CN109910013A - A kind of PTP method for planning track of the continuous bounded of SCARA robot acceleration - Google Patents
A kind of PTP method for planning track of the continuous bounded of SCARA robot acceleration Download PDFInfo
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Abstract
The invention discloses a kind of PTP method for planning track of the continuous bounded of SCARA robot acceleration, comprising: the forward kinematics solution that SCARA robot is established by DH parametric method acquires Inverse Kinematics Solution by analytic method；It is solved to obtain joint angles against starting point and halt of the solution to cartesian space by gained, 8 boundary conditions are obtained in conjunction with angle acceleration, angular acceleration and angular speed, 9 order polynomial forms of PTP trajectory planning are determined in combination with 2 status conditions of acceleration, acceleration intermediate time；The acceleration time t of PTP trajectory planning is calculated by the boundedness of accelerationjWith the coefficient of 9 order polynomials；By the boundedness constraint adjustment acceleration time t of accelerationjAnd calculate even accelerating sections time ta；Even accelerating sections time t is adjusted by the boundedness constraint of speedaAnd calculate at the uniform velocity section time tv.The continuous boundedness of acceleration slows down the mutation of joint driven torque, concussion in PTP trajectory planning, improves tracking accuracy.
Description
Technical field
The present invention relates to the trajectory planning field of SCARA robot, especially a kind of SCARA robot acceleration is continuous
The PTP method for planning track of bounded.
Background technique
With the rapid development of intelligence manufacture industry, the high-speed, high precision control of industrial robot becomes research hotspot.Machine
The trajectory planning mode of device people is divided into cartesian space trajectory planning and joint space trajectory planning.Cartesian space trajectory planning
The working path of robot end's coordinate system is influenced, while needing to consider that reachable tree and singular point are evaded and Inverse Kinematics Solutions is waited to ask
Topic；Joint space trajectory planning is not required to carry out complicated conversion, is directly given to joint of robot by motor side, therefore joint space
The flatness of planning directly influences the stationarity of motor torque output.
SCARA robot architecture is simple, operation efficiently, often by PTP movement realize the high speed crawl of point-to-point, sort,
The operation such as fitting.High speed PTP movement can bring track tracking error to become larger, and positioning time is elongated and torque is mutated oscillation problem.
Summary of the invention
The present invention regarding to the issue above and technical need, proposes a kind of continuous bounded of SCARA robot acceleration
PTP method for planning track.
Technical scheme is as follows:
A kind of PTP method for planning track of the continuous bounded of SCARA robot acceleration, comprising:
Step 1, the forward kinematics solution of SCARA robot is established by DH parametric method, and kinematics is acquired by analytic method
Inverse solution；
Step 2, it is solved to obtain joint angles against starting point and halt of the solution to cartesian space by gained, in conjunction with
Angle acceleration, angular acceleration and angular speed obtain 8 boundary conditions, in combination with acceleration, acceleration intermediate time 2
A status condition determines 9 order polynomial forms of PTP trajectory planning；
Step 3, the acceleration time t of PTP trajectory planning is calculated by the boundedness of accelerationjWith more than 9 times
The coefficient of item formula；
Step 4, by the boundedness constraint adjustment acceleration time t of accelerationjAnd calculate even accelerating sections time ta；
Step 5, even accelerating sections time t is adjusted by the boundedness constraint of speedaAnd calculate at the uniform velocity section time tv。
Its further technical solution are as follows: the forward kinematics solution that SCARA robot is established by DH parametric method, and lead to
It crosses analytic method and acquires Inverse Kinematics Solution, comprising:
SCARA joint of robot coordinate system and DH parameter list are established, and establishes the adjacent segment in each joint by DH parameter list
The matrix of a linear transformation of coordinate system；
Module and carriage transformation matrix by even multiplying adjacent segment obtains SCARA robot end coordinate system and base coordinate system
Module and carriage transformation matrix, that is, forward kinematics solution；
The inverse solution of SCARA robot kinematics is completed by analytic method, obtains cartesian space coordinate to joint space angle
Conversion.
Its further technical solution are as follows: determine the condition of the trajectory planning of 9 order polynomial are as follows:
Start 8 boundary conditions of halt and 2 status conditions of intermediate time:
Wherein, p is joint angles, and v is angular speed, and a is angular acceleration, and j is angle acceleration, tjWhen for acceleration
Between.
