CN110851775A - Motion analysis method of Mecanum wheel all-directional mobile platform - Google Patents
Motion analysis method of Mecanum wheel all-directional mobile platform Download PDFInfo
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Abstract
The invention discloses a motion analysis method of a Mecanum wheel omnibearing moving platform, which is characterized in that the wheel-ground staggered shaft friction wheel transmission analysis is applied to the motion speed of the Mecanum wheel omnibearing moving platform, and according to the driving condition of the Mecanum wheel, the speed analysis and calculation are carried out on the transmission relation formed by a waist drum-shaped roller of the Mecanum wheel and the ground to obtain the speed of the platform omnibearing moving (inclining, left-right, front-back and rotating). The invention solves the problem of complicated and abstract deduction calculation process in the prior art, and the analysis process is concise, clear and visual. Support is provided for the kinematic analysis of various forms of omni-directional mobile platforms based on Mecanum wheels and other devices based on ground-based crossed-axis friction wheel transmissions.
Description
Technical Field
The invention belongs to the technical field of robot walking, and particularly relates to a motion analysis method of a Mecanum wheel all-directional mobile platform based on a wheel-ground staggered shaft friction wheel transmission principle.
Background
The omnibearing moving platform is a robot technology which can move in any directions such as oblique, front-back, left-right, in-situ rotation and the like on the ground, has omnibearing motion performance based on a Mecanum wheel (Mecanum wheel) and has simple structure, good control performance and good trafficability, and is widely applied to the fields of manufacturing automation, storage material transportation, industrial robots, daily life and the like.
At present, in the aspect of motion analysis of an omni-directional mobile platform based on Mecanum wheels, in the prior art, a kinematic model is constructed by adopting a vector analysis method and a matrix transformation method to analyze motion parameters such as speed, displacement and the like of the system for the motion analysis of a Mecanum four-wheel omni-directional mobile system. The analysis process of the analysis method is complex and abstract, and the movement of a quantitative transmission relation analysis platform formed by alternate contact of a waist drum-shaped roller on a Mecanum wheel and the ground is not fully utilized.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a motion analysis method of a Mecanum wheel omnibearing moving platform based on a wheel-ground staggered shaft friction wheel transmission principle, which has the characteristics of simple and intuitive process analysis and is characterized by fully utilizing the quantitative transmission relation formed by the alternate contact of a waist drum-shaped roller on the Mecanum wheel and the ground to analyze the motion parameters (speed and displacement) of the platform omnibearing movement (slant, left and right, front and back and rotation).
In order to achieve the purpose, the invention adopts the technical scheme that:
a motion analysis method for an omnibearing moving platform of a Mecanum wheel determines the linear velocity direction of a waist drum-shaped roller and the moving speed direction of the waist drum-shaped roller along a supporting shaft, thereby judging a homodromous wheel set (the homodromous refers to the same moving speed direction of the waist drum-shaped roller on the Mecanum wheel along the supporting shaft), and respectively selecting the moving speed of the waist drum-shaped roller on one homodromous wheel along the supporting shaft for speed synthesis to obtain the omnibearing moving speed of the platform.
Further, the linear velocity direction of the crowned rollers is determined from the direction of rotation for a given Mecanum wheel angular velocity ω.
Further, the speed direction of the movement of the waist drum-shaped roller along the supporting shaft is as follows: when the waist drum shaped roller is contacted with the ground,the included angle between the speed direction of the waist drum-shaped roller moving along the supporting shaft and the linear speed direction of the supporting shaft isWhereinIs the offset angle of the crowned roller support shaft axis relative to the Mecanum wheel central axis.
Further, the same-direction acting wheel set is as follows: and judging that the Mecanum wheels with the same speed direction of the movement of the waist drum-shaped roller along the supporting shaft are the same-direction acting wheel set according to the speed direction of the movement of the waist drum-shaped roller along the supporting shaft.
Further, the speed of the platform is: speed V of moving waist drum-shaped roller on Mecanum wheel in different same-direction acting wheel sets along supporting shaftrVector synthesis is carried out, and a calculation equation of the omnibearing moving speed of the platform is obtained according to the speed synthesis result; vrNamely, it isWherein R is the radius of gyration of the axis of the support shaft around the central axis of the Mecanum wheel, and omega R is the linear velocity V of the rotation of the support shaft of the waist drum-shaped roller.
