CN107116549A - A kind of method for planning track of robot and anthropomorphic robot platform based on quadravalence cubic B-spline function - Google Patents
A kind of method for planning track of robot and anthropomorphic robot platform based on quadravalence cubic B-spline function Download PDFInfo
- Publication number
- CN107116549A CN107116549A CN201710155012.5A CN201710155012A CN107116549A CN 107116549 A CN107116549 A CN 107116549A CN 201710155012 A CN201710155012 A CN 201710155012A CN 107116549 A CN107116549 A CN 107116549A
- Authority
- CN
- China
- Prior art keywords
- mrow
- mtd
- mtr
- msub
- mfrac
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
Landscapes
- Engineering & Computer Science (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Manipulator (AREA)
Abstract
The invention provides a kind of method for planning track based on quadravalence cubic B-spline function and anthropomorphic robot platform, the specific action required for each joint is cooked up by the method, and build the Track Pick-up control system of a set of completion, it is ensured that to the stability contorting of anthropomorphic robot under ZMP stable conditions.Its trajectory planning part includes the construction of B-spline function and its derivation of mathematical modeling, the solution of quadravalence cubic B-spline function, the densification of joint trajectories.After desired trajectory is drawn, according to required shape value point editor's corresponding actions function into raspberry factions system, command adapted thereto is sent by smart mobile phone application software and calls the complete rear desired planned trajectory of corresponding actions function.The present invention ensure that using quadravalence cubic B-spline function programming movement track will not cause wedge angle problem at adjacent segment, it is to avoid the vibrations of articulated mechanical arm, improve stability of the anthropomorphic robot in motion process.
Description
Technical field
It is more particularly to a kind of to be based on quadravalence three times the present invention relates to robot joints trajectory planning control technology field
The method for planning track of robot and anthropomorphic robot platform of B-spline function.
Background technology
With service-delivery machine man-based development, domestic and international each research institution, universities and colleges, the research manufacture of manufacturer of robot
Go out to be suitable for the service robot product of household use.Wherein anthropomorphic robot is particularly closed as one of focus
Note, wherein the scholar of the state such as Japan and the United States has carried out extensive research in anthropomorphic robot field, achieves more theory
And practical result, realize from static walking to dynamic walking, from segregation reasons to real-time control, from level walking to slope,
Travelling up or down a flight of stairs, from simple biped walking mechanism to the development of the anthropomorphic robot with arm, head and waist.
The trajectory planning of robot has important effect in the control of robot, and work of its performance to robot is imitated
Rate, robust motion and energy expenditure have decisive significance.Require that robotic mechanical system exists in actual production application
It should be tried one's best in motion process steady shockproof, it is to avoid displacement, speed, the mutation of acceleration.The motion of mutation needs greatly dynamic
Power, and motor is limited by physics can not provide so big energy so as to cause wearing and tearing for joint of robot, reduction is used
Life-span.Suitable method must be chosen in order to meet these requirements to plan the movement locus of robot, machine can be made
Each joint motions of people are steadily shockproof, and energy-efficient, the purpose of quick response to desired locations can be reached again.
The content of the invention
It is an object of the invention to overcome shortcoming and deficiency of the prior art there is provided one kind based on quadravalence cubic B-spline
The method that function plans oint motion trajectory, generation can reach the gait walking of stable motion condition.By using quadravalence three
Secondary B-spline function constructs the movement locus of anthropomorphic robot so that the speed in each joint of robot, acceleration, acceleration
Derivative it is continuous, it is to avoid each joint steering wheel occurs interrupted, situations such as vibrations, realizes that the planned trajectory under ZMP stable conditions is moved
Make.The present invention is to walk each joint in space by can be maintained in particular track motion process with anthropomorphic robot arm and leg
Control method under ZMP stable conditions, the movement locus in each joint is planned by using quadravalence cubic B-spline function, by
Interarticular DC motor Driver joint generation movement locus simultaneously can do stable motion under robot ZMP stable conditions.
Meanwhile, the present invention builds a set of Motion Controller for Humanoid Robot during relative trajectory planning is carried out,
The action after corresponding Track Pick-up is completed, the track feasibility of its planning is verified.The present invention enters every trade suitable for anthropomorphic robot
Walk, nautch, during human-computer interaction, pass through the movement locus action set and complete particular task.Letter is acted in foundation
Before number, first joint action track as needed determines quadravalence cubic B-spline function, its track point coordinates of densification, according to obtaining
Track point coordinates construct function of movement on the time, the driving in each joint is controlled by Motion Controller for Humanoid Robot
Motor, completes to meet the trajectory planning motion under the conditions of ZMP.
