Proceedings of the ASME 2011 International Mechanical Engineering Congress & Exposition IMECE2011 November 11-17, 2011, Denver, Colorado, USA

Transcription

1 Proceeings of the ASME International Mechanical Engineering Congress & Exposition IMECE November -7,, Denver, Colorao, USA IMECE-6348 DESIGN AND ANALSIS OF A BIOMIMETIC WIRE-DRIVEN ROBOT ARM Zheng Li Institute of Precision Engineering, Dept. of Mechanical an Automation Engineering, Chinese University of ong Kong ong Kong, SAR zli@mae.cuhk.eu.hk Man Cheong Lei Institute of Precision Engineering Dept. of Mechanical an Automation Engineering, Chinese University of ong Kong ong Kong, SAR mclei@mae.cuhk.eu.hk Ruxu Du,ASME Fellow Institute of Precision Engineering, Dept. of Mechanical an Automation Engineering, Chinese University of ong Kong ong Kong, SAR ru@mae.cuhk.eu.hk Song Mei uan School of Mechanical Engineering & Automation, Beihang University Beijing, China yuansm@buaa.eu.cn ABSTRACT Inspire by the octopus an snakes, we esigne an built a wire-riven serpentine robot arm. The robot arm is mae of a number of rigi noes connecte by two sets of wires. The rigi noes act as the backbone while the wires work as the muscle, which enables the DOF bening. The forwar kinematics is erive using D- metho, while the inverse kinematics an its workspace can be solve by geometric analysis. To valiate the esign, a prototype is built. It is foun that the positioning error of the robot arm is generally less than %. The avantage of this robot arm is that with several noes fixe the rest noes are still controllable. The positioning error is smaller when the fixe noe is closer to the en effector.. INTRODUCTION Nowaays, robot arms are increasingly use both in inustry an aily life. In general, robot arms coul be ivie into three categories: iscrete, serpentine, an continuum [][]. Traitional sequential an parallel robots are of iscrete type. They are mae of several rigi links an joints, an can position accurately with large payloa. owever, they are usually big in size an have limite DOF, which constrain their performance in confine environment. Continuum robots are compact an theoretically have infinite DOF. As a result, they may be more suitable for confine environment. owever, because of the lack of high rigiity, they are limite by its positioning accuracy an payloa capacity. Accoring to literatures, existing continuum robots are mainly in the evelopment stage with few practical applications []. Serpentine robots have higher rigiity than continuum robots an are more flexible than iscrete robots. It has foun many applications, such as enoscope in minimally invasive surgery [3]. This paper presents our serpentine robot arm. It is well known that traitional robots are riven by servo motors arrange at each joint, however nature works ifferently. For example, a human finger is mae of three or four rigi bones an a number of flexible muscles an tenons [4]. As muscles can only prouce tension to realize reciprocate motion, a group of muscles woul work together: some exten while others contract. In the nature, such a bening mechanism is wiely seen, such as human spines, fishes, snakes, etc. Accoring to literatures, various artificial muscles have been evelope for bening robots, continuum or serpentine. There are mainly four types of artificial muscles: SMA (Shape Memory Alloy) wires [5], EAP (Electro Active Polymer) [6][7], PAM (Pneumatic Artificial Muscle) [8], an PZT (Piezoelectric Ceramic) [9]. For SMA artificial muscles, as heating an cooling process is necessary, the response is slow. Besies, high temperature makes it unsuite for bio-relate applications. For EAP artificial muscles, ue to the low rigiity of the polymer their payloa capacity is rather limite. PAM artificial muscles, typically McKibben actuator, can prouce large force an are easy to control. owever, they rely on air compressor system, Copyright by ASME

