CN110039544A - Apery Soccer robot gait planning based on cubic spline interpolation - Google Patents
Apery Soccer robot gait planning based on cubic spline interpolation Download PDFInfo
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- 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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
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- 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
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Abstract
Apery Soccer robot gait planning based on cubic spline interpolation, includes the following steps: step 1, establishes kinematics model by the structure of robot；Step 2, based on kinematics model, the gait of planning robot is carried out in conjunction with the method for space cubic spline interpolation；Step 3, the stability control algorithm optimization robot gait inhibited by vibration.The present invention improves the disadvantage of robot ambulation shakiness, so that robot has good robustness to realize walking and the behaviors of grade of playing football；Using cubic spline interpolation law of planning, it can be good at guaranteeing the geometrical relationship between each joint in NAO robot soccer movement gait planning, and also more convenient for the realization of optimizing stability later；Deflecting angle and offset distance in walking process have by new gait planning and algorithm optimization largely to be reduced, and the walking Stability and veracity of robot is enhanced.
Description
Technical field
The present invention relates to a kind of apery Soccer robot gait planning based on cubic spline interpolation, belongs to robot control
Field.
Background technique
Apery Soccer robot is the hot spot of current robot research, is related to robotics, intelligent control, computer vision
Etc. multiple fields.It simulates mankind's football using football match as platform, realizes autonomous, the functions such as play football, wherein
The cooperation being related between multiple agent provides one for robotics, multi-agent system theoretical research and technical application
Good experiment porch.
Walking planning and stability control research are in anthropomorphic robot research in occupation of critically important status, its realization
Very big contribution is made that the development of anthropomorphic robot.
Summary of the invention
The present invention propose the apery Soccer robot gait planning based on cubic spline interpolation, by the structure of robot come
Kinematics model is established, the method in conjunction with space cubic spline interpolation carrys out the gait of planning robot based on this, and passes through
Shake inhibit stability control algorithm optimization robot gait so that robot have good robustness realize walking and
Grade of playing football behaviors.
Apery Soccer robot gait planning based on cubic spline interpolation, includes the following steps:
Step 1, kinematics model is established by the structure of robot；
The kinematics model is established based on NAO biped robot, specifically with time resolution function to robot
Movement is decoupled, and the relationship between each joint angles of robot and each joint link lever pose, the kinematics model packet are solved
Include lateral movement modeling and Forward kinematics modeling；
Step 2, based on kinematics model, the step of planning robot is carried out in conjunction with the method for space cubic spline interpolation
State；
The planning of the gait uses the form of space planning, using the method for space cubic spline interpolation, with reference to machine
The traveling movement of robot is split as the coordinated movement of various economic factors in each joint, with space coordinate generation by the position of each joint of people in space
For time sequencing；
Step 3, the stability control algorithm optimization robot gait inhibited by vibration；
The stability control algorithm, the first initial centroid trajectory of solution robot simultaneously control rail as initial
Then mark constructs and solves the optimal control problem with restricted problem, finally applies it in robot walking planning.
Further, in the step 1, the lateral movement modeling connects NAO robot leg and hip joint
The place of connecing is reduced to five connecting rod models, and reference frame is established at robot ankle, by Forward Kinematics Analysis, according to geometry
Relationship obtains the position coordinates of each joint and each connecting rod mass center in a coordinate system；By Analysis of Inverse Kinematics, swung by given
The motion profile of leg ankle-joint and hip joint in fixed coordinate system, finds out the angle in each joint of robot.
Further, in the step 1, Forward kinematics modeling, it is specified that the upper body of robot is perpendicular to the ground, and
Hip joint keeps horizontal when moving, and obtaining robot when moving by geometrical relationship is the maximum for keeping stablizing body swing
Angle.
Further, the method for the space cubic spline interpolation in the step 2, specifically, when robot gait is planned
Upper limb is kept upright, then the pose of robot can be determined according to the ankle-joint of swinging kick, and the height for ankle-joint of leading leg is taken to become
Change situation is as reference variable, to cook up robot hip joint and the respective space motion path of ankle-joint of leading leg, and
The movement relation between each joint can be represented；By planning the time locus of the height change for ankle-joint of leading leg, machine is controlled
The position of the point of zero moment of device people in support polygon, guarantees that the size of stability margin in stability range, makes machine always
People's stabilized walking.