Further, the omni-directional movement of the platform includes a diagonal movement, a left-right movement, a front-back movement and a rotation movement.
The invention has the beneficial effects that: the method comprises the steps of firstly determining the linear velocity direction of the waist drum-shaped roller, then determining the moving speed direction of the waist drum-shaped roller along the supporting shaft, so as to judge the equidirectional acting wheel, selecting the speed of a platform for analyzing the moving speed of the waist drum-shaped roller on a Mecanum wheel along the supporting shaft, and finally obtaining the omnibearing moving speed of the platform. The motion analysis method of the Mecanum wheel omnibearing moving platform overcomes the limitations of a vector analysis method and a matrix transformation method in complex and abstract derivation and calculation complicated processes, and meanwhile, the transmission relation among motion components is clear, and the analysis process is concise, clear and intuitive. Support is provided for the kinematics analysis of various 3 and 8 Mecanum wheel omni-directional mobile platforms, crawler-type omni-directional mobile platforms, frog-type sports cars and the like.
Drawings
FIG. 1 is a schematic diagram of the tilting motion of an omni-directional mobile platform according to the present invention;
FIG. 2 is a schematic diagram of the side-to-side movement of the omni-directional mobile platform according to the present invention;
FIG. 3 is a schematic diagram of the fore-aft movement of the omni-directional mobile platform of the present invention;
FIG. 4 is a schematic diagram of the rotational motion of the omni-directional mobile platform according to the present invention.
Detailed Description
The invention will be further described with reference to the following figures and specific examples, but the scope of the invention is not limited thereto.
The invention applies the principle that a friction wheel driven by a wheel-ground staggered shaft friction wheel moves axially along a supporting shaft (the wheel-ground staggered shaft friction wheel drive principle), and the design and calculation method of the axial movement speed of the principle comprises the following steps(ω R is the linear speed of rotation of the axis of the friction wheel support shaft,is the offset angle of the friction wheel) the analysis is based on the motion speed of the Mecanum wheel omni-directional mobile platform. All direction movement platform comprises a plurality of Mecanum wheel, and the outer circumference equipartition of Mecanum wheel is waist drum shape roller of a certain amount. When the Mecanum wheel is driven, the waist drum-shaped rollers alternately contact with the ground to form transmission, and the transmission formed by the contact of the waist drum-shaped rollers and the ground belongs to wheel-ground staggered-shaft friction wheel transmission. According to the driving condition of the Mecanum wheels, the speed of the platform in all-directional movement (oblique, left-right, front-back and rotation) is calculated by analyzing the speed of the transmission relation formed by the waist drum-shaped rollers of the Mecanum wheels and the ground. The Mecanum wheel omnibearing mobile platform in the embodiment of the invention adopts a four-wheel structure.
EXAMPLE 1 oblique movement of the platform
When the platform moves obliquely, only two Mecanum wheels on one diagonal line (No. 1, No. 3 or No. 2, No. 4) of the platform rotate at an angular velocity omega, and at the moment, waist drum-shaped rollers which are in contact with the ground on the two Mecanum wheels on the diagonal line move along the axial direction of a supporting shaft of the waist drum-shaped rollers, so that the platform moves obliquely together. As shown in fig. 1, Mecanum wheels nos. 1 and 3 are selected as analysis objects in the present embodiment.
The method comprises the following steps: determining linear velocity direction of a crowned roller
According to the rotation direction of the angular velocity omega of the Mecanum wheel No. 1 and No. 3, the linear velocity V direction of the rotation of the supporting shaft of the waist drum-shaped roller on the Mecanum wheel when the waist drum-shaped roller is in contact with the ground is determined, as shown in figure 1.
Step two: determining the speed V of a crowned roller moving along a support axisrDirection of rotation
According to the transmission principle of a friction wheel with staggered axles on the ground, when the waist drum-shaped roller is in contact with the ground, the speed V of the waist drum-shaped roller moving along the supporting axler(1)、Vr(3)The included angle between the direction and the linear velocity V direction of the supporting shaft isWhereinIs the offset angle of the crowned roller support shaft axis relative to the Mecanum wheel center axis as shown in figure 1.