2 which is usually large, complex an expensive. For PZT artificial muscles, the require voltage is generally high, an the working range is small. Wire or cable can also function as muscles []. They are inexpensive, flexible, an can bear large tension with small iameter. In practice, they are wiely use to transmit force or motion. Researchers also use cable-riven mechanism to evelop parallel robot arms [4, 5], continuum robot arms [6, 7], etc. Current serpentine robots are mostly actuate by motors arrange at each joint or section, making the whole system very complicate [8, 9]. A recent systematic review about continuum robot can be foun in []. As pointe out in the paper, builing an effective continuum robot is still a challenge. In this paper, we introuce a wire-riven serpentine robot arm which is mae of multiple noes. Instea of using motors at each joint, two sets of wire are employe as muscles to rive the robot arm. The rest of the paper is organize as follows: Section escribes the esign of the robot; Section 3 presents the kinematics of the robot; Section 4 gives the experiment results; an Section 5 contains the conclusions.. ROBOT ARM DESIGN Our robot arm is inspire by snake an octopus tentacle. The skeleton of the robot is learnt from snake an the muscle arrangement imitates octopus tentacle. The backbone of snake has a number of short bones, as shown in Figure (a) []. The length of each bone is small, an multiple bones make up the whole backbone. The bening angle of each joint is small. owever, the backbone can easily ben over 36 egree. In our esign, we use a number of short noes with spherical joint as the robot arm skeleton, as shown in Figure (b). The noes are ivie into three types: start noe, mile noe an en noe. Mile noe is the major part of the skeleton, an its length is.5 mm. The number of mile noe can be etermine base on the nee. In each noe, there is a central hole an four pilot holes. The central hole has a iameter of 5 mm, an can be use to carry tooling or measuring instruments such as optic fiber. The pilot holes are for the wires. A gripper is arrange at the en noe of the robot arm. It is also riven by a wire an can be use for grasping or cutting. Octopus tentacle is highly flexible an can grasp objects freely in 3D space. Octopus tentacle has three types of muscle as shown in Figure (c) [6]: the longituinal muscles (L), the transversal muscles (T) an the external oblique muscles (O). With these muscles, it can exten, ben an twist. In our esign we use four wires, which are ivie into two groups, to imitate the longituinal muscles of octopus tentacle. As shown in Figure (), P an P3 are horizontal muscle group, while P an P4 are vertical muscle group. Due to the lack of transversal an external oblique muscles, our robot arm can only ben in ifferent irections but oes not have the fully function of octopus tentacle. In this esign, the wires o not only serve as muscles of the robot arm, but also play a role in connecting all the noes. The two groups of wire go through the whole robot arm an are fastene at the en noe. The other en is connecte to a wire coiler. All the wires are prestresse to prevent loose connection. (a) Skeleton of a snake Inspire Inspire (c) Octopus tentacle muscle arrangement (b) Backbone the robot arm P3 P4 P P () Wire arrangement in robot arm Fig. : Robot arm inspire by octopus an snake At the resting position, the lengths of P, P, P3 an P4 are the same an the robot arm is straight. When P extens an P3 contracts with P an P4 remain unchange, the robot will ben rightwar, as shown in Figure. When P contracts an P3 extens, the robot arm will ben leftwar. Similarly, the robot arm will ben forwar an backwar uner the control of P an P4. With the control of P, P, P3, an P4 the robot arm can ben in arbitrary irections. The relationship between the wire length an the bening angle will be iscusse in the subsequent section. The total bening angle is name as yaw angle, while is name as roll angle. Ben Leftwar Gripper Relax Straight Straight En Noe Mile Noe Start Noe Ben Rightwar Control Wire Fig. : Design of the wire-riven robot arm Gripper Grasp Copyright by ASME

