CN103365249B - Rapid solving method for failure workspace of six-degree-of-freedom parallel robot - Google Patents

Rapid solving method for failure workspace of six-degree-of-freedom parallel robot Download PDF

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CN103365249B
CN103365249B CN201310287277.2A CN201310287277A CN103365249B CN 103365249 B CN103365249 B CN 103365249B CN 201310287277 A CN201310287277 A CN 201310287277A CN 103365249 B CN103365249 B CN 103365249B
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parallel robot
pose
supporting leg
motion platform
degree
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CN201310287277.2A
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CN103365249A (en
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段学超
仇原鹰
保宏
崔传贞
杜敬利
满曰刚
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西安电子科技大学
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Abstract

The invention relates to a rapid solving method for the failure workspace of a six-degree-of-freedom parallel robot. The conventional methods have the defects that 1) a geometric method is high in engineering implementation difficulty and low in computational efficiency; and 2) a certain feasible pose solution capable of making a support leg corresponding to the pose solution right as long as that of a failing support leg is difficult to give by a kinematic inverse solution-based rapid searching method. The rapid solving method comprises the following steps of determining a minimum length value Li<min>(i=1,2, -,6) of each linear electrical executor and an extended stroke value delta Li(i=1,2, -6) which can be realized by each linear electrical executor according to the product performance of the adopted linear electrical executors; randomly generating N groups of support leg length data L<n> according to the data by using a pseudo-random method; solving the position p<n> of a motion platform according to known parallel robot pose parameters by utilizing a steepest descent position forward kinematics algorithm; and finally obtaining N motion platform pose points to obtain a motion space scatter diagram when the leg of the parallel robot fails. According to the method, the support leg failure workspace of a six-degree-of-freedom redundant drive parallel robot is more rapidly and accurately determined.

