CN110308699A - A kind of method for planning track - Google Patents
A kind of method for planning track Download PDFInfo
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- CN110308699A CN110308699A CN201910351225.4A CN201910351225A CN110308699A CN 110308699 A CN110308699 A CN 110308699A CN 201910351225 A CN201910351225 A CN 201910351225A CN 110308699 A CN110308699 A CN 110308699A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/35—Nc in input of data, input till input file format
- G05B2219/35338—Display virtual tool, locus, part to check possibility of execution next block
Abstract
The invention discloses a kind of method for planning track, this method, using the right angle transition portion between PH curve smoothing vertical motion and horizontal movement, determines motion profile first in cartesian space；The 1 dimension curve displacement of track is planned followed by polynomial motion, determines the position of motion profile interpolated point；Finally to minimize the Pick-and-Place operations period as objective optimization PH parameter of curve, and prove that the optimization method can obtain the smallest curvature difference under PH curve by deriving.The invention also discloses application of the parallel robot method for planning track in Delta robot system.The Pick-and-Place operations of method for planning track of the invention have the shorter period of motion, smooth trajectory and have stable kinetic characteristic.Delta robot of the present invention can carry out grasping manipulation with 90 beats/min of speed, realize the high-speed job of parallel robot.
Description
Technical field
The present invention relates to parallel robot technical fields, are about a kind of method for planning track specifically.
Background technique
Delta robot is using one of parallel institution the most successful.It is the parallel manipulator of a kind of high speed, underloading
People usually has 3~4 freedom degrees.Delta robot has many advantages, such as that speed is fast, registration, at low cost, high-efficient, quilt
Be widely used on the flow-wraps line of food, drug and electronic product and other items, for complete high-volume, repeatability, quickly
The operation such as sorting, crawl, assembly, and the control system of high-speed, high precision Delta parallel robot depends on state at present
Outer technology, therefore it is significant to China's equipment manufacture is promoted to study Delta robot.
Domestic and foreign scholars have carried out extensively kinematic accuracy when how to improve the work of Delta mechanism high-speed high frequency with stability
General, in-depth study shows that end effector of robot motion profile during the motion and the characteristics of motion will affect mechanism
Dynamic accuracy, therefore effective trajectory planning is most important.In fields such as above-mentioned crawl, sortings, Delta robot mainly into
Row Pick-and-Place operations (PPO).Pick-and-Place operations are frequently with door shape track, including vertical, horizontal, vertical 3 part is due to vertical direction
There are right angles with horizontal direction junction, therefore are easy to happen shock and vibration, the high-speed cruising of unfavorable Delta robot.To make
Door shape track is more smooth, the auspicious Pick-and-Place operations track for proposing the arc transition based on the modified trapezoid characteristics of motion, the party
Method reduces the impact of right angle transition, but in terms of still have room for promotion.Xie Zexiao proposes one kind
The Delta parallel robot Pick-and-Place operations method for planning track of inflection point smooth transition is carried out using Lam ' e curve, this method is subtracting
It works well in terms of manipulator residual oscillation in small motion process, but Lam ' e curve calculates complexity, is unfavorable for system and realizes in fact
Shi Xing.In recent years, many scholars study PH curve.Wang Yi etc. is for unmanned plane in a dynamic environment along reference locus
The problem of flight, propose the path tracking algorithm based on 3 dimension PH curves, PH curvature of curve is continuous, curve smoothing, is able to satisfy fortune
It is dynamic to learn constraint.Jahanpour et al. carries out turning transition using PH curve, so that the hysteresis quality of servo is pressed down in High-speed machining
System.
About PH curve: Farouki proposes PH curve equal to nineteen ninety, to establish between curve arc long and parameter
Exact relationship .PH curve is a kind of special Bezier, has many advantages, such as that arc length is represented by the polynomial function of parameter
Because of its peculiar advantage, application is throughout High-speed NC Machining, cutter path offset design and radius compensation, robot motion's rail
The numerous areas such as mark planning, the analysis of computer geometric tolerance, traffic route design.If P (τ) indicates a n times shellfish plug in plane
That curve, is defined as follows:
Wherein Pi=(xi, yi) is the control vertex of curve, i=0；...；N, n are most high-order term in curve multinomial
Number, τ are that parameter of curve makes if there is multinomial σ (τ):
Then claim P (τ)=(x (τ)；Y (τ)) it is n times PH curve.
