A Hybrid Multi-Objective Scheme Applied to Redundant Robot Manipulators
A Hybrid Multi-Objective Scheme Applied to
Redundant Robot Manipulators
Dechao Chen and Yunong Zhang,Member,IEEE
Abstract—In this paper,a hybrid multi-objective scheme is pro-posed to complete simultaneously four objectives,i.e.,the speci?ed primary task for the end-effector,obstacle avoidance,joint-phys-ical limits avoidance,and repetitive motion of redundant robot ma-nipulators.In addition,corresponding theoretical analysis is given, which guarantees the validity of the proposed scheme.Then,the proposed hybrid multi-objective scheme is reformulated as a dy-namical quadratic program(DQP)problem.The optimal solution of the DQP problem is found by the PLPE(piecewise-linear projec-tion equation)neural network,i.e.,PLPENN,and also by the corre-sponding numerical algorithm implemented on the computer.Fur-thermore,simulation and comparison based on a six-link planar redundant robot manipulator substantiate the effectiveness and accuracy of the proposed scheme.At last,a hardware experiment is conducted on a six-link physical robot manipulator system,which substantiates the physical realizability,operational stability,and safety of the proposed hybrid multi-objective scheme.
Note to Practitioners—This paper is motivated by the multi-ob-jective problem of redundant robot manipulators in practical applications.Note that redundant robot manipulators are usually required to handle the multiple objectives simultaneously in a complex environment.Thus,a physically realizable,operationally stable,and safe solution for such redundant robot manipulators is signi?cant for practitioners.This paper proposes a hybrid multi-objective scheme to complete simultaneously multiple objectives of redundant robot manipulators.Besides,for the convenience of practitioners to develop in applications,the corre-sponding numerical algorithm with its block diagram given for the optimal solution of the proposed scheme is also presented. Computer simulation based on a six-link planar redundant robot manipulator shows that the four mentioned objectives are com-pleted well.The proposed scheme is also applied to a six-link physical robot manipulator system to substantiate further its effectiveness.
Index Terms—Hybrid multi-objective scheme,joint-physical limits avoidance,obstacle avoidance,redundant robot manipula-tors,repetitive motion.
I.I NTRODUCTION
K INEMATIC redundancy occurs when a manipulator pos-sesses more degrees of freedom(DOF)than the required to perform a given end-effector primary task[1]–[12].Similar to
Manuscript received May31,2015;accepted August23,2015.This paper was recommended for publication by Associate Editor A.Pashkevich and Editor J.Wen upon evaluation of the reviewers’comments.This work was supported in part by the National Natural Science Foundation of China(61473323),in part by the Foundation of Key Laboratory of Autonomous Systems and Networked Control,Ministry of Education,China(2013A07),and in part by the Science and Technology Program of Guangzhou,China(2014J4100057).
The authors are with the School of Information Science and Technology, Sun Yat-sen University(SYSU),Guangzhou510006,China;the SYSU-CMU Shunde International Joint Research Institute,Foshan528300,China;and the Key Laboratory of Autonomous Systems and Networked Control,Ministry of Education,Guangzhou510640,China(e-mail:zhynong@https://www.sodocs.net/doc/6d953320.html,;jal-lonzyn@https://www.sodocs.net/doc/6d953320.html,;chdchao@https://www.sodocs.net/doc/6d953320.html,).
Color versions of one or more of the?gures in this paper are available online at https://www.sodocs.net/doc/6d953320.html,.
Digital Object Identi?er10.1109/TASE.2015.2474157the situation of our human arm or leg,elephant trunk and snake, the potential ef?cacy of a redundant manipulator is determined by the DOF number,as well as the manipulator's structure and its control scheme[13]–[18].For a manipulator with just enough DOF for a speci?c end-effector task(or simply,a nonredundant manipulator),it may not have the ability to complete secondary objectives when executing the primary task,due to the solution uniqueness.Besides,many studies have shown that the redun-dancy can improve the performance and versatility of the re-dundant robot manipulators in various aspects[19]–[22],such as repetitive motion[23],obstacle avoidance[24]and joint-physical limits avoidance[10],[25].Therefore,a hybrid mul-tipurpose(or termed,hybrid multi-objective)robot manipulator needs to be redundant if it is to be implemented effectively. For example,a7-DOF PA10robot manipulator equipped with a 1-DOF long tool has5redundant DOFs when we consider only the end-effector's positioning so that it can perform various sub-tasks in addition to the end-effector's primary path-tracking task [10],[25].
Redundancy-resolution problem(or termed,inverse-kine-matic problem)is one fundamental issue in operating the redundant robot manipulators,which thus has attracted a vast concern among the readers and researchers[1],[8],[9],[14]. That is,given the desired or user-de?ned Cartesian trajectories of the manipulator's end-effector,we need to generate the corresponding joint trajectories online or in real time.Note that,due to the in-depth research in redundancy resolution, multi-objective optimization has been viewed as a powerful alternative to motion planning of redundant robot manipu-lators[8],[12],[26].Two general approaches are available in multi-objective optimization[8],[27].The?rst approach combines individual objectives into a single composite function or moves all but one objective to the constraint set(e.g.,the repetitive motion,obstacle avoidance and joint-physical limits avoidance[25],[28]).This approach is sometimes termed as “multi-criteria optimization”and sometimes as“bi-criteria optimization”.Hou et al.[10]investigated the multi-criteria optimization for coordination of redundant robots.In another study,Zhang et al.[28],[29]presented different bi-criteria minimization schemes for motion planning of redundant robot manipulators.The second approach determines either the Pareto-optimal set,which is an entire set of trade-off optimal solutions,or a representative subset.In a different experiment, Machado et al.[8]developed and investigated a technique to solve the inverse kinematics of redundant robot manipulators by using a multi-objective genetic algorithm.Guigue et al.[26] presented an approach that obtains the Pareto-optimal set to solve multi-objective robotic trajectory planning problems. Generally speaking,multiple tasks or requirements will usu-ally occur in a complex operational environment for redundant
1545-5955?2015IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.
See https://www.sodocs.net/doc/6d953320.html,/publications_standards/publications/rights/index.html for more information.
robot manipulators.Regardless of the type of redundancy(e.g., kinematical or functional),a variety of tasks requiring sophis-ticated motion in a complex environment can be conducted by redundant robot manipulators[30].In particular,this includes working in hazardous or rough-and-tumble environment,car-rying heavy objects or radioactive materials,and exploring un-predictable regions[31].A speci?ed primary task,e.g.,motion tracking for the end-effector of the redundant robot manipulator can be viewed as a common objective.In this paper,based on the relation between the end-effector position vector and joint angle vector of the redundant robot manipulator,we can achieve the objective of a speci?ed primary task of the end-effector in the2-D(or3-D)space.
Obstacle avoidance is another essential issue in redundancy resolution[25],[32]–[34].It is very signi?cant for the motion planner to avoid collisions between the obstacles and robot manipulator during the end-effector task execution(otherwise, it may lead to the serious damage of the manipulator and/or objects).To complete the objective of obstacle avoidance for redundant robot manipulators,many researches have been re-ported[25],[32],[34],[35].The pseudoinverse method and its variants[36],[37],generally in the form of a minimum-norm particular solution plus a homogeneous solution,were proposed and investigated for no collision between obstacles and the robot manipulators.As another well-known technique,the methods based on arti?cial potential?eld were investigated for obstacle avoidance of robot manipulators[28],[38]in which obstacles were represented by repulsive surfaces,whereas the target position was represented as an attractive pole.Being different from the pseudoinverse approaches,the approaches based on quadratic programming have also been developed and investigated for obstacle avoidance of redundant robot manipulators.In[39],several methods were designed by Cheng et al.to maximize the distance between robot links and obstacles.In[40],the collision-free criterion was formulated as a dynamic equality constraint.In this paper,the obstacle avoidance is also considered as a secondary objective,but the collision-free criterion is formulated as an inequality constraint in the proposed scheme.
Note that almost all physical robot manipulators have the joint physical limits in practical applications[28],[41].In addi-tion,it would be desirable to obtain trajectories with continuous and smooth joint angle,so that the absolute value of the joint velocity keeps bounded[28].Limiting joint physical variables (e.g.,joint angle,and joint velocity)is very important,because high velocity values can lead to a low accuracy,and even worse, wear out the robot structure,for the end-effector to conduct the speci?ed primary task[42].More seriously,a nonsmooth phe-nomenon occurs.Vibrations induced by nonsmooth trajectories can damage the robot actuators,and further induce large errors while the robot is performing tasks such as path tracking[43]. The objective of repetitive motion requires that the robot manipulator maps closed paths in the task space(i.e.,cyclic sequences of tasks)to closed trajectories in the con?guration space(i.e.,cyclic sequences of con?gurations)[23],[44]–[46]. Non-repetitive problem is that joint angles do not return to their initial values when the end-effector traces a closed path in its workspace[23],[46].Non-repetitive scheme results in a joint angle drift phenomenon and may induce a problem that the manipulator's behavior is hard to control[23],[46],[47]; and it is then less ef?cient to readjust the manipulator's con?g-uration after every cycle via self-motion[47].For redundant robot manipulators with nonrepetitive motion,problem may arise from the robot manipulators'unpredictable behaviors, which leads to less ef?ciency in readjusting the manipulators' con?guration with self-motion at every cycle.Therefore,the repetitive motion is usually considered as a basic objective for the redundant robot manipulators.
The rest of this paper is organized into?ve sections.In Section II,the hybrid multi-objective scheme is proposed with the corresponding theoretical analysis given.In Section III, the proposed hybrid multi-objective scheme is reformulated into a uni?ed DQP which is solved by the PLPENN and also implemented by the corresponding numerical algorithm. Section IV illustrates the computer simulation and comparison. Hardware experimental veri?cation is given in Section V. Section VI concludes this paper with?nal remarks.Before ending this introductory section,it is worth pointing out the main contributions of this paper as follows.
1)In this paper,a hybrid multi-objective scheme is pro-
posed for completing simultaneously four objectives
(i.e.,the speci?ed primary task for end-effector,obstacle
avoidance,joint-physical limits avoidance,and repetitive motion)of the redundant robot manipulators.
2)Theoretical analysis about the obstacle avoidance con-
straint,joint-physical limits conversion,and repetitive motion criterion is given,which guarantees the validity of the proposed scheme.
3)The optimal solution of the DQP problem can be found by
the PLPENN,which is guaranteed by the corresponding convergence lemma.
4)The corresponding numerical algorithm with its block dia-
gram given for the optimal solution of the proposed scheme is also presented,which is convenient for practitioners to develop in practical applications.
5)Computer simulation and comparison based on a six-link
planar redundant robot manipulator substantiate the effec-tiveness and accuracy of the proposed scheme.
6)A hardware experiment is implemented on a physical
six-link robot manipulator system,which substantiates the physical realizability,operational stability and safety of the proposed hybrid multi-objective scheme.
II.H YBRID M ULTI-O BJECTIVE S CHEME AND
T HEORETICAL A NALYSIS
In this section,by using a redundancy-resolution scheme,i.e., hybrid multi-objective scheme,the redundant robot manipula-tors can achieve different secondary objectives(e.g.,obstacle avoidance,joint-physical limits avoidance,and repetitive mo-tion discussed in Section I)simultaneously when the end-ef-fector conducts the speci?ed primary task.Note that such objec-tives of redundant robot manipulators are formulated as the cor-responding equality constraint,one-sided inequality constraint and bound constraint(i.e.,two-sided inequality constraint)as well as the criterion in the ensuing subsections.Besides,the rel-ative theoretical analysis is given.
CHEN AND ZHANG:HYBRID MULTI-OBJECTIVE SCHEME APPLIED TO REDUNDANT ROBOT MANIPULATORS3
A.Direct Derivative End-Effector Constraint
When a speci?ed primary task of the end-effector is consid-ered(or say,a desired path is expected to be tracked by the end-effector),we have,where
is a continuous nonlinear forward-kinematics mapping with a known structure and parameters for a given manipulator,and
denotes the joint angle vector.To achieve the objective of the speci?ed primary task of the end-effector,we should?nd the relation between the joint angle vector and the end-effector effective position vector of the redundant robot ma-nipulator.Based on the forward kinematics,such a relation can be written mathematically as
(1) Considering the user-de?ned Cartesian path,we need to gen-erate the corresponding joint trajectory in real time so that,which is the general description of the inverse kinematics problem[25].Based on the direct-deriva-tive method,by differentiating(1)with respect to time,it can obtain the point-wise linear relation between the end-effector Cartesian velocity vector and the joint velocity vector as follows:
where is the Jacobian matrix of the end-effector de?ned as.