3 Compare to traitional robot arms, the wire-riven serpentine robot arm is more flexible. As shown in Figure 3, when the robot arm is constraine at one of the mile noe, the rest of the noes are still active, an can ben uner the control of the four wires. Different from the controllable DOF, this is calle passive DOF. Our robot arm has two active DOF an multiple passive DOF. pair, is the height of noe, an h is the original istance between two noes. D h r Bening h h l Fig. 5: The joint of wire-riven robot arm: at the resting position (left) an in bening (right) Constrain Active Fig. 3: Flexibility of the robot arm 3. KINEMATICS OF TE WIRE DRIVEN ROBOT ARM For both forwar an inverse kinematics, their mapping coul be ivie into two parts [] as illustrate in Figure 4. The first part is between the actuator space an the configuration space, i.e. between wire length l an the robot arm bening angles θ,. The forwar an inverse kinematics in this stage are efine as f an f - respectively. The secon part is between the configuration space an the task space, which is between the robot arm bening angles an the en effector position an orientation (x, y, z). The forwar an inverse kinematics are efine as f an f - respectively. Actuator space l, x, y, z Wire length f f Config. space Forwar Kinematics Forwar Kinematics Inverse Inverse Kinematics Kinematics f Bening Angle f Task space Position, Orientation Fig. 4: Kinematics efine by mapping between the spaces 3. Mapping from the Actuator Space to the Configuration Space The robot arm has multiple noes an two ajacent noes making a joint. In Figure 5, the left part shows two ajacent noes at the resting position an the right part shows the joint bening leftwar with an angle of θ. As shown in the figure, D is the iameter of the noe, is the istance between the wire At the resting position, the length of wire insie the joint is l = + h. When the joint bens left with an angle of θ, the left wire becomes l l = + h l an the right wire becomes l r = + h r. From the geometric relationship as shown in Figure 6, lengths of the wires are: hr h cos sin hl h cos sin h h h Fig. 6: Wire length change w.r.t. the bening angle Assuming the robot arm has N mile noes, an the length of the wire insie the robot arm is L. Then, the resting length of the left an the right wire is as follows: L L L ( N )( h ) + () l r S E where S is the length of the start noe, an E is the length of the en noe. Furthermore, assuming the friction of each joint is ientical, then the bening angle of each joint ue to the change of the wire length woul be the same. This is similar to constant () 3 Copyright by ASME

4 curvature assumption aopte in continuum robot []. At a bening angle of θ the total wire length becomes: Ll L( N ) sin hsin 4 Lr L( N ) sin hsin 4 Note that the other group of wires woul remain unchange as they lay in the neutral plane. It can be shown that the total bening angle of the robot arm is: Lr L ( N ) ( N ) arcsin l ( N ) In particularly, the maximum bening angle θ max is constraine by the esign of the noe: D an h. The relationship between the maximum bening angle an the noe parameter is: P 3 P 3 P max arctan h D P y P 4 P x P 4 (a) Bening irection an virtual axises P P 3 P P 3 b P a P 4 a P b P 4 (b) Distance from wires to virtual axises Fig.7: Wire group configuration: (a) the bening irection an the virtual axis, (b) the istance from wires to the virtual axis For our robot arm, the two groups of wires (P P 3 an P P 4 ) are configure as shown in Figure 7. When the robot arm bens about axis, P an P 4 are in the neutral plane an their length remains unchange. Similarly, when robot arm bens about axis, P an P 3 are in the neutral plane an their length remains unchange. Generally, the robot arm may ben arbitrarily an we name the virtual bening axis as, which lies in the neutral plane. The angle between an is the roll angle. To etermine the length of each wire, assume the roll angle is, an each joint bens θ. The configuration is equivalent to the robot arm actuate by a virtual group of wire locate at P an P 3. The length variation is proportional to the istance from the wire