A kind of method for planning track of robot based on quadravalence cubic B-spline function, it is characterised in that comprise the following steps：
Step 1：A B-spline function is defined, the mathematical modeling of B-spline function is shifted out onto by the B-spline function of definition；
Step 2：Solve quadravalence cubic B-spline function expression formula：By the B-spline function of definition, first assume quadravalence three
The expression formula of secondary B-spline function, will be connected by its boundary condition with single order, second order, three rank inverses at shape value point, can
The parametric solution of quadravalence cubic B-spline function is solved to draw 12 conditions, so as to obtain quadravalence cubic B-spline function
Expression formula；
Step 3：Track densification, carries out the densification of parameter, calculates the corresponding parameter value u of each interpolated point, then first
The coordinate that interpolated point is sought in batten parametric equation is brought into, the quadravalence cubic B-spline function geometric locus after densification can be obtained,
Complete the planned trajectory generation of each joint motions of anthropomorphic robot；
Step 4：Motion Controller for Humanoid Robot is built, by the motion control system for building each joint of anthropomorphic robot
System completes the function of movement that each joint generates track, realizes the motion control of anthropomorphic robot planning action；
Step 5：Judge motion state of the planned trajectory of generation under anthropomorphic robot ZMP stable conditions, be each pass
Section is edited into the function of movement of next shape value point, reaches and initial actuating point is set to after shape value point coordinates, under continuing to be designed into and reaching
The function of movement of one shape value point, the last shape value point until generating track judges whether robot reaches that ZMP is stable.
It is preferred that, a kind of method for planning track of robot based on quadravalence cubic B-spline function, it further comprises following
Step：
(1) B-spline function is defined, B-spline function mathematical modeling is derived；
1) B-spline function is defined as follows：
Wherein, k ＞ 1, i=0,1 ..., n-k, u be parameter；
2)：The mathematical modeling of B-spline function can be derived using above formula：If the mechanical arm of service robot is empty in joint
Between in have a series of data point P1、P2、...、Pm, m+2 control point V can be obtained by the condition of continuity and boundary condition0、
V1、...、Vm+1, whole piece track is divided into m-1 sections, can using each section of batten track as B-spline track a track region
Between, the end of every section of track is the top of next section of track, continuous at the whole story of every section of batten track, i-th section of B-spline curves
Connect PiAnd Pi+1Data point, then can be segmented the B-spline shape value locus of points curve for representing mechanical arm in joint space；
(2)：Solve quadravalence cubic B-spline function
If i-th section of curve is by Vi-1、Vi、Vi+1、Vi+2Four control points are controlled, if quadravalence cubic uniform B-spline function
Expression formula is：
θi(u)=X0(u)Vi-1+X1(u)Vi+X2(u)Vi+1+X3(u)Vi+2
In formula, u is parameter, and 0≤u≤1, Xi(u) it is parametric polynomial, θi(u) B-spline curves for i-th section, i.e., should
The geometric locus of section, in addition, in addition it is also necessary to meet the unvarying condition after Cauchy's relation, i.e. coordinate transform：
X0(u)+X1(u)+X2(u)+X3(u)=1
Xi(u) it is cubic polynomial, can obtain the polynomial coefficient according to above formula is：
The B-spline curves track that can determine i-th section according to the multinomial coefficient is：
There are m+2 numbers to need solution in above formula, but known according to solution procedure above, there is m known conditions, therefore will
Want to solve the unknown number that place has, in addition it is also necessary to two known conditions, it is as follows：
V1=V0Vm+1=Vm,
It can then obtain：
One group of V can be uniquely determined by above formulaiValue, it is possible thereby to determine the track of B-spline Curve；
(3)：Track densification method
For quadravalence cubic B-spline track densification, the densification of parameter is carried out first, the corresponding ginseng of each interpolated point is calculated
Numerical value u, is brought into the coordinate that interpolated point is sought in batten parametric equation；
If v (t) is interpolation rate：
Then have：
Wherein：
It can obtain：
Deployed using Taylor's single order：
Above formula (15) is substituted into (16) to obtain：
T is interpolation cycle, and u value can be calculated by the recurrence formula of formula (17), substitutes into cubic spline function formula Q
(u)=au3+bu2+ cu+d, it can be deduced that Q (u (T)), Q (u (2T)), etc., you can the position for calculating each interpolated point is sat
Mark；
Step 5：Robot joints track action command system is built, writes out different according to different tracks
Action command realizes the task action planned.
The present invention also provides a kind of apery machine of the method for planning track of robot based on the quadravalence cubic B-spline function
Device people's platform, is completed under the conditions of ZMP according to the track planned by DC motor Driver mechanical arm and each joint of lower limb
Stability contorting is moved；
(1) Motion Controller for Humanoid Robot based on quadravalence cubic B-spline lopcus function, including smart mobile phone are built
And its APP application software for the specific action developed, the bluetooth communication that raspberry factions unite and its are attached thereto, No. 16 rudders
Machine controller, anthropomorphic robot；
(2) raspberry factions system tune is passed to by Bluetooth communication by mobile phone application software transmission planned trajectory action password
With its corresponding actions function, 16 road servos control plates are passed to by serial communication, each articulated mechanical arm are driven by the shape of planning
Value point action, reaches desired action request, and examine whether it reaches stable state under the conditions of ZMP.