B.Obstacle Avoidance Constraint
The general description of the obstacle avoidance objective is
,where denotes a set.is the critical point location on the vulnerable link of the robot manipulator, and denotes the obstacle location in the Cartesian space.For such an objective of obstacle avoidance,there are two steps.The ?rst step is to locate the critical point on the vulnerable link of the robot manipulator by computing the distance between the obstacle point and the critical point on the link at any time interval.Secondly,an escape velocity is assigned at the critical point,which drives the vulnerable link away from the obstacle point.Thus,based on the previous work [30],an inequality-based constraint for obstacle avoidance of the redundant robot manipulator is depicted as
where is de?ned as
with for obstacle avoidance in2-D planar or for ob-stacle avoidance in3-D space.In addition,denotes the pairs of effective obstacle points and vulnerable-link critical points [30].Besides,denotes the Jacobian matrix of the critical point,and is de?ned as follows(when we consider ob-stacle avoidance in the general3-D space):
where and are,respectively,-,-and-axis coordinates of points and with regard to the base frame.In addition,denotes the transpose of a vector or matrix.Moreover,the vector-matrix multiplication operator is de?ned as
where column vector and row vector denotes the th row of matrix(with). Moreover,to remedy the possible discontinuity phenomenon, based on[53],the smoothing inequality constraint is further ob-tained
(2) where with the dis-tance-based smoothing function de?ned as
if
if
if
with being the minimum link-obstacle distance.Besides, and are the inner safety and outer safety threshold,respec-tively.In addition,is the vector-valued function for the maximal values between each components of and. Lemma1:The presented inequality-based obstacle avoid-ance constraint(2)is a variable-magnitude escape velocity method.
Proof:It can be generalized from[30],[53]and[54].
C.Joint Physical Limits Avoidance Constraint
As discussed in Section I,the joint physical limits are so sig-ni?cant that they are frequently considered as a constraint for redundant robot manipulators.Thus,limiting the joint physical variables in a safety range is an essential objective for redun-dant robot manipulators.In this paper,we consider joint phys-ical variables of redundant robot manipulators kept in a safety range as
(3)
(4) where and denote as the safety lower and upper bounds of the joint angle.In addition,and denote as the safety lower and upper bounds of the joint velocity.
For the reason that the hybrid multi-objective scheme will be reformulated as a DQP at the joint-velocity level and then solved by a PLPENN in the ensuing section,we give the following theorem about the joint physical limits conversion. Theorem1:If the joint physical limits[i.e.,(3)and(4)]for redundant robot manipulators are given,they can be converted into a bound constraint in terms of
(5) where the th elements of and are generally de?ned re-spectively as
4IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING
Note that the large value of parameter may cause quick joint deceleration when a joint approaches its limits [28].In mathematics,should be greater than or equal to
.
Proof:See Appendix A.
D.Repetitive Motion Criterion
The objective of repetitive motion can be generally depicted as,where denotes the task duration and denotes the initial state of the joint angle vector.Speci?-cally,repetitive motion requires that a redundant robot manipu-lator maps closed paths in the task space(i.e.,cyclic sequences of tasks)to closed trajectories in the con?guration space(i.e., cyclic sequences of con?gurations).To make the inverse-kine-matic solution repetitive,the minimization of the joint displace-ment between current and initial states should be exploited.In the proposed scheme,the repetitive motion criterion is used as follows:
(6) where with design parameter being used to scale the magnitude of the manipulator response to the joint displacement.Note that the design parameter should be set as large as the robot system would permit,or selected appropriately large for experimental and/or simulative purposes.In addition, the corresponding theoretical analysis for the effectiveness of criterion(6)on repetitive motion of the redundant robot manip-ulator is given as follows.
Theorem2:For a redundant robot manipulator,if the repet-itive motion criterion depicted in(6)is applied,then it can achieve the objective of repetitive motion.
Proof:See Appendix B.
E.Hybrid Multi-Objective Scheme
Based on the above detailed analysis of the four mentioned objectives of the redundant robot manipulator,in this paper,we propose the following hybrid multi-objective scheme for the re-dundant robot manipulators to complete the four mentioned ob-jectives simultaneously:
(7)
(8)
(9)
(10) where denotes the time derivative of the desired end-effector path.In addition,,,,,and are de?ned the same as those in previous subsections.
III.DQP F ORMULATION AND O PTIMAL S OLUTION
In the above section,we propose the hybrid multi-objective scheme(7)–(10)for the redundant robot manipulators with cor-responding theoretical analysis.In this section,the proposed hybrid multi-objective scheme(7)–(10)is uni?ed into a dy-namical quadratic program(DQP)with equality,inequality,and bound constraints.Then,such a DQP problem is solved by the PLPE(piecewise-linear projection equation)neural network, i.e.,PLPENN,and also by the corresponding numerical algo-rithm implemented on the computer.
A.DQP Formulation
Note that(7)can be rewritten as
In the light of the above minimization formula,with and ,the proposed hybrid multi-objective scheme(7)–(10) of robot manipulators is reformulated?nally as the following DQP:
(11)
(12)
(13)
(14) where,,,
,and.In addition,and are de?ned the same as before.Besides,a brief algorithm description for DQP formulation is listed in Algorithm1.
Algorithm1:DQP Formulation
1Input:Design parameters,e.g.,and
2Input:Joint physical limits,i.e.,and
3Input:The desired or user-de?ned Cartesian path
4Calculate:The repetitive motion variable in(11)
5Calculate:The obstacle avoidance variables and
in(13)
6Calculate:The safe joint bounds by Theorem1
7Output:The formulation of DQP(11)–(14)
Remark1:The proposed hybrid multi-objective scheme is resolved at the joint-velocity level,and thus,the decision vari-able vector for DQP(11)–(14)is.Based on the basic the-oretical results of quadratic programming[25],[55],to mini-mize in the DQP of which the decision vari-able vector is,is equivalent to minimize
with respect to the optimal DQP solution. In practical applications,is an alternative term for DQP (11)–(14),of which the decision variable vector is.To reduce the computational complexity and to develop the cor-responding neurodynamic solver(i.e.,PLPENN solution pro-posed in this paper),the alternative term can thus be set aside from criterion(7)for the DQP formulation.Therefore,cri-terion(7)is reformulated as the minimization of
(note that).
CHEN AND ZHANG:HYBRID MULTI-OBJECTIVE SCHEME APPLIED TO REDUNDANT ROBOT MANIPULATORS5
B.Optimal Solution via PLPENN
In the above subsection,we give the uni?ed DQP formulation (11)–(14)of the hybrid multi-objective scheme.In this subsec-tion,we?nd the optimal solution for the hybrid multi-objective scheme by utilizing the PLPENN.Based on the previous work [25],[28],the DQP problem(11)–(14)can be converted to the system of piecewise-linear equations.
Lemma2:DQP(11)–(14)is equivalent to the following linear variational inequality problem,i.e.,to?nd a vector such that
(15) with being the PLPE theoretical solution.Besides,the primal-dual decision variable vector,coef?cient vector and matrix are de?ned respectively as follows:
where and denote the dual decision variable vectors de?ned for equality constraint(12)and inequality con-straint(13),respectively.
Proof:It can be generalized from[28].
Note that linear variational inequality(15)is equivalent to the following piecewise-linear projection equation:
(16) where is a piecewise-linear projection operator[25], [28].It is worth mentioning that
is a projection operator.In addition, and denote respectively as
with,,and
.Note that is de?ned suf?ciently large(e.g.,)to replace numerically.Besides,the th element of is de?ned as
if
if
if
Thus,the proposed hybrid multi-objective scheme(7)–(10)and its corresponding DQP problem(11)–(14)[as well as the piece-wise-linear projection(16)]are solved via the PLPENN[46], [56],of which the dynamic equation is described as follows:
(17)where design parameter is used to scale the convergence rate of the PLPENN[57].
It is worth mentioning here that the PLPENN(17)solves the strictly-convex DQP problems in an inverse-free manner together with simple piecewise-linear dynamics and adap-tive-tuning nature[46],[56].Moveover,we have the following lemma to guarantee that the PLPENN(17)can globally gen-erate optimal solution to DQP(11)–(14)in real time. Lemma3:Assume the existence of optimal solution to DQP(11)–(14).Starting from any initial state,the PLPE variable vector of PLPENN(17)is globally and expo-nentially convergent to PLPE theoretical solution,of which the?rst elements constitute the optimal solution to DQP (11)–(14).In addition,the exponential convergence rate is pro-portional to the product of and the minimum eigenvalue of coef?cient matrix.
Proof:It can be generalized from[25],[46]and[56]. Besides,a brief algorithm description for PLPENN solution is listed in Algorithm2.
Algorithm2:PLPENN Solution
1Input:The design parameter
2Input:The DQP formulation(11)–(14)in Algorithm1
3Formulate:The PLPE variable vector by,
and
4Call:The piecewise-linear projection operator
5Call:The MATLAB ODE solver to calculate the PLPENN(17)
6Output:The optimal PLPENN solution
To show the computational speed superiority of proposed so-lution,we conduct a computer simulation to compare the com-putational time between the proposed PLPENN solution and the MATLAB(which is a commonly commercial and mathematic tool)function“QUADPROG”in Appendix C.
C.Optimal Solution via Numerical Algorithm
As discussed in the above subsection,the PLPENN(17)is a continuous-time model used to solve the hybrid multi-objective scheme and its corresponding DQP problem(11)–(14)as well as PLPE(16).For the purposes of the implementation of the proposed hybrid multi-objective scheme on a practical redun-dant robot manipulator,a numerical algorithm(viewed as a dis-crete-time method)is developed in this subsection.The design procedure of such a numerical algorithm can be simply depicted by the following steps.
Step 1.Calculate the coef?cient vector and matrix with the given variables,,,,,and.
Step 2.According to[48],[49],an error function at each iteration is de?ned as
(18)
Evidently,is the solution of(16)when
.
6IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING
Step 3.If[i.e.,is not the solution of(16)],the recursion is formulated as
(19)
where
(20)
(21) Since the objective function(11)of the DQP is strictly convex due to the positive de?niteness of,and the constraint region constructed by(12)–(14)is a convex set,by the Theorem3.4.2 of[58],we know that the constrained minimizer to DQP (11)–(14)is unique.Moreover,the relevant theoretical analyses on the global convergence result of the proposed optimal solu-tion via numerical algorithm can be seen in[59]for more details. Thus,given an initial state,the sequence generated by (18)–(21)converges globally and linearly to a solution point [of(16)],of which the?rst elements constitute the optimal solution to the DQP problem depicted in(11)through(14) [48],[49].
For the convenience of the readers and practitioners,the block diagram of numerical algorithm(18)–(21)is shown in Fig.1. Besides,a brief algorithm description for numerical solution is listed in Algorithm3.
Algorithm3:Numerical Solution
1Input:The given variables,,,,and
2Calculate:The coef?cient vector and matrix
3Initialize:The PLPE variable vector
4Formulate:The error function via(18)
5Calculate:via(20)and via(21)
6For do
7
8If or
9Then break
10Else
11End for
12Output:The optimal solution of the?rst elements of
IV.S IMULATION AND C OMPARISON
To validate the effectiveness of the hybrid multi-objective scheme(7)–(10)proposed in Section II-E,a computer simu-lation is performed based on a six-link planar redundant robot manipulator.Note that design parameters,,and .Besides,the inner and outer safety thresholds are
set as m and m.Fig.1.Block diagram of numerical algorithm(18)–(21)for DQP(11)–(14).
TABLE I
J OINT P HYSICAL L IMITS
AND P ARAMETERS U SED IN S IX-L INK P LANAR R EDUNDANT R OBOT M ANIPULATOR S IMULATIONS
Remark2:The design parameters and are termed convergence parameters for the proposed hy-brid multi-objective scheme,which are used to scale the conver-gence rate of solution.Note that and usually correspond to the reciprocals of capacitance parameters,of which the values should be set as large as the hardware would permit,or appro-priately large for practical applications purposes[60].
