CN103009389B - Track planning method of redundant space mechanical arm for on-track catching - Google Patents
Track planning method of redundant space mechanical arm for on-track catching Download PDFInfo
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- CN103009389B CN103009389B CN201210520049.0A CN201210520049A CN103009389B CN 103009389 B CN103009389 B CN 103009389B CN 201210520049 A CN201210520049 A CN 201210520049A CN 103009389 B CN103009389 B CN 103009389B
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Abstract
The invention relates to a track planning method of a redundant space mechanical arm for on-track catching. The catching operation of the space mechanical arm is divided into a rough catching stage and a fine catching stage, so that problems are simplified. By aiming at outstanding problems of different stages, different planning algorithms are adopted. In the rough catching stage, a track searching algorithm based on configuration space is adopted, and the algorithm is based on the test in the configuration space; and in the fine catching stage, a pseudo-inverse algorithm based on kinematics is adopted, and the final precise catching is guaranteed by compensating the relative movement of a target.
Description
Technical field
The present invention relates to the method for planning track that a kind of redundant space mechanical arm is arrested in-orbit, belong to Spacecraft Attitude Control field.
Background technology
Space manipulator is arrested in operation in-orbit, in order to fuel saving, the position of spatial manipulation platform is not controlled, only stability contorting is carried out to the attitude of spatial manipulation platform, belong to the free flying robot that attitude is controlled, each joint angle only having mechanical arm that therefore can be controlled arbitrarily in the variable of system model.Namely the basic demand of trajectory planning is that the position of the end effector expected and attitude are oriented to target, determine the Angle Position of each joint angle, angular speed and angular acceleration track by certain algorithm, thus realize mechanical arm by controller arrest operation.Here redundancy refers to, mechanical arm has 7 frees degree, arrive except end effector can be made except the position and attitude of specifying, also there is the unnecessary free degree for evading the collision with barrier, the collaborative manipulation of multiple mechanical arm can be adopted simultaneously, make to change end effector flexibly, firmly arrest noncooperative target safely and reliably.
If mechanical arm collides with barrier arresting in operation, then spatial manipulation platform is subject to the effect of unknown reaction force, unknown disturbances power and disturbance torque are brought to whole system, platform is made to occur unforeseen motion, destroy the attitude stabilization of platform and the motion stabilization of mechanical arm, not only can cause the failure of arresting operation, also may cause uncertain infringement to spatial manipulation platform.Therefore, evading collision is that space manipulator arrests the factor must considered in operation trace planning.In addition, the singular problem of mechanical arm and the compensation problem of target relative movement are also the problems must considered in trajectory planning.
The trajectory planning algorithm of mechanical arm mainly contains Pseudoinverse algorithm, Artificial Potential Field Method and the free-space Method based on configuration space.Pseudoinverse algorithm easily occurs unusual in solving.There is local minimum problem in Artificial Potential Field Method, and for challenge, amount of calculation is excessive, is comparatively applicable to the trajectory planning of mobile robot.In configuration space, the coordinate of configuration point is each joint angle of mechanical arm.By kinematic relation, affector object pose and barrier are mapped to configuration space by working space, obtain target configuration point and configuration space obstacle.Namely collision-free Trajectory Planning will search out and connect initial and target configuration point and without the path of obstacle in configuration space.Method all demand solution configuration spaces of current existence, very large for multi-degree-of-freemechanical mechanical arm amount of calculation, configuration space obstacle can only be obtained by discretization, need take a large amount of internal memory for improving precision.This causes existing algorithm cannot be applied to the space manipulator of computational resource anxiety, is difficult to be applied to space mission.
Summary of the invention
Technical problem to be solved by this invention is: overcome the deficiencies in the prior art, provides the method for planning track that a kind of collisionless is arrested in-orbit without unusual redundant space mechanical arm, and the method engineering construction is simple, can save computational resource.
Technical scheme of the present invention is:
The method for planning track that a kind of redundant space mechanical arm is arrested in-orbit; Described redundant space mechanical arm is arranged on spatial manipulation platform, and mechanical arm tail end installs end effector; Spatial manipulation platform is equipped with vision measurement sensor and spaceborne computer; Redundant space mechanical arm arrest in-orbit to as if space non-cooperative target; The operation of arresting of space manipulator is divided into the section of arresting and the meticulous section of arresting roughly,
The method for planning track of the section of arresting comprises the steps: roughly
(1.1) by desired locations and the attitude of the section of arresting end effector roughly, collisionless target configuration derivation algorithm is utilized to try to achieve collisionless target configuration;
(1.2) according to mechanical arm current configuration and target configuration, utilize collisionless path search algorithm, try to achieve the path in collisionless configuration space;
(1.3) utilize path optimization's algorithm, the path in collisionless configuration space is optimized to the motion sequence of each joint angle of the mechanical arm that acquisition is not collided with barrier;
The method for planning track of the meticulous section of arresting comprises the steps:
(2.1) movement locus of end effector position/attitude is designed in advance by the end effector position/attitude of the capture target expected and the position/attitude of current end affector, speed trajectory and acceleration trajectory;
(2.2) target relative movement obtained according to the measurement of vision measurement sensor is to the movement locus of described end effector position/attitude, speed trajectory and acceleration trajectory compensate the movement locus obtaining the end effector position/attitude after compensating, speed trajectory and acceleration trajectory;
(2.3) according to the movement locus of the end effector position/attitude after compensation, speed trajectory and acceleration trajectory adopt the angular speed track and the angular acceleration track that obtain each joint angle of mechanical arm based on kinematic Pseudoinverse algorithm.
