Stable Grasp and Manipulation in 3D Space with 2-Soft-Fingered Robot Hand

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1 Stable Grasp and Manipulation in 3D Space with 2-Soft-Fingered Robot Hand Tsuneo Yoshikawa 1, Masanao Koeda 1, Haruki Fukuchi 1, and Atsushi Hirakawa 2 1 Ritsumeikan University, College of Information Science and Engineering, Department of Human and Computer Intelligence Noji Higashi Kusatsu, Shiga, Japan. {yoshikawa, koeda, fukuchi}@robot.ci.ritsumei.ac.jp 2 Kyoto University (Currently with DENSO CORPORATION) Abstract. We report on our newly developed two-fingered robotic hand with soft and thin skin. This hand is basically controlled by a position-based control algorithm. However, it can realize desired grasping force due to the soft skin while maintaining stability of the system. For an experimental validation of this concept, we conducted following the three kinds of manipulation tasks: manipulating of a cubic object, opening and closing of a bottle cap, and turning of a crank. These results show that this two-fingered hand can perform various manipulation tasks of objects in three dimensional space. 1 Introduction Robotic hands with multiple multi-jointed fingers have been studied by many researchers because of their large potential for versatile and dexterous grasping and manipulation. It has usually been assumed that the fingers are rigid and make point contacts with grasped objects because of simplicity and convenience for their analysis and derivation of control algorithm. However, in practical applications, rigid fingers sometimes cause difficulties regarding stability of grasping and versatility of manipulation. Partly because of these difficulties, robot hands with fingers covered by soft materials have recently been studied by some researchers. Murakami et al.[1] developed a novel fingertip equipped with a soft skin and a nail. Arimoto et al.[2] suggested a geometry-based control method for dual soft-fingered manipulations. Xydas et al.[3] presented a model of contact mechanics for soft fingers. Maeno et al.[4] proposed a grasping force control scheme of an elastic finger. However, most of these analytical works and conducted experiments are limited to two dimensional manipulation, and dexterous manipulation in three dimensional space has not been studied in detail.

2 2 T. Yoshikawa, M. Koeda, H. Fukuchi, and A. Hirakawa This paper reports on our newly developed two-fingered robotic hand with soft and thin skin. Although this hand is basically controlled by a positionbased control algorithm, it can also realize desired grasping force due the soft skin while maintaining stability of the system. Experimental results are also presented which shows that this two-fingered hand can perform various manipulation tasks of objects in three dimensional space. 2 Long Term Goal and Current System Configuration Our long term goal is to develop a dexterous multi-fingered robot hand whose whole body is covered by a soft skin. Fig.1 is a conceptual sketch of a finger of this robot hand. For a preliminary analysis and an experimental validation of this concept, we have developed a 2-fingered robot hand with a soft fingertip. Each finger has three joint motors (YASKAWA Electric Corporation, AC servo motor, reduction gear ratio 1:80) and a force/torque sensor (BL Autotec, LTD., NANO /4). The motors have rotary encoders which output pulses per round. The force/torque sensor is mounted at the end of the each finger. The overview of the current system and the fingertip are shown in Fig.2. The displacement property of this soft finger tip is shown in Fig.3. The fingertip consists of two parts: a hard inner core and a soft outer skin. The inner core is a circular cylinder with round tip which is made of polyoxymethylene(pom). The diameter of the cylinder is 1[mm]. The outer skin is made of elastic gel and the thickness of the skin is [mm] at the part of tip and 3[mm] on the side surface (Fig.4). This finger shape features a symmetric elasticity around its axis, and simplicity for controlling and making motion planning. 6 Aixs Force/Torque Sensor Soft and Thin Skin Motors Hard Core 6 Aixs Force/Torque Sensor Fig. 1. Conceptual Sketch of Final Target

3 Stable Grasp and 3D Manipulation with 2-Soft-Fingered Robot Hand 3 3 Control Scheme In this section, we will explain the control scheme we have developed for stable manipulation in 3D space. The joint torque vector τ i R 3 for finger i (i = 1, 2) is given by the following simple PID control scheme: τ i (t) = k P q ei (t) + k I q ei (t)dt + k D q ei (t) (1) q ei (t) = q ti (t) q ci (t) (2) (a) Overall View (b) Soft Fingertip Fig. 2. Current System Overview Force Displacement force[n] (a) Experimental Condition displacement[mm] (b) Deformation Property Fig. 3. Displacement Property of Soft Finger