Further, in the step 3, the stability control algorithm for shaking inhibition specifically comprises the following steps:
Step 3-1 solves robot initial centroid trajectory: constructing line according to the position of mass center actual path and point of zero moment
Property inverted pendulum model, then wherein be added motion model using mass center reference acceleration as controlled volume, as joined acceleration
Constraint condition is spent, then available updated state model, can be obtained by centroid trajectory generator using with observation method, obtain
To Controlling object function, comparatively ideal centroid trajectory available at this time, but still need to further by the method for optimum control
Optimization；
Method in optimal control: optimization constraint condition is added, using unbound conjugate gradient in step 3-2 in Controlling object function
Method carrys out interative computation, after adding Hamilton function, can find out optimal objective value by 800 iteration.
What the present invention reached has the beneficial effect that apery Soccer robot gait planning of the proposition based on cubic spline interpolation,
Kinematics model is established by the structure of robot, plans machine in conjunction with the method for space cubic spline interpolation based on this
The gait of device people, and the stability control algorithm optimization robot gait inhibited by vibration improve robot ambulation shakiness
Disadvantage, so that robot has good robustness to realize walking and the behaviors of grade of playing football；It is planned using cubic spline interpolation
Method can be good at guaranteeing the geometrical relationship between each joint in NAO robot soccer movement gait planning, and for it
The realization of optimizing stability afterwards is also more convenient；Deflecting angle and offset distance in walking process by new gait planning and
Algorithm optimization, which has, largely to be reduced, and the walking Stability and veracity of robot is enhanced.
Detailed description of the invention
Fig. 1 is the design cycle schematic diagram of robot gait planning.
Fig. 2 is the schematic diagram of the lateral movement model of robot.
Fig. 3 is the forward model schematic diagram of robot.
Fig. 4 is the lateral inclination angle schematic diagram of robot.
Fig. 5 is the propulsion schematic diagram of robot.
Specific embodiment
Technical solution of the present invention is described in further detail with reference to the accompanying drawings of the specification.
Apery Soccer robot gait planning based on cubic spline interpolation, includes the following steps:
Step 1, kinematics model is established by the structure of robot.
The kinematics model is established based on NAO biped robot, specifically with time resolution function to robot
Movement is decoupled, and the relationship between each joint angles of robot and each joint link lever pose, the kinematics model packet are solved
Include lateral movement modeling and Forward kinematics modeling.
Step 2, based on kinematics model, the step of planning robot is carried out in conjunction with the method for space cubic spline interpolation
State.
The planning of the gait uses the form of space planning, using the method for space cubic spline interpolation, with reference to machine
The traveling movement of robot is split as the coordinated movement of various economic factors in each joint, with space coordinate generation by the position of each joint of people in space
For time sequencing.
Step 3, the stability control algorithm optimization robot gait inhibited by vibration.
The stability control algorithm, the first initial centroid trajectory of solution robot simultaneously control rail as initial
Then mark constructs and solves the optimal control problem with restricted problem, finally applies it in robot walking planning.
In the step 1, the lateral movement modeling simplifies NAO robot leg and hip joint junction
For five connecting rod models, and reference frame is established at robot ankle, by Forward Kinematics Analysis, obtained according to geometrical relationship
The position coordinates of each joint and each connecting rod mass center in a coordinate system；By Analysis of Inverse Kinematics, pass through given ankle-joint of leading leg
With motion profile of the hip joint in fixed coordinate system, the angle in each joint of robot is found out.
Specifically, as shown in Fig. 2, and reference frame is established at robot ankle, it is assumed that the length and matter of each connecting rod
Amount is respectively liAnd mi, (i=1,2,3,4,5), the distance for furthermore marking the mass center i to joint i of connecting rod is ai, each joint is opposite
In itself corner be αi, the angle of connecting rod i and vertical direction is θi.Then there is following relationship:
α=K θ (2.1)
Wherein θ=[θ1…θ5]T, α=[α1…α6]T。
Wherein θiCorner to be otherwise negative to rotating to be just on the left of Z axis positive direction.
Carry out Forward Kinematics Analysis, it is assumed that position of each artis in referential coordinate is (xi, zi), each connecting rod mass center
Position in rectangular coordinate system is (xci, zci), then each joint and each connecting rod mass center can be found out according to geometrical relationship and be sat at right angle
Coordinate in mark system.