In this section,a six-link planar robot manipulator is simulated for completing four objectives,i.e.,the speci-?ed primary task for end-effector,obstacle avoidance,joint physical limits avoidance,and repetitive motion.The end effector of the six-link planar robot manipulator is expected to track a circle path with the radius being0.10m.Note that the motion-task duration s.The initial joint state
rad.In ad-dition,the obstacle point is at(0.720,0.115)m.The joint physical limits and the physical parameters of the six-link planar robot manipulator used in the simulation are shown in Table I with symbol“m”standing for meter[61].The?rst joint of the six-link planar robot manipulator is driven by a servo motor.Being different from the?rst joint,the second to the sixth joints are driven by their corresponding push-rods,and each joint structure is like a triangle with three edges of the triangle being,and(with).In addition, denotes the length of the th link(with).As for the joint-velocity limits,Based on the previous research[61], the joint-velocity limit of each joint is variable and it can be
CHEN AND ZHANG:HYBRID MULTI-OBJECTIVE SCHEME APPLIED TO REDUNDANT ROBOT MANIPULATORS
7 Fig.2.End-effector of six-link planar robot manipulator tracks a circle path synthesized by the proposed hybrid multi-objective scheme:(a)simulated motion of six-link planar robot manipulator;(b)motion trajectories of each joint;(c)pro?les of joint angle;(d)minimum link-obstacle distance.
reformulated as(with), where, with and being the positive and negative rotation rate limits of the stepper motor,and denoting the elongation rate of the th push-rod(i.e.,the elongation length when the motor moves a full turn).For this six-link planar robot manipulator,
rot/s and m/rot. The corresponding simulative results synthesized by the proposed hybrid multi-objective scheme are illustrated in Figs.2and3.As we can see from Fig.2(a),the desired motion of the end effector is achieved successfully,showing that the speci?ed primary task for end-effector is completed.In addition,Fig.2(b)shows the motion trajectories of each joint clearly.All joint trajectories are closed.The?nal state
of the six-link planar manipulator coincides very well with initial state,which is illustrated in Fig.2(c).That is to say,the objective of repetitive motion is completed.Besides, as seen from Fig.2(d),the six-link planar robot manipulator avoids the obstacle point successfully,with the minimum link-obstacle distance being always greater than the inner safety threshold m during the motion task execution. It is worth pointing out that,when the effective obstacles are within the region of in?uence(i.e.,),the escape velocity is
generated by activating the obstacle avoidance Fig.3.End-effector positioning errors of six-link planar robot manipulator synthesized by the proposed hybrid multi-objective scheme.
constraint(2),which generates the corresponding escape ve-locity to change the joint con?guration and drive the affected link(s)of the six-link planar robot manipulator away from the obstacle point.In addition,as seen from Fig.3,the maximum end-effector positioning error is less than m,which is acceptable and suitable in practical applications.Moreover,
8IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING Fig.4.End-effector of six-link planar robot manipulator tracks a circle path synthesized by the VLMVN scheme:(a)simulated motion of six-link planar robot manipulator;(b)motion trajectories of each joint;(c)pro?les of joint angle;(d)minimum link-obstacle distance.
all the joint physical variables are kept in the given limit range. Thus,it can be said that the mentioned four objectives of the robot manipulator are completed well via the proposed hybrid multi-objective scheme(7)–(10).
In previous works[25],[29],the velocity-level minimum-velocity-norm(VLMVN)scheme has been proposed and in-vestigated for executing the primary task of redundant robot manipulators.For comparative purposes,the relative simula-tive results under the same simulation condition synthesized by the VLMVN scheme are presented in Fig.4.As we can see from Fig.4(b),the?nal state of the six-link planar manipulator does not coincide with initial state.Generally speaking,there are lots of factors(extrinsic and inherent),such as end-effector motion requirement,joint physical limits and optimization of secondary criterion,which have great effect on the motion planning of robot manipulators.If the redundancy-resolution schemes(e.g.,the conventional pseudoinverse-based schemes)are not suitable for some particular end-effector tasks, the?nal con?guration of the robot manipulators may not coin-cide well with the initial con?guration.This is the so-called joint angle drift phenomenon.Thus,we expect to?nd an effective redundancy-resolution scheme(i.e.,the hybrid multi-objective scheme proposed in this paper)to remedy such a phenomenon and achieve the repetitive motion,which is one of the motiva-tions of this work.Moreover,Fig.4(d)shows that,during the time interval s,the minimum link-obstacle distance
m.For such a close distance,it can be con-sidered as a collision that may result in serious damage of the robot manipulators and/or obstacles.Thus,based on the above discussion,we know that the proposed hybrid multi-objective scheme has the better performance than the VLMVN scheme in terms of repetitive motion and obstacle avoidance.
V.E XPERIMENTAL A PPLICATION
In this section,to verify the physical realizability and ef-fectiveness of the proposed hybrid multi-objective scheme (7)–(10),we perform such a scheme on a physical six-link robot manipulator system.Note that the experimental environment is a whole robot system which is composed of a host computer and a robot manipulator in Fig.5(a).The host computer is a personal digital computer with a Windows XP Professional operating system and with a Pentium E53002.6GHz CPU,4 GB DDR3memory hardware system,which sends instructions to the manipulator motion control module with a six-axis control card of peripheral component interconnect(PCI).
In this experiment,all the design parameters are set the same as those in Section IV and the joint physical limits of the phys-ical six-DOF planar robot manipulator are the same as those
CHEN AND ZHANG:HYBRID MULTI-OBJECTIVE SCHEME APPLIED TO REDUNDANT ROBOT MANIPULATORS
9
Fig.5.Hardware system of the practical six-link planar robot manipulator used for experimental application and snapshot at the end of the end-effector actual task execution with measurements:(a)hardware system of the practical six-link planar robot manipulator;(b)circle-motion task of end
effector.
Fig.6.Joint angles of the practical six-link planar robot manipulator synthesized by the proposed hybrid multi-objective scheme before the end-effector task
execution:(a)joint angle
;(b)joint angle ;(c)joint angle ;(d)joint angle ;(e)joint angle ;and (f)joint angle .shown in Table I.The manipulator's end-effector is expected
to track circle path,of which the radius being 0.01m.In ad-dition,the motion-task duration s,and the initial joint state rad.Besides,the obstacle point in this experiment is set to be (0.490,0.115)m.The corresponding experimental results are il-lustrated in Fig.5through Fig.8.Speci?cally,from Fig.5(b),the desired motion task of the end-effector is completed well with the maximal end-effector positioning error being about
m.The high precision of the primary task execu-tion also demonstrates that each joint of the physical six-link planar robot manipulator works within the joint physical limits shown in Table I.In addition,the joint angles of the practical six-link planar robot manipulator synthesized by the proposed hybrid multi-objective scheme are shown in Figs.6and 7.As we can compare these two ?gures,all joint angles before the end-effector primary task execution and after the end-ef-fector primary task execution are rad (i.e.,15degree)with
,which illustrates that the objective of repetitive
motion is also completed well.
Moreover,comparative results of obstacle avoidance for the practical robot manipulator synthesized by the hybrid multi-objective scheme and the VLMVN scheme are shown in Figs.8and 9.For the practical robot manipulator synthesized by the hybrid multi-objective scheme,as shown in Fig.8(a),at the initial position of the robot manipulator (i.e.,at the initial
10
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND
ENGINEERING
Fig.7.Joint angles of the practical six-link planar robot manipulator synthesized by the proposed hybrid multi-objective scheme after the end-effector task
execution:(a)joint angle
;(b)joint angle ;(c)joint angle ;(d)joint angle ;(e)joint angle ;and (f)joint angle .time instant s),the minimum link-obstacle distance
is 7.00cm.As we observed in the experiment process,just like the results shown in Fig.2(d),at about time instant s,the link of robot manipulator gets closest to the point obstacle with minimum link-obstacle distance cm,which is shown in Fig.8(b).Hereafter,the link of robot manipulator moves away the point obstacle.That is to say,is always greater than the inner safety threshold cm during the motion task,which implies that the objective of obstacle avoidance is completed successfully.For the practical robot manipulator synthesized by the VLMVN scheme,the relative experiment result is illustrated in Fig.9.At the initial position of the robot manipulator (i.e.,at the initial time instant s),the minimum link-obstacle distance is also 7.00cm.How-ever,the link of robot manipulator gets closest to the point obstacle with minimum link-obstacle distance cm,which illustrates that the VLMVN scheme fails to complete the objective of obstacle avoidance for the redundant robot manipulator in the practical applications.
Besides,to further show the scienti?c and practical contribu-tions of this paper,we discuss the acceptability of the developed technique for industrial robotic computer aided design (CAD)systems in terms of the manipulator precision,and provide a re-mark as follows.
Remark 3:We clarify two different types of precision pre-sented in this paper.One is the physical robot manipulator op-eration precision (termed,PRMOP),the other is the experiment measurement precision (termed,EMP).In experiments,for the purpose of implementing our proposed hybrid multi-objective scheme in a fast,simple and effective manner with a relatively low cost,we develop the physical six-link robot manipulator
system shown in Fig.5(a).Note that the PRMOP of the phys-ical six-link robot manipulator system is 1mm.As we can see from this experiment section,the execution results are relatively favorable even when the scheme is applied to such a system.Accordingly,for the reason that our robot system has an open operation environment which can be detected and measured on-line,directly and conveniently,we design the corresponding measurement device for the physical six-link robot manipulator system.Note that the EMP of the measurement device is 0.1mm (with the minimum scale of measurement tool being 1mm and the estimate measurement being 0.1mm)according to the PRMOP being 1mm of the robot system.Thus we present all the measurement results with the precision being of 0.1mm level.Moreover,such experimental results are also consistent with the computer simulation results shown in Section IV with the max-imum positioning error being about 0.1mm level.It is worth mentioning here that the modular/integrated robots scheme de-veloped in recent years have a rather high precision,e.g.,2.3mm via PID and 0.26mm via PID with embedded FPGA [62].So our proposed hybrid multi-objective scheme in this paper with the maximal end-effector positioning error being of 0.1mm level is comparatively effective.Besides,in practical applica-tions,the acceptable precision of robot-based water jet cutting presented in [63]is 3mm.Thus our proposed hybrid multi-ob-jective scheme with the PRMOP being 1mm and the EMP being 0.1mm is relatively acceptable for the robotic CAD systems in practical applications [64]–[67].
VI.C ONCLUSION
A hybrid multi-objective scheme has been proposed to exe-cute simultaneously four objectives,i.e.,the speci?ed primary
CHEN AND ZHANG:HYBRID MULTI-OBJECTIVE SCHEME APPLIED TO REDUNDANT ROBOT MANIPULATORS
11
Fig.8.Point obstacle avoidance of practical six-link planar robot manipulator synthesized by the proposed hybrid multi-objective scheme:(a)initial position of robot manipulator and point obstacle;(b)?nal position of robot manipulator and point
obstacle.
Fig.9.Point obstacle avoidance of practical six-link planar robot manipulator synthesized by the comparative VLMVN scheme without considering the point obstacle avoidance objective:(a)initial position of robot manipulator and point obstacle;(b)?nal position of robot manipulator and point obstacle.
task for end-effector,obstacle avoidance,joint physical limits avoidance,and repetitive motion of the redundant robot ma-nipulators in this paper.In addition,corresponding theoretical analysis has been given,which has guaranteed the validity of the proposed scheme.Then,the proposed hybrid multi-objec-tive scheme has been reformulated as a dynamical quadratic program (DQP)problem.The optimal solution for the redundant robot manipulators to execute the four objectives has been found by the PLPE (piecewise-linear projection equation)neural net-work,i.e.,PLPENN.Besides,the optimal solution has also been found by the corresponding numerical algorithm for the fur-ther implementation on the computer.Furthermore,simulation and relative comparison based on a six-link planar redundant robot manipulator have substantiated the effectiveness and ac-curacy of the proposed scheme.At last,a hardware experiment has been conducted on a practical six-link robot manipulator system,which has substantiated the physical realizability,oper-ational stability,and safety of the proposed hybrid multi-objec-tive scheme.
A PPENDIX A
P ROOF OF J OINT P HYSICAL L IMITS C ONVERSION (5)As mentioned previously,the dynamical quadratic program problem is solved at the joint-velocity level,and thus,the joint physical limits (3)and (4)have to be converted into the expres-sion(s)in terms of joint velocity .
Based on the analysis in [50]–[52],we assume that the joint physical limits are avoided at current time .Therefore,the focus is that the limits should be avoided at next sampling time instant
,where is the sampling time.In other words,the
joint physical limits of robot manipulators at the next time step should be described as
(22)(23)
12IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING
Firstly,let us handle the joint-angle constraint(22).By using the backward difference,the joint velocity could be approximated as follows:
which can be rewritten as
Thus,the joint-angle constraint(22)could be reformulated as which is then rewritten in the following form:
Based on the above analysis,the joint physical constraints (22)–(23)can be reformulated as
which are rewritten respectively as
where.