4 4 T. Yoshikawa, M. Koeda, H. Fukuchi, and A. Hirakawa Elastic Gel POM [mm] 3[mm] 1 Fig. 4. Inner Structure of Soft Fingertip where k P, k I, and k D are proportional, integral, and derivative gains, and q ei (t) the error of the joint angle between the target joint angle q ti (t) and the current joint angle q ci (t). Current joint angles q ci (t) are acquired by rotary encoder mounted on each motor. To control the grasping force between the two fingers, the thickness of the soft material is controlled by changing the target joint angle q ti (t). To reduce the noise of force sensors the following filter is used: F i (t) = γf ri (t) + (1 γ)f i (t t) (3) where t is the sampling period and F ri (t) is raw data and γ is a parameter of the filter which corresponds to the inverse of the time constant. To keep the stability of the system, γ is taken to be small. In this paper, γ was selected as γ = 0.01 empirically. The minimum value of the grasping force exerted by the two fingers is assumed to be given by F min (t) = min { F i (t) }, i = 1, 2 (4) and the error of grasping force can be written as F e (t) = F t (t) F min (t) () where F t (t) is the target force. To reduce the influence of an excessive error, the maximum modification distance per one sampling period is limited. Taking error ratio e(t) = F e (t)/f t (t) into account, to control the current distance between fingertips D(t), the target distance D t (t) is adjusted by the following equation: { D(t) + D 0 e(t) D t (t) = δ, if e(t) δ (6) D(t) + D 0 sgn {e(t)}, otherwise where D 0 is a constant parameter that decides the maximum velocity of the fingertip and δ is a parameter that determines the saturation region of e(t).

5 Stable Grasp and 3D Manipulation with 2-Soft-Fingered Robot Hand The values D0 = -0.[mm] and δ = 0.1 are applied in this experiment. Each target joint angle qti (t) is calculated from Dt (t) by solving the inverse kinematics problem. 4 Experiment Using the above robot hand system we have conducted the three kinds of manipulation tasks. The results are shown below. 4.1 Manipulating of Cubic Object We have conducted an experiment to manipulate a wooden cubic object in free space. The size of cube is 0[mm] on a side and the weight is 77[g]. To grasp the cube, the distance between the two fingertips was made smaller by (a) initial pose (b) grasp (c) lift up (d) rotate 30[deg] (vertically) (e) rotate -30[deg] (vertically) (f) rotate 30[deg] (horizontally) (g) rotate -30[deg] (horizontally) (h) rotate 30[deg] (diagonally) (i) rotate -30[deg] (diagonally) Fig.. Manipulation of Cubic Object

6 6 T. Yoshikawa, M. Koeda, H. Fukuchi, and A. Hirakawa Force [N] finger0 finger Time [sec] (a) Target Force 3[N] Force [N] finger0 finger Time [sec] (b) Target Force [N] Fig. 6. Change of Grasping Force during the Task Distance [mm] current distance target distance Time [sec] (a) Target Force 3[N] Distance [mm] current distance target distance Time [sec] (b) Target Force [N] Fig. 7. Change of Distance between Fingers during the Task using position control until the grasping force became a target value. When the grasping force reached the target value, the cube was lifted upward by 30[mm]. Then, with keeping the grasping force to the desired force, each fingertip was moved following some circular paths in a horizontal plane, vertical plane, and diagonal plane. The sequential images of this experiment are shown in Fig.. Experiments have been conducted for two cases: F t = 3[N] and F t = [N]. Fig.6 and 7 show the change of target and measured values of both grasping force and distance between the fingertips for these cases. Both force and distance have followed well the desired values, and accurate and stable manipulation has been achieved. The servo control period was 1[ms]. 4.2 Opening and Closing of Bottle Cap Secondly, we conducted a task of opening and closing a bottle cap which needs both rotation and translation motion of the fingers. At first, to grasp the bottle cap, the distance between the fingers was brought close until the

