阅读说明：本技术 一种基于神经动力学的三轮全向移动机器人状态调整方法 (Three-wheel omnidirectional mobile robot state adjusting method based on neurodynamics ) 是由 郭东生 李煊鲜 刘庆平 黎子豪 殷海波 于 2021-09-28 设计创作，主要内容包括：本发明公开了一种基于神经动力学的三轮全向移动机器人状态调整方法,基于神经动力学公式,设计新型性能指标；最小化该新型性能指标,建立相应的速度层状态调整方案,受约束于移动平台的运动学方程、移动平台三个全向驱动轮的旋转角度极限和旋转角速度极限、机器人关节的角度极限和速度极限；将状态调整方案转化为一个二次型优化问题,并采用数值算法对其进行求解；根据求解结果,下位机控制器驱动移动平台的三个全向轮和机器人的各个关节使得移动机器人调整到期望状态。该方法操作方便,能规范、有效地在速度层上实现三轮全向移动机器人在不同状态之间的自动调整,使其快速、精确地到达期望状态。(The invention discloses a three-wheel omnidirectional mobile robot state adjusting method based on neurodynamics, which is based on a neurodynamics formula and designs a novel performance index; minimizing the novel performance index, and establishing a corresponding speed layer state adjustment scheme which is restricted by a kinematic equation of the mobile platform, rotation angle limits and rotation angle speed limits of three omnidirectional driving wheels of the mobile platform, and angle limits and speed limits of a robot joint; converting the state adjustment scheme into a quadratic optimization problem, and solving the quadratic optimization problem by adopting a numerical algorithm; and according to the solving result, the lower computer controller drives the three omnidirectional wheels of the mobile platform and each joint of the robot so that the mobile robot is adjusted to a desired state. The method is convenient to operate, and can be used for normatively and effectively realizing the automatic adjustment of the three-wheeled omnidirectional mobile robot among different states on a speed layer, so that the three-wheeled omnidirectional mobile robot can quickly and accurately reach an expected state.)

1. A three-wheel omnidirectional mobile robot state adjusting method based on neurodynamics is characterized by comprising the following steps:

designing a novel performance index described on a speed layer based on a neurodynamic formula;

minimizing the novel performance index, and establishing a corresponding speed layer state adjustment scheme; the state adjustment scheme is restricted by a kinematic equation of the mobile platform, rotation angle limits and rotation angular velocity limits of three omnidirectional driving wheels of the mobile platform, and angle limits and velocity limits of a robot joint;

converting the state adjustment scheme into a quadratic optimization problem, and solving the quadratic optimization problem by adopting a numerical algorithm;

and according to the solving result of the algorithm, the lower computer controller drives the three omnidirectional wheels of the mobile platform and each joint of the robot so that the mobile robot is adjusted to a desired state.

2. The method for adjusting the state of a three-wheeled omnidirectional mobile robot based on the neurodynamics of claim 1, wherein the three-wheeled omnidirectional mobile robot is composed of a mobile platform with three symmetrically distributed omnidirectional driving wheels and a robot with n degrees of freedom mounted on the mobile platform; based on a neurodynamic formula, a novel performance index described on a velocity layer is designed as follows:

wherein, lambda is larger than 0 and belongs to R to represent the adjusting parameter of the performance index, and T represents the transposition of a matrix or a vector;represents a velocity vector of the three-wheeled omnidirectional mobile robot, anTheta represents a position vector of the three-wheeled omnidirectional mobile robot, andp_xe.g. R and p_ye.R represents the coordinates of the mobile platform on the horizontal ground along the X-axis direction and the Y-axis direction respectively; φ e R represents the orientation angle of the mobile platform,andrespectively represents p_x，p_yAnd the time derivative of phi;which represents the joint angle of the robot,representing a joint velocity of the robot; nonlinear mapping:

p_xd∈R，p_yde R respectively represents the expected coordinates of the mobile platform on the horizontal ground along the X-axis direction and the Y-axis direction; phi is a_dE R represents the desired orientation angle of the mobile platform,representing a desired angle of a robot joint; accordingly, vector is augmentedRepresenting the desired state of the three-wheeled omnidirectional mobile robot.