Analysis of Inverse Kinematics is carried out, for the Inverse Kinematics of robot, passes through given ankle-joint and the hip pass of leading leg
The motion profile in fixed coordinate system is saved, the angle in each joint of robot is found out.The robot that we are studied is one
The system that typical case has towering remaining, theoretically analyzing Inverse Kinematics Problem has infinite multiresolution, and when research is relative complex.To obtain
Unique solution, can be behind the track that lead leg ankle-joint and hip joint has been determined, in addition geometry constraint conditions, then acquires each connecting rod
With the angle theta of Z axis positive directioni(i=1,2,3,4,5), the final walking posture constraint condition for combining setting, so that it may obtain only
One solution.
Assuming that hip joint coordinate is (xh, zh), ankle-joint coordinate of leading leg is (xe,ze), then each joint angles solve mode
It is as follows:
1.θ1And θ2It solves:
θ1And θ2Geometrical constraint are as follows:
Constraint condition: -68.15 °≤θ1≤ 52.86 °, -5.29 °≤θ2≤121.04°
Thus it solves:
2.θ4And θ5It solves:
θ4And θ5Geometrical constraint are as follows:
Constraint condition: -5.29 °≤θ4≤ 121.04 °, -68.15 °≤θ5≤52.86°
Thus it solves:
In the step 1, Forward kinematics modeling is, it is specified that the upper body of robot is perpendicular to the ground, and when moving
Hip joint keeps horizontal, and obtaining robot when moving by geometrical relationship is the maximum angle for keeping stablizing body swing.
As shown in figure 3, stabilization and upper body to guarantee robot must meet perpendicular to the ground when left foot is to swing foot
Angle requirement are as follows: | θ6|=| θ7|, | θ8|=| θ9|.Guarantee that robot upper body when both feet are stood is parallel to the ground, also needs volume
The angle requirement of outer satisfaction are as follows: | θ6|=| θ8|, | θ7|=| θ9|.To sum up, to guarantee robot stabilization, we arrange arbitrarily
Moment, lateral model met constraint condition:
|θ6|=| θ7|=| θ8|=| θ9|=| θsd| (2.8)
NAO robot in walking must be rotated by lateral joint, so that robot is obtained center of gravity and is projected between two feet
Conversion.When robot static state is stood, we solve θsd, as shown in Figure 4.
Indicate that a is distance of the robot stabilized center of gravity apart from connecting rod boundary in figure, mark b is robot stabilized center of gravity distance
The distance on ground may make up a right angled triangle in this way.It is hereby achieved that robot is to keep stablizing body when moving
The maximum angle of swing:
θsd=tan-1(a/b) (2.9)
In the walking process of robot for a period of time, its center of gravity projection changes constantly, therefore can be with parameter
Form setting, and its value is limited in θsd≤|tan-1(a/b) | angular range in.
The method of space cubic spline interpolation in the step 2, specifically, upper limb keeps straight when robot gait is planned
Vertical, then the pose of robot can be determined according to the ankle-joint of swinging kick, take the height change situation conduct for ankle-joint of leading leg
Reference variable to cook up robot hip joint and the respective space motion path of ankle-joint of leading leg, and can represent each
Movement relation between joint；By planning the time locus of the height change for ankle-joint of leading leg, the zero-g of robot is controlled
The position of square point in support polygon, guarantees that the size of stability margin in stability range, makes robot stabilized walking always.