In described step (1.1), collisionless target configuration derivation algorithm is as follows:
First target configuration is calculated according to target configuration derivation algorithm;
Target configuration derivation algorithm be input as each current joint angle of mechanical arm, and the position of end effector needed for capture target and attitude, each joint angle that target configuration derivation algorithm utilizes numerical integration method to solve mechanical arm inverse kinematics equation to obtain needed for capture target, i.e. target configuration;
Whether the target configuration then utilizing collision detection algorithm to judge to calculate collides with barrier, if collided with barrier, then current to the mechanical arm inputing to target configuration derivation algorithm joint angle adjusts, calculating is re-started, until obtain collisionless target configuration according to target configuration derivation algorithm.
In described step (1.2), the total angle of rotation of each joint angle from current configuration to target configuration is divided into N part by collisionless path search algorithm, each joint angle is turned over every part of corner and be defined as a son motion, thus define pN son motion, wherein p is joint number;
The son motion of note i-th joint angle is son motion i, i=1,2 ..., P, pN son motion with the arrangement of suitable order, is formed the motion sequence of a pN step by collisionless path search algorithm;
Setting serial number gencration function F (i), this function generates next step sub-motion sequence number that will sound out by current sub-motion sequence number i; F (i) is for increasing progressively, successively decreasing or randomly generated test problems;
Represent step number with m, T represents exploration total degree, T
maxexpression can accept maximum exploration number of times;
Collisionless path search algorithm step is as follows:
1) initialize, make m=1, T=1, choose i, T is set
max;
2) judge whether m equals pN+1;
If m=pN+1, then export collisionless joint motions sequence, and terminate searching algorithm; Otherwise utilize collision detection algorithm, judge that mechanical arm m walks execution motion i and whether collides with barrier; If do not collided, mechanical arm performs and gives motion i, and keeps a record, and performs step 3); If collision, perform step 4);
3) m=m+1, i=F (i), T=T+1, perform step 6);
4) judge whether m step has soundd out all possible son motion i, if so, performs step 5); Otherwise i=F (i), T=T+I, perform step 6);
5) rebound m-1 walks, and makes m=m-1; Judge whether m step has soundd out all possible son motion, if re-execute step 5); Otherwise make i=F (i (m)), i (m) refers to the original sub-motion sequence number adopted of m step, and T=T+1, performs step 6);
6) judge whether T equals T
max,
If T=T
max, then output algorithm is searched for unsuccessfully and is terminated searching algorithm, otherwise performs step 2);
If algorithm search failure, then different explorations rule F (i) or increase path segmentation constant N is adopted to re-execute collisionless path search algorithm.
In described step (1.3), path optimized algorithm method is as follows: two son motions adjacent in the motion sequence of each joint angle of the collisionless mechanical arm searched by collisionless path search algorithm are merged into a son motion, and whether the son motion after then adopting collision detection algorithm combining data detection collides with barrier; If do not collided, then these two motions are merged; If collide, cancel merging; Son motion adjacent in the motion sequence obtained repeats said process, until cannot merge further.
Described collision detection algorithm method is as follows: mechanical arm is reduced to the line segment that some connect, then discretization is spatially carried out, the discrete a series of point turned on mechanical arm, barrier is merotomized, every part finds the envelope of a convex polyhedron, then replaces barrier itself with these convex polyhedrons are approximate; Remember that the central point in i-th face of certain convex polyhedron is P
i, the exterior normal vector in i-th face is
remember that point to be detected is P
t, then P is put
tthe sufficient and necessary condition being positioned at this convex polyhedron is: all faces for convex polyhedron have
if it is inner at barrier to there is measuring point to be checked, then thinks that mechanical arm and barrier are collided, otherwise think that mechanical arm and barrier can not collide.
The angular speed track of each joint angle of the mechanical arm in described step (2.3)
formula is:
Wherein, X
er(t) and
for movement locus and the speed trajectory of the end effector position/attitude after compensation, X
et () is the position/attitude of end effector in mechanical arm actual motion process; δ (X
er(t)-X
e(t)) proportion adjustment item for adding, wherein δ > 0; J
+=J
t(JJ
t)
-1for the pseudoinverse of Jacobian matrix J;
The joint angle acceleration trajectory of each joint angle of described mechanical arm
for:
Wherein,
for the acceleration trajectory of the end effector position/attitude after compensation;
for the time-derivative of the pseudoinverse of Jacobian matrix J.
The method for planning track of the described meticulous section of arresting also comprises the steps: the redundant degree of freedom utilizing mechanical arm, adopts idle running to make mechanical arm away from singular configuration.
The angular speed track of each joint angle of the mechanical arm of band idle running is
P
j=(I-J
t(JJ
t)
-1j) be the orthogonal intersection cast shadow matrix of Jacobian matrix J; Column vector y=α v;
ξ (q) is unusual tolerance: ξ (q)=det (JJ
t); Scalar parameter α is chosen for:
subscript ". " represents derivative operation; Transpose operation is asked in subscript " T " representative; Subscript "-1 " represents inversion operation;
represent scalar ξ and gradient is asked to vector q.
