两自由度机械手的一个平行四边形的.pdf

Task based kinematic design of a two DOF manipulator with a parallelogram fi ve-bar link mechanism J.Y. Kim * Department of Mechatronics Engineering, Tongmyong University of Information Technology, 535, Yongdang-dong, Nam-gu, Busan 608-711, Republic of Korea Received 19 May 2005; accepted 22 January 2006 Abstract As the demand for modular manipulators or special purpose manipulators has increased, task based design to design an optimal manipulator for given tasks become more and more important. However, manipulator design problems usually are very complex due to a large number of design parameters, their nonlinear and implicit relationship, and so on. To achieve task based design successfully, it is necessary to develop a methodology that can solve the complexity. This paper addresses how to determine the kinematic parameters of a two degrees of freedom manipulator with a parallelogram fi ve-bar link mechanism from a given task, namely, how to map a given task into the kinematic parameters. With a simplifi ed example of designing a manipulator with a fi ve-bar link mechanism, a methodology for task based design is presented. And it introduces formulations of task specifi cations and manipulator specifi cations, and presents a new dexterity measure as an optimality criterion for manipulator design. Also it fi nds out an optimal design solution for the manipulator by using a genetic algorithm that has robust search performance in complex spaces. ? 2006 Elsevier Ltd. All rights reserved. Keywords: Task based design; Five-bar link mechanism; Task specifi cation; Manipulator specifi cation; Optimality criterion; Measure of dynamic isotropy 1. Introduction One of the largest characteristics of a robot manipulator is to be able to carry out various tasks by changing its pro- gram. Therefore, manipulator design until now has been focused on general purpose manipulators that can adapt to more tasks. In other words, the designed manipulator specifi cations such as workspace, joint angle limit, torque limit do not aim some specifi c tasks only, but many and unspecifi edtasks.However,eventhemanipulators designed for general purpose have the limitation on the executable tasks, and thus most robots carry out only a task or a couple of tasks in the working fi elds. In order to accomplish given tasks successfully, a manip- ulator must be having the specifi cations required for the tasks, for example, workspace, DOF (degrees of freedom), velocity, accuracy, and so on. But, over-specifi cations to the given tasks are not desirable. In other words, it is desir- able to design the most appropriate manipulator satisfy- ing the required specifi cations which are necessary to the accomplishment of the given tasks. It is the objective of task based design. Task based design will be of good use for the design of a modular manipulator or a special pur- pose manipulator. Recently, the application area of a robot manipulator is being expanded widely to nonindustrial fi elds such as space, undersea, nuclear power plant, medical service as well as industrial fi elds such as loading/unloading, welding, or assembly. And thus, the necessity of special purpose manipulators for a specifi c task is increasing. In designing a special purpose manipulator, it is necessary to endow the manipulator with the functions and performances opti- mal to a given task, namely, to determine the appropriate values of workspace, accuracy, velocity, payload, and so on. 0957-4158/$ - see front matter ? 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2006.01.004 * Tel.: +82 51 610 8360; fax: +82 51 610 8845. E-mail address: kjy97tit.ac.kr Mechatronics 16 (2006) 323329 As the researches on task based design, Yoshikawa 1 and Salisbury 2 each proposed a kinematic dexterity mea- sure called the manipulability and the condition number, and carried out rudimentary task based kinematic design to determine the link lengths of a manipulator on the basis of the proposed dexterity measures in case that one task point was given as a task specifi cation. Tsai 3 carried out task based kinematic design to determine the link length, the joint angle limit and the base position of a serial drive manipulator from its workspace with advance infor- mation on some kinematic parameters. Paredis 4 carried out a kind of task based kinematic design to fi nd out DenavitHartenberg parameters of a serial drive manipulator satisfying task specifi cations of task points, joint angle limit, obstacle avoidance. Au 5 carried out task based kinematic design of a fault tolerant manipulator in the same way as Paredis described above. Snyman 6 carried out task based kinematic design to determine the link lengths and the base position required for execution of a tool moving task in a serial drive planar manipulator. Kim 7,8 proposed a framework of task based design including kinematic specifi cations and param- eters. He carried out task based design through formula- tion of task specifi cations and a performance index for optimization. Huang 9 and Muller 10 carried out a kind of task based kinematic design of parallel manipulators. On the other hand, there are the researches on manipu- lator redesign though they are not task based design. Asada 11, Yoshjkawa 12, and Khatib 13 each proposed a dynamic performance index such as the generalized inertia ellipsoid and the dynamic manipulability, and redesigned a manipulator by changing the link lengths and mass distribution in order to enhance dynamic perfor- mances. Inoue 14 carried out design of a serial drive manipulator based on mechanical parts database in consid- eration of both of kinematic and dynamic specifi cations. This study attempted performance enhancement by modi- fying original design parameters. However, none of above researches on task based design deals with a parallel drive manipulator like a fi ve-bar link- age. And none determined design