Thus,the above bound constraints can be generally converted into the expression in terms of joint velocity:, where the th elements of and are
Besides,for more details about the common techniques of the joint physical limits conversion,please refer to[25],[47]and
[61].The proof is thus completed.
A PPENDIX B
P ROOF OF R EPETITIVE M OTION C RITERION(6)
The repetitive motion criterion(6)can be rewritten as the minimization of
(24) where denotes the Euclidean norm of a vector.When the feasible solution exists,minimizing the performance index(24) is equivalent to force to zero with respect to.Note that is rewritten as
(25)
Let and design parameter is used to adjust the exponential convergence rate of to zero. Equation(25)can be rewritten as which guaran-tees that converges to zero globally and exponentially[i.e.,
with rate].
TABLE II
C OMPUTATIONAL T IME OF PLPENN(17)AN
D MATLAB F UNCTION
“QUADPROG”(26)U SED TO S OLVE DQP(11)–(14)AT
D IFFERENT T IM
E I NSTANTS
Based on the above analysis,we thus achieve repetitive mo-tion of redundant robot manipulators,that is, in mathematics,or when is large enough in practical applications.Thus,we have the conclusion that the ma-nipulators can achieve the objective of repetitive motion when criterion(6)is applied.The proof is thus completed.
A PPENDIX C
C OMPUTATIONAL S PEE
D VIA PLPENN(17)S OLUTION Computational speed,or computational time,is also an important issue which should be considered in robot motion planning.To show the superiority of the proposed solution,we conduct a computer simulation to compare the computational time between the proposed PLPENN solution and the MATLAB function“QUADPROG”.As presented in Section III-B,DQP (11)–(14)is solved by PLPENN(17).For comparative purpose, the MATLAB function“QUADPROG”is also exploited to solve the same DQP.In general,when the MATLAB function “QUADPROG”is used to solved such a DQP,the syntax can be described as
(26) where the initial value is set as in the com-puter simulative tests.Table II shows the computational time of PLPENN(17)and MATLAB function“QUADPROG”
(26)used to solve DQP(11)–(14)at different time instants for the manipulator to complete simultaneously four objectives.As seen from the table,the maximal computational time of DQP via the proposed PLPENN is s.By contrast,the maximal computational time of DQP via the MATLAB func-tion“QUADPROG”is0.224s.Such numerical results compar-atively illustrate that the proposed PLPENN solution is supe-rior to the MATLAB function in terms of computational speed. Moreover,an approach with the computational time being about 1ms1000instructions per second(IPS)can be acceptable for the existing commercial robotic CAD systems[68]–[70].Thus the proposed PLPENN solution has a potentially high enough computational speed that can achieve the real-time control in practical applications.
A CKNOWLEDGMENT
The authors would like to thank the editors and anonymous reviewers for their time and effort spent in handling the paper,
CHEN AND ZHANG:HYBRID MULTI-OBJECTIVE SCHEME APPLIED TO REDUNDANT ROBOT MANIPULATORS13
as well as many constructive comments provided for improving the presentation and quality of this paper.
R EFERENCES
[1]J.Na,X.Ren,and D.Zheng,“Adaptive control for nonlinear pure-
feedback systems with high-order sliding mode observer,”IEEE Trans.
Neural Netw.Learn.Syst.,vol.24,no.3,pp.128–135,Mar.2013.
[2]S.Hong,Y.Oh,D.Kim,and B.-J.You,“Real-time walking pattern
generation method for humanoid robots by combining feedback and
feedforward controller,”IEEE Trans.Ind.Electron.,vol.61,no.1,pp.
355–364,Jan.2014.
[3]C.Yang,Z.Li,and J.Li,“Trajectory planning and optimized adap-
tive control for a class of wheeled inverted pendulum vehicle models,”
IEEE Trans.Cybern.,vol.43,no.1,pp.24–36,Feb.2013.
[4]H.Cheng,H.Chen,and B.W.Mooring,“Accuracy analysis of
dynamic-wafer-handling robotic system in semiconductor manufac-
turing,”IEEE Trans.Ind.Electron.,vol.61,no.3,pp.1402–1410,
Mar.2014.
[5]R.C.Luo and https://www.sodocs.net/doc/6d953320.html,i,“Enriched indoor map construction based on
multisensor fusion approach for intelligent service robot,”IEEE Trans.
Ind.Electron.,vol.59,no.8,pp.3135–3145,Aug.2012.
[6]C.Guarino,L.Bianco,and F.Ghilardelli,“Real-time planner in the
operational space for the automatic handling of kinematic constraints,”
IEEE Trans.Autom.Sci.Eng.,vol.11,no.3,pp.730–739,Jul.2014.
[7]Q.Chen,W.Chen,G.Yang,and R.Liu,“An integrated two-level
self-calibration method for a cable-driven humanoid arm,”IEEE Trans.
Autom.Sci.Eng.,vol.10,no.2,pp.380–391,Apr.2013.
[8]M.G.Marcos,J.A.T.Machado,and T.-P.Azevedo-Perdicoulis,“A
multi-objective approach for the motion planning of redundant manip-
ulators,”Appl.Soft Comput.,vol.12,no.2,pp.589–599,2012.
[9]L.Ren,https://www.sodocs.net/doc/6d953320.html,ls,and D.Sun,“Trajectory tracking control for a
3-DOF planar parallel manipulator using the convex synchronized con-
trol method,”IEEE Trans.Control Syst.Technol.,vol.16,no.4,pp.
613–623,Jul.2008.
[10]Z.Hou,L.Cheng,and M.Tan,“Multicriteria optimization for coordi-
nation of redundant robots using a dual neural network,”IEEE Trans.
Syst.,Man,Cybern.B,vol.40,no.4,pp.1075–1087,Aug.2010.
[11]G.Hu,N.Gans,N.Fitz-Coy,and W.Dixon,“Adaptive homography-
based visual servo tracking control via a quaternion formulation,”IEEE
Trans.Control Syst.Technol.,vol.18,no.1,pp.128–135,Jan.2010.
[12]E.J.S.Pires,J.A.T.Machado,and P.B.M.OliveiraY,“Manipulator
trajectory planning using a MOEA,”Appl.Soft Comput.,vol.7,no.3,
pp.659–667,2007.
[13]A.Vergnano,C.Thorstensson,B.Lennartson,P.Falkman,M.Pellic-
ciari,F.Leali,and S.Biller,“Modeling and optimization of energy
consumption in cooperative multi-robot systems,”IEEE Trans.Autom.
Sci.Eng.,vol.9,no.2,pp.423–428,Apr.2012.
[14]B.Siciliano and O.Khatib,Springer Handbook of Robotics.Heidel-
berg,Germany:Springer-Verlag,2008.
[15]W.Shang,S.Cong,and Y.Ge,“Coordination motion control in the
task space for parallel manipulators with actuation redundancy,”IEEE
Trans.Autom.Sci.Eng.,vol.10,no.3,pp.665–673,Jun.2013.
[16]H.I.Chen and M.C.Shih,“Visual control of an automatic manip-
ulation system by microscope and pneumatic actuator,”IEEE Trans.
Autom.Sci.Eng.,vol.10,no.1,pp.215–218,Feb.2013.
[17]S.Toyoshima,M.Tanaka,and F.Matsuno,“A study on sinus-lifting
motion of a snake robot with sequential optimization of a hybrid
system,”IEEE Trans.Autom.Sci.Eng.,vol.11,no.1,pp.139–144,
Feb.2014.
[18]D.Guo and Y.Zhang,“Simulation and experimental veri?cation of
weighted velocity and acceleration minimization for robotic redun-
dancy resolution,”IEEE Trans.Autom.Sci.Eng.,vol.11,no.4,pp.
1203–1217,Aug.2014.
[19]H.D.Taghirad and Y.B.Bedoustani,“An analytic-iterative redun-
dancy resolution scheme for cable-driven redundant parallel manipu-
lators,”IEEE Trans.Robot.,vol.27,no.6,pp.1137–1143,Dec.2011.
[20]Y.Xia,G.Feng,and J.Wang,“A primal-dual neural network for online
resolving constrained kinematic redundancy in robot motion control,”
IEEE Trans.Syst.,Man,Cybern.B,vol.35,no.1,pp.54–64,Feb.2005.
[21]R.O'Flaherty and M.Egerstedt,“Low-dimensional learning for com-
plex robots,”IEEE Trans.Autom.Sci.Eng.,vol.12,no.1,pp.19–27,
Feb.2015.
[22]K.Yu,J.Yi,and J.W.Shan,“Motion control,planning and manip-
ulation of nanowires under electric-?elds in?uid suspension,”IEEE
Trans.Autom.Sci.Eng.,vol.12,no.1,pp.37–49,Feb.2015.[23]K.Tchon and J.Jakubiak,“A repeatable inverse kinematics algorithm
with linear invariant subspaces for mobile manipulators,”IEEE Trans.
Syst.,Man,Cybern.B,vol.35,no.5,pp.1051–1057,Oct.2005. [24]G.C.H.E.de Croon,E.de Weerdt,C.D.Wagter,B.D.W.Remes,and
R.Ruijsink,“The appearance variation cue for obstacle avoidance,”
IEEE Trans.Robot.,vol.28,no.2,pp.529–534,Apr.2012.
[25]Y.Zhang and Z.Zhang,Repetitive Motion Planning and Control of Re-
dundant Robot Manipulators.New York,NY,USA:Springer-Verlag, 2013.
[26]A.Guigue,M.Ahmadi,https://www.sodocs.net/doc/6d953320.html,nglois,and M.J.D.Hayes,“Pareto op-
timality and multiobjective trajectory planning for a7-DOF redundant manipulator,”IEEE Trans.Robot.,vol.26,no.6,pp.1094–1099,Dec.
2010.
[27]A.Konak,D.W.Coit,and A.E.Smith,“Multiobjective optimization
using genetic algorithms:A tutorial,”Reliab.Eng.Syst.Saf.,vol.91, no.9,pp.992–1007,2006.
[28]Y.Zhang,S.S.Ge,and T.H.Lee,“A uni?ed quadratic program-
ming based on dynamical system approach to joint torque optimization of physically constrained redundant manipulators,”IEEE Trans.Syst., Man,Cybern.B,vol.34,no.5,pp.2126–2132,Oct.2004.
[29]Y.Zhang,D.Guo,and S.Ma,“Different-level simultaneous minimiza-
tion of joint-velocity and joint-torque for redundant robot manipula-tors,”J.Intell.Rob.Syst.,vol.72,no.3–4,pp.301–323,2013. [30]D.Guo and Y.Zhang,“A new inequality-based obstacle-avoidance
MVN scheme and its application to redundant robot manipulators,”
IEEE Trans.Syst.,Man,Cybern.C,vol.42,no.6,pp.1326–1340,Nov.
2012.
[31]A.Iborra,J.A.Pastor,B.Alvarez,C.Fernandez,and J.M.F.Merono,
“Robots in radioactive environments,”IEEE Robot.Autom.Mag.,vol.
10,no.4,pp.12–22,Dec.2003.
[32]S.Wen,W.Zheng,J.Zhu,X.Li,and S.Chen,“Elman fuzzy adaptive
control for obstacle avoidance of mobile robots using hybrid force/po-sition incorporation,”IEEE Trans.Syst.,Man,Cybern.C,vol.42,no.
4,pp.603–608,Jul.2012.
[33]M.Joo Er and C.Deng,“Obstacle avoidance of a mobile robot using
hybrid learning approach,”IEEE trans.Ind.Electron.,vol.52,no.3, pp.898–905,Jun.2005.
[34]T.Sugie,K.Fujimoto,and Y.Kito,“Obstacle avoidance of manipula-
tors with rate constraints,”IEEE Trans.Robot.Autom.,vol.19,no.1, pp.168–174,Feb.2003.
[35]H.Li,S.X.Yang,and M.L.Seto,“Neural-network-based path plan-
ning for a multirobot system with moving obstacles,”IEEE Trans.
Syst.,Man,Cybern.C,vol.39,no.4,pp.410–419,Jul.2009. [36]A.A.Maciekewski and C.A.Klein,“Obstacle avoidance for kinemat-
ically redundant manipulators in dynamicall varying environments,”
Int.J.Robot.Res.,vol.4,no.3,pp.109–117,1985.
[37]L.Sciavicco and B.Sicilino,“A solution algorithm to the inverse kine-
matic problem for redundant manipulators,”IEEE J.Robot.Autom., vol.4,no.4,pp.403–410,Aug.1988.
[38]S.S.Ge and Y.J.Cui,“New potential functions for mobile robot path
planning,”IEEE Trans.Robot.Autom.,vol.16,no.5,pp.615–620, Oct.2000.