to the neutral plane, as shown in Figure 7, the length insie the robot arm for each wire is as follows: P (3) (4) (5) P : P : P 3 : P 4 : L L ( N ) b sin sin h 4 L L ( N ) a sin sin h 4 L 3 L ( N ) b sin sin h 4 L 4 L ( N ) a sin sin h 4 where, a sin( ) is the istance from P, P4 to the virtual bening axis ; b cos( ) is the istance from P, P3 to. Equations (6) ~ (9) efine the forwar mapping between the actuator space an the configuration space i.e. f. The two bening angles, an θ, can be solve analytically using the equations below: arctan L L 4 L L3 L ( ) ( ) arcsin L3 N N ( N ) cos( ) (6) (7) (8) (9) () () These two equations give the inverse mapping between the actuator space an the configuration space f Mapping from the Configuration Space to the Task Space The position of the en effector can be etermine using the D- (Denavit artenberg) metho [3]. Figure 8 shows the coorinate system an Table shows the D- parameters. Assume the friction on each noe is the same. Then all θ i are equal, an let it be θ. Z i Z N i Z N i N N N Z Z N Fig. 8: Coorinate frame setting for the D- Metho Z w w Z w 4 Copyright by ASME

5 i ai i S 3 h i i ( ) i h ( ) i N+ ( h ) N Table : The D- parameter of our robot arm Base on the D- table, the transform matrix from coorinate i- to i is: i i ci si ai sic i c ic i s i s i i T si s i c is i c i c ii () where cθ i enotes cos(θ i ) an sθ i means sin(θ i ); c i- is cos( i- ) an s i- enotes sin( i- ). Accoringly, the en effector position in the worl coorinate can be calculate from the following equation: x E y w i N N T T it NT N T z (3) where i =,,, N+. Moreover, the close form solution of en effector position is as Eq. (4). When one of the mile noes is fixe, by taking the fixe noe as the start noe we can get the en effector position in the same way. S, arctan y x Z O Fig. 9: Robot Arm Bening E ( x, y, z) E (5) To solve the angle θ, let A = E, B = ( + h ), C = U x y, an V z C. It follows that: N N sin N U AcosN B cos sin sin N V Asin N B sin sin tan( ) By using the trigonometric formula sin( ) tan ( ) tan ( ) cos( ), an let tan ( ) equation is obtaine: U A u V u (6) an N utan, the following ( ) ( ) (7) As u is a real number, the two complex roots are iscare. Thus, the bening angle of each joint θ is: N xe sin N h sin i cos i N ye sin N h sin i sin i N zsecos N h cosi i (4) z arctan N x y (8) Moreover, the total bening angle of the robot arm is as shown in Eq. (9). The inverse kinematics between the configuration space an the task space is shown in figure 9. In the figure, the re curve represents the robot arm, an E is the en effector position. From the position an orientation of the en effector, the roll angle an yaw angle θ coul be solve analytically. From the geometric relationship, it is straightforwar to solve as: z N arctan x y (9) Equation (4) gives the forwar kinematics from configuration space to task space f, while Eq. (5) an (9) give the inverse one f -. 5 Copyright by ASME

6 Relative Error(%) position (mm) Z position (mm) 3.3. The Workspace of the Robot Arm From the forwar kinematics, the relationship between the en effector position an the wire length can be foun. This is the workspace efine below: sin ( U A) V A cos B N N sin () Note that the workspace is a surface not a volume. Moreover, from Eq. (), it is seen that the workspace is a spheroial surface, as shown in Figure. In planes parallel to - plane, the locus of en effector is a circle, whose raius epens on the robot arm total length an joint bening angle. If a mobile platform is ae along the Z axis, the robot arm will be able to carry out many applications MCU Wire Coiler Servo Motor Rubber tube Wire Wire Base Fig. : Experiment setup DC Power Supply Robot Arm In the first experiment, the en effector move from the left most position to the right most position. The experiment result is summarize in Figure. In the figure, the re line is the preicte trajectory using Eq. (4), while the blue stars are the recore positions. 