parameters in consider- ation of dynamics excluding some studies on redesign. With this motivation, this paper carries out task based kinematic design to determine kinematic design parameters of a two DOF manipulator with a parallelogram 5-bar link mechanism, and proposes a methodology for task based design, which takes dynamics as well as kinematics into consideration by presenting a new dexterity measure for manipulator design. Robot manipulators with a 5-bar linkage are applied to a variety of fi elds nowadays, especially to many industrial fi elds such as welding, painting, handling, sealing, de- burring, assembly, and so on. Fig. 1 shows a schematic diagram of a serial drive mechanism and a parallel drive mechanism. In a serial drive mechanism, the lower link is drived by motor 1 located at the base, and the upper link is drived by motor 2 located between the lower link and the upper link. Also the weight of motor 2 becomes a load on motor 1, and the reaction torque of motor 2 has infl u- ence on motor 1. However, in case of a parallel drive mech- anism with a 5-bar linkage, all of two motors are located at the base of the mechanism. And thus, the weight and the reaction torque of one motor do not have a direct eff ect on another motor 15. A 5-bar link mechanism has small power dissipation compared with a serial drive mechanism with the same motor power and the same workspace. Especially, in case of a parallelogram 5-bar link mechanism shown in Fig. 2, the inertia tensors of the manipulator links can be invariant and decoupled, and thus it results in simplifi ed dynamics and large structural stiff ness 15. Summarizing the advan- tages of a parallelogram 5-bar link mechanism compared with a serial drive mechanism, there are small power dissi- pation, simplifi ed dynamics, large structural stiff ness, no direct infl uence between the motors, and so on. Due to the advantages, the application of manipulators with a 5-bar link mechanism will increase more and more. However, the design problem of a parallelogram 5-bar link mechanism is more complex compared with a serial drive mechanism due to its complex structure. Therefore, it is certain that a methodology for task based design of a (b) parallel drive(a) serial drive motor 1 motor 2 link 1 (lower link) link 2 (upper link) link 3 link 4 link 2 link 1 motor 1 motor 2 0 Fig. 1. A serial and a parallel drive mechanism. X Z 1 2 2 3 1 m1 m2 m3 m4 d1 d2 d4 d3 (Px, Pz) link 3 link 2 link 4 link 1 I3 I1 I4 I2 X Fig. 2. A two DOF manipulator with a parallelogram 5-bar link mechanism. 324J.Y. Kim / Mechatronics 16 (2006) 323329 manipulator with a 5-bar link mechanism will be able to be applied easily to design of a serial drive manipulator. This paper is organized as follows: Section 2 describes a methodology and problem statements for task based design. Section 3 describes task based design of a parallel- ogram 5-bar link mechanism which takes kinematics only into consideration by using a kinematic dexterity measure. Section 4 presents a new dynamic dexterity measure as a performance index for manipulator design, and carries out task based design considering both of kinematics and dynamics by using the proposed dexterity measure. Finally, some conclusions are made in Section 5. 2. Problem statements of task based design The objective of task based design is to decide kinematic and dynamic design parameters of a manipulator optimal to given tasks. Task specifi cations can be categorized into kinematic specifi cations and dynamic specifi cations. The former has infl uence on kinematics only, and includes workspace, allowable maximum value of the position error due to kinematic factors, etc. The latter has infl uence on both of kinematics and dynamics, and includes payload, maximum joint velocity and acceleration, etc. Similarly, manipulator design can be divided into two stages of kinematic design and dynamic design. Kinematic design is to determine kinematic design parameters of a manipulator like DenavitHartenberg parameters, and dynamic design is to determine dynamic design parameters like mass center, mass moment of inertia 16. On the other hand, in order to satisfy both of kinematic specifi cations and dynamic specifi cations, it is desirable to carry out kinematic design and dynamic design iteratively because kinematic design parameters determined in the fi rst kinematic design stage can be changed by dynamic design. Fig. 3 shows an iterative manipulator design procedure. First, task specifi cations are given. Next, kinematic design, dynamic design, detailed structure design, and controller design are carried out in regular sequence and iteratively. This iterative design method can be equally applied to task based design, too. As the elements constituting task based design, there are task specifi cations, manipulator specifi cations, and an optimality criterion. Task specifi cations are just the same as they are described above. In manipulator specifi cations, there are joint angle limit, base position constraint, con- straints on manipulator design parameters, and so on. As an optimality criterion, a dexterity measure for task points, and total weight or cost of a manipulator, etc. can be used. A task based design problem is to determine kinematic and dynamic design parameters such as the dimension and the mass of each link, and DOF and type of a manip- ulator from task specifi cations and manipulator specifi ca- tions by using an optimality criterion. Fig. 4 shows such a framework for task based design. Thereafter, motion planning and control parameter decision can be done. Fig. 5 shows the diff erence between task based design and other optimal design which is not task based design. Task based design searches for design parameters conforming to given task specifi cations. On the other hand, there are a lot of design parameters to determine, and their relations are very complicated and