Summary of the invention
To make Delta robot system that there is the shorter period of motion and preferable movenent performance, its working efficiency is improved
And precision, extend its mechanical life, Pick-and-Place operations track of the invention uses polynomial motion, and transition portion is adopted in track
Optimize PH parameter of curve with PH curve, and by minimizing the Pick-and-Place operations period.By repeatedly studying, a kind of parallel connection is obtained
Method for planning track of robot, flute card when which can solve existing Delta parallel robot high-speed job
The rough problem of youngster's space tracking.Therefore, the primary purpose of the present invention is that providing a kind of method for planning track.Of the invention
Second purpose is to provide the application of the method for planning track.
To achieve the above object, the invention provides the following technical scheme:
A kind of method for planning track, includes the following steps:
Step A, in picking up the cartesian space put in operation using between PH curve smoothing vertical motion and horizontal movement
Right angle transition portion, determines motion profile；
Step B, the 1 dimension curve displacement of track is planned using polynomial motion, determines motion profile interpolation
The position of point；
Step C, to minimize the Pick-and-Place operations period as objective optimization PH parameter of curve, and the optimization side is proved by deriving
Method can obtain the smallest curvature difference under PH curve, that is, realize the most smooth motion trajectories under the minimum movement period.
According to the present invention, the constraint condition of objective optimization PH parameter of curve mainly has: each master arm angular speed, angular acceleration
No more than joint maximum limitation angular speed, maximum limitation angular acceleration, the speed, acceleration of robot end is not more than maximum limit
Speed processed, maximum limitation acceleration etc..
A kind of application of method for planning track described above in Delta robot system.
Parallel robot method for planning track of the invention, beneficial aspects are: Pick-and-Place operations have shorter movement week
Phase, smooth trajectory and there is stable kinetic characteristic.
Grasping manipulation can be carried out with 90 beats/min of speed by using the Delta robot of the method for planning track, be realized
The high-speed job of parallel robot.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of Pick-and-Place operations track of the invention.
Fig. 2 is the PH curve and coordinate system of embodiment 2.The transition portion BC in Pick-and-Place operations track that the figure is Fig. 1.
Fig. 3 is the period of motion differential chart of embodiment 4.
Motion profile figure in the case where Fig. 4 is the track kinetic characteristic emulation testing of embodiment 41.
Fig. 5 is the tip speed curve in situation 1 under the method for planning track based on PH curve.
Fig. 6 is the end accelerating curve in situation 1 under the method for planning track based on PH curve.
Fig. 7 is the tip speed curve in situation 1 under the method for planning track based on modified trapezoid rule.
Fig. 8 is the end accelerating curve in situation 1 under the method for planning track based on modified trapezoid rule.
Fig. 9 is each joint position under the method for planning track based on PH curve.
Figure 10 is each joint angle rate curve under the method for planning track based on PH curve.
Figure 11 is each joint angle accelerating curve under the method for planning track based on PH curve.
Figure 12 is each joint position under the method for planning track based on modified trapezoid rule.
Figure 13 is each joint angle rate curve under the method for planning track based on modified trapezoid rule.
Figure 14 is each joint angle accelerating curve under the method for planning track based on modified trapezoid rule.
Figure 15 is the motion profile figure in situation 2.
Figure 16 is the tip speed curve in situation 2 under the method for planning track based on PH curve.
Figure 17 is the end accelerating curve in situation 2 under the method for planning track based on PH curve.
Figure 18 is the tip speed curve in situation 2 under the method for planning track based on modified trapezoid rule.
Figure 19 is the end accelerating curve in situation 2 under the method for planning track based on modified trapezoid rule.
Figure 20 is the experimental enviroment figure of prototype test.
Figure 21 is each joint moment curve under the method for planning track based on PH curve.
Figure 22 is each joint moment curve under the method for planning track based on modified trapezoid rule.
Specific embodiment
Below in conjunction with specific attached drawing, method for planning track of the invention is described in further details.
1 Pick-and-Place operations track of embodiment (Pick-and-place operation trajectory)
As shown in Figure 1, Pick-and-Place operations track be curve ABCDEFG, horizontal motion distance | AG |=w, vertical direction
Move distance | AH |=| GI |=h, | AB |=| GF |=n, | BH |=| FI |=l, | HC |=| EI |=k. curve BC instead of
The right angle transition portion being made of BH and HC, curve EF is instead of the right angle transition portion being made of EI and IF.