5 Preicte Experiment position (mm) -5 position (mm) Fig. : The workspace of the robot arm EPERIMENT VALIDATION To valiate the presente esign, we built a prototype as shown in Figure. The noes are built using Rapi Prototyping (RP). There are totally noes, an the maximum bening angle of the robot arm is = 8.5 o (4.5 o for each joint). It is note that the friction of the joints coul be uneven, which makes the bening non-uniform. To eliminate this problem, a rubber tube is place through the central hole of each noe. It serves as the backbone of the robot arm. The tube puts a soft constraint to the bening motion of the whole robot arm: the bening curve of the robot arm is approximately piecewise constant curvature arc []. The wires are fishing lines, an are fastene onto a wire coiler, which is riven by servo motors. The motor is controlle by a MCU (Moel: AVR ATmega 6). Because of the symmetry, only a group of wire is teste in the experiment. During the experiment, the en effector positions are recore at ifferent bening angles using a gri paper. Two sets of experiments are conucte position (mm) Fig. : The trajectory of the en effector 3-4 Error -5 Error Dist. Error Sample Num. Fig. 3: Robot arm positioning error 6 Copyright by ASME

7 Positioning Error(%) position (mm) It is note that the actual position is very close to the preicte one. As shown in Figure 3, the position error is generally within % (black ash line). More specifically, the position error in irection (re line) an irection (blue line) are less than 3% with few exceptions, such as at the two bening limits. Compare to traitional robot arms, the positioning error is large. This may be attribute to a number of factors, such as the lack of rigiity as well as the friction among the noes. It is expecte that the errors can be minimize when feeback control is introuce. with the isplacement an velocity being amplifie, the loaing capability of the robot arm is reuce. 5 5 Simu Simu 3 Simu 5 Exp Exp 3 Exp 5 Fixe noe 5 4 En Effector Trajectory -5 - Mile Noe No. 3 Fixture position (mm).5 Fig. 5: Robot Arm trajectory with Obstacle Fig. 4: The motion of the robot arm with constraints In the secon experiment, part of the en effector is constraine as shown in Figure 4. As iscusse previously, the motion of the robot arm will be ifferent. Figure 5 shows the experiment result. There are three curves in the figure: the curve in re is the preicte trajectory of the en effector when the first mile noe is fixe (re square shows the location of the fixe noe). The re circles are the recore en effector positions. The curve in green is the preicte trajectory of the en effector when the thir mile noe (green square) is fixe an iamons show the experiment results. The curve in blue is the preicte trajectory of the en effector when the fifth mile noe (blue square) is fixe an stars show the result of the thir case. Moreover, the three squares enote the position where the fixe noe is. In all three cases, the experiment results are quite close to the preictions. As shown in Figure 6, for Case, the positioning error is less than.5% (re ash-ot line); for case, the error is below.75% (green ash line); for case 3, the error is below.35% (blue soli line). As expecte, with the fixe noe closer to the en effector, the positioning error is smaller. This is because with less active noes, the uncertainty brought by the robot arm is smaller. It shall be pointe out that from the kinematic point of view, the isplacement an the velocity of the en effector are amplifie compare to the isplacement an the velocity of the riven wire. As a result, the wire-riven robot arm can be use as a isplacement an / or velocity amplifier. On the other han, st noe fixe 3r noe fixe 5th noe fixe Sample Num. Fig. 6: Positioning Error when Noes are fixe 5. CONCLUSION This paper introuces a wire-riven robot arm. It is mae up by a start noe, an en noe an a number of ientical mile noes. The robot arm has two active bening DOF (roll an yaw) an multiple passive bening DOF. The range of the bening is etermine by the number of noes. For each joint, the maximum bening angle is given by noe iameter an joint initial istance. The robot arm is equippe with a gripper, which coul be use to grasp or cut. It has a central hole that can be use to carrying tools such as measuring evices. Both forwar an inverse kinematics of the robot arm are erive. It is foun that the robot arm can achieve isplacement an velocity amplification, an the amplification ratio is etermine by the length of the robot arm an the istance 7 Copyright by ASME