The space path of hip joint plans that the center due to the center of gravity of robot from two hip joints is closer, so hip joint
Motion conditions being affected for ZMP point, so the initial position of hip joint is just especially heavy in space path planning
It wants, and since its initial position has certain influence to the inertia force of robot, and inertia force has an impact to ZMP point, so wanting
Ensure that the projection of ZMP point can fall on both feet in the supporting zone on ground.By Fig. 5 robot propulsion schematic diagram, if hip
The initial position in joint is H1(Lb,H1), then symmetrical last bit is set to H3(Lf,H3), and middle position is hip pass in traveling process
The extreme higher position of section, is set as H2(Lm,Hh).It is available by imposing a condition using above three point as interpolation point:
Above-mentioned formula is brought into 3.2 and is obtained:
And then M1 is found out, the value of M2, M3 can obtain after bringing into:
With xhFor variable, one, second dervative is asked to obtain z respectively above formulah'(xh), zh”(xh)。
Ankle-joint obtains path planning, corresponding with hip joint, and it is R that initial time ankle-joint, which obtains position,1(0,hfoot), when end
The position for carving ankle-joint is R3(Ds,hfoot), it is R that ankle-joint of leading leg, which reaches highest to obtain position,2(Ds/2,Hs), hip is closed at this time
The direction the x coordinate x of sectionhIt is set as reference variable, cooks up and obtains function on the direction ankle-joint x are as follows:
xr=f (xh)=xr(xh) (3.6)
Due to:
xh(0)=Lb,xr(0)=0, xh(TS)=Lf,xr(TS)=DS,xh(TS/ 2)=Lm,xr(TS/ 2)=DS/2
Available ankle-joint of leading leg obtains three interpolation in the x direction:
(Lb,0),(Lm,DS/2),(Lf,DS)
Then obtained by sample interpolation theorem three times:
As hip joint, with xhFor variable, a second dervative is asked to obtain x above formulai'(xh),xi”(xh)。
When carrying out the derivation of equation, we are by xhIt is set as reference variable, so not when carrying out robot space gait planning
It needs to consider dynamics problem, it is only necessary to consider that other joints obtain position relative to hip joint, then ZMP obtains equation of locus then
Are as follows:
In the step 3, the stability control algorithm for shaking inhibition specifically comprises the following steps:
Step 3-1 solves robot initial centroid trajectory: constructing line according to the position of mass center actual path and point of zero moment
Property inverted pendulum model, then wherein be added motion model using mass center reference acceleration as controlled volume, as joined acceleration
Constraint condition is spent, then available updated state model, can be obtained by centroid trajectory generator using with observation method, obtain
To Controlling object function, comparatively ideal centroid trajectory available at this time, but still need to further by the method for optimum control
Optimization.
Specifically, being solved by taking the movement on the direction y as an example, first according to mass center actual pathWith the position of ZMP
yzmp(t) linear inverted pendulum model is constructed are as follows:
Motion model is added on the basis of above formulaAnd using mass center reference acceleration as controlled volume u, as plus
Entered acceleration constraint condition, then available:
Wherein set motion model are as follows:
State model is converted by 4.2 formulas, centroid trajectory generator is can be obtained by using with observation method, controls target letter
Number are as follows:
Wherein R value takes 1, Q to can use 113.5 according to experiment experience, comparatively ideal centroid trajectory available at this time, still
The value of ZMP does not reach requirement but, so by u0(t) it is used as initial track, is advanced optimized by the method for optimum control.
Method in optimal control: optimization constraint condition is added, using unbound conjugate gradient in step 3-2 in Controlling object function
Method carrys out interative computation, after adding Hamilton function, can find out optimal objective value by 800 iteration.
To reach the requirement of anticipation, the constraint of pre- observation frame must be got rid of, is modified to control target, it will be therein
Q removes, and optimization constraint condition is added and obtains:
According to experiment, generally take
Since there are inequation constraint conditions for (4.5) formula, changed here using the more high unbound conjugate gradient method of efficiency
Optimal objective value can be found out by 800 iteration after adding Hamilton function for operation.
The foregoing is merely better embodiment of the invention, protection scope of the present invention is not with above embodiment
Limit, as long as those of ordinary skill in the art's equivalent modification or variation made by disclosure according to the present invention, should all be included in power
In the protection scope recorded in sharp claim.
Claims (5)
1. the apery Soccer robot gait planning based on cubic spline interpolation, characterized by the following steps:
Step 1, kinematics model is established by the structure of robot；
The kinematics model is established based on NAO biped robot, specifically uses movement of the time resolution function to robot
It is decoupled, solves the relationship between each joint angles of robot and each joint link lever pose, the kinematics model includes side
It is modeled to Kinematic Model and Forward kinematics；
Step 2, based on kinematics model, the gait of planning robot is carried out in conjunction with the method for space cubic spline interpolation；
The planning of the gait uses the form of space planning, each with reference to robot using the method for space cubic spline interpolation
The traveling movement of robot is split as the coordinated movement of various economic factors in each joint, when being replaced with space coordinate by the position of joint in space
Between sequence；
Step 3, the stability control algorithm optimization robot gait inhibited by vibration；
The stability control algorithm, the first initial centroid trajectory of solution robot simultaneously control track as initial, so
The optimal control problem with restricted problem is constructed and solved afterwards, is finally applied it in robot walking planning.