Method for planning track of the embodiment 2 based on PH curve
1, the method for planning track based on PH curve refers to that curve BC and EF are adopted in the Pick-and-Place operations track of embodiment 1
With PH curve.
The transition portion of the Pick-and-Place operations track of the present embodiment uses 3 PH curves.3 PH curves are as follows:
As a result as shown in Figure 2.Wherein, Fig. 2 is the transition portion BC in Pick-and-Place operations track, using PH curve, Li PH
Curve controlled polygonal side length, i=0；1；2, θ 1 and θ 2 respectively represents P1P2To P1P0And P2P3To P2P1Corner counterclockwise, then P
(τ) is the necessary and sufficient condition of 3 PH curves are as follows:
And
θ1=θ2 (5)
It can be drawn a conclusion by 3 PH Curve Properties:
(1) parameter of curve expression formula is
P (τ)=P0(1-τ)3+3P1(1-τ)2τ+3P2(1-τ)τ2+P3τ3, τ ∈ [0,1] (6)
(2) curve passes through the 1st and the 4th control point, it may be assumed that
(3) it is right angle in conjunction with track vertical direction and horizontal direction by formula (5), can obtains under the UOV coordinate system of Fig. 2:
(4) l and k in Fig. 2 is combined by formula (8), obtained:
Formula (4) are substituted into above formula, can be obtained:
If therefore known l and k, formula (10) substitution formula (8) can be obtained into control point coordinates, and then acquire formula (6), i.e. PH is bent
Line:
(5) it is obtained by PH Curve Property:
Wherein, PH Curve Property is carried out using the method for following document: the curvature of Zheng Zhihao, Wang Guozhao cubic PH curve
Monotonicity and easement curve construction [J] CAD and graphics journal, 2014,26 (8): 1219-1224.
It is obtained by PH curve arc long calculation formula:
Wherein, PH curve arc long calculation formula referring to following document method calculate: Duan little Juan cubic interpolation PH batten with
The Hangzhou research [D] of F- knee of curve and singular point: Zhejiang University, 2009.
Obtaining arc > P0P3 length is
2, by the multinomial acceleration and deceleration motion law-analysing of the above-mentioned method for planning track based on PH curve
Since 3-4-5 order polynomial characteristics of motion formula is simple and is easily achieved, therefore it is widely used in picking up and puts in operation
Cartesian space trajectory planning.In conjunction with boundary conditions such as whole story positions, the 3-4-5 order polynomial movement met the requirements is advised
It restrains as follows:
P (Γ)=lall(10Γ3-15Γ4+6Γ5) (15)
Wherein, Γ=t/T and Γ ∈ [0；1], lallFor the total length of Pick-and-Place operations track in Fig. 1, T is robot completion
The period of motion of Pick-and-Place operations.Unilateral PH length of a curve, which can be obtained, by formula (14) is Motion profile bilateral symmetry, it is total can to obtain Pick-and-Place operations track in conjunction with parameter in Fig. 1
Length is
In Pick-and-Place operations movement, the 1 dimension curve displacement of track is subjected to trajectory planning by the characteristics of motion of formula (16):
S (t)=p (Γ) (16)
T be time set robot end in the t=0 moment from point A along curvilinear motion to point G, on time by period of motion T
Between interval of delta t discretization:
ti=i Δ t (17)
Δ t can determine according to factors such as interpolation precisions, i 1；2；3；...；N, N are equal part number.In conjunction with Fig. 1, can must transport
It is dynamic to have with the next stage:
(1) when robot end moves from point A to point B, i.e. 0≤s (ti)≤n, robot end along the vertical direction to
Upper movement, robot end should be moved under robot basis coordinates system by following coordinate at this time:
(XA, YA, ZA+s(ti)) (18)
(2) when robot end moves from point B to point C, i.e.,Robot end
Along PH curvilinear motion, thus need to obtain UOV coordinate system in Fig. 2 to robot basis coordinates system XYZO transition matrix, if UOV is sat
The transition matrix of mark system to robot basis coordinates system XYZO are To, then have:
Coordinate of point B, C, P1, the P2 in UOV coordinate system and XYZO coordinate system in Fig. 2 is respectively obtained, To can be acquired.