The present invention compared with prior art, has the following advantages and feature：
(1) in humanoid robot system, the movement locus in each joint generally carries out interpolation using straight line and circular arc, for
Complicated geometric locus is difficult to, with simple straight line and arc representation, interpolation fitting be carried out to these complicated geometric locuses, must
Geometric locus must be divided into the straight line or circular arc of many segments, this will cause to calculate complicated, and interpolation efficiency is low, and joint action delays
Slowly, it is impossible to reach control speed and required precision.Complex curve can be reduced using three rank B-spline function moving interpolation tracks
Interpolation problem, its speed, acceleration, acceleration can continuously be led, and can be prevented effectively from machinery pass caused by path acceleration wedge angle
The friction of section, vibration problems.
(2) function of movement that the track shape value point generated using quadravalence cubic B-spline function is write.In anthropomorphic robot control
In system processed, corresponding planned trajectory is made by each articulated mechanical arm DC motor Driver and acted, it is ensured that be under the conditions of ZMP steady
Determine motion state.
Brief description of the drawings
Fig. 1 is interpolating method at anthropomorphic robot adjacent segment；
Fig. 2 is the densification method of anthropomorphic robot planned trajectory；
Fig. 3 is the corresponding trajectory planning control system for the anthropomorphic robot built.
Embodiment
It is an object of the invention to overcome the shortcoming and deficiency of prior art there is provided one kind to be based on quadravalence cubic B-spline letter
Several method for planning track of robot and anthropomorphic robot platform.
Wherein, a kind of method for planning track of robot based on quadravalence cubic B-spline function, is comprised the following steps：
Step 1：A B-spline function is defined, the mathematical modeling of B-spline function is shifted out onto by the B-spline function of definition；
Step 2：Solve quadravalence cubic B-spline function expression formula：By the B-spline function of definition, first assume quadravalence three
The expression formula of secondary B-spline function, will be pointed out in shape value with single order, second order, three rank inverses by its boundary condition and be connected, can
The parametric solution of quadravalence cubic B-spline function is solved to draw 12 conditions, so as to obtain quadravalence cubic B-spline function
Expression formula；
Step 3：Track densification, carries out the densification of parameter, calculates the corresponding parameter value u of each interpolated point, then first
The coordinate that interpolated point is sought in batten parametric equation is brought into, the quadravalence cubic B-spline function geometric locus after densification can be obtained,
Complete the planned trajectory generation of each joint motions of anthropomorphic robot；
Step 4：Motion Controller for Humanoid Robot is built, by the motion control system for building each joint of anthropomorphic robot
System completes the function of movement that each joint generates track, realizes the motion control of anthropomorphic robot planning action；
Step 5：Judge motion state of the planned trajectory of generation under anthropomorphic robot ZMP stable conditions, be each pass
Section is edited into the function of movement of next shape value point, reaches and initial actuating point is set to after shape value point coordinates, under continuing to be designed into and reaching
The function of movement of one shape value point, the last shape value point until generating track judges whether robot reaches that ZMP is stable.
It is preferred that, a kind of method for planning track of robot based on quadravalence cubic B-spline function, specific implementation step is such as
Under：
(1) the oint motion trajectory design based on quadravalence cubic B-spline function.
The present invention realizes the oint motion trajectory based on quadravalence cubic B-spline function using following steps.
Step 1：A B-spline function is defined, it is as follows that we can define B-spline function：
Wherein, k ＞ 1, i=0,1 ..., n-k, u be parameter.
Step 2：The mathematical modeling of B-spline function is shifted out onto by the B-spline function of definition, if the machinery of service robot
Arm has a series of data point P in joint space1、P2、...、Pm, m+2 can be obtained by the condition of continuity and boundary condition
Control point V0、V1、...、Vm+1, whole piece track is divided into m-1 sections, can regard each section of batten track as the one of B-spline track
Individual track is interval, and the end of every section of track is the top of next section of track, continuous at the whole story of every section of batten track, i-th section of B
SPL connects PiAnd Pi+1Data point.The B-spline shape value locus of points for representing mechanical arm in joint space can be then segmented
Curve.