3. The method of claim 2, wherein minimizing the new performance metric and establishing a corresponding velocity layer state adjustment scheme comprises:

minimization

Is constrained by:

wherein the equation constraint formula (2) represents a kinematic equation of the mobile platform,representing velocity vectors by a mobile robotOf the first three elements, i.e. vectorsM represents a matrix composed of the structural parameters of the mobile platform, namely:

r > 0 ∈ R represents each omnidirectional of the mobile platformThe radius of the driving wheel, l is larger than 0 and belongs to R, and the distance from the center point of the mobile platform to the omnidirectional driving wheel is represented;andrespectively representing the rotation angles and rotation angular velocities of three omnidirectional driving wheels of the mobile platform;andrespectively indicating the rotation angle of the omni-directional driving wheelOmnidirectional driving wheel rotation angular velocityRobot joint angleAnd robot joint velocityThe limit of (c).

4. The method of claim 1, wherein the augmented angle vector and the velocity vector of the mobile robot are defined asAndaccordingly, the，Andrespectively represent v and(iii) a limit of (d);

definition ofConverting the speed layer state adjustment schemes (1) to (6) into a quadratic optimization problem as follows:

and (3) minimizing: x is the number of^TQx/2+p^Tx (7)

Constraint conditions are as follows: x is the number of^-≤x≤x⁺ (8)

Wherein Q is N^TN∈R^(3+n)×(3+n)，N＝[M,0；0,I]∈R^(3+n)×(3+n)，

p＝λN^Tf(θ)∈R³⁺ⁿ，I∈R^n×nRepresenting an identity matrix; x is the number of^±The limit of x is expressed, and,mu > 0 epsilon R represents the regulating parameter of the limit transition.

5. The method for adjusting the state of the three-wheeled omnidirectional mobile robot based on the neurodynamics as recited in claim 4, wherein the solving of the state is performed by a numerical algorithm, and comprises the following steps:

converting the quadratic optimization problems (7) - (8) into a piecewise linear projection equation:

F_Ω(x-(Qx+p))-x＝0∈R³⁺ⁿ (9)

(9) in the formula, F_Ω(. h) represents a piecewise linear projection operator;

solving equation (9) using the following numerical algorithm:

e(x^k)＝x^k-F_Ω(x^k-(Qx^k+p)) (10)

x^k+1＝F_Ω(x^k-ρ(x^k)δ(x^k)) (11)

δ(x^k)＝Q^Te(x^k)+Qx^k+p (12)

wherein e represents a calculation error, and δ and ρ represent a specific vector and a constant in the algorithm calculation process respectively; the superscript k denotes the number of iterations and k is 0,1,2, …; i | · | purple wind₂A two-norm representation of a vector; given an initial value x⁰∈R³⁺ⁿThe numerical solution of the piecewise linear projection equation (9) can be obtained through continuous iterative calculation of numerical algorithms (10) - (13).

Technical Field

The invention relates to the field of motion planning of three-wheeled omnidirectional mobile robots, in particular to a three-wheeled omnidirectional mobile robot state adjusting method based on neurodynamics.

Background

The three-wheel omnidirectional mobile robot consists of a mobile platform with three symmetrically distributed omnidirectional driving wheels and a robot with n degrees of freedom; the device is widely concerned due to flexibility and mobility, and is currently applied to various fields such as article transportation, fire scene search and rescue, space exploration and the like. After the mobile robot completes a planning task in a working space, the current structural state is often required to be adjusted to a specified structural state; i.e., the desired state; thereby efficiently executing the next planning task.

The adjustment of the state of the mobile robot is generally done in two steps: firstly, adjusting the position of a mobile platform, and then adjusting the joints of the robot; or the joints of the robot are adjusted first, and then the position of the mobile platform is adjusted. However, both of the above methods are cumbersome, time consuming and have significant drawbacks: each adjustment may require measuring the position and orientation angle of the mobile platform and the joint angle of the robot for many times to enable the mobile robot to accurately reach the specified structural state; also, inaccuracies in any one quantity for position, orientation angle and joint angle may result in the three-wheeled omnidirectional mobile robot failing to successfully complete the planned task.