nonlinear. Accordingly, there is a need to decide them based on the priority order, and thus an iterative design method can be of good use. Selection of an optimization algorithm is also the point to see. In optimizing a lot of Detailed structure design Task requirements Kinematic design Dynamic design Controller design Kinematic analysis Dynamic analysis Dynamic analysis Structure analysis Database of machine elements Motion planning Detailed structure design Task requirements Kinematic design Dynamic design Controller design Kinematic analysis Dynamic analysis Dynamic analysis Structure analysis Database of machine elements Motion planning Fig. 3. An iterative manipulator design procedure. Task specification : -reachability -obstacle avoidance -singularity avoidance -joint angle change -positional error -dextrous workspace -velocity, acceleration -payload Manipulator specification : -joint angle limit -dimension constraint minmaxi -base position constraint -joint limit interval Design : Mapping tasks onto design parameters DOF selection Type generation Optimization algorithm Output : -degree of freedom -type, dimension, pose (D-H parameters) -base position -joint torque -mass and inertia of link -position of mass center Optimality criterion : -dexterity measure -cost (total mass of a robot) i : () Fig. 4. A framework for task based design of a manipulator. J.Y. Kim / Mechatronics 16 (2006) 323329325 design parameters on many task points or workspace, it is necessary to use an optimization algorithm with strong search capacity and excellent convergence performance to global optimum because the design parameters have very nonlinear and complex relations. In such a framework shown in Fig. 4, the formulation of task specifi cations and manipulator specifi cations is neces- sary, and the selection and the formulation of a perfor- mance index as an optimality criterion also need to be carried out. This paper presents a basic framework for manipulator design through task based design of a two DOF manipulator with a parallelogram 5-bar link mech- anism. But, in order to simplify the design problem, it determines the DenavitHartenberg parameters only which belong to kinematic design parameters. Through a formu- lation of manipulator specifi cations and proposal of a new performance index considering dynamics, this study deter- mines design parameters on consideration of dynamics as well as kinematics. And a genetic algorithm with excellent convergence performance to global optimum is used for optimization. 3. Kinematic design by a kinematic performance index In this section, task based kinematic design to determine DenavitHartenberg parameters of a two DOF manipula- tor with a parallelogram 5-bar link mechanism is carried out on consideration of only kinematics. As shown in Fig. 6, 12 task points are given as task specifi cations to be carried out. The design parameters to be determined are (1, 2, 3, h1, h2) as shown in Fig. 2, which are the DenavitHartenbergparametersofthemanipulator. Because a link length 1 has no eff ect on the kinematic end position of the manipulator, it is not determined in this design example, and it is excluded in the design parameters of this example. On the other hand, joint angles h1, h2can be obtained by inverse kinematics after link lengths 2, 3 are determined. As kinematic constraints which belong to manipulator specifi cations, the joint angle ranges are assumed to be h1,min6 h16 h1,max, h1+ h2,rmin6 h26 h1+ h2,rmax, h2,min6 h26 h2,max, and then they can be formulated as follows: Cj ?wj X t i1 X d k62 max 0;hik? hk;max ? max 0;hk;min? hik ? max 0;hi2? hi1 h2;rmax ? max 0; hi1 h2;rmin ? ? hi2 ?# 1 where Cjrepresents the joint angle range constraint as a component of the fi tness function for optimization, and Cjhas the maximum value 0 when all joint angle range con- straints are satisfi ed. And wjrepresents a weight factor of the joint angle range constraint, and hk,max, hk,minrepresent the upper limit, the lower limit of joint angle of each link, and h2,rmax, h2,rminrepresent the upper limit, the lower limit of the diff erence between h1and h2, and hikrepresents the joint angle of kth link at ith task point, and t represents the number of task points, and d represents the degrees of freedom. On the other hand, this design used the measure of isot- ropy D as a performance index for optimization, which is independent on the order and the scale of a manipulator 7. The D is suitable as a kinematic performance index formanipulatordesignconsideringkinematicsonly ab required task space performance index design parameter by Non TBD : a by TBD : b Fig. 5. Comparison of task based design and nontask based design. 1 23 4 5 6 7 9 10 11 12 8 Pz(cm) Px(cm) -100-50 0 50100150 -100 -50 50 100 -150 ( No. of task points = 12 ) 1 5 6 7 9 10 11 12 8 150 Fig. 6. Task points for an example of task based kinematic design. 326J.Y. Kim / Mechatronics 16 (2006) 323329 because of order-independence and scale-independence. It is formulated as follows: Cp wp X t i1 D wp X t i1 Mi W wp X t i1 ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi detJJT m p traceJJT=m wp X t i1 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi k1k2?km m p k1 k2 ? km=m 2 where Cprepresents the performance index component of the fi tness function, and the larger a performance index D is, the larger Cpis. And wprepresents a weight factor of the performance index component, Mirepresents the order-independent manipulability, J represents a Jacobian matrix, m represents the order of J, kirepresents an eigen- value of JJT, W represents the arithmetic mean of the eigen- values of JJT, and t represents the number of task points. From the formulation of manipulator specifi cations and a performance index described in Eqs. (1) and (2), the fi t- ness function F for optimization is given by F = Cj+ Cp. In order to obtain optimal design parameters maximizing the fi tness fu