The present invention's beneficial effect is compared with prior art:
(1) the present invention be a kind of completely newly arrest the collisionless of operation in-orbit without unusual trajectory planning algorithm for spatial redundancy mechanical arm.By the operation of arresting of space manipulator is divided into the section of arresting and the meticulous section of arresting roughly, problem is simplified.For the outstanding problem of different phase, have employed different planning algorithms.Adopt the track search algorithm based on configuration space in the section of arresting roughly, this algorithm is based on the exploration in configuration space; Adopt based on kinematic Pseudoinverse algorithm in the meticulous section of arresting, by ensureing final accurately arresting to the compensation of target relative movement.
(2) the method is in the section of arresting roughly by the track search algorithm based on configuration space, achieves evading barrier.Configuration space is with the abstract space of each joint angle of mechanical arm higher-dimension that is coordinate.This track search algorithm based on souning out in configuration space, do not need to solve configuration space, soundd out by collision detection and just can find out collisionless path in configuration space, compared with prior art, computational resource and internal memory are saved, be applicable to the quick planning of the track of the space manipulator of computational resource anxiety, for aerospace engineering application provides a kind of simple effective method.By track optimizing algorithm, the final track obtained is comparatively level and smooth, is easy to Project Realization.
(3) the method the meticulous section of arresting by add target relative movement compensate based on kinematic Pseudoinverse algorithm, can by the metrical information of the visual acuity device on spatial manipulation platform, obtain the relative motion of target, the relative motion of target is incorporated in Pseudoinverse algorithm, realizes the compensation to target relative movement.In addition, in Pseudoinverse algorithm, additional proportion regulates item, compensates the tracking error of track, increases antijamming capability and the robustness of system, ensure that in the meticulous section of arresting, mechanical arm accurately arresting target.
(4) involved in the present invention methods engineering is implemented simple, and popularizing application prospect is good.The method not only meets the basic demand of space manipulator collisionless without unusual trajectory planning, and algorithm is simply easy to implement, save computing time, save computational resource and internal memory, be specially adapted to the quick trajectory planning of the space manipulator of computational resource anxiety.The method is particularly useful for space manipulator arresting fast noncooperative target, is also applicable to the collision-free Trajectory Planning of mechanical arm on lunar rover.
Accompanying drawing explanation
Fig. 1 is that extraterrestrial target schematic diagram arrested by spatial manipulation platform of the present invention;
Fig. 2 is the schematic flow sheet of collisionless of the present invention without unusual mechanical arm trajectory planning algorithm;
Fig. 3 is the schematic flow sheet of collisionless path search algorithm in the present invention;
Fig. 4 is initial configuration and the rotating shaft positive direction of 7 degree-of-freedom manipulators in the present invention;
Fig. 5 is the level and smooth front collisionless path of algorithm in the present invention;
Fig. 6 is the level and smooth front joint angle speed of algorithm in the present invention; Wherein in Fig. 6 (a) curve 11,12,13 be the 1st respectively, 2, the angular speed change curve in 3 joints; In Fig. 6 (b) curve 14,15,16 be the 4th respectively, 5, the angular speed change curve in 6 joints;
Fig. 7 be in the present invention algorithm level and smooth after collisionless path;
Fig. 8 be in the present invention algorithm level and smooth after joint angle speed; Wherein in Fig. 8 (a) curve 21,22,23 be the 1st respectively, 2, the angular speed change curve in 3 joints; In Fig. 8 (b) curve 24,25,26 be the 4th respectively, 5, the angular speed change curve in 6 joints.
Detailed description of the invention
The invention provides collisionless that a kind of redundant space mechanical arm arrests in-orbit without unusual method for planning track, as shown in Figure 1, the equipment that method is relied on comprises spatial manipulation platform 1 and is arranged on the mechanical arm system 3 on spatial manipulation platform; Spatial manipulation platform is equipped with vision measurement sensor and spaceborne computer; Mechanical arm tail end is provided with end effector; Mechanical arm arrest to as if space non-cooperative target 2.Generally can refer to the controllable satellite in-orbit with mechanical arm for spatial operation platform, space non-cooperative target refers generally to the uncontrollable satellite in space etc.Mechanical arm system 3 comprises n portion mechanical arm, and every portion mechanical arm comprises p joint 4, is designated as the 1st joint from spatial manipulation platform successively, and the 2nd joint ... p joint, p joint is installed end effector 5.The collisionless being mechanical arm system 3 capture target provided by the invention is without unusual method for planning track.
Such as mechanical arm system 3 can comprise 3 mechanical arms, and each mechanical arm has 7 frees degree.
Below in conjunction with accompanying drawing 2 and example, the present invention is elaborated.As shown in Figure 2 space manipulator whole is arrested operation and be divided into the section of arresting and the meticulous section of arresting roughly.In the section of arresting roughly, the trajectory planning problem of space manipulator is reduced to the trajectory planning problem of fixed pedestal mechanical arm, adopt the track search algorithm based on configuration space, end effector is moved to the state of position close to capture target and attitude, revised by the meticulous section of arresting in the lump with the position of final capture target and the difference of attitude and the section of arresting is caused by target relative movement roughly error.And the meticulous section of arresting operational ton is very little, target relative movement is not obvious, adopts simultaneously and carries out trajectory planning based on kinematic Pseudoinverse algorithm, and carry out real-Time Compensation to the relative motion of target in the algorithm, final realization is accurately arrested.