Disclosure of Invention

In view of the above problems, the present invention provides a method for adjusting the state of a three-wheeled omnidirectional mobile robot based on neurodynamics, which at least solves some of the above technical problems, and the method is convenient to operate, has low workload and standard operation, and can automatically and simultaneously adjust the mobile platform and the robot to quickly and accurately reach the desired state.

The embodiment of the invention provides a three-wheel omnidirectional mobile robot state adjusting method based on neurodynamics, which comprises the following steps:

designing a novel performance index described on a speed layer based on a neurodynamic formula;

minimizing the novel performance index, and establishing a corresponding speed layer state adjustment scheme; the state adjustment scheme is restricted by a kinematic equation of the mobile platform, rotation angle limits and rotation angular velocity limits of three omnidirectional driving wheels of the mobile platform, and angle limits and velocity limits of a robot joint;

converting the state adjustment scheme into a quadratic optimization problem, and solving the quadratic optimization problem by adopting a numerical algorithm;

and according to the solving result of the algorithm, the lower computer controller drives the three omnidirectional wheels of the mobile platform and each joint of the robot so that the mobile robot is adjusted to a desired state.

Furthermore, the three-wheel omnidirectional mobile robot consists of three mobile platforms with symmetrically distributed omnidirectional driving wheels and a robot with n degrees of freedom, wherein the robot is arranged on the mobile platforms; based on a neurodynamic formula, a novel performance index described on a velocity layer is designed as follows:

wherein, lambda is larger than 0 and belongs to R to represent the adjusting parameter of the performance index, and T represents the transposition of a matrix or a vector;represents a velocity vector of the three-wheeled omnidirectional mobile robot, anTheta represents a position vector of the three-wheeled omnidirectional mobile robot, andp_xe.g. R and p_ye.R represents the coordinates of the mobile platform on the horizontal ground along the X-axis direction and the Y-axis direction respectively; φ e R represents the orientation angle of the mobile platform,andrespectively represents p_x，p_yAnd the time derivative of phi;which represents the joint angle of the robot,representing a joint velocity of the robot; nonlinear mapping:

p_xd∈R，p_yde R respectively represents the expected coordinates of the mobile platform on the horizontal ground along the X-axis direction and the Y-axis direction; phi is a_dE R represents the desired orientation angle of the mobile platform,representing a desired angle of a robot joint; accordingly, vector is augmentedRepresenting the desired state of the three-wheeled omnidirectional mobile robot.

Further, minimizing the new performance index and establishing a corresponding speed layer state adjustment scheme includes:

minimization

Is constrained by:

wherein the equation constraint formula (2) represents a kinematic equation of the mobile platform,representing velocity vectors by a mobile robotOf the first three elements, i.e. vectorsM represents a matrix composed of the structural parameters of the mobile platform, namely:

r is larger than 0 and belongs to R to represent the radius of each omnidirectional driving wheel of the mobile platform, and l is larger than 0 and belongs to R to represent the distance from the central point of the mobile platform to the omnidirectional driving wheel;andrespectively representing the rotation angles and rotation angular velocities of three omnidirectional driving wheels of the mobile platform;andrespectively indicating the rotation angle of the omni-directional driving wheelOmnidirectional driving wheel rotation angular velocityRobot joint angleAnd robot joint velocityThe limit of (c). Further, an angle vector and a velocity vector of the mobile robot are respectively defined asAndaccordingly, the number of the first and second electrodes,andrespectively represent v and(iii) a limit of (d);

definition ofConverting the speed layer state adjustment schemes (1) to (6) into a quadratic optimization problem as follows:

and (3) minimizing: x is the number of^TQx/2+p^Tx (7)

Constraint conditions are as follows:x^-≤x≤x⁺ (8)

wherein Q is N^TN∈R^(3+n)×(3+n)，N＝[M,0；0,I]∈R^(3+n)×(3+n)，

p＝λN^Tf(θ)∈R³⁺ⁿ，I∈R^n×nRepresenting an identity matrix; x is the number of^±The limit of x is expressed, and,mu > 0 epsilon R represents the regulating parameter of the limit transition.