Step three: wheel set for judging equidirectional action
Determining the speed V of the waist drum-shaped roller moving along the supporting shaft according to the step twor(1)、Vr(3)Direction, determining the speed V of the movement of the crowned roller along the support axisr(1)、Vr(3)The same direction acting wheel set with the same direction is a Mecanum wheel set No. 1 and No. 3, as shown in FIG. 1.
Step four: platform velocity analysis
Because only one group of diagonal wheels move in the oblique movement, the speed of the platform in the oblique movement is Vr(1)According to the wheel-ground staggered shaft friction wheel transmission principle, V can be obtainedr(1)Is composed ofWherein R is the radius of gyration of the axis of the support shaft around the central axis of the Mecanum wheel, and omega R is the linear velocity V of the rotation of the support shaft of the waist drum-shaped roller.
Step five: calculation equation of oblique movement velocity of all-directional mobile platform
According to the fourth step, the speed V of the platform can be obtained1Comprises the following steps:
example 2 side-to-side movement of the platform
When the platform moves left and right, the 4 Mecanum wheels all rotate at an angular speed omega, the rotation direction is shown in figure 2, and the movement of the waist drum-shaped rollers contacted with the ground on the 2 groups of Mecanum wheels (No. 1, No. 3, No. 2 and No. 4) on two diagonal lines of the platform along the axial direction of the supporting shaft of the waist drum-shaped rollers causes the platform to move left and right.
The method comprises the following steps: determining linear velocity direction of a crowned roller
According to the rotation direction of the given Mecanum wheel angular velocity ω, the linear velocity V direction of the rotation of the support shaft of the waist drum roller on the Mecanum wheel when the waist drum roller is in contact with the ground is determined, as shown in fig. 2.
Step two: determining the speed V of a crowned roller moving along a support axisrDirection of rotation
According to the transmission principle of the friction wheel with staggered axles on the wheel, when the waist drum-shaped rollers are contacted with the ground, the speed V of the waist drum-shaped rollers on the 4 Mecanum wheels moving along the supporting axler(1)、Vr(2)、Vr(3)、Vr(4)The included angle between the direction and the linear velocity V direction of the supporting shaft isWhereinIs the offset angle of the crowned roller support shaft axis relative to the Mecanum wheel center axis as shown in figure 2.
Step three: wheel set for judging equidirectional action
Determining the speed V of the waist drum-shaped roller moving along the supporting shaft according to the step twor(1)、Vr(2)、Vr(3)、Vr(4)Direction, determining the speed V of the movement of the crowned roller along the support axisr(1)、Vr(2)、Vr(3)、Vr(4)The same-direction acting wheel sets with the same direction are No. 1 and No. 3 Mecanum wheel sets and No. 2 and No. 4 Mecanum wheel sets (generally on diagonal lines), and the moving speed of the waist drum-shaped roller on one Mecanum wheel in the different-direction acting wheel sets along the supporting shaft is set as Vr(13)、Vr(24)As shown in fig. 2.
Step four: platform velocity analysis
Speed V of moving waist drum-shaped roller on Mecanum wheel in different same-direction acting wheel sets along supporting shaftr(13)、Vr(24)Vector synthesis is carried out, and V can be obtained according to the wheel-ground staggered shaft friction wheel transmission principler(13)、Vr(24)Are all made ofWherein R is the radius of gyration of the axis of the support shaft around the central axis of the Mecanum wheel, and omega R is the linear velocity V of the rotation of the support shaft of the waist drum-shaped roller.
Step five: calculation equation of left and right movement speed of omnibearing mobile platform
V of step fourr(13)、Vr(24)Carrying out synthetic analysis to obtain the speed V of the platform2Comprises the following steps:
EXAMPLE 3 platform Back and forth motion
When the platform moves back and forth, the 4 Mecanum wheels all rotate at an angular velocity omega, the rotating direction is as shown in figure 3, and the waist drum-shaped rollers contacted with the ground on the 2 groups of Mecanum wheels (No. 1, No. 3, No. 2 and No. 4) on two diagonal lines of the platform move along the axial direction of the supporting shaft of the waist drum-shaped rollers, so that the platform moves back and forth together.
