Joint Coupling Design of Underactuated Grippers

This paper examines the nature of joint coupling in underactuated grippers for environments where object properties and location may not be well known. A grasper consisting of a pair of two-link planar fingers with compliant revolute joints was simulated as it was actuated after contact with a target object. The joint coupling configuration of the gripper was varied in order to maximize successful grasp range and minimize contact forces for a wide range of target object size and position. A normal distribution of object position was assumed in order to model sensing uncertainty and weight the results accordingly. The results show that proximal-distal joint torque ratios of around 0.6 produced the best results for cases in which sensory information available for the task was poor, and ratios of around 1.0 produced the best results for cases in which sensory information available for the task was good. INTRODUCTION After years of experimenting with complex, fullyarticulated anthropomorphic hands, researchers have begun to embrace the idea that much of the functionality of a hand can be retained by careful selection of joint coupling schemes, reducing the number of actuators and the overall complexity of the grasping mechanism. Many of these grippers are ‘underactuated’, having fewer actuators than degrees-offreedom. These types of hand have also been referred to as ‘adaptive’ or ‘selfadaptable’. Other simplified hands have fixed-motion coupling between joints, reducing the overall degrees-of-freedom of the mechanism. These two classes of simplified grippers can be easier to control, much lighter, and less expensive than their fully-actuated counterparts. The very nature of unstructured environments precludes full utilization of a complex, fully-actuated hand. In order to appropriately use the added degrees of actuation, an accurate model of the task environment is necessary. A gripper with a reduced number of actuators is not only simpler to use, it is more appropriate based on the quality of information available for the unstructured grasping task. The joint coupling necessary to allow for underactuation is often accomplished through compliance in the manipulator structure. Compliance is perhaps the simplest way to allow for coupling between joints without enforcing the fixed-motion coupling relationship inherent with gear or linkage couplings. Compliant couplings are a simple way to allow a joint to passively deflect without causing a fixed-motion proportional change in the joints to which it is coupled. Compliant underactuated grippers show particular promise for use in unstructured environments, where object properties are not known a priori and sensing is prone to error. Finger compliance allows the gripper to passively conform to a wide range of objects while minimizing contact forces. Passive compliance offers additional benefits, particularly in impacts, where control loop delays may lead to poor control of contact forces [1,2]. Compliance can also lower implementation costs by reducing the sensing and actuation required for the gripper. In previous work, we examined the optimization of the preshape and joint stiffness of simple two-fingered grippers with passive springs in the joints. This study showed that for a particular set of joint stiffnesses and rest angles, the widest range of range of uncertainty in object size and location could be allowed for. Contact forces were also minimized at approximately the same gripper configuration. In addition to simulation studies, these results were confirmed with experimental tests using a reconfigurable gripper [3]. In this paper, we explore the role of the joint coupling scheme in grasping in unstructured environments, where poor sensing may mean that object size and location uncertainty can span a wide range. In particular, we examine the performance of a two-fingered compliant underactuated gripper as joint torque ratio and joint compliance are varied. Performance is compared on the basis of the maximum range of object size and location that can be successfully grasped and the magnitude of contact forces. We begin with a survey of underactuated and fixed-motion coupled robotic hands, describing in depth the nature of the coupling schemes and/or compliance in each. We then describe the details of the gripper and grasping scenario that we are studying. Finally we provide the results of a simulation of the 1 Copyright © 2006 by DEAS – Harvard University TABLE I UNDERACTUATED AND FIXED-MOTION COUPLED ROBOT HANDS Hand # fingers Pitch joints per finger Pitch actuators per finger Coupling scheme (*indicates compliant coupling ^indicates adaptive mechanism) Coupling ratio Source of compliance and/or adaptability 100G [4] 2 2 1/2 prox:*:dist unknown tendon routing, spring-loaded joints Barrett [5] 3 2 1 prox:^:dist (3:4) "TorqueSwitch" differential Belgrade/USC [6] 4+1 3+0 1/2+1 (prox;med;dist)+(prox;dist) (~9;8;7) rocker arm coupling of fingers DLR I and II [7,8] 4 3 2 med;dist (1;1) none Domo [9] 3 3 1 prox;med:*:dist (1;1:passive) unactuated