Further, solving the problem by adopting a numerical algorithm comprises the following steps:

converting the quadratic optimization problems (7) - (8) into a piecewise linear projection equation:

F_Ω(x-(Qx+p))-x＝0∈R³⁺ⁿ (9)

(9) in the formula, F_Ω(. h) represents a piecewise linear projection operator;

solving equation (9) using the following numerical algorithm:

e(x^k)＝x^k-F_Ω(x^k-(Qx^k+p)) (10)

x^k+1＝F_Ω(x^k-ρ(x^k)δ(x^k)) (11)

δ(x^k)＝Q^Te(x^k)+Qx^k+p (12)

wherein e represents a calculation error, and δ and ρ represent a specific vector and a constant in the algorithm calculation process respectively; the superscript k denotes the number of iterations and k is 0,1,2, …; i | · | purple wind₂A two-norm representation of a vector; given an initial value x⁰∈R³⁺ⁿThe numerical solution of the piecewise linear projection equation (9) can be obtained through continuous iterative calculation of numerical algorithms (10) - (13).

The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:

the embodiment of the invention provides a three-wheel omnidirectional mobile robot state adjusting method based on neurodynamics, which is based on a neurodynamics formula and designs a novel performance index described on a speed layer; minimizing the novel performance index, and establishing a corresponding speed layer state adjustment scheme; the state adjustment scheme is restricted by a kinematic equation of the mobile platform, rotation angle limits and rotation angular velocity limits of three omnidirectional driving wheels of the mobile platform, and angle limits and velocity limits of a robot joint; converting the state adjustment scheme into a quadratic optimization problem, and solving the quadratic optimization problem by adopting a numerical algorithm; and according to the solving result of the algorithm, the lower computer controller drives the three omnidirectional wheels of the mobile platform and each joint of the robot so that the mobile robot is adjusted to a desired state. The method is convenient to operate, can realize automatic adjustment of the three-wheeled omnidirectional mobile robot among different states on a speed layer in a standard and effective manner, and avoids the complex process that the three-wheeled omnidirectional mobile robot needs to measure the horizontal position and the orientation angle of the mobile platform and the joint angle of the robot for multiple times when executing different tasks. And the mobile platform and the robot can be automatically and simultaneously adjusted to quickly and accurately reach the expected state.

Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.

The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:

fig. 1 is a flowchart of a state adjustment method for a three-wheeled omnidirectional mobile robot based on neurodynamics according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of an adjustment method provided by an embodiment of the invention;

fig. 3 is a schematic structural diagram of a three-wheeled omnidirectional mobile robot according to an embodiment of the present invention.

Detailed Description

Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

Referring to fig. 1, a method for adjusting a state of a three-wheeled omnidirectional mobile robot based on neurodynamics according to an embodiment of the present invention includes:

s10, designing a novel performance index described on a velocity layer based on a neurodynamic formula;

s20, minimizing the novel performance index, and establishing a corresponding speed layer state adjustment scheme; the state adjustment scheme is restricted by a kinematic equation of the mobile platform, rotation angle limits and rotation angular velocity limits of three omnidirectional driving wheels of the mobile platform, and angle limits and velocity limits of a robot joint;

s30, converting the state adjustment scheme into a quadratic optimization problem, and solving the quadratic optimization problem by adopting a numerical algorithm;

and S40, driving the three omnidirectional wheels of the mobile platform and each joint of the robot by the lower computer controller according to the solution result of the algorithm to adjust the mobile robot to a desired state.

The method is convenient to operate, can realize automatic adjustment of the three-wheeled omnidirectional mobile robot among different states on a speed layer in a standard and effective manner, and avoids the complex process that the three-wheeled omnidirectional mobile robot needs to measure the horizontal position and the orientation angle of the mobile platform and the joint angle of the robot for multiple times when executing different tasks. And the mobile platform and the robot can be automatically and simultaneously adjusted to quickly and accurately reach the expected state.

As shown in fig. 2, the method for adjusting the state of the three-wheeled omnidirectional mobile robot based on the neurodynamics mainly comprises six parts, namely designing a novel performance index 1 based on the neurodynamics, establishing a speed layer state adjustment scheme 2, converting into a quadratic optimization problem 3, solving a numerical algorithm by a solver 4, controlling a lower computer by a controller 5, and controlling the three-wheeled omnidirectional mobile robot by a controller 6.