One, the trajectory planning of the section of arresting roughly
Specifically comprise the steps:
(1.1) by desired locations and the attitude of the section of arresting end effector roughly, collisionless target configuration derivation algorithm is utilized to try to achieve collisionless target configuration;
The desired locations of the section of arresting end effector and attitude are the position and attitude expecting at the end of the section of arresting roughly to reach roughly, the position of the end effector namely needed for capture target and attitude.
First described collisionless target configuration derivation algorithm calculates target configuration according to target configuration derivation algorithm;
Target configuration derivation algorithm be input as each current joint angle of mechanical arm, i.e. Current mechanical arm configuration, and the position of end effector needed for capture target and attitude, export each joint angle needed for capture target, i.e. target configuration.The method adopted solves mechanical arm inverse kinematics equation for utilizing numerical integration method (as 4 rank Runge-Kutta methods)
The initial joint angle of inverse kinematics equation integration is current each joint angle of mechanical arm, and the end value of integration is the output of algorithm: each joint angle needed for capture target, i.e. target configuration.In equation, X
efor mechanical arm tail end affector position/orientation vector;
for mechanical arm tail end affector position/orientation vector X that the position of the end effector needed for the position of current end affector and attitude, capture target and attitude and time of arresting are designed
ethe characteristics of motion, can be the polynomial function about the time or SIN function; Q is joint of mechanical arm angle column vector;
for joint of mechanical arm angular speed column vector; J
+(q)=J
t(JJ
t)
-1for the generalized inverse of Jacobian matrix J; Subscript ". " represents derivative operation; Subscript " T " represents transpose operation; Subscript "-1 " represents inversion operation.
Whether the target configuration then utilizing collision detection algorithm to judge to calculate collides with barrier, if the target configuration that integration obtains and barrier are collided, then can to the input of target configuration derivation algorithm: the current joint angle of mechanical arm adjusts (as changed the angle of first joint angle) arbitrarily, calculating is re-started according to target configuration derivation algorithm, obtain the target configuration of end effector position and the attitude met needed for capture target, until obtain collisionless target configuration.The said process just joint angle current to the mechanical arm inputing to target configuration derivation algorithm adjusts, and the current joint angle of mechanical arm does not change.
(1.2) according to mechanical arm current configuration and target configuration, utilize collisionless path search algorithm, try to achieve the path in collisionless configuration space;
As shown in Figure 3, collisionless path search algorithm thinking is as follows: algorithm is input as the configuration (initial configuration) of Current mechanical arm, the parameter of the target configuration that mechanical arm will arrive and barrier, exports the motion sequence of each joint angle for the mechanical arm of not colliding with barrier.Make positive integer N be path segmentation constant, the total angle of rotation of each joint angle from current configuration to target configuration is divided into N part, each joint angle is turned over every part of corner and be defined as a son motion, just define pN son motion, wherein p is joint number.As long as so N is enough large, path is split enough thin, just can become a collisionless dog leg path with this pN son motion by suitable sequential concatenation.
The son motion of note i-th joint angle is son motion i, i=1,2 ..., p, the task of searching algorithm is by constantly souning out the order determining this pN son motion.Be divided into pN step by total path, by pN son motion with the arrangement of suitable order, form the motion sequence of a pN step.
Setting serial number gencration function F (i), this function generates next step sub-motion sequence number that will sound out by current sub-motion sequence number i, and F (i) can choose as required, as increased progressively, successively decreasing or stochastic generation.Represent step number with m, T represents exploration total degree, T
maxexpression can accept maximum exploration number of times, and algorithm is as follows:
1) initialize, m=1, T=1, choose i, arranges T
max;
2) if m=pN+1, algorithm successfully terminates, Output rusults, otherwise utilizes collision detection algorithm, judges that mechanical arm m walks execution motion i and whether collides with barrier.If do not collided, mechanical arm performs son motion i (this is simulation in a computer), and keeps a record, and performs step 3); If collision, perform step 4);
3) m=m+1, i=F (i), T=T+1, perform step 6);
4) judge whether m step has soundd out all possible son motion, if so, performs step 5); Otherwise i=F (), T=T+1, perform step 6);
5) rebound m-1 walks, and makes m=m-1.Judge whether m step has soundd out all possible son motion, if re-execute step 5); Otherwise make i=F (i (m)), i (m) refers to the original sub-motion sequence number adopted of m step, and T=T+1, performs step 6);
6) if T=T
max, algorithm unsuccessfully terminates, otherwise performs 2.
If this algorithm search failure, then can adopt different explorations rule F (i) or increase path segmentation constant N and again search for.Souning out rule F (i) can have multiple, and according to random exploration, each result soundd out all can be different.Sound out the diversity of rule, ensure that the validity of searching algorithm.Increase the success rate that path segmentation constant N then can increase search, but this is to increase amount of calculation for cost.
