armature current is proportional to the output torque, the system calibration parameters are used to estimate the torque applied by the gripper at the rollers and to control the grasp, ultimately.
4 Experimental Results
We have executed many experiments with the scrollic gripper grasping and manipulating several objects of different shapes, textures and weights within the nominal capacities of the gripper. It was possible to produce successful grasps of rigid objects using the same algorithm despite uncertainties on the position, orientation, weight and shape of the objects. The characteristic objects used for the experiments were light wooden or rubber pieces with shapes such as a cone, a tetrahedron, a rectangular cube, a sphere, a hexahedron, a cylinder and a thin bar. Also, convex objects of an undefined shape were used. Fig. 7 shows various situations of the scrollic gripper grasping different shaped objects, when mounted in an arm manipulator Movemaster-ET2.
5 Conclusion
The method presented in this paper is available to control the trajectory of objects grasped by the scrollic gripper from the outside of the workspace, and its advantage relies on the fact that sensorial feedback information about the object's local geometry, as well as the contact position, are not required, thus allowing the gripper to grasp objects of arbitrary shape.
The control strategy method is verified by the manipulation experiments, treating various kind of objects in shape and size - such as a tetrahedron showed the adaptability of the gripper's graspability. The scrollic gripper's system is characterized by its soft grasping and its algorithmic simplicity and the efficiency in implementation. The gripper has been attached to an arm manipulator to perform pick-and-place tasks treating various kinds of shapes and sizes of objects. Experimental results had shown that flexibility of the scrollic gripper is great very clexible.
Acknowledgements:This research was carried out under a Graduate Scholarship Program from the Ministry of Education of Japan (grant number 91-ER-910697).
7 References
- [1] R.C. Brost, Automatic grasp planning in the presence of uncertainty. The Int. J. of Robotics Res., 7(1):3-17, 1988.
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- [3] J.R. Kerr. An analysis of multi-fingered hands. Ph.D. Thesis. Stanford University, 1984.
- [4] D.J. Montana, The kinematics of multi-fingered manipulation. IEEE Trans. Robotics Automat., 11:491-503, 1995.
- [5] V. Nguyen, Constructing force-closure grasps. Int. J. Robotics Res., 7:3-16, 1988.
- [6] T. Okada, Computer control of multijointed finger system for precise object-handling. IEEE Trans. Syst. Man Cybern., SMC-12(3):289-299, 1982.
- [7] A.S. Rao and K.Y. Goldberg. Orienting generalized polygonal parts. In Proc. IEEE Int. Conf. on Robotics and Automation, pages 2263-2268, 1992.
- [8] P.F.F. Rosa and T. Okada. 3d firm grasps with the scrollic gripper. In Proc. IEEE Int. Conf. on Robotics and Automation, Nagoya, pages 1662-1667, 1995.
- [9] D.E. Whitney, Quasi-static assembly of compliantly supported rigid parts. J. of Dyn. Sys., Meas., and Contr., 104:65-77, 1992.
Publication Dates
-
Publication in this collection
08 Oct 1998 -
Date of issue
Apr 1998