[39]F.-T.Cheng,Y.-T.Lu,and Y.-Y.Sun,“Window-shaped obstacle
avoidance for a redundant manipulator,”IEEE Trans.Syst.,Man, Cybern.B,vol.28,no.6,pp.806–815,Dec.1998.
[40]W.Tang,https://www.sodocs.net/doc/6d953320.html,m,and J.Wang,“Kinematic control and obstacle avoid-
ance for redundant manipulators using a recurrent neural network,”in Proc.Int.Conf.Artif.Neural Netw.,2001,pp.922–929.
[41]L.Xiao and Y.Zhang,“A new performance index for the repetitive
motion of mobile manipulators,”IEEE Trans.Cybern.,vol.44,no.2, pp.280–292,Feb.2014.
[42]S.Macfarlane and E.A.Croft,“Jerk-bounded manipulator trajectory
planning:Design for real-time applications,”IEEE Trans.Robot.
Autom.,vol.19,no.1,pp.42–52,Feb.2003.
[43]A.Gasparetto and V.Zanotto,“A new method for smooth trajectory
planning of robot manipulators,”Mech.Mach.Theory,vol.42,no.4, pp.455–471,2007.
[44]R.G.Roberts and A.A.Maciejewski,“Repeatable generalized inverse
control strategies for kinematically redundant manipulators,”IEEE Trans.Autom.Control,vol.38,no.5,pp.689–698,May1993. [45]T.Shamir and Y.Yomdin,“Repeatability of redundant manipulators:
Mathematical solution of the problem,”IEEE Trans.Autom.Control, vol.33,no.11,pp.1004–1009,Nov.1988.
[46]Y.Zhang,Z.Tan,K.Chen,Z.Yang,and X.Lv,“Repetitive motion of
redundant robots planned by three kinds of recurrent neural networks and illustrated with a four-link planar manipulator's straight-line ex-ample,”Robot.Auton.Syst.,vol.57,no.6–7,pp.645–651,2009.
14IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING
[47]Z.Zhang and Y.Zhang,“Acceleration-level cyclic-motion generation
of constrained redundant robots tracking different paths,”IEEE Trans.
Syst.,Man,Cybern.B,vol.42,no.4,pp.1257–1269,Aug.2012. [48]B.He,“A new method for a class of linear variational inequalities,”
Math.Program.,vol.66,no.1–3,pp.137–144,1994.
[49]B.He,“Solving a class of linear projection equations,”Numer.Math.,
vol.68,no.1,pp.71–80,1994.
[50]F.-T.Cheng,T.-H.Chen,and Y.-Y.Sun,“Resolving manipulator re-
dundancy under inequality constraints,”IEEE Trans.Robot.Autom., vol.10,no.1,pp.65–71,Jan.1994.
[51]F.-T.Cheng,R.-J.Sheu,and T.-H.Chen,“The improved compact QP
method for resolving manipulator redundancy,”IEEE Trans.Syst., Man,Cybern.,vol.25,no.11,pp.1521–1530,Nov.1995.
[52]K.C.Park,P.H.Chang,and S.H.Kim,“The enhanced compact
QP method for redundant manipulators using practical inequality con-straints,”in Proc.IEEE Int.Conf.Robot.Autom.,1998,pp.107–114.
[53]Y.Zhang and J.Wang,“Obstacle avoidance for kinematically redun-
dant manipulators using a dual neural network,”IEEE Trans.Syst., Man,Cybern.B,vol.34,no.1,pp.752–759,Feb.2004.
[54]D.Guo and Y.Zhang,“Acceleration-level inequality-based MAN
scheme for obstacle avoidance of redundant robot manipulators,”
IEEE Trans.Ind.Electron.,vol.61,no.12,pp.6903–6914,Dec.2014.
[55]Y.Zhang,Y.Wang,D.Chen,C.Peng,and Q.Xie,“Neurodynamic
solvers,robotic applications and solution nonuniqueness of linear pro-gramming,”in Linear Programming:Theory,Algorithms and Appli-cant,Y.Truma,Ed.New York,NY,USA:Nova Science Publishers, 2014,pp.27–100.
[56]Y.Zhang,Z.Li,H.-Z Tan,and Z.Fan,“On the simpli?ed LVI-based
primal-dual neural network for solving LP and QP problems,”in Proc.
IEEE Int.Conf.Control Autom.,2007,pp.3129–3134.
[57]C.Mead,Analog VLSI and Neural Systems.Reading,MA,USA:Ad-
dison-Wesley,1989.
[58]M.S.Bazaraa,H.D.Sherali,and C.M.Shetty,Nonlinear Program-
ming-Theory and Algorithms.New York,NY,USA:Wiley,1993. [59]Y.Zang and J.Wang,“A dual neural network for convex quadratic pro-
gramming subject to linear equality and inequality constraints,”Phys.
Lett.A,vol.298,no.4,pp.271–278,2002.
[60]Y.Zhang,W.Ma,and B.Cai,“From Zhang neural network to Newton
iteration for matrix inversion,”IEEE Trans.Circuits Syst.I,Reg.Pa-pers,vol.56,no.7,pp.1405–1415,Jul.2009.
[61]Z.Zhang and Y.Zhang,“Variable joint-velocity limits of redundant
robot manipulators handled by quadratic programming,”IEEE/ASME Trans.Mech.,vol.18,no.2,pp.674–686,Apr.2013.
[62]W.Zhu,https://www.sodocs.net/doc/6d953320.html,marche,E.Dupuis,D.Jameux,P.Barnard,and G.
Liu,“Precision control of modular robot manipulators:The VDC approach with embedded FPGA,”IEEE Trans.Robot.,vol.29,no.5, pp.1162–1179,Oct.2013.
[63]T.Yao,Y.Gai,S.Fu,and H.Liu,“Mechanical design of7-DOF ma-
nipulator for water jet cutting,”in Proc.Int.Conf.Mechatron.Autom., 2009,pp.2746–2751.
[64]https://www.sodocs.net/doc/6d953320.html,o,N.Mendes,J.N.Pires,and A.P.Moreira,“CAD-based robot
programming:The role of fuzzy-PI force control in unstructured en-vironments,”in Proc.the6th IEEE Conf.Autom.Sci.Eng.,2010,pp.
362–367.
[65]F.Mazzini,D.Kettler,J.Guerrero,and S.Dubowsky,“Tactile robotic
mapping of unknown surfaces,with application to oil wells,”IEEE
Trans.Instrum.Meas.,vol.60,no.2,pp.420–429,Feb.2011.
[66]N.Chakraborty,S.Akella,and J.T.Wen,“Coverage of a planar point
set with multiple robots subject to geometric constraints,”IEEE Trans.
Autom.Sci.Eng.,vol.7,no.1,pp.111–122,Jan.2010.
[67]L.A.Burhanuddin,M.N.Islam,and S.M.Yusof,“Evaluation of colli-
sion avoidance path planning algorithm,”in Proc.Int.Conf.Res.Innov.
Inf.Syst.,2013,pp.360–365.
[68]D.Meike,M.Pellicciari,and G.Berselli,“Energy ef?cient use of mul-
tirobot production lines in the automotive industry:Detailed system
modeling and optimization,”IEEE Trans.Autom.Sci.Eng.,vol.11,
no.3,pp.798–809,Jul.2014.
[69]H.Zhang,C.Reardon,and L.E.Parker,“Real-time multiple human
perception with color-depth cameras on a mobile robot,”IEEE Trans.
Cybern.,vol.43,no.5,pp.1429–1441,Oct.2013.
[70]D.Kim,S.Lee,and B.Choi,“A real-time stereo depth extraction hard-
ware for intelligent home assistant robot,”IEEE Trans.Consum.Elec-
tron.,vol.56,no.3,pp.1782–1788,Aug.
2010.
Dechao Chen received the B.S.degree in electronic
information science and technology from the Guang-
dong University of Technology,Guangzhou,China,
in2013.He is currently pursuing the Ph.D.degree
in communication and information systems at the
School of Information Science and Technology,Sun
Yat-sen University,Guangzhou,China,under the
direction of Prof.Y.Zhang.
He is also with the SYSU-CMU Shunde Interna-
tional Joint Research Institute,Foshan,China,for
cooperative research.His research interests include robotics,neural networks,and nonlinear dynamics
systems.
Yunong Zhang(S'02–M'03)received the B.S.
degree from the Huazhong University of Science and
Technology,Wuhan,China,in1996,the M.S.degree
from the South China University of Technology,
Guangzhou,China,in1999,and the Ph.D.degree
from the Chinese University of Hong Kong,Shatin,
Hong Kong,China,in2003.
He is currently a Professor with the School of
Information Science and Technology,Sun Yat-sen
University,Guangzhou,China.Before joining Sun
Yat-sen University in2006,Yunong had been with the National University of Singapore;the University of Strathclyde,U.K.;and the National University of Ireland at Maynooth.In addition,he is also with the SYSU-CMU Shunde International Joint Research Institute,Foshan,China, for cooperative research.His main research interests include robotics,neural networks,computation and optimization.His web page is now available at https://www.sodocs.net/doc/6d953320.html,/~zhynong.
Web性能测试方案
Web性能测试方案 1测试目的 此处阐述本次性能测试的目的，包括必要性分析与扩展性描述。 性能测试最主要的目的是检验当前系统所处的性能水平，验证其性能是否能满足未来应用的需求，并进一步找出系统设计上的瓶颈，以期改善系统性能，达到用户的要求。 2测试范围 此处主要描述本次性能测试的技术及业务背景，以及性能测试的特点。 编写此方案的目的是为云应用产品提供web性能测试的方法，因此方案内容主要包括测试环境、测试工具、测试策略、测试指标与测试执行等。 2.1测试背景 以云采业务为例，要满足用户在互联网集中采购的要求，实际业务中通过云采平台询报价、下单的频率较高，因此云采平台的性能直接决定了业务处理的效率，并能够支撑业务并发的压力。 例如：支撑100家企业用户的集中访问，以及业务处理要求。 2.2性能度量指标 响应时间（TTLB） 即“time to last byte”，指的是从客户端发起的一个请求开始，到客户端接收到从服务器端返回的响应结束，这个过程所耗费的时间，响应时间的单位一般为“秒”或者“毫秒”。响应时间＝网络响应时间+应用程序响应时间。 响应时间标准：
事务能力TPS（transaction per second） 服务器每秒处理的事务数； 一个事务是指一个客户机向服务器发送请求然后服务器做出反应的过程。 客户机在发送请求时开始计时，收到服务器响应后结束计时，一次来计算使用的时间和完成的事务个数。它是衡量系统处理能力的重要指标。 并发用户数 同一时刻与服务器进行交互的在线用户数量。 吞吐率（Throughput） 单位时间内网络上传输的数据量，也可指单位时间内处理的客户端请求数量，是衡量网络性能的重要指标。 吞吐率=吞吐量/传输时间 资源利用率 这里主要指CPU利用率（CPU utilization），内存占用率。 3测试内容 此处对性能测试整体计划进行描述，包括测试内容以及关注的性能指标。Web性能测试内容包含：压力测试、负载测试、前端连接测试。 3.1负载测试 负载测试是为了测量Web系统在某一负载级别上的性能，以保证Web系统在需求范围内能正常工作。负载级别可以是某个时刻同时访问Web系统的用户数量，也可以是在线数据处理的数量。例如：Web应用系统能允许多少个用户同时在线？如果超过了这个数量，会出现什么现象？Web应用系统能否处理大
α-突触核蛋白与帕金森病
soluble protein which one kind of central nervous system synapse, expresses, gets sick the morbidity with Parkinson to have the close relationship. Alpha - the synapse nucleoalbumin in each physiology, under environmental factor's influence exceptionally expresses and gathers, through biochemistry and so on a series of oxidized stress responded, has produced to neuron's toxic effect, thus participated in the occurrence which Parkinson gets sick. To Alpha - the synapse nucleoalbumin's chemical property, the accumulation mechanism and influencing factor's understanding and the research, will be very advantageous the prevention which and the treatment will get sick in Parkinson. 【Key words】Alpha - synapse nucleoalbumin; Parkinson sickness; Louis minute 帕金森病是一种中老年人常见的运动障碍疾病，以黑质多巴胺能神经元变性缺失和路易小体形成为病理特征，临床上表现为静止性震颤，运动迟缓，肌强直和姿势步态异常等。 α-突触核蛋白是一种在健康人的脑组织中广泛分布的 可溶性蛋白，它是帕金森病的发病机制中最重要的蛋白，因为它是路易小体的主要结构成分，α-突触核蛋白聚集与路易小体的形成及多巴胺能神经元的死亡密切相关。本文就α-
品质体系框架图.