(1.3) utilize path optimization's algorithm, the path in collisionless configuration space is optimized to the motion sequence of each joint angle of the mechanical arm that acquisition is not collided with barrier.
Algorithm is input as the motion sequence of each joint angle of the mechanical arm of not colliding with barrier that collisionless path search algorithm obtains, and exports the motion sequence of each joint angle of the mechanical arm of not colliding with barrier after for optimization.Attempt two son motions adjacent in the motion sequence of each joint angle of the collisionless mechanical arm searched by collisionless path search algorithm and be merged into a son motion, two son motions that in chronological sequence order is carried out in turn before carried out, whether the son motion then after combining data detection collides with barrier simultaneously.If do not collided, then these two son motions are merged; If collide, cancel merging.Continuous trial, until son motion adjacent in the motion sequence obtained cannot merge further.
Described collision detection algorithm can detect a motion process of mechanical arm or whether some configurations collide with barrier.
Collision detection algorithm method is as follows: the some motion processes being input as mechanical arm to be detected of algorithm, i.e. each joint angle characteristics of motion in time.First the motion process of mechanical arm is carried out temporal discretization, the discrete mechanical arm for being in a series of configuration; Under each configuration, mechanical arm being reduced to the line segment that some connect, then carrying out discretization spatially, the discrete a series of point turned on mechanical arm, is whether test point is inner at barrier by problem reduction; Barrier is merotomized, and every part finds the envelope of a convex polyhedron, then replaces barrier itself with these convex polyhedrons are approximate.Remember that the central point in i-th face of certain convex polyhedron is P
i, the exterior normal vector in i-th face is
remember that point to be detected is P
t, then P is put
tthe sufficient and necessary condition being positioned at this convex polyhedron is: all faces for convex polyhedron have
if it is inner at barrier to there is measuring point to be checked, then thinks that mechanical arm and barrier are collided, otherwise think that mechanical arm and barrier can not collide.
Two, the trajectory planning of the meticulous section of arresting
The method for planning track of the meticulous section of arresting comprises the steps:
(2.1) movement locus of end effector position/attitude is designed in advance by the end effector position/attitude of the capture target expected and the position/attitude of current end affector, speed trajectory and acceleration trajectory;
After the section of arresting terminates roughly, the visual acuity device on spatial operation platform is utilized to carry out measuring the position/attitude of the end effector obtaining the capture target expected to the position/attitude of target being arrested a little, and do difference with the position/attitude of current end affector, then the end effector position connecting desired value and currency/attitude motion track, speed trajectory and an acceleration trajectory is designed.
The speed trajectory of the end effector position/attitude designed in advance and acceleration trajectory are 0 in the starting point operated and destination county.
(2.2) target relative movement obtained according to the measurement of vision measurement sensor is to the movement locus of described end effector position/attitude, speed trajectory and acceleration trajectory compensate the movement locus obtaining the end effector position/attitude after compensating, speed trajectory and acceleration trajectory; Thus the real-Time Compensation realized the relative motion of target;
(2.3) according to the movement locus of the end effector position/attitude after compensation, speed trajectory and acceleration trajectory adopt the angular speed track and the angular acceleration track that obtain each joint angle of mechanical arm based on kinematic Pseudoinverse algorithm; Thus the position of end effector and attitude can be made to follow the movement locus designed in advance, the mechanical arm of speed trajectory and acceleration trajectory.
The angular speed track of each joint angle of mechanical arm
formula is:
Wherein, X
er(t) and
for movement locus and the speed trajectory of the end effector position/attitude after compensation, X
et () is the position/attitude of end effector in mechanical arm actual motion process; δ (X
er(t)-X
e(t)) proportion adjustment item for adding, can compensate the tracking error of actual motion with the track designed in advance, increase antijamming capability and robustness, wherein the δ > 0 of system; J
+=J
t(JJ
t)
-1for the pseudoinverse of Jacobian matrix J;
Subscript " " represents derivative operation; Subscript " T " represents transpose operation; Subscript "-1 " represents inversion operation.
Joint angle acceleration trajectory is:
Wherein,
for the acceleration trajectory of the end effector position/attitude after compensation;
for the time-derivative of the pseudoinverse of Jacobian matrix J.
(2.4) utilize the redundant degree of freedom of mechanical arm, adopt idle running to make mechanical arm away from singular configuration.
Utilize the redundant degree of freedom of mechanical arm, adopt idle running to make mechanical arm away from singular configuration, final joint angle speed is
Wherein
for the Basic Solutions of inverse kinematics obtained in step (203); P
j=(I-J
t(JJ
t)
-1j) be the orthogonal intersection cast shadow matrix of Jacobian matrix J; Column vector y=α v;
ξ (q) is unusual tolerance: ξ (q)=det (JJ
t); Scalar parameter α is chosen for:
subscript " " represents derivative operation; Transpose operation is asked in subscript " T " representative; Subscript "-1 " represents inversion operation;
represent scalar ξ and gradient is asked to vector q.
Embodiment 1
Embodiment 1 is mainly used in verifying the validity of the algorithm of the section of arresting roughly.