Step 3：Quadravalence cubic B-spline function is solved, if i-th section of curve is by Vi-1、Vi、Vi+1、Vi+2Four control points are controlled
System, if the coordinate at control point is as follows：
Vi-1(vi-1, qi-1), Vi(vi, qi), Vi+1(vi+1, qi+1), Vi+2(vi+2, qi+2) (1)
Can set the expression formula of quadravalence cubic uniform B-spline function as：
θi(u)=X0(u)Vi-1+X1(u)Vi+X2(u)Vi+1+X3(u)Vi+2 (2)
In formula, u is parameter, and 0≤u≤1, Xi(u) it is parametric polynomial, θi(u) B-spline curves for i-th section, i.e., should
The geometric locus of section, the geometric locus is connected by the top of end and i+1 the section track of the i-th -1 section track, then and adjacent two
The B-spline curves θ of data pointiAnd θ (u)i+1(u) following condition is met at u=0 and u=1 respectively：
θi(1)=θi+1(0) (3)
Above-mentioned two formula, which is merged, to be obtained：
X0(1)=X3(0)=0, X1(1)=X0(0), X2(1)=X1(0), X3(1)=X2(0) (4)
Single order, second order and three order derivatives of B-spline curves between two data points will be at i-1 sections end and i+1
The top of section is connected, and physical relationship is as follows：
θ′i(1)=θ 'i+1(0), θ "i(1)=θ "i+1(0), θ " 'i(1)=θ " 'i+1(0) (5)
It can thus be concluded that 12 conditions are：
In addition, in addition it is also necessary to meet the unvarying condition after Cauchy's relation, i.e. coordinate transform：
X0(u)+X1(u)+X2(u)+X3(u)=1 (7)
Xi(u) it is cubic polynomial, can obtain the polynomial coefficient according to above formula is：
There are m+2 numbers to need solution in above formula (8), but know there be m known conditions according to solution procedure above, because
This wants to solve the unknown number that place has, in addition it is also necessary to two known conditions, as follows：
V1=V0, Vm+1=Vm (9)
It can then obtain：
One group of V can be uniquely determined by formula (10)iValue, it is possible thereby to determine the track of quadravalence B-spline Curve.
Step 4：Track densification method, for quadravalence cubic B-spline track densification, we carry out the densification of parameter first,
The corresponding parameter value u of each interpolated point is calculated, the coordinate that interpolated point is sought in batten parametric equation is brought into.Referring specifically to accompanying drawing
1 is interpolating method at anthropomorphic robot adjacent segment, and accompanying drawing 2 is the densification method of anthropomorphic robot planned trajectory.
If v (t) is interpolation rate：
Then have：
Wherein：
Formula (13), which is brought into formula (12), to be obtained：
Deployed using Taylor's single order：
Above formula (15) is substituted into (16) to obtain：
T is interpolation cycle, and u value can be calculated by the recurrence formula of formula (17), substitutes into cubic spline function formula
Q (u)=au3+bu2+cu+d (18)
Q (u (T)), Q (u (2T)) can be drawn, etc., you can calculate the position coordinates of each interpolated point.
Step 5：Robot joints track action command system is built, writes out different according to different tracks
Action command realizes the task action planned.Such as complete stable walking, performance of squatting down, arm, which is saluted, to be acted etc..
Fig. 3 is the corresponding trajectory planning control system for the anthropomorphic robot built, and the present invention relates to a kind of anthropomorphic robot
Oint motion trajectory planing method, with reference to mobile phone, raspberry factions system, mechanical arm steering engine controller, anthropomorphic robot, has been erected
Whole anthropomorphic robot movement locus moving system.Instructed by smart mobile phone sending action, being received on raspberry factions system should
Instruction, calls relevant action function, transmits the function of movement to 16 road steering engine controllers, each joint Execution plan of driving robot
Good track action.Its method for planning track uses quadravalence cubic B-spline function tectonic movement track, can by track densification
To obtain each shape value point coordinates in track, corresponding actions function is edited, it is corresponding that driving joint steering engine controller completes anthropomorphic robot
Action.
The present invention also provides a kind of based on the quadravalence cubic B-spline function anthropomorphic robot trajectory planning control method
Anthropomorphic robot platform, is completed in ZMP bars according to the track planned by DC motor Driver mechanical arm and each joint of lower limb
Stability contorting motion under part；
(1) Motion Controller for Humanoid Robot based on quadravalence cubic B-spline lopcus function, including smart mobile phone are built
And its APP application software for the specific action developed, the bluetooth communication that raspberry factions unite and its are attached thereto, No. 16 rudders
Machine controller, anthropomorphic robot；
(2) raspberry factions system tune is passed to by Bluetooth communication by mobile phone application software transmission planned trajectory action password
With its corresponding actions function, 16 road servos control plates are passed to by serial communication, each articulated mechanical arm are driven by the shape of planning
Value point action, reaches desired action request, and examine whether it reaches stable state under the conditions of ZMP.
Above-described embodiment is preferably embodiment, but embodiments of the present invention are not by above-described embodiment of the invention
Limitation, other any Spirit Essences without departing from the present invention and the change made under principle, modification, replacement, combine, simplification,
Equivalent substitute mode is should be, is included within protection scope of the present invention.