Ask under the period robot basis coordinates system that specific step is as follows for coordinate:
Step1 seeks t by formula (16)iCorresponding s (ti)；
Step2 is by s (t required by Step1i) period (1) corresponding length is subtracted, convolution (13) can acquire parameter ε's
Value, specific method can be solved with Newton iteration method；
ε required by Step2 is substituted into formula (11) by Step3, can acquire the coordinate under UOV coordinate system；
Step4 is converted to the coordinate under robot basis coordinates system by formula (19).
(3) when robot end moves from point C to point E, i.e.,
Robot end is along horizontal motion, if CE and the angle of robot basis coordinates system X-axis are θ, then this opportunity
Coordinate of the device people end under basis coordinates system be
(4) when being moved as robot end from point E to point F, i.e.,
Robot end is along PH curvilinear motion, and the calculation method of trajectory coordinates point is similar with period (2) at this time.
(5) when being moved as robot end from point F to point G, i.e.,
Robot end moves vertically downwards, and the calculation method of trajectory coordinates point is similar with period (1) at this time.
3, the trajectory parameters of the above-mentioned method for planning track based on PH curve are optimized and is constrained
The period of motion, which can be obtained, by the characteristics of motion of formula (16) is
Wherein 0≤l≤h, 0≤k≤w/2, amaxFor moving platform peak acceleration.Different parameter l and k can obtain difference
PH curved path, it is contemplated that high speed sort object demand, the period of motion should be made most short, i.e., should minimize T.Due to l2+k2≥
2lk is obtained:
T is minimum when above formula takes equal sign, and equal sign is set up when l=k.Therefore l=k is taken, to minimize Pick-and-Place operations cycle T.
Because l is bigger, smaller on the right of inequality (22), then corresponding T is smaller when taking equal sign.Therefore ginseng is taken as follows
Number:
(1) as h≤w/2, l=k=h is taken；
(2) as h >=w/2, l=k=w=2 is taken.
As l=k, take parameter that the smallest PH curve of curvature difference can be obtained according to the above method.
Conclusion: it to keep the curvature difference of PH curve in Pick-and-Place operations track minimum, then needs to calculate maximum curvature and minimum
Curvature, therefore the curvature of PH curve two-end-point and the curvature of extreme point need to be calculated.
It can be obtained by 3 PH curvature of curve calculation formula [14]:
So that
This 3 points of corresponding curvature must include maximum curvature and minimum curvature in curve.By l=k, L is obtained0=L1=L2, because
This k (0)=k (1).Curvature difference J is minimized to obtain:
Therefore maximum L need to be taken by minimizing curvature difference0, and
Conclusion: taking maximum l that the smallest curvature difference can be obtained, i.e., takes parameter that curvature difference can be obtained according to the above method the smallest
PH curve.
In above-mentioned Pick-and-Place operations motion process, constraint condition mainly has: each master arm angular speed, angular acceleration are little
Angular speed, maximum limitation angular acceleration are limited in joint maximum, the speed, acceleration of robot end is no more than maximum limitation speed
Degree, maximum limitation acceleration etc..Mapping relations between the speed and master arm tarnsition velocity of robot end use " Zhang Li
Delta high-speed parallel manipulator Integrated Optimal Design technique study [D] Tianjin of the quick based on dynamics index: University Of Tianjin,
Rate pattern in 2011. ", the mapping relations between the acceleration and master arm angular acceleration of robot end use " Zhang Li
Delta high-speed parallel manipulator Integrated Optimal Design technique study [D] Tianjin of the quick based on dynamics index: University Of Tianjin,
Fast track surgery in 2011. ".
During the motion, the maximum speed v of robot end can be obtained by displacement expression formula (15)maxWhen appearing in T/2
It carves:
By maximum speed v in motion processmaxDelta robot end's movement velocity upper limit v is not to be exceededlim:
vmax≤vlim (30)
That is Pick-and-Place operations movement should meet:
Each parameter limits all in above-mentioned constraint condition without departing from maximum in entire Pick-and-Place operations movement.
Pick-and-Place operations track after parameter optimization has the shortest period of motion, and curvature difference is minimum.After optimizing
Most smooth track under the most short period of motion.