7 Stable Grasp and 3D Manipulation with 2-Soft-Fingered Robot Hand 7 (a) initial pose (b) grasp (c) opening (d) lift up (e) put down (f) closing Fig. 8. Opening and Closing of Bottle Cap exerted force became [N] (Fig.8-(a), (b)). Next, to open the cap, both fingertips were moved simultaneously along a circular path and the bottle cap was rotated horizontally for 30[deg] (Fig.8-(c)). To lift the cap, the fingertips were translated upward for 20[mm] (Fig.8-(d)). Finally, both fingertips were moved downward and rotated in the inverse direction (Fig.8-(e),(f)), and the bottle cap was closed. The grasping and manipulation was stable through out the task. 4.3 Crank Turning Finally, we conducted a crank turning task. The motion of the crank is constrained to a circle. To turn the crank smoothly, it is necessary to control both the position and force of the fingertips adequately according to the constraint. However, it is usually difficult to know both the position and the attitude of the crank accurately beforehand. Our approach is to give a rough path of the fingertips and to use the proposed control method for fine adjustment. We used a pencil sharpener for the crank, and it is 40[mm] in length, and the diameter of the handle is 10[mm]. Since the radius of the crank was too large for a complete rotation by the two fingers, only a partial revolution was specified as the task. The following input path was used(see Fig.9). 1. grasp the handle from 0[sec] to 2[sec] 2. move 2[mm] along x axis from 2[sec] to 3[sec] 3. move -0[mm] along x axis from 3[sec] to [sec] 4. move 2[mm] along x axis from [sec] to 6[sec]

8 8 T. Yoshikawa, M. Koeda, H. Fukuchi, and A. Hirakawa X Z Crank Constraint (a) grasp handle (b) 2[mm] Input Path Fig. 9. Crank Constraint and Input Path (c) -2[mm] (d) 0[mm] Fig. 10. Turning of Crank The input path was just on a straight line. As a result of adjustment of the finger positions by force information, the actual path was modified to follow the crank constraint as shown in Fig.10 ((a),(b),(c), and (d) correspond to the above steps 1, 2, 3, and 4 respectively). Fig.11 and 12 show the grasping force and the paths of the fingertips while this task was being executed. The robot hand kept holding the handle of the crank during the task though the holding power vibrated a little. Conclusion We have presented our newly developed two-fingered robotic hand with soft and thin skin. This hand is basically controlled by a position-based control

9 Stable Grasp and 3D Manipulation with 2-Soft-Fingered Robot Hand 9 4 finger0 finger1 Force [N] (a) (b) (c) (d) Time [sec] Fig. 11. Grasping Force Z [mm] (b) (d) (a) 0 X [mm] actual path input path (c) -2 Fig. 12. Path of Fingertip algorithm but it can also realize desired grasping force due the soft skin while keeping stability of the system. Experimental results have also been presented which show that this two-fingered hand can perform various manipulation tasks of objects in three dimensional space very stably. A future research topic will be to develop a multi-fingered robot hand that is completely covered by soft skin. Acknowledgment This research was supported by Grant-in-Aid for Scientific Research (No ) from Ministry of Education, Science, Sports, and Culture, Japan.

10 10 T. Yoshikawa, M. Koeda, H. Fukuchi, and A. Hirakawa References 1. K. Murakami and Tsutomu Hasegawa, Novel Fingertip Equipped with Soft Skin and Hard Nail for Dexterous Multi-fingered Robotic Manipulation, In Proceedings of IEEE International Conference on Robotics and Automation, pp , S. Arimoto, P. A. N. Nguyen, H.-Y. Han, and Z. Doulgeri, Dynamics and control of a set of dual fingers with soft tips, Robotica, Vol. 18, pp , N. Xydas and I. Kao, Modeling of contact mechanics and friction limit surfaces for soft fingers in robotics, with experimental results, International Journal of Robotics Research, Vol. 18, No. 8, pp , T. Maeno, S. Hiromitsu, and T. Kawai, Control of grasping force control by detecting stick/slip distribution at the curved surface of an elastic finger, In Proceedings of IEEE International Conference on Robotics and Automation, pp , 2000.