compliant distal joint Graspar [10] 3 3 1 prox:^:med:^:dist (~5:4.2:2.9) tendon differential mechanism Hirose [11] 2 10 1/2 prox:(all):distal (55:::28:::10:::1) tendon routing Laval 10-DOF [12] 3 3 1/3 prox:^:med:^:dist unknown adaptive linkage mechanism NAIST [13] 3+1 3+3 2+2 (med;dist)+(med;dist) (1;1.15) none Obrero [14] 3 2 1 prox:*:dist (4:3) series elastic actuation Robonaut [15] 2+2+1 3+3+2 2+1+2 (med;dist)+(prox;med;dist)+0 (1;1)+(1;1;1)+0 compliant connector, no adaptability Rutgers [16] 4+1 3+3 2+2 med:dist unknown tendon routing Salford [17] 4+1 3+3 2+3 (med;dist)+0 unknown none SDM [18] 2 2 1 (prox:*:dist) (4.5:1) tendon routing, joints made of springs Shadow [19] 4+1 3+2 2+2 (med:dist)+0 unknown McKibbons, unknown adaptability Southampton [20] 3 3 1 prox:^:med:^:dist unknown differential unit SPRING [21] 2+1 3+2 1/3+1/3 (prox:*:med:*:dist)+(prox:*:dist) (2.9:1.6:1) series elastic actuation TBM [22] 4+1 3+2 1+1 (prox;med;dist)+(prox;dist) (~2;1;1)+(~2;1) none UB III [23] 2+2+1 3+3+3 3+2+2 0+(med:*:dist)+(med:*:dist) (~6:7) tendon routing, joints made of springs grasping process for a wide range of target object size and position, identifying optimal joint coupling schemes for various levels of sensory information available for the grasping task. SURVEY OF UNDERACTUATED HANDS Table I provides an overview of some of the most wellknown underactuated and fixed-motion coupled robotic hands. An ‘underactuated’ hand has fewer actuators than degrees-offreedom, and therefore demonstrates adaptive behavior. In these hands, motion of the distal links can continue after contact on the coupled proximal links occurs, allowing the finger to passively adapt to the object shape. In a ‘fixed-motion coupled’ hand, each actuator controls a single degree-offreedom, and the mechanism has no ‘adaptability’ (final column). In these hands, motion of one joint always results in a proportional motion of the joint(s) coupled to it. In the same way, if contact occurs on one joint fixing its position, all coupled joints are thereby fixed. The ‘# fingers’ column gives the number of fingers of each different type used in the hand, separated by ‘+’. Cases where two types are given indicate that some number of identical fingers and one thumb are used in the design. Cases where three types are given mean that two different finger designs are used in addition to a thumb. For example, the Robonaut hand [15] incorporates two “grasping” fingers, two “dexterous” fingers, and a thumb. The second column indicates the number of ‘pitch’ joints per finger, leaving out ‘yaw’ and ‘roll’ joints, if any exist. Entries correspond to the data in the ‘# fingers’ column. For the Robonaut hand, the grasping and dexterous fingers and thumb have three pitch joints each. The next column corresponds to the number of actuators per finger that control the pitch joints. Note that the degree of underactuation ranges from a single actuator for twenty joints (Hirose’s “Soft Gripper” [11]) to twelve actuators for fifteen joints (UB III hand [23]). The coupling scheme is indicated in the next column. ‘Prox’ indicates the proximal joint (nearest to the base), ‘med’ is the medial joint (for three phalanx fingers), and ‘dist’ is the distal joint (farthest from the base). A ‘:*:’ between two joints indicates that the coupling between the two joints is compliant, such as those hands with joints made of springs. A ‘:^:’ between two joints indicates that the coupling between the two joints is based on a mechanism that allows for decoupling. The BarrettHand [5], for example, achieves this effect by means of a “TorqueSwitch” differential gear mechanism that actively decouples the two joints once contact has been made on the inner link and a preset torque limit has been reached. A ’;’ between joints indicates that the coupling is fixed-motion, and therefore has no adaptability. The next column indicates the coupling ratio (prox:med:dist) between the joints. For a finger with some method of adaptability, this ratio is the relative angular motion between joints when the finger is freely actuated (i.e. no external contact). For Hirose’s “Soft Gripper” [11], every third value is given. The final column indicates the method by which the hand is passively compliant and/or adaptive, if at all. METHODS We select for this study a simple gripper with two fingers, each with two revolute degrees of freedom (Fig. 1). This gripper, proposed by Hirose [11], is perhaps the simplest 2 Copyright © 2006 by DEAS – Harvard University configuration that is able to grasp a wide range of objects. This mechanism is the same as that used in the 100G hand [4] and the SDM hand [18], and is similar to the planar, power-grasp configurations of the BarrettHand [5], Domo hand [9], Laval 10-DOF hand [12], Obrero hand [14], and SPRING hand [21], among others. TABLE II NOMENCLATURE parameter definition φ1, φ2 spring rest link angles ψ1, ψ2 deflected angles ∆ψi small joint deflection due to fingerpad compliance k1, k2 kr joint stiffness values stiffness ratio (k2/k1) ks τ1, τ2 τr finger skin stiffness joint torque values torque ratio (t2/t1)