Description

Six-degree-of-freedom parallel robot fail operation space fast solution method
Technical field
The invention belongs to parallel robot technical field, determine a fast method for its work space after specifically breaking down based on the six-degree-of-freedom parallel robot supporting leg of forward kinematics solution, be used to guide or the performance evaluation of auxiliary six-degree-of-freedom parallel robot and supporting leg break down after maintenance and debugging.
Background technology
Six-degree-of-freedom parallel robot is widely used in motion simulation, pose adjustment and digital-control processing system.The work space of parallel robot is the perform region that robotic manipulator can arrive, it is the important indicator weighing robot performance, the Analytical Solution of six-degree-of-freedom parallel robot work space is a very complicated problem, so far also imperfect method, so can only adopt the work space of numerical solution to six-degree-of-freedom parallel robot to analyze at present.In actual production process, certain a set of drive unit of 6DOF parallel robot can not move according to steering order once there occurs fault, then must by controlling the motion of other 5 supporting legs, make end effector platform and load movement thereof to home (i.e. mechanism stable position, caving in of operating platform can not be caused because removing a supporting leg), then fault supporting leg is overhauled or changed.And so-called supporting leg fail operation space, just refer to when a supporting leg break down can not move time 6DOF parallel robot operating platform all possible space pose points that can reach.From with co-relation, the home of aforesaid operating platform must be positioned within parallel robot fail operation space.Therefore, determine that fail operation space is the prerequisite of the home that selection operation platform will be stopped.Motion planning after breaking down to instruct six-degree-of-freedom parallel robot supporting leg, for guaranteeing payload security and the maintenance of accessory drive component, the fast solution method in research six-degree-of-freedom parallel robot supporting leg fail operation space, this is very important.
At present, at home and abroad disclosed Workspace Determination for Parallel Manipulator method mainly contains several as follows:
(1) analytical method: this kind of method is the geometric properties of a sphere based on imagination single open chain end bar reference point movement locus when given moving platform attitude and limit restraint long by bar, working envelope is constructed the junction region Solve problems be summed up as 12 sphere sheets.J. P. Merlet. Geomet rical det erminat ion of workspace of a const rained parallel manipulators. In:ARK. France, 1992, pp326-329 has done Workspace Analysis by introducing hinge restraining on this basis. Z Ji. Workspace analysis of Stewart plat forms via vertex space. J Robot ic Systems, vol.11, no.7, 1994, the spheric motion track definition of moving platform hinge during given attitude is space, summit by pp631-638, solving of working envelope is summed up as space, summit and asks friendship problem.In addition, J. P. Merlet. Determination of the orientation workspace of parallel manipulators. Journal of Intelligent and Robotic Systems, 1995,13:143-160 is investigated fixing moving platform reference point, solves the analytic method in corresponding extreme attitude space.Huang Tian, Wang Jingsong, Stewart parallel robot locational space is resolved, " Chinese science (E collects) ", the 28th volume the 2nd phase, 1998, with set theory and infinitesimal geometry for instrument, a kind of Stewart parallel manipulators Workspace modeling method is proposed.On the basis of definition work space, under being derived and frame linking ball pivot cone angle allowable constraint condition long at bar, solve the closed solution of working envelope.
(2) numerical method: mainly contain fast polar coordinate searching method, gridding method.These algorithms generally need depend on position-based routing, and need fixation ends actuator attitude, as J. P. Merlet. Determination of the orientation workspace of parallel manipulators. Journal of Intelligent and Robotic Systems, 1995,13:143-160 adopts fixation ends actuator attitude to search for position work space.Therefore, these algorithms are also existing poor for applicability, counting yield and the shortcoming such as solving precision is low in varying degrees.In fact, the motion of the sextuple space of SPM end effector is extremely complicated, causes many scholars to think to set up the general analytic model of work space to be very difficulty.
There is following defect when determining 6DOF parallel robot supporting leg fail operation space in the Workspace Determination for Parallel Manipulator method that document proposes above: 1) geometric method Project Realization difficulty is large, and operation efficiency is low.2) fast search process based on Inverse Kinematics Solution is difficult to provide some pose feasible solutions, makes a leg length of its correspondence just equal fault and props up leg length.
Summary of the invention
The object of the invention is to avoid now methodical deficiency, a kind of six-degree-of-freedom parallel robot fail operation space fast solution method is provided, the maintenance and debugging after the performance evaluation of guidance or auxiliary parallel robot and supporting leg break down; It is relatively applicable to adopting the electric cylinder of braking device as the motion control after the heavy load parallel robot generation supporting leg fault of driver part and Breakdown Maintenance, to improve the motion fault-tolerance of system, to shorten the security of maintenance time, raising maintenance process.
For achieving the above object, technical scheme of the present invention is, determines the shortest length value of each linear electrical actuator according to the properties of product of adopted linear electrical actuator , and the extended travel value that linear electrical actuator can realize ; According to these data, by Pseudorandom method, produce at random group supporting leg length data ; The position of steepest down position normal solution Algorithm for Solving motion platform is utilized according to known parallel robot pose parameter ; Finally obtain individual motion platform pose point, can obtain space scatter diagram during parallel robot leg fault.Detailed process comprises:
(1) for the linear electrical actuator with band brake apparatus as driving the six-degree-of-freedom parallel robot of supporting leg, determine the shortest length value of each linear electrical actuator according to the properties of product of adopted linear electrical actuator , and the extended travel value that linear electrical actuator can realize .When parallel robot supporting leg linear electrical actuator moves and controls fault, the length variations amount of fault supporting leg vanishing, for the supporting leg number broken down;
(2) adopt Pseudorandom method, produce at random ngroup leg long data ;
(3) by the zero-bit pose of parallel robot as parallel robot position forecast initial pose point, as known leg length of normal solution, according to the Jacobi matrix of parallel robot utilize the pose of steepest down position normal solution Algorithm for Solving motion platform ;
(4) above-mentioned process (3) is repeated nsecondary, draw ngroup supporting leg length data corresponding motion platform pose point, pointwise is drawn and is obtained work space figure.
" adopting Pseudorandom method, producing at random described in step (2) ngroup leg long data " carry out according to the following procedure:
A) adopt Pseudorandom method, provide the random number of 6 normal distributions between 0 to 1 ;