品质体系框架图 图中各缩写词含义如下： QC：Quality Control 品质控制 QA：Quality Assurance 品质保证 QE：Quality Engineering 品质工程 IQC：Incoming Quality Control 来料品质控制 LQC：Line Quality Control 生产线品质控制 IPQC：In Process Quality Control 制程品质控制 FQC：Final Quality Control 最终品质控制 SQA：Source (Supplier) Quality Assurance 供应商品质控制 DCC：Document Control Center 文控中心 PQA：Process Quality Assurance 制程品质保证 FQA：Final Quality Assurance 最终品质保证 DAS：Defects Analysis System 缺陷分析系统 FA：Failure Analysis 坏品分析 CPI：Continuous Process Improvement 连续工序改善 CS：Customer Service 客户服务 TRAINNING：培训 一供应商品质保证（SQA） 1.SQA概念 SQA即供应商品质保证，识通过在供应商处设立专人进行抽样检验，并定期对供应商进行审核、评价而从最源头实施品质保证的一种方法。是以预防为主思想的体现。
2.SQA组织结构 3.主要职责 1）对从来料品质控制（IQC）/生产及其他渠道所获取的信息进行分析、综合，把结果反馈给供应商，并要求改善。 2）耕具派驻检验远提供的品质情报对供应商品质进行跟踪。 3）定期对供应商进行审核，及时发现品质隐患。 4）根据实际不定期给供应商导入先进的品质管理手法及检验手段，推动其品质保证能力的提升。 5）根据公司的生产反馈情况、派驻人员检验结果、对投宿反应速度及态度对供应商进行排序，为公司对供应商的取舍提供依据。 4.供应商品质管理的主要办法 1）派驻检验员 把IQC移至供应商，使得及早发现问题，便于供应商及时返工，降低供应商的品质成本，便于本公司快速反应，对本公司的品质保证有利。同时可以根据本公司的实际使用情况及IQC的检验情况，专门严加检查问题项目，针对性强。 2）定期审核 通过组织各方面的专家对供应商进行审核，有利于全面把握供应商的综合能力，及时发现薄弱环节并要求改善，从而从体系上保证供货品质定期排序，此结果亦为供应商进行排序提供依据。 一般审核项目包含以下几个方面 A．品质。 B．生产支持。 C．技术能力及新产品导入。 D．一般事务. 具体内容请看“供应商调查确认表”. 3）定期排序 排序的主要目的是评估供应商的品质及综合能力，以及为是否保留、更换供应商提供决策依据.排序主要依据以下几个方面的内容： A.SQA批通过率：一般要求不低于95%。 B.IQC批合格率：一般要求不低于95%。
天线分集技术的原理
天线分集技术的原理 最初，许多设计者可能会担心区域规范的复杂性问题，因为在全世界范围内，不同区域规范也各异。然而，只要多加研究便能了解并符合不同区域的法规，因为在每一个地区，通常都会有一个政府单位负责颁布相关文件，以说明“符合特定目的的发射端相关的规则。 无线电通信中更难于理解的部分在于无线电通信链路质量与多种外部因素相关，多种可变因素交织在一起产生了复杂的传输环境，而这种传输环境通常很难解释清楚。然而，掌握基本概念往往有助于理解多变的无线电通信链接品质，一旦理解了这些基本概念，其中许多问题可以通过一种低成本、易实现的被称作天线分集(antenna diversity)的技术来实现。 环境因素的考虑 影响无线电通信链路持续稳定的首要环境因素是被称为多径/衰落和天线极化/分集的现象。这些现象对于链路质量的影响要么是建设性的要么是破坏性的，这取决于不同的特定环境。可能发生的情况太多了，于是，当我们试着要了解特定的环境条件在某个时间点对无线电通信链接的作用，以及会造成何种链接质量时，这无疑是非常困难的。 天线极化/分集 这种被称为天线极化的现象是由给定天线的方向属性引起的，虽然有时候把天线极化解释为在某些无线电通信链路质量上的衰减，但是一些无线电通信设计者经常利用这一特性来调整天线，通过限制收发信号在限定的方向范围之内达其所需。这是可行的，因为天线在各个方向上的辐射不均衡，并且利用这一特性能够屏蔽其他（方向）来源的射频噪声。 简单的说，天线分为全向和定向两种。全向天线收发信号时，在各个方向的强度相同，而定向天线的收发信号被限定在一个方向范围之内。若要打造高度稳固的链接，首先就要从了解此应用开始。例如：如果一个链路上的信号仅来自于特定的方向，那么选择定向天线获
性能测试流程规范
目录 1前言 (2) 1.1 文档目的 (2) 1.2 适用对象 (2) 2性能测试目的 (2) 3性能测试所处的位置及相关人员 (3) 3.1 性能测试所处的位置及其基本流程 (3) 3.2 性能测试工作内容 (4) 3.3 性能测试涉及的人员角色 (5) 4性能测试实施规范 (5) 4.1 确定性能测试需求 (5) 4.1.1 分析应用系统，剥离出需测试的性能点 (5) 4.1.2 分析需求点制定单元测试用例 (6) 4.1.3 性能测试需求评审 (6) 4.1.4 性能测试需求归档 (6) 4.2 性能测试具体实施规范 (6) 4.2.1 性能测试起始时间 (6) 4.2.2 制定和编写性能测试计划、方案以及测试用例 (7) 4.2.3 测试环境搭建 (7) 4.2.4 验证测试环境 (8) 4.2.5 编写测试用例脚本 (8) 4.2.6 调试测试用例脚本 (8) 4.2.7 预测试 (9) 4.2.8 正式测试 (9) 4.2.9 测试数据分析 (9) 4.2.10 调整系统环境和修改程序 (10) 4.2.11 回归测试 (10) 4.2.12 测试评估报告 (10) 4.2.13 测试分析报告 (10) 5测试脚本和测试用例管理 (11) 6性能测试归档管理 (11) 7性能测试工作总结 (11) 8附录：............................................................................................. 错误！未定义书签。
1前言 1.1 文档目的 本文档的目的在于明确性能测试流程规范，以便于相关人员的使用，保证性能测试脚本的可用性和可维护性，提高测试工作的自动化程度，增加测试的可靠性、重用性和客观性。 1.2 适用对象 本文档适用于部门内测试组成员、项目相关人员、QA及高级经理阅读。 2性能测试目的 性能测试到底能做些什么，能解决哪些问题呢？系统开发人员，维护人员及测试人员在工作中都可能遇到如下的问题 1.硬件选型，我们的系统快上线了，我们应该购置什么样硬件配置的电脑作为 服务器呢？ 2.我们的系统刚上线，正处在试运行阶段，用户要求提供符合当初提出性能要 求的报告才能验收通过，我们该如何做？ 3.我们的系统已经运行了一段时间，为了保证系统在运行过程中一直能够提供 给用户良好的体验（良好的性能），我们该怎么办？ 4.明年这个系统的用户数将会大幅度增加，到时我们的系统是否还能支持这么 多的用户访问，是否通过调整软件可以实现，是增加硬件还是软件，哪种方式最有效？ 5.我们的系统存在问题，达不到预期的性能要求，这是什么原因引起的，我们 应该进行怎样的调整？ 6.在测试或者系统试点试运行阶段我们的系统一直表现得很好，但产品正式上 线后，在用户实际环境下，总是会出现这样那样莫名其妙的问题，例如系统运行一段时间后变慢，某些应用自动退出，出现应用挂死现象，导致用户对我们的产品不满意，这些问题是否能避免，提早发现？ 7.系统即将上线，应该如何部署效果会更好呢？ 并发性能测试的目的注要体现在三个方面：以真实的业务为依据，选择有代表性的、关键的业务操作设计测试案例，以评价系统的当前性能；当扩展应用程序的功能或者新的应用程序将要被部署时，负载测试会帮助确定系统是否还能够处理期望的用户负载，以预测系统的未来性能；通过模拟成百上千个用户，重复执行和运行测试，可以确认性能瓶颈并优化和调整应用，目的在于寻找到瓶颈问题。
敲除α-突触核蛋白保护多巴胺能神经元
敲除α-突触核蛋白保护多巴胺能神经元 甲基苯丙胺诱导的帕金森病模型中多巴胺能神经元死亡的主要因素是α-突触核蛋白过表达。中国南方医科大学王慧君博士所在团队发现，立体定位注射α-syn-shRNA慢病毒抑制右侧纹状体α-syn mRNA和蛋白的表达后，帕金森病模型大鼠抑郁表现减弱，且纹状体中多巴胺水平和酪氨酸羟化酶及超氧化物歧化酶活性显著增加，而活性氧生成量、一氧化氮合酶活性、一氧化氮含量和丙二醛含量下降，同时纹状体中凋亡细胞的数量明显降低。作者认为，α-突触核蛋白具有通过抑制氧化应激和改善多巴胺能系统功能扭转甲基苯丙胺诱导的神经毒性的能力。相关文献发表于《中国神经再生研究（英文版）》杂志2014年5月第9期。 TUNEL染色结果显示，以立体定向注射α-syn-shRNA慢病毒敲除右侧纹状体中α-syn后，腹腔注射甲基苯丙胺建立帕金森病模型大鼠纹状体中凋亡细胞的数量显著降低 Article: " Protective effect of alpha-synuclein knockdown on methamphetamine-induced neurotoxicity in dopaminergic neurons," by Yunchun Tai1, Ling Chen1, Enping Huang1, Chao Liu1, 2, Xingyi Yang1, Pingming Qiu1, Huijun Wang1 (1 Department of Forensic Medicine, School of Basic Medical Sciences, Southern Medical University, Guangzhou, Guangdong Province, China; 2 Guangzhou Forensic Science Institute, Guangzhou, Guangdong Province, China) Tai YC, Chen L, Huang EP, Liu C, Yang XY, Qiu PM, Wang HJ. Protective effect of alpha-synuclein knockdown on methamphetamine-induced neurotoxicity in dopaminergic neurons. Neural Regen Res. 2014;9(9):951-958. 欲获更多资讯： Neural Regen Res
浅析发射分集与接收分集技术
浅析发射分集与接收分集技术 1 概述 1.1 多天线信息论简介 近年来,多天线系统(也称为MIMO系统)引起了人们很大的研究兴趣,多天线系统原理如图1所示，它可以增加系统的容量,改进误比特率(BER).然而,获得这些增益的代价是硬件的复杂度提高,无线系统前端复杂度、体积和价格随着天线数目的增加而增加。使用天线选择技术，就可以在获得MIMO系统优势的同时降低成本。 图1 MIMO系统原理 有两种改进无线通信的方法：分集方法、复用方法。分集方法可以提高通信系统的鲁棒性，利用发送和接收天线之间的多条路径，改善系统的BER。在接收端，这种分集与RAKE接收提供的类似。分集也可以通过使用多根发射天线来得到，但是必须面对发送时带来的相互干扰。这一类主要是空时编码技术。 另外一类MIMO技术是空间复用，来自于这样一个事实：在一个具有丰富散射的环境中，接收机可以解析同时从多根天线发送的信号，因此，可以发送并行独立的数据流，使得总的系统容量随着min( , )线性增长，其中
和 是接收和发送天线的数目。 1.2 空时处理技术 空时处理始终是通信理论界的一个活跃领域。在早期研究中，学者们主要注重空间信号传播特性和信号处理，对空间处理的信息论本质探讨不多。上世纪九十年代中期，由于移动通信爆炸式发展，对于无线链路传输速率提出了越来越高的要求，传统的时频域信号设计很难满足这些需求。工业界的实际需求推动了理论界的深入探索。 在MIMO技术的发展，可以将空时编码的研究分为三大方向：空间复用、空间分集与空时预编码技术，如图2所示。 图2 MIMO技术的发展
1.3 空间分集研究 多天线分集接收是抗衰落的传统技术手段，但对于多天线发送分集，长久以来学术界并没有统一认识。1995年Telatarp[3]首先得到了高斯信道下多天线发送系统的信道容量和差错指数函数。他假定各个通道之间的衰落是相互独立的。几乎同时， Foschini和Gans在[4]得到了在准静态衰落信道条件下的截止信道容量(Outage Capacity)。此处的准静态是指信道衰落在一个长周期内保持不变，而周期之间的衰落相互独立，也称这种信道为块衰落信道(Block Fading)。 Foschini和Gans的工作，以及Telatar的工作是多天线信息论研究的开创 性文献。在这些著作中，他们指出，在一定条件下，采用多个天线发送、多个天线接收(MIMO)系统可以成倍提高系统容量，信道容量的增长与天线数目成线性关系 1.4 空时块编码 (STBC) 本文我们主要介绍一类高性能的空时编码方法——空时块编码( STBC: Space Time Block Code)。 STBC编码最先是由Alamouti[1]在1998年引入的，采用了简单的两天线发分集编码的方式。这种STBC编码最大的优势在于，采用简单的最大似然译码准则，可以获得完全的天线增益。 Tarokh[5]进一步将2天线STBC编码推广到多天线形式，提出了通用的正交设计准则。 2 MIMO原理及方案