8 between the wire pair. Though, the amplification will result in reuce loaing capacity, as the loaing is also amplifie. The friction between the noes plays an important role. To minimize the effects of friction, a rubber tube is place in the center. Base on the experiments, the positioning error of this robot arm is generally less than %. The robot arm is still controllable with several mile noes being constraint. The positioning error is smaller when the fixe noe is closer to the en effector. It is believe that with further improvement, this robot arm will fin many practical applications in the future. ACKNOWLEDGMENTS This work is partially supporte by Major Project of the Science an Technology Ministry in China. The grant number is Z44-5. REFERENCES [] G. Robinson an J. B. C. Davies, Continuum Robots a State of the Art, Proceeings of the 999 IEEE International Conference on Robotics an Automation, pp , May, 999. [] P. E. Dupont, J. Lock, B. Itkowitz an E. Butler. Design an Control of Concentric-Tube Robots, IEEE Transactions on Robotics. vol. 6, No., p.9-5,. [3] W. J. oon, P.G. Reinhall an E. J. Seibel, Analysis of Electro-active Polymer Bening: A Component in a Low Cost Ultrathin Scanning Enoscope, Sensors an Actuators A: Phys, 33 pp.56-57, 7. [4] Anatomy Wrist an Forearm motions at: Mechanism.htm [5] V. D. Sars, S. yliyo an J. Szewczyk. A practical approach to the esign an control of active enoscopes, Mechatronics. vol., pp. 5-64,. [6] C. Laschi, B. Mazzolai, V. Mattoli, etc. Design of a biomimetic robotic octopus arm, Bioinspiration & Biomimetic, oi:.88/748-38/4//56, 9 [7] C. Laschi, B. Mazzolai, V. Mattoli, etc. Design an Development of A Soft Actuator for a Robot Inspire By the Octopus Arm Experimental Robotics: The th Intern. Symp. STAR 54, pp. 5-33, 9 [8] B. A. Jones an I. D. Walker, Kinematics for Multisection Continuum Robots, IEEE Transactions on Robotics, vol., No., pp.43-57, Feb. 6. Phys, 54, pp , 996. [] M W. annan, an Ian D. Walker, Kinematics an the Implementation of an Elephant s Trunk Manipulator an other Continuum Style Robots, J. of Robotics Systems,vol., Issue, pp 45-63, Feb. 3 [] D. Drew, Skeleton (InfoActive), at: 8visual.info/ia_skeleton.html [] R. J. Webster Ⅲ an B. A. Jones. Design an Kinematic Moeling of Constant Continuum Robots: A Review, Int. J. of Robotics Research, vol.9, pp ,. [3] R. artenberg an J. Denavit, Kinematic Synthesis of Linkages, New ork: McGraw-ill, 964 [4] R. Dekker, A. Khajepour, an S. Behzaipour, Design an testing of an ultra-high-spee cable robot, Int. J. of Robotics an Automation, vol., no., pp. 5 34, 6. [5] S. K. Mustafa, G. J. ang, an et al. Self-Calibration of a Biologically Inspire 7 DOF Cable-Driven Robotic Arm, IEEE/ASME transactions on mechatronics, vol. 3, No., pp , Feb. 8. [6] C. Q. Li an C. D. Rahn, Design of Continuous Backbone, Cable-Driven Robots, J. of Mechanical Design, vol. 4, pp. 65-7, [7] K. u an N. Simaan, Analytic Formulation for Kinematics, Statics, an Shape Restoration of Multibackbone Continuum Robots Via Elliptic Integrals, J. of Mechanisms an Robotics, vol., oi: 6- Feb.. [8] C. Wright, A. Johnson, an at el. Design of a Moular Snake Robot, Proceeings of the 7 IEEE/RSJ International Conference on Intelligent Robots an Systems, San Diego, CA, USA, pp , Oct 9-Nov, 7. [9] J. Borenstein, M. ansen, an. Nguyen, The OmniTrea OT-4 Serpentine Robot for Emergencies an azarous Environments, 6 Int. Joint Topical Meeting: Sharing Solutions for Emergencies an azarous Environments, Feb -5, Salt Lake City, Utah, USA. [9] T. Iogaki, T. Tominaga, K. Sena, an et al. Bening an expaning motion actuators, Sensors an Actuators A: 8 Copyright by ASME