B) random number produced a) is utilized , the random square formation of structure 6 dimension ;
C) 6 dimensional vectors of supporting leg length elongation amount are calculated, Qi Zhong iindividual component is ;
D) the random square formation produced b) is utilized , calculate supporting leg length data .
" Jacobi matrix of parallel robot " described in step (3) carries out according to the following procedure:
A) according to known , and base platform six Hooke's hinges center vector , the center vector of motion platform six ball pivots solve supporting leg vector
In formula for moving platform center position vector under global coordinate system, for relatively rotating Transition of Coordinate matrix
B) according to supporting leg vector , solve and obtain parallel robot Jacobi matrix and be:
In formula , be the vector of unit length of bar supporting leg.
Tool of the present invention has the following advantages:
(1) the parallel robot normal solution algorithm iteration number of times proposed is few, fast convergence rate, solving precision are high; In algorithm, convergence precision can adaptability be determined according to the application background of algorithm, thus can make normal solution error-reduction, and increases the weight of the burden of computing hardly.
(2) in the real-time control of parallel robot, this algorithm can be adopted to calculate the pose of end component according to the measurement value of feedback of a leg joint, realize the pose monitoring to end effector or feedback, avoid and adopt multidimensional sensor to the measurement of end component, greatly reduce measurement cost.
(3) premised on position forecast, parallel robot can be launched and study, to improve control performance based on the control strategy of work space.
Accompanying drawing explanation
Fig. 1 is six-degree-of-freedom parallel robot schematic diagram;
Fig. 2 is pose solution procedure schematic diagram;
Fig. 3 solves work space process flow diagram;
Fig. 4 is the process flow diagram of solving condition process flow diagram;
Fig. 5 is experiment parallel robot schematic diagram;
Fig. 6 is work space three-dimensional plot;
Fig. 7 is work space y, z face perspective view;
Fig. 8 is work space x, y face perspective view;
Fig. 9 is work space x, z face perspective view.
Embodiment
Referring to accompanying drawing, the present invention is described in further detail.
With reference to Fig. 1, assistant adjustment of the present invention uses six-degree-of-freedom parallel robot model, MATLAB software.
As shown in Figure 1, respectively with the center of base platform and motion platform for initial point sets up global coordinate system and local coordinate system . be respectively the center of individual Hooke's hinge, ball pivot.With represent ? in position vector, represent ? in position vector .
Vector for the position vector of moving platform center p under global coordinate system, represent the position of moving platform and attitude, then the ithe vector of bar supporting leg under world coordinates is:
(1)
In formula, r for p- xyzrelatively o- xYZrotating Transition of Coordinate matrix:
Then ithe length of bar supporting leg is:
Order , by (1) formula two ends respectively to time variable differentiate:
In formula, be ithe vector of unit length of bar supporting leg.Gained knowledge can be obtained by robot motion:
In formula, for moving platform is around three coordinate axis x, ywith zvelocity of rotation.Comprehensively (2) (3) Shi Ke get:
In formula, be ithe vector of unit length of bar supporting leg, above formula two ends are with being multiplied by vector , arrangement can obtain:
Therefore, the Jacobi matrix of 6-UPS parallel robot is:
See Fig. 2, solve motion platform pose process, in Fig. 2 represent the initial pose point of motion platform, , wherein be the pose point of finally trying to achieve.
With reference to Fig. 3, the implementation process of the inventive method is as follows:
the first step,according to determining parallel robot supporting leg shortest length value , and variable quantity , determine supporting leg length data .
With the linear electrical actuator of band brake apparatus as driving the six-degree-of-freedom parallel robot of supporting leg, the shortest leg length of six-degree-of-freedom parallel robot can be determined according to the properties of product of adopted linear electrical actuator , supporting leg length variations amount can be obtained according to the extended travel value that adopted linear electrical actuator can realize , when parallel robot supporting leg linear electrical actuator moves and controls fault, the length variations amount of fault supporting leg vanishing, for the supporting leg number broken down.
second step,according to with , adopt Pseudorandom method, produce at random ngroup leg long data .
Adopt Pseudorandom method, provide the random number of 6 normal distributions between 0 to 1 , the random square formation of structure 6 dimension .Calculate 6 dimensional vectors of supporting leg length elongation amount, Qi Zhong iindividual component is .Utilize random square formation , calculate supporting leg length data .
3rd step, according to the zero-bit pose of parallel robot , utilize the pose of steepest down position normal solution Algorithm for Solving motion platform .
With reference to Fig. 4, specific implementation process is as follows:
A) knownly known the leg length of normal solution is carried out , based on a leg length of Inverse Kinematics Solution gained .
B) basis obtain supporting leg length difference:
C) basis calculate direction of steepest descent (negative gradient direction):
If two norms in the negative gradient direction of trying to achieve are less than the convergence precision of requirement , then tried to achieve motion platform pose ; Otherwise, new pose turn back to step a) to recalculate, until the convergence precision met the demands.
4th step,draw ngroup supporting leg length data corresponding motion platform pose point, pointwise is drawn and is obtained work space figure.
Above-mentioned process (3) is repeated nsecondary, use MATLAB to carry out drawing and obtain work space scatter diagram shape.
Advantage of the present invention further illustrates by the wave filter debugging application in Practical Project below:
Work space aided debugging method of the present invention is artificially set supporting leg fault and carries out experimental verification.Accompanying drawing 5 is shown in by the empirical model that this parallel robot space solves.The parameter of this empirical model is:
The pose of moving platform center under global coordinate system
Leg electric cylinder shortest length is:
The variation range of leg length:
Based on MATLAB software program, random generation one group of data , the random leg produced is long therefrom:
Conveniently will for drawing , hinge coordinate position parameter is all multiplied by , then tried to achieve corresponding to the long pose of leg by step 2 , given algorithm convergence precision .Below provide wherein one group of leg and grow solving of corresponding pose, for reference:
Random generation leg is long:
Supporting leg length variations amount
Jacobi matrix
Above data are brought into , try to achieve
, new pose
Continue to repeat above computation process, finally try to achieve , motion platform pose:
Be more than the process that one group of data solves, obtain the pose corresponding to 4000 groups of legs length so successively, show that the loose point of work space is as shown in Fig. 6, Fig. 7, Fig. 8, Fig. 9.
Above-mentioned numerical experiment results shows, adopt the present invention can than more quickly, determine the supporting leg fail operation space of 6DOF redundantly driven parallel device people exactly.