Claims (3)
1. a kind of method for planning track of robot based on quadravalence cubic B-spline function, it is characterised in that comprise the following steps：
Step 1：A B-spline function is defined, the mathematical modeling of B-spline function is shifted out onto by the B-spline function of definition；
Step 2：Solve quadravalence cubic B-spline function expression formula：By the B-spline function of definition, first assume three B samples of quadravalence
The expression formula of bar function, will be connected at shape value point with single order, second order, three rank inverses by its boundary condition, can obtained
Go out 12 conditions to solve the parametric solution of quadravalence cubic B-spline function, so as to obtain the expression of quadravalence cubic B-spline function
Formula；
Step 3：Track densification, carries out the densification of parameter, calculates the corresponding parameter value u of each interpolated point, then bring into first
The coordinate of interpolated point is sought into batten parametric equation, the quadravalence cubic B-spline function geometric locus after densification can be obtained, is completed
The planned trajectory generation of each joint motions of anthropomorphic robot；
Step 4：Motion Controller for Humanoid Robot is built, it is complete by the kinetic control system for building each joint of anthropomorphic robot
The function of movement of track is generated into each joint, the motion control of anthropomorphic robot planning action is realized；
Step 5：Judge motion state of the planned trajectory of generation under anthropomorphic robot ZMP stable conditions, be that each joint is compiled
The function of movement to next shape value point is collected, reaches and initial actuating point is set to after shape value point coordinates, continue to be designed into up to next
The function of movement of shape value point, the last shape value point until generating track judges whether robot reaches that ZMP is stable.
2. a kind of method for planning track of robot based on quadravalence cubic B-spline function as claimed in claim 1, its feature exists
Further comprise the steps in it：
(1) B-spline function is defined, B-spline function mathematical modeling is derived；
1) B-spline function is defined as follows：
Wherein, k ＞ 1, i=0,1 ..., n-k, u be parameter；
2)：The mathematical modeling of B-spline function can be derived using above formula：If the mechanical arm of service robot is in joint space
There is a series of data point P1、P2、...、Pm, m+2 control point V can be obtained by the condition of continuity and boundary condition0、
V1、...、Vm+1, whole piece track is divided into m-1 sections, can using each section of batten track as B-spline track a track region
Between, the end of every section of track is the top of next section of track, continuous at the whole story of every section of batten track, i-th section of B-spline curves
Connect PiAnd Pi+1Data point, then can be segmented the B-spline shape value locus of points curve for representing mechanical arm in joint space；
(2)：Solve quadravalence cubic B-spline function
If i-th section of curve is by Vi-1、Vi、Vi+1、Vi+2Four control points are controlled, if the expression of quadravalence cubic uniform B-spline function
Formula is：
θi(u)=X0(u)Vi-1+X1(u)Vi+X2(u)Vi+1+X3(u)Vi+2
In formula, u is parameter, and 0≤u≤1, Xi(u) it is parametric polynomial, θi(u) it is i-th section of B-spline curves, i.e. this section
Geometric locus, in addition, in addition it is also necessary to meet the unvarying condition after Cauchy's relation, i.e. coordinate transform：
X0(u)+X1(u)+X2(u)+X3(u)=1
Xi(u) it is cubic polynomial, can obtain the polynomial coefficient according to above formula is：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>X</mi>
<mn>0</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<mn>6</mn>
</mfrac>
<mo>,</mo>
<msub>
<mi>X</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msup>
<mi>u</mi>
<mn>3</mn>
</msup>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo>-</mo>
<msup>
<mi>u</mi>
<mn>3</mn>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>X</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<msup>
<mi>u</mi>
<mn>3</mn>
</msup>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mi>u</mi>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<mo>,</mo>
<msub>
<mi>X</mi>
<mn>3</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msup>
<mi>u</mi>
<mn>3</mn>
</msup>
<mn>6</mn>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
The B-spline curves track that can determine i-th section according to the multinomial coefficient is：
<mrow>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<mo>&lsqb;</mo>
<msup>
<mi>u</mi>
<mn>3</mn>
</msup>
<mo>,</mo>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
<mo>,</mo>
<mi>u</mi>
<mo>,</mo>
<mn>1</mn>
<mo>&rsqb;</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
<mtd>
<mn>3</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mn>3</mn>
</mrow>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mn>6</mn>
</mrow>
</mtd>
<mtd>
<mn>3</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>3</mn>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>3</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>4</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