金蝶ERP性能测试经验分享
ERP性能测试总结分享
1分享 (3) 1.1测试环境搭建 (3) 1.2并发量计算及场景设计 (3) 1.3测试框架搭建 (4) 1.4测试脚本开发/调试 (5) 1.5场景调试/执行 (5) 1.6性能监控分析 (6) 1.7结果报告 (7) 2展望 (8) 2.1业务调研及场景确定 (8) 2.2场景监控与分析 (8)
1分享 1.1 测试环境搭建 在我们进行性能测试之前，通常需要搭建一个供测试用的环境，使用这个环境来录制脚本，根据在这个环境下执行测试的结果，得出最终的测试结论。 有些时候，测试环境就是生产环境，例如：一个新的项目上线前进行的性能测试，通常就是在未来的生产环境下进行的。在这种情况下，可以排除测试环境与生产环境差异带来影响，测试结果相对比较准确。 反之，如果测试环境与生产环境不是同一环境，这个时候，为了保证测试结果的准确性，需要对生产环境进行调研。在搭建测试环境时，尽量保证搭建的测试环境和生成环境保持一致（环境主体框架相同，服务器硬件配置相近，数据库数据相近等）。 另外，最好输出一个测试环境搭建方案，召集各方参加评审确认。同时，在测试方案、测试报告中，对测试环境进行必要的阐述。 1.2 并发量计算及场景设计 首先，在确定场景及并发量之前，需要对业务进行调研，调研的对象最好是业务部门，也可以通过数据库中心查询数据，进行辅助。 场景选取一般包括：登陆场景、操作频繁的核心业务场景、涉及重要信息（如：资金等）业务场景、有提出明确测试需求的业务场景、组合场景等。 每个场景的并发量，需要根据业务调研的结果进行计算。可以采用并发量计算公式：C=nL / T 进行计算（其中C是平均的并发用户数，n是平均每天访问用户数，L是一天内用户从登录到退出的平均时间（操作平均时间），T是考察时间长度（一天内多长时间有用户使用系统））。 每个场景的思考时间，也可以通过业务调研获得。 另外，也可以采用模拟生产业务场景TPS（每秒通过事务数）的方式，来确定场景。相比上一种方式，模拟生产业务场景TPS，能更加准确模拟生产压力。本次ERP性能测试采用的就是这种方式：首先，通过调研确定业务高峰时段，各核心业务TPS量及产生业务单据量。然后，通过调整组合场景中，各单场景的Vusr（虚拟用户数）和Thinktime（思考时间），使每个场景的TPS接近业务调研所得到的TPS量,每个场景相同时间（即高峰时间段长度）通过事务数接近调研业务单据量，从而确定一个，可以模拟生成环境压力的基准场景。最后，通
人α-突触核蛋白(α-SYN)ELISA试剂盒使用说明书
人α-突触核蛋白(α-SYN)ELISA试剂盒使用说明书 本试剂仅供研究使用目的：本试剂盒用于测定人血清，血浆及相关液体样本中人α-突触核蛋白(α-SYN)含量。 实验原理： 本试剂盒应用双抗体夹心法测定标本中人α-突触核蛋白(α-SYN)水平。用纯化的人α-突触核蛋白(α-SYN)抗体包被微孔板，制成固相抗体，往包被单抗的微孔中依次加入α-突触核蛋白(α-SYN)，再与HRP标记的α-突触核蛋白(α-SYN)抗体结合，形成抗体-抗原-酶标抗体复合物，经过彻底洗涤后加底物TMB显色。TMB在HRP酶的催化下转化成蓝色，并在酸的作用下转化成最终的黄色。颜色的深浅和样品中的α-突触核蛋白(α-SYN)呈正相关。用酶标仪在450nm波长下测定吸光度（OD值），通过标准曲线计算样品中人α-突触核蛋白(α-SYN)浓度。 试剂盒组成： 样本处理及要求： 1.血清：室温血液自然凝固10-20分钟，离心20分钟左右（2000-3000转/分）。仔细收集上 清，保存过程中如出现沉淀，应再次离心。 2.血浆：应根据标本的要求选择EDTA、者柠檬酸钠或肝素作为抗凝剂，混合10-20分钟后， 离心20分钟左右（2000-3000转/分）。仔细收集上清，保存过程中如有沉淀形成，应该再次离心。 3.尿液：用无菌管收集，离心20分钟左右（2000-3000转/分）。仔细收集上清，保存过程中 如有沉淀形成，应再次离心。胸腹水、脑脊液参照实行。 4.细胞培养上清：检测分泌性的成份时，用无菌管收集。离心20分钟左右（2000-3000转/分）。仔细收集上清。检测细胞内的成份时，用PBS（PH7.2-7.4）稀释细胞悬液，细胞浓度达到100万/ml左右。通过反复冻融，以使细胞破坏并放出细胞内成份。离心20分钟
CS架构性能测试
C/S测试 通常，客户/ 服务器软件测试发生在三个不同的层次： 1.个体的客户端应用以“ 分离的” 模式被测试——不考虑服务器和底层网络的运行； 2.客户端软件和关联的服务器端应用被一起测试，但网络运行不被明显的考虑； 3.完整的 C/S 体系结构，包括网络运行和性能，被测试。 下面的测试方法是 C/S 应用中经常用到的： 应用功能测试客户端应用被独立地执行，以揭示在其运行中的错误。 服务器测试——测试服务器的协调和数据管理功能，也考虑服务器性能（整体反映时间和数据吞吐量）。 数据库测试——测试服务器存储的数据的精确性和完整性，检查客户端应用提交的事务，以保证数据被正确地存储、更新和检索。 事务测试——创建一系列的测试以保证每类事务被按照需求处理。测试着重于处理的正确性，也关注性能问题。 网络通信测试——这些测试验证网络节点间的通信正常地发生，并且消息传递、事务和相关的网络交通无错的发生。 C/S结构与B/S结构的特点分析 为了区别于传统的C/S模式，才特意将其称为B/S模式。认识到这些结构的特征，对于系统的选型而言是很关键的。 1、系统的性能 在系统的性能方面，B/S占有优势的是其异地浏览和信息采集的灵活性。任何时间、任何地点、任何系统，只要可以使用浏览器上网，就可以使用B/S系统的终端。 不过，采用B/S结构，客户端只能完成浏览、查询、数据输入等简单功能，绝大部分工作由服务器承担，这使得服务器的负担很重。采用C/S结构时，客户端和服务器端都能够处理任务，这虽然对客户机的要求较高，但因此可以减轻服务器的压力。而且，由于客户端使用浏览器，使得网上发布的信息必须是以HTML 格式为主，其它格式文件多半是以附件的形式存放。而HTML格式文件（也就是Web页面）不便于编辑修改，给文件管理带来了许多不便。
沙发性能测试
1. 作用 家具性能测试是一种加速使用的疲劳和强度承受能力的测试方法，可以用来评估产品能否达到预期的设计要求。 2.GSA沙发性能测试 2.1 测试方法 GSA性能测试基于循环递增加载模式（图1）。测试开始时先给沙发加一个起始载荷，这个载荷以20次/分的频率循环加力25000/次。循环结束后，载荷增加一定量，然后再循环25000次。当载荷达到所需求的水平，或沙发框架或部件破环时测试才结束。 2.2测度设备 GSA沙发性能测试是在一套特别设计的汽缸-管道支架系统上进行的（如照片所示）。气缸在压缩空气机的推动下，以20次/分的循环频率对被测沙发加载。加载循环次数是由一个可编程逻辑控制器和可重置电子记数系统进行记录的。当沙发框架或部件破坏时，限制开关被激活并停止测试。 2.3主要的测试类型 图2所示是沙发的基本框架图，沙发框架可以分成3个部分：坐基框架系统、侧边扶手框架系统和后靠框架系统。根据沙发通常的受力状态，可以进行以下几种测试： 3 测试数据的讨论 3.1垂直坐力测试（seat foundation load test）（图3）， 在垂直坐力作用下，主要的座位支撑框架部位承受很大的应力，如果其中任何一个部件破坏，整个沙发也就很快破坏了。 前横档和后横档破坏的主要原因是其尺寸大小，不过实木横档上有太多交叉纹理和太大太多的节疤刀会引起横档破坏。横档底部的节疤破坏性最大，因为这里所受的拉应力最大，如果支撑框架部件主要是由木榫钉为主要连接件，横档破坏常常起于横档上用于连接座位撑档的榫钉孔处，然后扩大到整个横档截面上。另外在测试中，前横档和前支柱的接头也经常是破坏发生的地方，既有在垂直面的破坏，也有前后方向的破坏。这些破坏的接头大多是由于没有加用涂胶支撑木块来加强连接，而
品质体系框架图
品质体系框架图 1
品质体系框架图 图中各缩写词含义如下： QC：Quality Control 品质控制 QA：Quality Assurance 品质保证 QE：Quality Engineering 品质工程 IQC：Incoming Quality Control 来料品质控制 LQC：Line Quality Control 生产线品质控制IPQC：In Process Quality Control 制程品质控制FQC：Final Quality Control 最终品质控制 SQA：Source (Supplier) Quality Assurance 供应商品质控制DCC：Document Control Center 文控中心 PQA：Process Quality Assurance 制程品质保证FQA：Final Quality Assurance 最终品质保证
DAS：Defects Analysis System 缺陷分析系统 FA：Failure Analysis 坏品分析 CPI：Continuous Process Improvement 连续工序改进 CS： Customer Service 客户服务 TRAINNING：培训 一供应商品质保证（SQA） 1.SQA概念 SQA即供应商品质保证，识经过在供应商处设立专人进行抽样检验，并定期对供应商进行审核、评价而从最源头实施品质保证的一种方法。是以预防为主思想的体现。 2.SQA组织结构 3.主要职责 1）对从来料品质控制（IQC）/生产及其它渠道所获取的信息进行分析、综合，把结果反馈给供应商，并要求改进。 2）耕具派驻检验远提供的品质情报对供应商品质进行跟踪。 3）定期对供应商进行审核，及时发现品质隐患。
α—突触核蛋白与帕金森病相互关系研究进展
α—突触核蛋白与帕金森病相互关系研究进展α-突触核蛋白是一种可溶性小分子蛋白主要在中枢神经系统的突出前末梢 表达。近年来关于α-突触核蛋白和帕金森病等神经退行性病的密切关系被广泛报道越来越多。在本综述中，详细介绍了α突触核蛋白的构成、生理功能和作用、病理生理、聚合机制等方面的研究进展，从α-突触核蛋白的角度理解帕金森病的发生机制。 标签：α-突触核蛋白；中枢神经系统 帕金森病（Parkinson’s Disease，PD）发病率在65岁以上人群中高达1%，神经系统退行性疾病中排在第二位，尤其男性罹患为多[1]。PD的临床特点集中在严重的运动性症状，包括静止性震颤、肌强直、姿势反射异常以及运动减少[2-3]。这些症状障碍可以与自主神经功能障碍、抑郁障碍、痴呆等其他神经精神功能障碍伴发[4]。病理学上PD特点为黑质致密部多巴胺神经元显著的退行性变，导致纹状体投射区或脑干多巴胺神经元投射的减少以及一系列运动皮质系统有关的运动功能障碍。这一神经退行性变伴随着存活多巴胺神经元和受累神经细胞胞浆和突触中路易小体的表现，但具体机制目前尚不清楚[5]。 尽管许多研究者试图阐明选择性多巴胺神经退化的机制，但PD仍是一种病理研究不明的散发性神经退行性疾病。基因和环境危险因素目前收到广泛的关注，但神经退行过程的始动因素目前仍不清楚[6]。基于目前研究，迟发型原发性PD是由于复杂的多重易感基因和环境因素引起的。此外，若干PD单基因家族类型以發病早和显性或隐性以遗传染色体病为特征。在众多与PD可能的基因中，四种PD有关的突变包括α-synuclein[7]、parkin[8]、泛素羧基末端水解酶（ubiquitin carboxy-terminal hydrolase L-1）[9]和DJ-1[10]。 尽管伴有特殊基因缺陷的家族性PD患者只占所有发病人群的一小部分，但对这些病例的研究可以有助于我们发现造成多因素散发性PD的核心蛋白通路。与α-syn编码有关的基因突变受到的重视，原因就在于在大多数家族性或散发性PD患者中，病理发现其路易小体中存在大量α-Syn纤维沉积[11-12]。 这一观察发现说明了尽管α-syn属于PD患者中不常见突变，但通过一些不正常的代谢性过程的积累，这些蛋白在家族或散发性PD的病例中起到了重要作用。 1 α-syn的分布和结构 α-Syn和β-Syn、γ-Syn同属于synuclein家族[13]，该家族蛋白只存在于脊椎动物中。α-Syn在脑部（尤其是新皮层、海马、纹状体、丘脑和小脑）的突触前末梢中广泛表达[14-15]。α-syn基因定位于4q21[16]。所有突触核蛋白的基因排序均类似，但是只有alfa-Syn与疾病相关。α-Syn最初在太平洋电鳗”加州电鯆”的放电器官中被发现。数百种保守的α-syn蛋白类似物存在于人类、鸟类、小鼠、
品质体系的一般架构
品质体系的一般架构 图中各缩写词含义如下： QC：Quality Control 品质控制 QA：Quality Assurance 品质保证 QE：Quality Engineering 品质工程IQC：Incoming Quality Control 来料品质控制LQC：Line Quality Control 生产线品质控制IPQC：In Process Quality Control 制程品质控制FQC：Final Quality Control 最终品质控制SQA：Source (Supplier) Quality Assurance 供应商品质控制DCC：Document Control Center 文控中心PQA：Process Quality Assurance 制程品质保证FQA：Final Quality Assurance 最终品质保证DAS：Defects Analysis System 缺陷分析系统FA：Failure Analysis 坏品分析CPI：Continuous Process Improvement 连续工序改善CS：Customer Service 客户服务TRAINNING：培训