Its further technical solution are as follows: the trajectory planning form of 9 order polynomial are as follows:
Wherein, p (t) is the expression formula of joint angle at any time, ki(i=0~9) are 9 order polynomial coefficients.
Its further technical solution are as follows: the boundedness of the acceleration is the largest acceleration constraint Jmax, described
The acceleration time t of PTP trajectory planning is calculated by the boundedness of accelerationjWith the side of the coefficient of 9 order polynomials
Method is the direct matrix of multi head linear equation group, comprising:
Coefficient to be solved is 10 multinomial coefficients and 1 acceleration runing time coefficient totally 11, by 8 perimeter strips
The equation group that part, 2 status conditions and 1 acceleration constraint condition form 11 nonlinear correlations altogether is solved.
Its further technical solution are as follows: the boundedness constraint of the acceleration is the largest acceleration value Amax, it is described by
The boundedness constraint adjustment acceleration time t of accelerationjAnd calculate even accelerating sections time taCondition are as follows: a (t)max=Amax。
Its further technical solution are as follows: the boundedness constraint of the speed is the largest velocity amplitude Vmax, described by speed
Boundedness constraint adjust even accelerating sections time taAnd calculate at the uniform velocity section time tvCondition are as follows: v (t)max=Vmax。
The method have the benefit that:
1, the continuous boundedness of joint space acceleration guarantees the low rate of change of driving moment, to reduce driving moment
Mutation, slow down the fluctuation of driving moment.
2, on the one hand, gentle joint driven torque can effectively reduce joint trajectories tracking error, on the other hand, put down
Slow joint driven torque can effectively slow down mechanical concussion, improve the service life of robot.
Detailed description of the invention
Fig. 1 is a kind of track the PTP rule of the continuous bounded of SCARA robot acceleration provided by one embodiment of the present invention
The flow chart for the method for drawing.
Fig. 2 is the structural schematic diagram of SCARA robot provided by one embodiment of the present invention.
Fig. 3 is SCARA robot links coordinate system diagram provided by one embodiment of the present invention.
Fig. 4 is a kind of track PTP for the continuous bounded of SCARA robot acceleration that another embodiment of the present invention provides
The flow chart of planing method.
Specific embodiment
The following further describes the specific embodiments of the present invention with reference to the drawings.
Fig. 1 is a kind of track the PTP rule of the continuous bounded of SCARA robot acceleration provided by one embodiment of the present invention
The flow chart for the method for drawing, as shown in Figure 1, this method may include:
Step 1, the forward kinematics solution of SCARA robot is established by DH parametric method, and kinematics is acquired by analytic method
Inverse solution.
In conjunction with referring to figs. 2 and 3, Fig. 2 has gone out the structural schematic diagram of SCARA robot, and Fig. 3 shows SCARA robot
Link rod coordinate system figure, SCARA robot architecture's schematic diagram according to Fig.2, establish the link rod coordinate system figure of SCARA robot, figure
Y-axis is omitted in 3.
Table 1 shows the DH parameter list of SCARA robot:
Table 1
| Connecting rod i | αi-1 | ai-1 | di | θi |
| 1 | 0 | 0 | 0 | θ1 |
| 2 | 0 | l1 | 0 | θ2 |
| 3 | π | l2 | d3 | 0 |
| 4 | 0 | 0 | 0 | θ4 |
Optionally, step 1 may include:
The first step establishes SCARA joint of robot coordinate system and DH parameter list, and the phase in each joint is established by DH parameter list
The matrix of a linear transformation of adjacent joint coordinate system.
The DH parameter list of SCARA robot is obtained by the link rod coordinate system figure of SCARA robot.
Transformation square between connecting rod and between end effector and railing 0 (pedestal) can be calculated by DH parameter list
Battle array:
Wherein, s1Indicate sin θ1, c1Indicate cos θ1, s2Indicate sin θ2, c2Indicate cos θ2。
Second step, the module and carriage transformation matrix by even multiplying adjacent segment obtain SCARA robot end coordinate system and pedestal
Module and carriage transformation matrix, that is, forward kinematics solution of coordinate system.