The method for planning track of arc transition of the embodiment 3 based on modified trapezoid
The present embodiment use " Tianjin Zhang Xiang High Speed Light parallel manipulator control method research [D]: University Of Tianjin,
The method for planning track of the 2005. " arc transition based on the modified trapezoid characteristics of motion.
The Acceleration Formula of modified trapezoid acceleration and deceleration motion rule is as follows:
In the method for planning track, horizontal direction and vertical direction of the robot in Pick-and-Place operations track are all made of amendment
The trapezoidal characteristics of motion.If T1For Fig. 1 mid point of curve A to the time of point C, T2For Fig. 1 mid point of curve B to the time of point F, T3For
The time of Fig. 1 mid point of curve E to point G have following 2 kinds of situations:
(1) as h≤w, then when t=0, vertical direction starts to move upwards, t=T1When/2, horizontal direction setting in motion,
T=T1/2+T2-T3When/2, vertical direction starts to move downward.The Pick-and-Place operations period of motion is at this time
(2) as h >=w, then when t=0, vertical direction starts to move upwards, t=T1-T2When/2, horizontal direction starts to transport
It is dynamic, t=T1When, vertical direction starts to move downward.The Pick-and-Place operations period of motion is at this time
4 simulation and analysis of embodiment
Computer CPU used by the present embodiment is Intel Core i3M330, inside saves as 6GB, and operating system is 32
Windows 7 is tested with method of the Matlab R2012a to embodiment 2 and embodiment 3.
1, track period of motion emulation testing
If robot end's main movement plane is z=-800mm, taking vertical climb h is 100mm, amax=50m/
s2.Table 1 is the Optimal Parameters obtained using the method for planning track based on PH curve and period of motion result.Table 2 is using base
In the Pick-and-Place operations cycle result that the method for planning track of the arc transition of the modified trapezoid characteristics of motion obtains.
1 different location trajectory parameters of table and period of motion experimental result
Period of motion experimental result of the table 2 based on modified trapezoid rule
When vertical climb h range is 0≤h≤0≤0.3m, when distance w range is 0≤w≤1m between horizontal coordinate point,
By the Pick-and-Place operations period under the method for planning track based on PH curve in embodiment 2 and embodiment 3 and based on modified trapezoid
The Pick-and-Place operations period under method for planning track subtracts each other, and obtains period of motion differential chart, as shown in Figure 3.
Can be obtained by Fig. 3: 98.8% period of motion difference is less than 0.
Conclusion: the method for planning track based on PH curve is compared with the method for planning track based on modification model, movement week
Phase is shorter.
2, track kinetic characteristic emulation testing
Situation 1: do not have in movement 2.1.2 save in stage (3), such as when starting point coordinate be (- 100mm, 0 ,-
800mm), coordinate of ground point is (100mm, 0, -800mm), when climb h is 100mm.Respectively to the track based on PH curve
The method for planning track of planing method and the arc transition based on the modified trapezoid characteristics of motion carries out experiment simulation, obtains robot
Track of the end under robot basis coordinates system, as shown in Figure 4.In the Pick-and-Place operations based on PH curve transition, tip speed
Curve is as shown in figure 5, accelerating curve is as shown in Figure 6.In the Pick-and-Place operations of the arc transition based on the modified trapezoid characteristics of motion
In, tip speed curve is as shown in fig. 7, accelerating curve is as shown in Figure 8.In addition, establishing kinematics model and being imitated
True experiment has obtained angular position of the Pick-and-Place operations based on PH curve in joint space, as shown in figure 9, angular speed is as schemed
Shown in 10, angular acceleration is as shown in figure 11.Figure 12~14 be angular position in modified trapezoid characteristics of motion hypozygal space,
Angular speed, angular acceleration curve.
Above-mentioned 2 kinds of methods are emulated respectively, obtain track of the robot end under robot basis coordinates system, are such as schemed
Shown in 15.Pick-and-Place operations lower end speed based on PH curve transition is as shown in figure 16, and acceleration as shown in figure 17 is being based on repairing
The Pick-and-Place operations lower end velocity and acceleration of trapezoid is as shown in Figure 18,19.
Conclusion, the method for planning track under the 3-4-5 order polynomial acceleration and deceleration motion rule based on PH curve are able to achieve flat
Sliding track, compared with the method for planning track based on modification model, movement is steady, there is preferable dynamic characteristic.