The method comprises the following steps: determining linear velocity direction of a crowned roller
According to the rotation direction of the given Mecanum wheel angular velocity ω, the linear velocity V direction of the rotation of the support shaft of the waist drum roller on the Mecanum wheel when the waist drum roller is in contact with the ground is determined, as shown in fig. 3.
Step two: determining the speed V of a crowned roller moving along a support axisrDirection of rotation
According to the transmission principle of the friction wheel with staggered axles on the wheel, when the waist drum-shaped rollers are contacted with the ground, the speed V of the waist drum-shaped rollers on the 4 Mecanum wheels moving along the supporting axler(1)、Vr(2)、Vr(3)、Vr(4)The included angle between the direction and the linear velocity V direction of the supporting shaft isWhereinIs the offset angle of the crowned roller support shaft axis relative to the Mecanum wheel center axis as shown in figure 3.
Step three: wheel set for judging equidirectional action
Determining the speed V of the waist drum-shaped roller moving along the supporting shaft according to the step twor(1)、Vr(2)、Vr(3)、Vr(4)Direction, determining the speed V of the movement of the crowned roller along the support axisr(1)、Vr(2)、Vr(3)、Vr(4)The same-direction acting wheel sets with the same direction are No. 1 and No. 3 Mecanum wheel sets and No. 2 and No. 4 Mecanum wheel sets (generally on diagonal lines), and the moving speed of the waist drum-shaped roller on one Mecanum wheel in the different-direction acting wheel sets along the supporting shaft is set as Vr(13)、Vr(24)As shown in fig. 3.
Step four: platform velocity analysis
Speed V of moving waist drum-shaped roller on Mecanum wheel in different same-direction acting wheel sets along supporting shaftr(13)、Vr(24)Vector synthesis is carried out, and V can be obtained according to the wheel-ground staggered shaft friction wheel transmission principler(13)、Vr(24)Are all made ofWherein R is the radius of gyration of the axis of the support shaft around the central axis of the Mecanum wheel, and omega R is the linear velocity V of the rotation of the support shaft of the waist drum-shaped roller.
Step five: calculation equation of front and back motion speed of omnibearing moving platform
V of step fourr(13)、Vr(24)Carrying out synthetic analysis to obtain the speed V of the platform3Comprises the following steps:
EXAMPLE 4 platform rotational movement
During the rotation, the 4 Mecanum wheels all rotate at an angular speed omega, the rotation direction is shown in fig. 4, the waist drum-shaped rollers contacted with the ground on the four Mecanum wheels (1, 2, 3 and 4) of the platform move along the axial direction of the supporting shaft, and the platform is enabled to generate the rotation motion under the combined action.
The method comprises the following steps: determining linear velocity direction of a crowned roller
The direction of the linear velocity V in which the support shaft rotates when the drum roller on the Mecanum wheel is in contact with the ground is determined from the direction of rotation of the given Mecanum wheel angular velocity ω, as shown in fig. 4.
Step two: determining the speed V of a crowned roller moving along a support axisrDirection of rotation
According to the transmission principle of the friction wheel with staggered axles on the wheel, when the waist drum-shaped rollers are contacted with the ground, the speed V of the waist drum-shaped rollers on the 4 Mecanum wheels moving along the supporting axler(1)、Vr(2)、Vr(3)、Vr(4)The included angle between the direction and the linear velocity V direction of the supporting shaft isWhereinIs the offset angle of the crowned roller support shaft axis relative to the Mecanum wheel center axis as shown in figure 4.
Step three: wheel set for judging equidirectional action
Determining the speed V of the waist drum-shaped roller moving along the supporting shaft according to the step twor(1)、Vr(2)、Vr(3)、Vr(4)Direction, determining the speed V of the movement of the crowned roller along the support axisr(1)、Vr(2)、Vr(3)、Vr(4)The equidirectional acting wheel sets with the same direction are No. 1, 2, 3 and 4 Mecanum wheels, and belong to the rotating equidirectional acting wheel set, as shown in FIG. 4.