(1) 7 degree-of-freedom manipulators are devised.The geometric parameter of mechanical arm is as shown in table 1, and wherein Section 1 arm mounting points represents in base coordinate system.Initial configuration when each joint angle is 0 and the positive direction of each corner are shown in Fig. 4, and in figure, black line segment represents mechanical arm, and black circles representative connects the joint of each joint mechanical arm, and juxta-articular arrow represents the positive direction of each joint rotation angle.Now the body coordinate system of base coordinate system and Ge Jie arm overlaps, and sees the coordinate system oxyz in Fig. 4.In Fig. 4,6 is the pedestal mounting points of mechanical arm, and 7 is the end effector of mechanical arm, i.e. Section 7 arm.The validity of the algorithm of the section of arresting roughly is verified below for this mechanical arm.
Table 1 respectively saves the mounting points location parameter of arm
(2) set the initial configuration of mechanical arm as q
s, each joint angle is (-1.5707,3.1414,1,0,0,0,0) rad.Following parameter describes in base coordinate system: at the end of the section of arresting roughly of expectation, end effector endpoint location is (2.0,0.3,0.5) m; At the end of the section of arresting roughly expected, end effector axis direction cosine is (0.4699 ,-0.1987,0.8601); Barrier is the seamed edge cuboid parallel with reference axis, and coordinate range is χ: 1.2 ~ 1.7m, y:0 ~ 0.5m, z:0 ~ 0.5m.Note, object pose does not retrain the rotation of end effector along axis, and Section 7 arm axle line and the 7th joint angle shaft parallel, so the 7th joint angle can not move, be in fact the end effector pose requirement that a 6DOF mechanical arm meets 5DOF.
(3) first by collisionless target configuration derivation algorithm, solve one and meet the requirement of end effector pose and the target configuration qE do not collided with barrier, each joint angle is (-0.0567,4.6127,1.4569 ,-2.1691,0.9561 ,-0.3024,0) rad.
(4) then a path of not colliding with barrier is searched out by collisionless path search algorithm, constant N=10 is separated in path, 7th joint angle corner does not change, it is in fact the search problem of 6 dimension spaces, be divided into into 6N=60 son motion, function F (i) adopts and increases progressively exploration.Sound out through 64 times, find a collisionless motion sequence: 1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,2,3,4,5,6,2,3,4,5,6,2,3,4,5,6,1,1,1.Can see that the previous section of sequence is identical with exploration order, not adjust, adjust to avoid obstacle to exploration order at the algorithm below of sequence.Here the collisionless path obtained not is final result, but in order to the necessity of path optimization's algorithm is described, we provide the motion process of mechanical arm in the collision-free motion sequence do not optimized and the curve movement of joint angle here.After obtaining the joint angle motion sequence of mechanical arm, also need to provide the characteristics of motion that mechanical arm to complete in sequence each joint angle needed for step.Setting each cross-talk time of doing exercises is 4s, and the joint angle characteristics of motion adopts about the multinomial of time, ensure the motion of every height start and at the end of, joint angle speed and angular acceleration are 0.The motion process of mechanical arm is shown in Fig. 5, records the position of one-time mechanical arm in figure at set intervals, and in figure, 8 is mechanical arm initial configuration, and 9 is the target configuration slightly at the end of the section of arresting, and 6 is the pedestal mounting points of mechanical arm, and 10 is barrier.As shown in Figure 5, mechanical arm reaches target configuration from bottom cut-through thing.Fig. 6 gives the angular speed curve of each joint angle.As can be seen from Figure 6, joint angle speed is level and smooth not as a whole.Therefore it is necessary for being optimized this path.
(5) adopt path smooth algorithm smoothing to dog leg path obtained above below.Found that the sequence of original 60 son motion compositions only need be divided into 2 steps to get final product avoiding obstacles, the 1st step moves to neutral configuration by initial configuration, and the 2nd step is by neutral configuration to target configuration, and each configuration is shown in Table 2.Obtain initial configuration of each step and terminate after configuration, also needing to provide the characteristics of motion that mechanical arm completes each joint angle needed for step.Setting each step run duration is 20s, and the joint angle characteristics of motion adopts about the multinomial of time, ensure each step start and at the end of, joint angle speed and angular acceleration are 0.The motion process of mechanical arm as shown in Figure 7, records the position of one-time mechanical arm at set intervals in figure, in figure, 8 is mechanical arm initial configuration, 9 is the target configuration at the end of the slightly section of arresting, 6 is the pedestal mounting points of mechanical arm, and 10 is barrier, and 11 is the neutral configuration of mechanical arm.The mechanical arm first step moves to neutral configuration 11 by initial configuration 8, and second step moves to target configuration 9 by neutral configuration 11.As seen from Figure 7, mechanical arm reaches target configuration from bottom cut-through thing, and mechanical arm, in this two steps motion process, does not all have to collide with barrier.Fig. 8 gives the angular speed curve of each joint angle.As can be seen from Figure 8, compared with Fig. 6, the characteristics of motion of each joint angle of mechanical arm is very level and smooth, be easy to realize, and the operating time reduces greatly, is convenient to arresting fast noncooperative target.
Three crucial configurations (rad) in the level and smooth rear path of table 2
Embodiment 2
Embodiment 2 gives the control method of the whole capture process of redundant space mechanical arm.