Formula (1)~(4) connecting rod transformation matrix is connected the multiplied pose to end effector of robot under base coordinate system to become
Change matrix are as follows:
Wherein, s12Indicate sin (θ1+θ2), c12Indicate cos (θ1+θ2), s12-4Indicate sin (θ1+θ2-θ4), c12-4It indicates
cos(θ1+θ2-θ4)。
I.e. the end pose of robot indicates are as follows:
Function is derived as known machine person joint angle and seeks ending coordinates system pose problem, the i.e. movement of SCARA robot
Normal solution is learned, seeks Inverse Kinematics Solution below, i.e. the pose of known machine people end seeks the angle in each joint of robot.
Third step completes the inverse solution of SCARA robot kinematics by analytic method, obtains cartesian space coordinate to joint sky
Between angle conversion.
Seek joint variable θ1:
By formula (6) both sides simultaneously multiplied byHaveThat is:
It enables the element (1,4) in the matrix of left and right and (2,4) is equal obtains:
It can thus be concluded that:
Wherein,φ=atan2 (px,py)。
Seek joint variable θ2:
Acquire θ1Generation, which goes back to formula (6), to be had:
Seek joint variable d3:
It enables in formula (6) that left and right matrix element (3,4) is equal, has:
d3=-pz (11)
Seek joint variable θ4:
It enables in formula (6) that the right and left matrix element (1,1) and (2,1) are equal, has:
Acquire θ1And θ2Afterwards, above formula is substituted into obtain:
θ4=θ2-atan2(-s1nx+c1ny,c1nx+s1ny) (13)
Step 2, it is solved to obtain joint angles against starting point and halt of the solution to cartesian space by gained, in conjunction with
Angle acceleration, angular acceleration and angular speed obtain 8 boundary conditions, in combination with acceleration, acceleration intermediate time 2
A status condition determines 9 order polynomial forms of PTP trajectory planning.
Expression formula and condition of the joint angles p about time t are as follows:
Wherein, p (t) is the expression formula of joint angle at any time, ki(i=0~9) are 9 order polynomial coefficients；V is angular speed,
A is angular acceleration, and j is angle acceleration, tjFor the acceleration time.It is obtained by joint angles p by 1,2,3 order derivatives, θ is
Joint rotation angle size.In order to guarantee the continuous bounded of angle acceleration, boundary condition needs have met the angular speed of rest point, angle adds
Speed and angle acceleration are 0, and the angle for playing rest point is given size totally 8 boundary conditions；While in order to guarantee acceleration and deceleration
Balanced and acceleration when avoiding uniform velocity mutation, in t=0.5tjWhen, two states of angular acceleration and angle acceleration
The value of condition is also respectively 0.ki(i=0 ..., 9) is 10 coefficients of 9 order polynomials, tjFor track operation acceleration when
Between.
Step 3, the acceleration time t of PTP trajectory planning is calculated by the boundedness of accelerationjWith more than 9 times
The coefficient of item formula.
The boundedness of acceleration, that is, maximum acceleration constrains Jmax, calculate plus add by the boundedness of acceleration
Velocity Time tjIt is the direct matrix of multi head linear equation group with the coefficient methods of 9 order polynomials, specifically: coefficient to be solved is
10 multinomial coefficients and 1 acceleration runing time coefficient totally 11, by 8 boundary conditions, 2 status conditions and 1
The equation group that acceleration constraint condition forms 11 nonlinear correlations altogether is solved.
Starting point condition p (0), v (0), a (0) and j (0) can calculate for 0, then midpoint and stopping are substituted into:
Matrixing obtains:
Multinomial coefficient is substituted into j (t), acquires maximum value:
By the Bounded Conditions j (t) of angle accelerationmax=Jmax:
Formula (17), (19) are substituted into formula (14), acquire p (t) expression formula are as follows:
Wherein, τ=t/tfFor time scale, value interval is [0,1].
Formula (20) is asked 1,2 and 3 time respectively and leads to obtain:
Step 4, by the boundedness constraint adjustment acceleration time t of accelerationjAnd calculate even accelerating sections time ta。
The boundedness constraint of acceleration is maximum acceleration value Amax, by the boundedness constraint adjustment plus acceleration of acceleration
Spend time tjAnd calculate even accelerating sections time taCondition are as follows: a (t)max=Amax。
It can be convenient to obtain maximum value acquirement in τ=0.173 of angular acceleration by formula (22):
If a (τ)maxMore than the KB limit A of angular accelerationmax, then acceleration section runing time t is adjustedj, so that a
(τ)max=Amax, it may be assumed that
Formula (20) are substituted into, the stroke for adding accelerating sections is obtained are as follows:
Uniform acceleration section runing time taMeet following relationship:
Amaxta 2+(0.654Amaxtj+2V1)ta-θ+θj=0 (27)
Wherein, V1Velocity amplitude when for τ=0.173, formula (27) can be solved by radical formula.