Step four: platform velocity analysis
Speed V of the movement of the crowned rollers along the supporting axis of the rollers rotating the same-direction-of-action wheelsr(1)、Vr(2)、Vr(3)、Vr(4)Corresponding to the distance r from the vertical centerline of the platform at that speed1The radius is the linear velocity rotating around the vertical central line of the platform, and V can be obtained according to the transmission principle of the friction wheel with alternately arranged shaftsr(1)、Vr(2)、Vr(3)、Vr(4)Are all made ofWhere R is the radius of rotation of the axis of the support shaft about the central axis of the Mecanum wheel and ω R is the linear velocity V of the rotation of the support shaft of the crowned roller, as shown in fig. 4.
Step five: calculation equation of rotating angular velocity of all-directional mobile platform
V of step fourr(4)And (3) obtaining a platform rotation angular velocity omega calculation equation as the linear velocity rotating around the platform vertical central line:
then:
wherein:r is the distance from the center of the Mecanum wheel to the center of the platform, and α is the included angle between the r axis and the y axis;
wherein: l1=rcosα,l2=rsinα;
Then:
when the waist drum roller has a specific offset angleAt 45 °, the speeds of the four motion modes of the platform are:
the left and right movement speeds are as follows:
the forward and backward movement speed is:
the above embodiments are only used for illustrating the design idea and features of the present invention, and the purpose of the present invention is to enable those skilled in the art to understand the content of the present invention and implement the present invention accordingly, and the protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes and modifications made in accordance with the principles and concepts disclosed herein are intended to be included within the scope of the present invention.
Claims (6)
1. A motion analysis method of a Mecanum wheel all-directional mobile platform is characterized in that: and determining the linear speed direction of the waist drum-shaped rollers and the moving speed direction of the waist drum-shaped rollers along the supporting shaft, so as to judge the wheel sets acting in the same direction, and selecting the moving speed of the waist drum-shaped rollers on one of the wheels acting in the same direction along the supporting shaft for speed synthesis to obtain the omnibearing moving speed of the platform.
2. The motion analysis method of the Mecanum wheel omni-directional mobile platform according to claim 1, wherein: the linear speed direction of the crowned rollers is determined by the direction of rotation of a given Mecanum wheel angular velocity ω.
3. The motion analysis method of the Mecanum wheel omni-directional mobile platform according to claim 1, wherein: the speed direction of the movement of the waist drum-shaped roller along the supporting shaft is as follows: when the waist drum-shaped roller is contacted with the ground, the included angle between the speed direction of the waist drum-shaped roller moving along the supporting shaft and the linear speed direction of the supporting shaft isWhereinIs the offset angle of the crowned roller support shaft axis relative to the Mecanum wheel central axis.
4. The motion analysis method of the Mecanum wheel omni-directional mobile platform according to claim 1, wherein: the equidirectional acting wheel set comprises: and judging that the Mecanum wheels with the same speed direction of the movement of the waist drum-shaped roller along the supporting shaft are the same-direction acting wheel set according to the speed direction of the movement of the waist drum-shaped roller along the supporting shaft.
5. The motion analysis method of the Mecanum wheel omni-directional mobile platform according to claim 1, wherein: the speed of the platform is: one Mecanum wheel in different same-direction acting wheel groupsSpeed V of upper waist drum type roller moving along supporting shaftrVector synthesis is carried out, and a calculation equation of the omnibearing moving speed of the platform is obtained according to the speed synthesis result; vrNamely, it isWherein R is the radius of gyration of the axis of the support shaft around the central axis of the Mecanum wheel, and omega R is the linear velocity V of the rotation of the support shaft of the waist drum-shaped roller.
6. The motion analysis method of the Mecanum wheel omni-directional mobile platform according to claims 1 to 5, wherein: the all-directional movement of the platform comprises oblique movement, left-right movement, front-back movement and rotation movement.
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US20070150096A1 (en) * | 2005-12-26 | 2007-06-28 | Industrial Technology Research Institute | Mobile robot platform and method for sensing movement of the same |
CN105667632A (en) * | 2016-01-04 | 2016-06-15 | 江苏科技大学 | Omnidirectional mobile platform for Mecanum wheels |
CN109765894A (en) * | 2019-01-22 | 2019-05-17 | 济南大学 | Steering wheel drives omni-directional mobile robots motion control method |
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