(1) mechanical arm in embodiment 1 is arranged on a spatial operation platform, a noncooperative target is arrested.First measuring by arresting mission requirements and sensor, determining noncooperative target arrests a little, the position of end effector required when calculating capture target and attitude.
(2) whole capture process is divided into the section of arresting and the meticulous section of arresting roughly.The initial state of the section of arresting is the current configuration of mechanical arm roughly, the done state of the section of arresting roughly is set as the end effector of mechanical arm is positioned at and arrests a distance, a top (such as 20cm).
(3) at the end of the section of arresting roughly set by previous step, the position of end effector and attitude, by collisionless target configuration derivation algorithm, obtain collisionless target configuration.By current configuration and the target configuration of mechanical arm, try to achieve level and smooth collisionless joint angle motion sequence by collisionless path search algorithm and path optimization's algorithm.According to the time requirement of the task of arresting, the run duration (such as each walks 20s consuming time) of each step in setting collision-free motion sequence.Then according to the run duration of setting, the design joint angle characteristics of motion is the polynomial function of time, ensure each step start and at the end of, joint angle speed and angular acceleration are 0.Subsequently, the control system of spatial operation platform, adopt certain control method (such as PID controller), the motor at driving device shoulder joint place, follow the given joint angle characteristics of motion, thus realize the target of the section of arresting roughly, the end effector of mechanical arm is moved to without collision and arrests a distance, top.
(4) after the section of arresting terminates roughly, by the sensor on spatial operation platform, measure the position of arresting a little obtained now, design the movement locus of end effector position and attitude, speed trajectory and acceleration trajectory, adopt based on kinematic Pseudoinverse algorithm, real-time resolving goes out the position at joint of mechanical arm angle, speed and acceleration information, by the control system of spatial operation platform, adopt certain control method (such as PID controller), the motor at driving device shoulder joint place, follow the joint angle characteristics of motion that real-time resolving goes out.Simultaneously, by the sensor on spatial operation platform, measurement target arrest a little relative to the motion of spatial operation platform, in Pseudoinverse algorithm, the relative motion of target is compensated, thus realize final accurately arresting, namely end effector accurately moves to and target to arrest some place by mechanical arm.
This detailed description of the invention part is arrested for the redundant mechanical arm target of 7 frees degree and is achieved collisionless without unusual trajectory planning, and engineering demands, is easy to engineer applied, has good promotion prospect.
The content be not described in detail in description of the present invention belongs to the known technology of those skilled in the art.
Claims (5)
1. the redundant space mechanical arm method for planning track of arresting in-orbit; Described redundant space mechanical arm is arranged on spatial manipulation platform, and mechanical arm tail end installs end effector; Spatial manipulation platform is equipped with vision measurement sensor and spaceborne computer; Redundant space mechanical arm arrest in-orbit to as if space non-cooperative target; It is characterized in that, the operation of arresting of space manipulator is divided into the section of arresting and the meticulous section of arresting roughly,
The method for planning track of the section of arresting comprises the steps: roughly
(1.1) by desired locations and the attitude of the section of arresting end effector roughly, collisionless target configuration derivation algorithm is utilized to try to achieve collisionless target configuration;
Collisionless target configuration derivation algorithm is as follows:
First target configuration is calculated according to target configuration derivation algorithm; Target configuration derivation algorithm be input as each current joint angle of mechanical arm, and the position of end effector needed for capture target and attitude, each joint angle that target configuration derivation algorithm utilizes numerical integration method to solve mechanical arm inverse kinematics equation to obtain needed for capture target, i.e. target configuration; Mechanical arm inverse kinematics equation is
the initial joint angle of inverse kinematics equation integration is current each joint angle of mechanical arm, end value each joint angle needed for capture target of integration; X
efor mechanical arm tail end affector position/orientation vector;
for mechanical arm tail end affector position/orientation vector X that the position of the end effector needed for the position of current end affector and attitude, capture target and attitude and time of arresting are designed
ethe characteristics of motion, be the polynomial function about the time; Q is joint of mechanical arm angle column vector;
for joint of mechanical arm angular speed column vector; J
+q () is the generalized inverse of Jacobian matrix J;
Whether the target configuration then utilizing collision detection algorithm to judge to calculate collides with barrier, if collided with barrier, then current to the mechanical arm inputing to target configuration derivation algorithm joint angle adjusts, calculating is re-started, until obtain collisionless target configuration according to target configuration derivation algorithm;
(1.2) according to mechanical arm current configuration and target configuration, utilize collisionless path search algorithm, try to achieve the path in collisionless configuration space;
(1.3) utilize path optimization's algorithm, the path in collisionless configuration space is optimized to the motion sequence of each joint angle of the mechanical arm that acquisition is not collided with barrier;
The method for planning track of the meticulous section of arresting comprises the steps:
(2.1) the visual acuity device on spatial operation platform is utilized to carry out measuring the position/attitude of the end effector obtaining the capture target expected to the position/attitude of target being arrested a little, and do difference with the position/attitude of current end affector, then end effector position/attitude motion track that connects desired value and currency is designed, speed trajectory and acceleration trajectory, the speed trajectory of design and acceleration trajectory are 0 in the starting point operated and destination county;
(2.2) target relative movement obtained according to the measurement of vision measurement sensor is to the movement locus of described end effector position/attitude, speed trajectory and acceleration trajectory compensate the movement locus obtaining the end effector position/attitude after compensating, speed trajectory and acceleration trajectory;
(2.3) according to the movement locus of the end effector position/attitude after compensation, speed trajectory and acceleration trajectory adopt the angular speed track and the angular acceleration track that obtain each joint angle of mechanical arm based on kinematic Pseudoinverse algorithm;
(2.4) utilize the redundant degree of freedom of mechanical arm, adopt idle running to make mechanical arm away from singular configuration;
The angular speed track of each joint angle of the mechanical arm of band idle running is
P
j=(I-J
t(JJ
t)
-1j) be the orthogonal intersection cast shadow matrix of Jacobian matrix J; Column vector y=α v;
ξ (q) is unusual tolerance: ξ (q)=det (JJ
t); Scalar parameter α is chosen for:
subscript " " represents derivative operation; Transpose operation is asked in subscript " T " representative; Subscript "-1 " represents inversion operation;
represent scalar ξ and gradient is asked to vector q.