5 prototype test of embodiment
The experimental system of the present embodiment includes Delta robot master system, motion controller, servo-system, machinery
Structure, industrial camera etc..Prototype test environment is as shown in figure 20, and wherein the silent flatform radius of Delta robot is 150mm, moves
Platform radius is 51mm, and active arm lengths are 325mm, and driven arm lengths are 800mm.
The test result of the model machine shows that robot is able to achieve high speed crawl under this method.Maximum crawl rate in experiment
Up to 90 beats/min, the improvement of mechanical structure can be such that robot crawl rate is further promoted.
The parameters such as rated speed of motor in Binding experiment model machine demonstrate the parameters such as motor torque in motion process and exist
In restrictive condition.By N=60jw/2 π (wherein N is motor speed, and j is reduction ratio, and w is angular speed), according to maximum angular rate and
Reduction ratio can acquire maximum (top) speed, and compare and check whether to be more than rated speed；By T=J α, (wherein T is motor torque, and J is to turn
Dynamic inertia, α is angular acceleration), torque capacity can be acquired according to maximum angular acceleration and rotary inertia, and compare and check whether to surpass
Cross nominal torque；By P=T × N/9550, maximum power can be acquired according to maximum (top) speed and torque capacity, and compare and check whether
More than rated power.
Model machine is tested, by serial acquisition torque data, is obtained each under the method for planning track based on PH curve
The M curve in a joint, as shown in figure 21；And the M curve in each joint under modification model is obtained, as shown in figure 22.Point
The data in above-mentioned figure are analysed it can be found that the method for planning track based on PH curve is than the method for planning track under modification model
M curve is smoother, and has the shorter period of motion.Delta method for planning track of robot based on PH curve realizes
High-speed job of the robot in sorting field.
In conclusion the Pick-and-Place operations of method for planning track of the invention have the shorter period of motion, smooth trajectory and
There is stable kinetic characteristic；Using the Delta robot of the method for planning track can be grabbed with 90 beats/min of speed
Operation, realizes the high-speed job of parallel robot.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of art technology
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (3)
1. a kind of method for planning track, which comprises the steps of:
Step A, the right angle put and utilized between PH curve smoothing vertical motion and horizontal movement in the cartesian space in operation is being picked up
Transition portion determines motion profile；
Step B, the 1 dimension curve displacement of track is planned using polynomial motion, determines motion profile interpolated point
Position；
Step C, to minimize the Pick-and-Place operations period as objective optimization PH parameter of curve, and the optimization method energy is proved by deriving
The smallest curvature difference under PH curve is obtained, that is, realizes the most smooth motion trajectories under the minimum movement period.
2. method for planning track as described in claim 1, which is characterized in that the pact of the objective optimization PH parameter of curve of step C
Beam condition mainly has: each master arm angular speed, angular acceleration accelerate no more than joint maximum limitation angular speed, maximum limit angles
Degree, the speed, acceleration of robot end is no more than maximum limitation speed, maximum limitation acceleration.
3. a kind of application of planing method as claimed in claim 1 or 2 in Delta robot system.
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| CN112925306A (en) * | 2021-01-12 | 2021-06-08 | 河南科技大学 | Delta robot-based trajectory planning method |
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| CN113485250A (en) * | 2021-07-15 | 2021-10-08 | 深圳市汇川技术股份有限公司 | Trajectory planning method, apparatus and computer-readable storage medium |
| CN113485347B (en) * | 2021-07-16 | 2023-11-21 | 上海探寻信息技术有限公司 | Motion trail optimization method and system |
| CN113485347A (en) * | 2021-07-16 | 2021-10-08 | 上海探寻信息技术有限公司 | Method and system for optimizing motion trail |
| CN113589754A (en) * | 2021-07-23 | 2021-11-02 | 哈尔滨工业大学（深圳） | Groove grinding processing method of variable helix angle micro drill bit |
| CN113589754B (en) * | 2021-07-23 | 2022-07-29 | 哈尔滨工业大学（深圳） | Groove grinding processing method of variable helix angle micro drill bit |
| CN114609929A (en) * | 2022-03-08 | 2022-06-10 | 南京理工大学 | Three-hinge-point multi-stage hydraulic rapid erecting constant-power track planning method |
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