There are m+2 numbers to need solution in above formula, but know there be m known conditions according to solution procedure above, therefore want to ask
The unknown number that solution place has, in addition it is also necessary to two known conditions, it is as follows：
V1=V0, Vm+1=Vm
It can then obtain：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>6</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mn>6</mn>
</mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>4</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>4</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>4</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mn>6</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mn>6</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>V</mi>
<mn>0</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>V</mi>
<mn>1</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>V</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>...</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>V</mi>
<mi>m</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>V</mi>
<mrow>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mn>6</mn>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>P</mi>
<mn>1</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>P</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>P</mi>
<mi>m</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
One group of V can be uniquely determined by above formulaiValue, it is possible thereby to determine the track of B-spline Curve；
(3)：Track densification method
For quadravalence cubic B-spline track densification, the densification of parameter is carried out first, the corresponding parameter value of each interpolated point is calculated
U, is brought into the coordinate that interpolated point is sought in batten parametric equation；
If v (t) is interpolation rate：
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi>s</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi>s</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>u</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi>u</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
Then have：
<mrow>
<mfrac>
<mrow>
<mi>d</mi>
<mi>u</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>d</mi>
<mi>s</mi>
<mo>/</mo>
<mi>d</mi>
<mi>u</mi>
</mrow>
</mfrac>
</mrow>
Wherein：
<mrow>
<mfrac>
<mrow>
<mi>d</mi>
<mi>s</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>u</mi>
</mrow>
</mfrac>
<mo>=</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mrow>
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mfenced open = "" close = "}">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>x</mi>
<mo>=</mo>
<msub>
<mi>Q</mi>
<mi>x</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>y</mi>
<mo>=</mo>
<msub>
<mi>Q</mi>
<mi>y</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>z</mi>
<mo>=</mo>
<msub>
<mi>Q</mi>
<mi>z</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mtd>
<mtd>
<mfenced open = "" close = "}">
<mtable>
<mtr>
<mtd>
<mrow>
<mover>
<mi>x</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>dQ</mi>
<mi>x</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>d</mi>
<mi>u</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mover>
<mi>y</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>dQ</mi>
<mi>y</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>d</mi>
<mi>u</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mover>
<mi>z</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>dQ</mi>
<mi>z</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>d</mi>
<mi>u</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mtd>
</mtr>
</mtable>
</mfenced>
It can obtain：
<mrow>
<mfrac>
<mrow>
<mi>d</mi>
<mi>u</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
Deployed using Taylor's single order：
<mrow>
<mi>u</mi>
<mrow>
<mo>(</mo>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
<mi>T</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>u</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mi>T</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>T</mi>
<mo>&CenterDot;</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi>u</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
<msub>
<mo>|</mo>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mi>K</mi>
<mi>T</mi>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
Above formula (15) is substituted into (16) to obtain：
<mrow>
<mi>u</mi>
<mrow>
<mo>(</mo>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
<mi>T</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>u</mi>
<mrow>
<mo>(</mo>
<mi>K</mi>
<mi>T</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>T</mi>
<mo>&CenterDot;</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
<msub>
<mo>|</mo>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mi>K</mi>
<mi>T</mi>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>17</mn>
<mo>)</mo>
</mrow>
</mrow>
T is interpolation cycle, and u value can be calculated by the recurrence formula of formula (17), substitute into cubic spline function formula Q (u)=
au3+bu2+ cu+d, it can be deduced that Q (u (T)), Q (u (2T)), etc., you can calculate the position coordinates of each interpolated point；
Step 5：Robot joints track action command system is built, different actions are write out according to different tracks