2. the apery Soccer robot gait planning according to claim 1 based on cubic spline interpolation, it is characterised in that:
In the step 1, NAO robot leg and hip joint junction are reduced to five connecting rods by the lateral movement modeling
Model, and reference frame is established at robot ankle, by Forward Kinematics Analysis, according to geometrical relationship obtain each joint and
The position coordinates of each connecting rod mass center in a coordinate system；By Analysis of Inverse Kinematics, pass through given lead leg ankle-joint and hip joint
Motion profile in fixed coordinate system finds out the angle in each joint of robot.
3. the apery Soccer robot gait planning according to claim 1 based on cubic spline interpolation, it is characterised in that:
In the step 1, the Forward kinematics modeling is, it is specified that the upper body of robot is perpendicular to the ground, and hip joint is protected when moving
Water holding is flat, and obtaining robot when moving by geometrical relationship is the maximum angle for keeping stablizing body swing.
4. the apery Soccer robot gait planning according to claim 1 based on cubic spline interpolation, it is characterised in that:
The method of space cubic spline interpolation in the step 2, specifically, upper limb is kept upright when robot gait is planned, then machine
The pose of device people can be determined according to the ankle-joint of swinging kick, and the height change situation for ankle-joint of leading leg is taken to be used as with reference to change
Amount, to cook up robot hip joint and lead leg the respective space motion path of ankle-joint, and can represent each joint it
Between movement relation；By planning the time locus of the height change for ankle-joint of leading leg, the point of zero moment of robot is controlled
Position in support polygon, guarantees that the size of stability margin in stability range, makes robot stabilized walking always.
5. the apery Soccer robot gait planning according to claim 1 based on cubic spline interpolation, it is characterised in that:
In the step 3, the stability control algorithm for shaking inhibition specifically comprises the following steps:
Step 3-1 solves robot initial centroid trajectory: linear according to the building of the position of mass center actual path and point of zero moment
Then vertical pendulum model is added motion model using mass center reference acceleration as controlled volume wherein, as joined acceleration about
Beam condition, then available updated state model, can be obtained by centroid trajectory generator using with observation method, is controlled
Objective function processed, comparatively ideal centroid trajectory available at this time, but still need to advanced optimize by the method for optimum control；
Step 3-2, method in optimal control: in Controlling object function be added optimization constraint condition, using unbound conjugate gradient method come
Interative computation can find out optimal objective value by 800 iteration after adding Hamilton function.
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| CN112486177A (en) * | 2020-12-02 | 2021-03-12 | 南京邮电大学 | Humanoid robot gait planning method based on vertical body movement and robot walking movement controller |
| CN112859856A (en) * | 2021-01-11 | 2021-05-28 | 常州工程职业技术学院 | Humanoid robot gait generation method based on centroid height compensation |
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| CN110315543A (en) * | 2019-07-29 | 2019-10-11 | 北京理工大学 | A kind of biped robot's gait generates and optimization method |
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| CN112486177A (en) * | 2020-12-02 | 2021-03-12 | 南京邮电大学 | Humanoid robot gait planning method based on vertical body movement and robot walking movement controller |
| CN112859856A (en) * | 2021-01-11 | 2021-05-28 | 常州工程职业技术学院 | Humanoid robot gait generation method based on centroid height compensation |
| CN112859856B (en) * | 2021-01-11 | 2022-12-09 | 常州工程职业技术学院 | Humanoid robot gait generation method based on centroid height compensation |
| CN113134833A (en) * | 2021-03-30 | 2021-07-20 | 深圳市优必选科技股份有限公司 | Robot and gait control method and device thereof |
| CN113183164A (en) * | 2021-05-10 | 2021-07-30 | 上海工程技术大学 | Bionic mechanical cow based on crank-rocker mechanism and control method |
| CN114355964A (en) * | 2021-12-29 | 2022-04-15 | 深圳市优必选科技股份有限公司 | Multi-degree-of-freedom single-leg kinematics solving method and device and robot |
| CN114355964B (en) * | 2021-12-29 | 2023-08-18 | 深圳市优必选科技股份有限公司 | Multi-degree-of-freedom single-leg kinematics solving method, device and robot |
| CN115447692A (en) * | 2022-10-10 | 2022-12-09 | 日照中兴汽车有限公司 | Multi-foot motion simulation robot based on virtual prototype technology and simulation method |
| CN117742134A (en) * | 2023-12-21 | 2024-03-22 | 桂林电子科技大学 | Walking planning and control method for biped robot |
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