2. a kind of redundant space mechanical arm according to claim 1 method for planning track of arresting in-orbit, it is characterized in that: in described step (1.2), the total angle of rotation of each joint angle from current configuration to target configuration is divided into N part by collisionless path search algorithm, each joint angle is turned over every part of corner and be defined as a son motion, thus define pN son motion, wherein p is joint number;
The son motion of note i-th joint angle is son motion i, i=1,2 ..., p, pN son motion with the arrangement of suitable order, is formed the motion sequence of a pN step by collisionless path search algorithm;
Setting serial number gencration function F (i), this function generates next step sub-motion sequence number that will sound out by current sub-motion sequence number i; F (i) is for increasing progressively, successively decreasing or randomly generated test problems;
Represent step number with m, T represents exploration total degree, T
maxexpression can accept maximum exploration number of times;
Collisionless path search algorithm step is as follows:
1) initialize, make m=1, T=1, choose i, T is set
max;
2) judge whether m equals pN+1;
If m=pN+1, then export collisionless joint motions sequence, and terminate searching algorithm; Otherwise utilize collision detection algorithm, judge that mechanical arm m walks execution motion i and whether collides with barrier; If do not collided, mechanical arm performs son motion i, and keeps a record, and performs step 3); If collision, perform step 4);
3) m=m+1, i=F (i), T=T+1, perform step 6);
4) judge whether m step has soundd out all possible son motion i, if so, performs step 5); Otherwise i=F (i), T=T+1, perform step 6);
5) rebound m-1 walks, and makes m=m-1; Judge whether m step has soundd out all possible son motion, if re-execute step 5); Otherwise make i=F (i (m)), i (m) refers to the original sub-motion sequence number adopted of m step, and T=T+1, performs step 6);
6) judge whether T equals T
max,
If T=T
max, then output algorithm is searched for unsuccessfully and is terminated searching algorithm, otherwise performs step 2);
If algorithm search failure, then different explorations rule F (i) or increase path segmentation constant N is adopted to re-execute collisionless path search algorithm.
3. a kind of redundant space mechanical arm according to claim 1 method for planning track of arresting in-orbit, it is characterized in that: in described step (1.3), path optimized algorithm method is as follows: two son motions adjacent in the motion sequence of each joint angle of the collisionless mechanical arm searched by collisionless path search algorithm are merged into a son motion, and whether the son motion after then adopting collision detection algorithm combining data detection collides with barrier; If do not collided, then these two motions are merged; If collide, cancel merging; Son motion adjacent in the motion sequence obtained repeats said process, until cannot merge further.
4. the method for planning track that a kind of redundant space mechanical arm according to the arbitrary claim of claim 2 to 3 is arrested in-orbit, it is characterized in that: described collision detection algorithm method is as follows: mechanical arm is reduced to the line segment that some connect, then discretization is spatially carried out, the discrete a series of point turned on mechanical arm, barrier is merotomized, every part finds the envelope of a convex polyhedron, then replaces barrier itself with these convex polyhedrons are approximate; Remember that the central point in i-th face of certain convex polyhedron is P
i, the exterior normal vector in i-th face is
remember that point to be detected is P
t, then P is put
tthe sufficient and necessary condition being positioned at this convex polyhedron is: all faces for convex polyhedron have
if it is inner at barrier to there is measuring point to be checked, then thinks that mechanical arm and barrier are collided, otherwise think that mechanical arm and barrier can not collide.
5. a kind of redundant space mechanical arm according to claim 1 method for planning track of arresting in-orbit, is characterized in that: the angular speed track of each joint angle of the mechanical arm in described step (2.3)
formula is:
Wherein, X
er(t) and
for movement locus and the speed trajectory of the end effector position/attitude after compensation, X
et () is the position/attitude of end effector in mechanical arm actual motion process; δ (X
er(t)-X
e(t)) proportion adjustment item for adding, wherein δ > 0; J
+=J
t(JJ
t)
-1for the pseudoinverse of Jacobian matrix J;
The joint angle acceleration trajectory of each joint angle of described mechanical arm
for:
Wherein,
for the acceleration trajectory of the end effector position/attitude after compensation;
for the time-derivative of the pseudoinverse of Jacobian matrix J.
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