The task action planned is realized in instruction.
3. a kind of apery machine of the method for planning track of robot of the quadravalence cubic B-spline function based on described in claim 1 or 2
Device people's platform, is completed under the conditions of ZMP according to the track planned by DC motor Driver mechanical arm and each joint of lower limb
Stability contorting is moved；
(1) build the Motion Controller for Humanoid Robot based on quadravalence cubic B-spline lopcus function, including smart mobile phone and its
The APP application software for the specific action developed, the bluetooth communication that raspberry factions unite and its are attached thereto, 16 road steering wheel controls
Device processed, anthropomorphic robot；
(2) raspberry factions system is passed to by Bluetooth communication by mobile phone application software transmission planned trajectory action password and calls it
Corresponding actions function, 16 road servos control plates are passed to by serial communication, drive each articulated mechanical arm by the shape value point of planning
Action, reaches desired action request, and examine whether it reaches stable state under the conditions of ZMP.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710155012.5A CN107116549A (en) | 2017-03-15 | 2017-03-15 | A kind of method for planning track of robot and anthropomorphic robot platform based on quadravalence cubic B-spline function |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710155012.5A CN107116549A (en) | 2017-03-15 | 2017-03-15 | A kind of method for planning track of robot and anthropomorphic robot platform based on quadravalence cubic B-spline function |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN107116549A true CN107116549A (en) | 2017-09-01 |
Family
ID=59717395
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710155012.5A Pending CN107116549A (en) | 2017-03-15 | 2017-03-15 | A kind of method for planning track of robot and anthropomorphic robot platform based on quadravalence cubic B-spline function |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107116549A (en) |
Cited By (15)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108037661A (en) * | 2017-11-30 | 2018-05-15 | 江苏省生产力促进中心 | Its Track Design method for cameras people |
| CN108081288A (en) * | 2018-02-02 | 2018-05-29 | 南京工业职业技术学院 | A kind of intelligent robot |
| CN108415427A (en) * | 2018-02-11 | 2018-08-17 | 昆山艾派科技有限公司 | The path joining method that robot multistep continuously moves |
| CN108731701A (en) * | 2018-05-30 | 2018-11-02 | 苏州工业职业技术学院 | Biped robot's mileage travelled metering device |
| CN108919750A (en) * | 2018-07-27 | 2018-11-30 | 深圳市雷赛控制技术有限公司 | A kind of real-time method and device for planning of machining locus based on uniform B-Spline |
| CN110427046A (en) * | 2019-07-26 | 2019-11-08 | 沈阳航空航天大学 | A kind of three-dimensional smooth random walk unmanned aerial vehicle group mobility model |
| CN111208807A (en) * | 2018-11-06 | 2020-05-29 | 苏州艾吉威机器人有限公司 | AGV motion control method based on B spline curve |
| CN112100869A (en) * | 2020-11-16 | 2020-12-18 | 北京云圣智能科技有限责任公司 | Power line point supplementing method and device and electronic equipment |
| CN112269356A (en) * | 2020-10-27 | 2021-01-26 | 南京溧航仿生产业研究院有限公司 | NURBS track interpolation method for robot |
| CN113031511A (en) * | 2019-12-24 | 2021-06-25 | 沈阳智能机器人创新中心有限公司 | Multi-axis system real-time guiding track planning method based on high-order B spline |
| CN113520275A (en) * | 2021-08-13 | 2021-10-22 | 元化智能科技(深圳)有限公司 | Trajectory tracking system, apparatus and medium for wireless capsule endoscope |
| CN113635296A (en) * | 2021-06-30 | 2021-11-12 | 苏州艾吉威机器人有限公司 | Method for tracking arbitrary curve path |
| WO2021248797A1 (en) * | 2020-06-08 | 2021-12-16 | 苏州艾吉威机器人有限公司 | B-spline curve-based path planning method and system, and motion control method and system |
| CN114035512A (en) * | 2021-11-22 | 2022-02-11 | 广东工业大学 | Minimum speed fluctuation interpolation method based on two-time Taylor expansion |
| CN114193449A (en) * | 2021-12-09 | 2022-03-18 | 中国煤炭科工集团太原研究院有限公司 | Anchor rod support robot working arm track planning method |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103770111A (en) * | 2012-10-24 | 2014-05-07 | 中国人民解放军第二炮兵工程大学 | Gait planning and synthetic method for humanoid robot |
| CN103802113A (en) * | 2012-11-08 | 2014-05-21 | 沈阳新松机器人自动化股份有限公司 | Industrial robot route planning method based on task and spline |
-
2017
- 2017-03-15 CN CN201710155012.5A patent/CN107116549A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103770111A (en) * | 2012-10-24 | 2014-05-07 | 中国人民解放军第二炮兵工程大学 | Gait planning and synthetic method for humanoid robot |
| CN103802113A (en) * | 2012-11-08 | 2014-05-21 | 沈阳新松机器人自动化股份有限公司 | Industrial robot route planning method based on task and spline |
Non-Patent Citations (1)
| Title |
|---|
| 赵皓等: "基于三次非均匀B样条的6DOF机械臂轨迹规划", 《机器人技术与应用》 * |
Cited By (21)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108037661A (en) * | 2017-11-30 | 2018-05-15 | 江苏省生产力促进中心 | Its Track Design method for cameras people |
| CN108081288A (en) * | 2018-02-02 | 2018-05-29 | 南京工业职业技术学院 | A kind of intelligent robot |
| CN108415427A (en) * | 2018-02-11 | 2018-08-17 | 昆山艾派科技有限公司 | The path joining method that robot multistep continuously moves |