一供应商品质保证（SQA） 1.SQA概念 SQA即供应商品质保证，识通过在供应商处设立专人进行抽样检验，并定期对供应商进行审核、评价而从最源头实施品质保证的一种方法。是以预防为主思想的体现。 2.SQA组织结构 3.主要职责 1）对从来料品质控制（IQC）/生产及其他渠道所获取的信息进行分析、综合，把结果反馈给供应商，并要求改善。 2）耕具派驻检验远提供的品质情报对供应商品质进行跟踪。 3）定期对供应商进行审核，及时发现品质隐患。 4）根据实际不定期给供应商导入先进的品质管理手法及检验手段，推动其品质保证能力的提升。 5）根据公司的生产反馈情况、派驻人员检验结果、对投宿反应速度及态度对供应商进行排序，为公司对供应商的取舍提供依据。 4.供应商品质管理的主要办法 1）派驻检验员 把IQC移至供应商，使得及早发现问题，便于供应商及时返工，降低供应商的品质成本，便于本公司快速反应，对本公司的品质保证有利。同时可以根据本公司的实际使用情况及IQC的检验情况，专门严加检查问题项目，针对性强。 2）定期审核 通过组织各方面的专家对供应商进行审核，有利于全面把握供应商的综合能力，及时发现薄弱环节并要求改善，从而从体系上保证供货品质定期排序，此结果亦为供应商进行排序提供依据。 一般审核项目包含以下几个方面 A．品质。 B．生产支持。 C．技术能力及新产品导入。
CS和CSS架构的软件性能测试分析
1. C S/C SS系统架构的基本概念 1.1系统架构定义 虽然B/S结构、J2EE架构愈来愈成为流行模式，但基于传统的C/S结构的应用程序还广泛地应用于各种行业。尤其是金融行业中的商业银行柜面－核心帐务系统等。一方面由于传统商业银行一般都有大量的字符终端等需要复用的设备，一方面也是因为他们存在大量密集的对实时性要求很高的高柜业务，使用传统的基于C/S结构或者C/S/S结构的应用效率更有保证。 C/S结构即CLIENT/SERVER结构。传统的C/S结构一般分为两层：客户端和服务器端。该结构的基本工作原理是，客户程序向数据服务器发送SQL请求，服务器返回数据和结果。客户端负责实现用户接口功能，同时封装了部分应用逻辑。服务器端的数据库服务器主要提供数据存储功能，也通过触发器和存储过程提供部分应用逻辑。 C/S/S结构即客户/应用服务器/数据库服务器三层结构，中间增加了应用服务器，通常实现应用逻辑，是连接客户与数据库服务器的桥梁。它响应用户发来的请求执行某种业务任务，并与数据库服务器打交道，技术实现上通常选用中间件产品，如BEA公司的TUXEDO （事实上J2EE架构的应用也属于这种三层或多层结构，这里不包括。）和IBM公司的CICS等。 三层或多层C/S结构与两层C/S结构相比，它的优势主要表现在：安全性加强、效率提高、易于维护、可伸缩性、可共享性、开放性好等。 1.2系统架构示意图 1.3CS/CSS系统架构中性能测试的特点 1.3.1CS/CSS系统架构的性能影响因素 由于CS/CSS系统的以下特性，测试工程师对一个CS/CSS系统实施性能测试具有很大的难度： *整个系统的各个部分使用多种操作系统，性能上有差别； *整个系统架构的各个环节上使用多种数据库，同样在性能上有差别； *应用是多个，分属多个种类，分布在不同设备上，包括自行开发的应用、第三方的应用； *系统中的设备、组件通过不同协议进行连接、通讯； *系统的内部接口多，性能瓶颈多；而系统的整体性能往往取决于最差的部分；需要分别测试和联合测试 *系统的性能指标不光同应用系统架构有关，还和具体行业应用的业务模式有关； *采用此架构的行业应用往往是一个7×24小时系统； *采用此架构的行业应用可能高柜业务多，这样会影响对性能度量项的选取和转换； *各个环节基本上以交换数据报文的方式通信，其格式经常会比较复杂。 因此这样的系统对于对测试工程师的知识的深度和广度都是一个考验。对于这样的系统，到底如何使用什么样的测试策略、如何分析测试需求、如何选取性能度量项的转换计算模型、如何确定测试内容和轮次、如何设计性能测试案例等等以及规划和实施性能测试中的其它诸多问题，都需要遵循一个系统的方法来解决。 1.3.2CS/CSS系统架构中性能测试的基本策略 1. 确定好测试工作范围 首先可以分析压力测试中最容易出现瓶颈的地方，从而有目的地调整测试策略或测试环境，使压力测试结果真实地反映出软件的性能。例如，服务器的硬件限制、数据库的访问性能设置等常常会成为制约软件性能的重要因素，但这些因素显然不是用户最关心的，我们在测试之前就要通过一些设置把这些因素的影响调至最低。 另外，用户更关心整个系统中哪个环节的性能情况也会影响工作范围。如有的环节是全
品质体系的一般架构
品质体系的一般架构 图中各缩写词含义如下: QC : Quality Con trol 品质控制QA : Quality Assura nee 品质保证QE : Quality Engin eeri ng 品质工程 IQC : Incoming Quality Con trol 来料品质控制 LQC :Line Quality Control 生产线品质控制IPQC :In Process Quality Control 制程品质控制FQC Fi nal Quality Co ntrol 最终品质控制SQA :Source (Supplier) Quality Assura nee 供应商品质控制DCC :Docume nt Con trol Cen ter 文控中心 PQA :Process Quality Assura nee 制程品质保证FQA :Final Quality Assura nee 最终品质保证DAS :Defects An alysis System 缺陷分析系统FA : Failure An alysis 坏品分析 CPI : Con ti nu ous Process Improveme nt 连续工序改善 CS : Customer Service 客户服务TRAINNING : 培训
一供应商品质保证(SQA) 1. SQA概念 SQA即供应商品质保证，识通过在供应商处设立专人进行抽样检验，并定期对供应商进行审核、评价而从最源头实施品质保证的一种方法。是以预防为主思想的体现。 2. SQA组织结构 3. 主要职责 1) 对从来料品质控制(IQC) /生产及其他渠道所获取的信息进行分析、综合，把结果反馈给 供应商，并要求改善。 2) 耕具派驻检验远提供的品质情报对供应商品质进行跟踪。 3) 定期对供应商进行审核，及时发现品质隐患。 4) 根据实际不定期给供应商导入先进的品质管理手法及检验手段，推动其品质保证能力的 提升。 5) 根据公司的生产反馈情况、派驻人员检验结果、对投宿反应速度及态度对供应商进行排 序，为公司对供应商的取舍提供依据。 4. 供应商品质管理的主要办法 1) 派驻检验员 把IQC移至供应商，使得及早发现问题，便于供应商及时返工，降低供应商的品质成本，便于本公司快速反应，对本公司的品质保证有利。同时可以根据本公司的实际使用情况及IQC的检验情况，专门严加检查问题项目，针对性强。 2) 定期审核 通过组织各方面的专家对供应商进行审核，有利于全面把握供应商的综合能力，及时发现薄弱环节并要求改善，从而从体系上保证供货品质定期排序，此结果亦为供应商进行排序提供依据。 一般审核项目包含以下几个方面 A. 品质。 B. 生产支持。 C. 技术能力及新产品导入。 般事务? 具体内容请看“供应商调查确认表”
分集接收技术
题目：多径衰落信道下分集接收技术性能仿 真 学科门类（文、理、工、医）：工 院 系：信息工程学院 专 业：通信与信息系统 初 审： 评 审： 2014年郑州大学第九届研究生论文大赛
多径衰落信道下分集接收技术性能仿真 摘要:随着信息时代的到来，近几年来，在通信领域，很多的技术都得到了发展和应用，通信质量问题也得到越来越多的关注，当信号在实际的无线通信系统中传输时，多径传输的存在会而使信号产生衰落，衰落会影响通信的质量，多径效应是影响无线通信质量的一个重要因素，多径效应通常会影响信号的传输，然而分集技术可以有效的减弱多径效应带给无线信道的不良的影响。使用分集技术可以获得分集增益，通过获得分集增益来提高通信的质量。 本设计介绍了有关通信系统仿真的方法和概念，也对多径衰落信道做了详细的介绍，论文的最后一章用MATLAB仿真了多径衰落信道，通过仿真可以比较直观的看出此信道的特点，论文详细的介绍了几种分集合并技术，并对这几种技术做了简单的分析和比较，仿真了信号在不同的分集接收技术上的BER。 关键词：信号；多径效应；分集技术；通信仿真 The performance simulation of diversity reception technology on Rayleigh fading channel Abstract:With the information age coming, in recent years, in the field of communication, many techniques are making a big development, the communication quality issues have been more and more attention, when the signal transmit in a real communication system .In multipath transmission signal will be fading, fading affects the quality of the communication .multipath effect is an important factor affecting the quality of the radio communication, multipath effects usually affect the signal transmission, however, the diversity technique can be effectively reduced multipath effects bring the adverse effects of the radio channel. Diversity gain can be obtained by obtaining the diversity gain to improve the quality of the communication using the diversity technique. This topic provides information communication system simulation methods and concepts. In this paper, I make a detailed introduction about multipath fading channel .In final chapter, MATLAB is used to simulate the multipath fading channel, Through the simulation we can see this channel characteristics more intuitive, the paper describes in detail several diversity combining techniques, and these types of technology to do a simple analysis and comparison of simulated signals in different diversity reception technology BER. Keywords: signal Multi-path effects diversity reception technology 1 绪论 1.1 引言 达接收端的信号路径不只有一条。即存在多径传输。多径传输会给信号带来多径衰落。多径衰落会使到达接收机的信号在实际的无线通信中，信号在传输过程中存在反射、折射、绕射等现象使到与原来的发射信号相差较大，造成错码，因此，怎样提高信号的输出信噪比，提高信道特性是现在通信领域的重要研究课题。 分集技术的关键是“分”，“分”的含义就是要使信号通过多个信道，这里所说的信道可以是空间的，可以是时间的，也可以是频率的。通过多个信道传送同一信号，然后在接收端会接收到多个信道信息，因为每个信道的特性不可能完全相同，在不同信道上传输的多路信号的衰落就不尽相同。多径信号叠加后在每个时间点上的信号就会减少衰落，多条信号叠加后所包含的的信息比较接近原来的信号，这样接收机就能比较准确的恢复原来的信号。因此分集技术可以降低衰落，如果不用分集技术，在这种情况下要想获得比较高的输出信号信噪比，发射机必须要有较高的信号发射功率，信号的发射功率较小会使到达接收端的衰落信号