Claims (4)

1. six-degree-of-freedom parallel robot fail operation space fast solution method, the step of the method is as follows:
(1) for the linear electrical actuator with clamping device as driving the six-degree-of-freedom parallel robot of supporting leg, determine the shortest length value of every bar supporting leg according to the properties of product of adopted linear electrical actuator, , and the extended travel value that linear electrical actuator can realize ; When parallel robot supporting leg linear electrical actuator moves and controls fault, the length variations amount of fault supporting leg vanishing, for the supporting leg number broken down;
(2) adopt Pseudorandom method, produce at random ngroup leg long data ;
(3) by the zero-bit pose of parallel robot as parallel robot position forecast initial pose point, as known leg length of normal solution, utilize the pose of steepest down position normal solution Algorithm for Solving motion platform ; Parameter represent the 6DOF pose of parallel robot motion platform, wherein for the position coordinates vector at motion platform center, for the attitude angle vector that motion platform defines according to Eulerian angle;
(4) above-mentioned process (3) is repeated nsecondary, draw ngroup supporting leg length data corresponding motion platform pose point, pointwise is drawn and is obtained work space figure.
2. six-degree-of-freedom parallel robot fail operation space according to claim 1 fast solution method, is characterized in that " adopting Pseudorandom method, producing at random described in step (2) ngroup leg long data " carry out according to the following procedure:
2a) adopt Pseudorandom method, provide the random number of 6 normal distributions between 0 to 1 ;
2b) utilize 2a) the middle random number produced , the random square formation of structure 6 dimension ;
2c) calculate 6 dimensional vectors of supporting leg length elongation amount, Qi Zhong iindividual component is ;
2d) utilize 2b) the middle random square formation produced , calculate supporting leg length data .
3. six-degree-of-freedom parallel robot fail operation space according to claim 1 fast solution method, is characterized in that " utilizing the pose of steepest down position normal solution Algorithm for Solving motion platform described in step (3) " carry out according to the following procedure:
3a) knownly carry out known the leg length of normal solution , zero-bit pose ;
3b) based on known pose carry out a leg length of Inverse Kinematics Solution gained ; According to , obtain supporting leg length difference ;
3c) according to the Jacobi matrix of parallel robot calculate direction of steepest descent, i.e. negative gradient direction:
If two norms in the negative gradient direction of trying to achieve are less than default convergence precision , then tried to achieve motion platform pose ; Otherwise, new pose turn back to step 3b) recalculate, until meet the convergence precision preset;
3d) finally obtain the result pose of parallel robot position forecast .
4. six-degree-of-freedom parallel robot fail operation space according to claim 3 fast solution method, is characterized in that step 3c) described in " the Jacobi matrix of parallel robot " carry out according to the following procedure:
4a) according to known and the center vector of base platform six Hooke's hinges , the center vector of motion platform six ball pivots solve supporting leg vector
In formula for moving platform center position vector under global coordinate system, for relatively rotating Transition of Coordinate matrix
4b) according to supporting leg vector , solve and obtain parallel robot Jacobi matrix and be:
In formula be the vector of unit length of bar supporting leg; c, srepresent sin respectively, cos function, parameter for the attitude angle variable that motion platform defines according to Eulerian angle.
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