Step 5, even accelerating sections time t is adjusted by the boundedness constraint of speedaAnd calculate at the uniform velocity section time tv。
The boundedness constraint of speed is the largest velocity amplitude Vmax, the even accelerating sections time is adjusted by the boundedness constraint of speed
taAnd calculate at the uniform velocity section time tvCondition are as follows: v (t)max=Vmax。
As angular acceleration maximum value a (τ)maxIt is not above acceleration limits value AmaxWhen, angular speed maximum value is in τ=0.5
When obtain:
If v (τ)maxMore than the KB limit V of angular speedmax, then acceleration section runing time t is adjustedj, so that v
(τ)max=Vmax, it may be assumed that
Add accelerating sections stroke θjIt is still calculated by formula (14), travel at the uniform speed time tvAre as follows:
If acceleration maximum value transfinites, add runing time, stroke and the even accelerating sections time of accelerating sections respectively by formula
(13), (14) and (15) determine, then corresponding angular speed maximum value are as follows:
If v (τ)maxMore than the KB limit V of angular speedmax, then uniform acceleration section runing time t is adjusteda, so that v
(τ)max=Vmax, it may be assumed that
Even accelerating sections stroke θaAre as follows:
θa=Amaxta 2+(0.654Amaxtj+2V1)ta (33)
At the uniform velocity section runing time tvAre as follows:
Fig. 4 institute can also be briefly described into the PTP method for planning track of the continuous bounded of above-mentioned SCARA robot acceleration
The flow chart shown, this method may include:
S101 seeks the inverse solution of SCARA robot kinematics.
S102 determines 9 order polynomials by 2 status conditions of 8 boundary conditions of trajectory planning start and stop moment and intermediate time
Form.
S103 calculates the coefficient of acceleration time and 9 order polynomials by the boundedness of acceleration.
S104 adjusts the acceleration time by the boundedness constraint condition of acceleration and determines the even accelerating sections time.
S105 adjusts the even accelerating sections time by the boundedness constraint condition of speed and determines the at the uniform velocity section time.
Above-described is only preferred embodiments of the invention, and present invention is not limited to the above embodiments.It is appreciated that this
The other improvements and change that field technical staff directly exports or associates without departing from the spirit and concept in the present invention
Change, is considered as being included within protection scope of the present invention.
Claims (7)
1. a kind of PTP method for planning track of the continuous bounded of SCARA robot acceleration characterized by comprising
Step 1, the forward kinematics solution of SCARA robot is established by DH parametric method, and Inverse Kinematics Solution is acquired by analytic method；
Step 2, solved to obtain joint angles against starting point and halt of the solution to cartesian space by gained, in conjunction with angle plus
Acceleration, angular acceleration and angular speed obtain 8 boundary conditions, in combination with acceleration, 2 shapes of acceleration intermediate time
State condition determines 9 order polynomial forms of PTP trajectory planning；
Step 3, the acceleration time t of PTP trajectory planning is calculated by the boundedness of accelerationjWith 9 order polynomials
Coefficient；
Step 4, by the boundedness constraint adjustment acceleration time t of accelerationjAnd calculate even accelerating sections time ta；
Step 5, even accelerating sections time t is adjusted by the boundedness constraint of speedaAnd calculate at the uniform velocity section time tv。
2. the PTP method for planning track of the continuous bounded of SCARA robot according to claim 1 acceleration, feature
It is, the forward kinematics solution that SCARA robot is established by DH parametric method, and Inverse Kinematics Solution is acquired by analytic method,
Include:
SCARA joint of robot coordinate system and DH parameter list are established, and establishes the adjacent segment coordinate in each joint by DH parameter list
The matrix of a linear transformation of system；
Module and carriage transformation matrix by even multiplying adjacent segment obtains the pose of SCARA robot end coordinate system and base coordinate system
Transformation matrix, that is, forward kinematics solution；
The inverse solution of SCARA robot kinematics is completed by analytic method, cartesian space coordinate is obtained and turns to joint space angle
It changes.