| CN108731701A (en) * | 2018-05-30 | 2018-11-02 | 苏州工业职业技术学院 | Biped robot's mileage travelled metering device |
| CN108919750A (en) * | 2018-07-27 | 2018-11-30 | 深圳市雷赛控制技术有限公司 | A kind of real-time method and device for planning of machining locus based on uniform B-Spline |
| CN108919750B (en) * | 2018-07-27 | 2020-01-21 | 深圳市雷赛控制技术有限公司 | Non-uniform B-spline-based real-time planning method and device for processing track |
| CN111208807A (en) * | 2018-11-06 | 2020-05-29 | 苏州艾吉威机器人有限公司 | AGV motion control method based on B spline curve |
| CN110427046A (en) * | 2019-07-26 | 2019-11-08 | 沈阳航空航天大学 | A kind of three-dimensional smooth random walk unmanned aerial vehicle group mobility model |
| CN110427046B (en) * | 2019-07-26 | 2022-09-30 | 沈阳航空航天大学 | Three-dimensional smooth random-walking unmanned aerial vehicle cluster moving model |
| CN113031511A (en) * | 2019-12-24 | 2021-06-25 | 沈阳智能机器人创新中心有限公司 | Multi-axis system real-time guiding track planning method based on high-order B spline |
| CN113031511B (en) * | 2019-12-24 | 2022-03-22 | 沈阳智能机器人创新中心有限公司 | Multi-axis system real-time guiding track planning method based on high-order B spline |
| WO2021248797A1 (en) * | 2020-06-08 | 2021-12-16 | 苏州艾吉威机器人有限公司 | B-spline curve-based path planning method and system, and motion control method and system |
| CN112269356A (en) * | 2020-10-27 | 2021-01-26 | 南京溧航仿生产业研究院有限公司 | NURBS track interpolation method for robot |
| CN112269356B (en) * | 2020-10-27 | 2022-03-18 | 南京溧航仿生产业研究院有限公司 | NURBS track interpolation method for robot |
| CN112100869A (en) * | 2020-11-16 | 2020-12-18 | 北京云圣智能科技有限责任公司 | Power line point supplementing method and device and electronic equipment |
| CN113635296A (en) * | 2021-06-30 | 2021-11-12 | 苏州艾吉威机器人有限公司 | Method for tracking arbitrary curve path |
| CN113520275A (en) * | 2021-08-13 | 2021-10-22 | 元化智能科技(深圳)有限公司 | Trajectory tracking system, apparatus and medium for wireless capsule endoscope |
| CN114035512A (en) * | 2021-11-22 | 2022-02-11 | 广东工业大学 | Minimum speed fluctuation interpolation method based on two-time Taylor expansion |
| CN114035512B (en) * | 2021-11-22 | 2022-09-23 | 广东工业大学 | Minimum speed fluctuation interpolation method based on two-time Taylor expansion |
| CN114193449A (en) * | 2021-12-09 | 2022-03-18 | 中国煤炭科工集团太原研究院有限公司 | Anchor rod support robot working arm track planning method |
| CN114193449B (en) * | 2021-12-09 | 2023-08-11 | 中国煤炭科工集团太原研究院有限公司 | Working arm track planning method of anchor bolt support robot |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107116549A (en) | A kind of method for planning track of robot and anthropomorphic robot platform based on quadravalence cubic B-spline function | |
| CN111046589B (en) | Intelligent production line testable digital twin body modeling method | |
| CN102662350B (en) | Track teaching and planning method of master-slave mode multi-robot cooperative system | |
| CN108089578B (en) | Walking motion planning method for biped walking robot | |
| CN104192221B (en) | A kind of electric drive Hexapod Robot kinetic control system and method | |
| CN103147577B (en) | Control method, device and system for multi-joint mechanical arm support and engineering machinery | |
| CN104808590B (en) | Mobile robot visual servo control method based on key frame strategy | |
| WO2017092463A1 (en) | Method of controlling walking posture of biped robot and device | |
| CN106863306A (en) | A kind of robotic joint space smooth track planing method | |
| CN103324196A (en) | Multi-robot path planning and coordination collision prevention method based on fuzzy logic | |
| CN108724191A (en) | A kind of robot motion's method for controlling trajectory | |
| CN103770111A (en) | Gait planning and synthetic method for humanoid robot | |
| CN113687659B (en) | Optimal trajectory generation method and system based on digital twinning | |
| JPWO2002066210A1 (en) | Robot controller | |
| CN107121930A (en) | Six Degree-of-Freedom Parallel Platform motion control method based on dummy model | |
| CN117655468A (en) | Portal frame arc welding robot path planning method and system | |
| Fan et al. | Integrated planning and control of large tracked vehicles in open terrain | |
| CN104267598A (en) | Method for designing fuzzy PI controller of Delta robot movement mechanism | |
| CN104915481A (en) | Spherical motor cooperative control based on virtual prototype modeling and periodic planning | |
| CN114800523B (en) | Mechanical arm track correction method, system, computer and readable storage medium | |
| Agrawal et al. | Bipedal robotic running on stochastic discrete terrain | |
| CN113867157B (en) | Optimal trajectory planning method and device for control compensation and storage device | |
| CN113885540B (en) | Motion planning and control method for climbing and crossing of wall surface of underwater hexapod robot | |
| CN112256028B (en) | Method, system, equipment and medium for controlling compliant gait of biped robot | |
| CN103978484A (en) | Efficient and high-precision leg type gait planning method based on planet wheel mechanism legged robot |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| WD01 | Invention patent application deemed withdrawn after publication | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20170901 |