3. the PTP method for planning track of the continuous bounded of SCARA robot according to claim 1 acceleration, feature
It is, determines the condition of the trajectory planning of 9 order polynomial are as follows:
Start 8 boundary conditions of halt and 2 status conditions of intermediate time:
Wherein, p is joint angles, and v is angular speed, and a is angular acceleration, and j is angle acceleration, tjFor the acceleration time.
4. the PTP method for planning track of the continuous bounded of SCARA robot according to claim 3 acceleration, feature
It is, the trajectory planning form of 9 order polynomial are as follows:
Wherein, p (t) is the expression formula of joint angle at any time, ki(i=0~9) are 9 order polynomial coefficients.
5. the PTP method for planning track of the continuous bounded of SCARA robot according to claim 1 acceleration, feature
It is, the boundedness of the acceleration is the largest acceleration constraint Jmax, the boundedness calculating by acceleration
Obtain the acceleration time t of PTP trajectory planningjMethod with the coefficient of 9 order polynomials is the inverse square of multi head linear equation group
The tactical deployment of troops, comprising:
Coefficient to be solved is 10 multinomial coefficients and 1 acceleration runing time coefficient totally 11, by 8 boundary conditions, 2
The equation group that a status condition and 1 acceleration constraint condition form 11 nonlinear correlations altogether is solved.
6. the PTP method for planning track of the continuous bounded of SCARA robot according to claim 1 acceleration, feature
It is, the boundedness constraint of the acceleration is the largest acceleration value Amax, described to be added by the boundedness constraint adjustment of acceleration
Acceleration time tjAnd calculate even accelerating sections time taCondition are as follows: a (t)max=Amax。
7. the PTP method for planning track of the continuous bounded of SCARA robot according to claim 1 acceleration, feature
It is, the boundedness constraint of the speed is the largest velocity amplitude Vmax, described that even accelerating sections is adjusted by the boundedness constraint of speed
Time taAnd calculate at the uniform velocity section time tvCondition are as follows: v (t)max=Vmax。
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| CN110333722A (en) * | 2019-07-11 | 2019-10-15 | 北京电影学院 | A kind of robot trajectory generates and control method, apparatus and system |
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| CN111158318A (en) * | 2020-01-16 | 2020-05-15 | 江南大学 | Flexible acceleration and deceleration planning method for asymmetric quartic curve |
| CN111158318B (en) * | 2020-01-16 | 2022-10-18 | 江南大学 | Flexible acceleration and deceleration planning method for asymmetric quartic curve |
| CN112720455B (en) * | 2020-12-01 | 2022-05-10 | 深圳众为兴技术股份有限公司 | Optimal joint acceleration and deceleration calculation method and device and application thereof |
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| CN112757306B (en) * | 2021-01-25 | 2022-03-01 | 北京交通大学 | Inverse solution multi-solution selection and time optimal trajectory planning algorithm for mechanical arm |
| CN112757306A (en) * | 2021-01-25 | 2021-05-07 | 北京交通大学 | Inverse solution multi-solution selection and time optimal trajectory planning algorithm for mechanical arm |
| CN113478479A (en) * | 2021-06-17 | 2021-10-08 | 北京工业大学 | Acceleration selection method based on industrial robot quintic polynomial trajectory planning intermediate point |
| CN113478479B (en) * | 2021-06-17 | 2023-08-01 | 北京工业大学 | Acceleration selection method based on five-time polynomial trajectory planning intermediate point of industrial robot |
| CN113878585A (en) * | 2021-11-03 | 2022-01-04 | 上海景吾智能科技有限公司 | Five-degree-of-freedom robot motion control method and system |
| CN114227687A (en) * | 2021-12-28 | 2022-03-25 | 深圳市优必选科技股份有限公司 | Robot control method and device, terminal equipment and storage medium |
| CN114227687B (en) * | 2021-12-28 | 2023-08-15 | 深圳市优必选科技股份有限公司 | Robot control method and device, terminal equipment and storage medium |
| CN116079696A (en) * | 2023-04-07 | 2023-05-09 | 广东毕要科技有限公司 | SCARA robot positioning updating method and device based on vibration signals |
| CN116079696B (en) * | 2023-04-07 | 2023-06-13 | 广东毕要科技有限公司 | SCARA robot positioning updating method and device based on vibration signals |
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Application publication date: 20190621 |