Firstly, designing a novel performance index described on a speed layer based on a neurodynamic formula according to the thought of minimizing the error between the current state and the expected state of the mobile robot; then, a corresponding speed layer state adjustment scheme is established by combining with a novel performance index needing to be minimized, and the scheme is converted into a quadratic optimization problem, so that the quadratic optimization problem is solved by adopting a corresponding numerical algorithm; finally, the solution result is used for driving three omnidirectional wheels of the mobile platform and each joint of the robot, so that the mobile robot is quickly and accurately adjusted to a desired state from the current state, namely: initial state when different planning tasks are performed.

The above steps will be described in detail below.

The three-wheel omnidirectional mobile robot consists of three mobile platforms with omnidirectional driving wheels which are symmetrically distributed and a robot with n degrees of freedom which is arranged on the mobile platforms; as shown in fig. 3.

In step S10, according to the idea of minimizing the error between the current state and the expected state of the three-wheeled omnidirectional mobile robot, based on the neurodynamic formula, the novel performance index described on the velocity layer is designed as:

wherein, lambda is larger than 0 and belongs to R to represent the adjusting parameter of the performance index, and T represents the transposition of a matrix or a vector;three wheels for indicationA velocity vector of the omni-directional mobile robot, andtheta represents a position vector of the three-wheeled omnidirectional mobile robot, andp_xe.g. R and p_yE R represents the coordinates of the mobile platform on the horizontal ground along the X-axis and Y-axis directions, respectively, i.e., the position where the robot is fixed to the mobile platform; φ e R represents the orientation angle of the mobile platform,andrespectively represents p_x，p_yAnd the time derivative of phi;which represents the joint angle of the robot,representing a joint velocity of the robot; nonlinear mapping:

p_xd∈R，p_yde R respectively represents the expected coordinates of the mobile platform on the horizontal ground along the X-axis direction and the Y-axis direction; phi is a_dE R represents the desired orientation angle of the mobile platform,representing a desired angle of a robot joint; accordingly, vector is augmentedRepresenting the expected shape of the three-wheeled omnidirectional mobile robot, i.e. the starting state when performing different planning tasks. Wherein, R isRepresenting a space of numbers, Rⁿ、Rⁿ⁺³Etc. and other references to R appearing below, all represent the dimensions of a matrix or vector.

In step S20, in combination with the performance index (1) that needs to be minimized, the state adjustment scheme of the three-wheeled omnidirectional mobile robot speed layer is established as follows:

minimization

Is constrained by:

wherein the equation constraint formula (2) represents a kinematic equation of the mobile platform,representing velocity vectors by a mobile robotOf the first three elements, i.e. vectorsM represents a parameter composed of the structure of the mobile platformThe matrix, namely:

as shown in fig. 3, R > 0 ∈ R denotes the radius of each omnidirectional driving wheel of the mobile platform, and l > 0 ∈ R denotes the distance from the center point of the mobile platform to the omnidirectional driving wheel;andrespectively representing the rotation angles and rotation angular velocities of three omnidirectional driving wheels of the mobile platform;andrespectively indicating the rotation angle of the omni-directional driving wheelOmnidirectional driving wheel rotation angular velocityRobot joint angleAnd robot joint velocityThe limit of (c).

For convenience of the following description, the augmented angle vector and velocity vector of the mobile robot are defined asAndaccordingly, the number of the first and second electrodes,andrespectively represent v andthe limit of (c).

In step S30, defineThe above speed layer state adjustment schemes (1) to (6) can be converted into a quadratic optimization problem as follows:

and (3) minimizing: x is the number of^TQx/2+p^Tx (7)

Constraint conditions are as follows: x is the number of^-≤x≤x⁺ (8)

Wherein Q is N^TN∈R^(3+n)×(3+n)，N＝[M,0；0,I]∈R^(3+n)×(3+n)，

p＝λN^Tf(θ)∈R³⁺ⁿ，I∈R^n×nRepresenting an identity matrix; x is the number of^±The limit of x is expressed, and,mu > 0 epsilon R represents the regulating parameter of the limit transition.

Solving the quadratic optimization problem (7) - (8) may be equivalent to solving the piecewise-linear projection equation as follows:

F_Ω(x-(Qx+p))-x＝0∈R³⁺ⁿ (9)

wherein, F_Ω(. cndot.) represents a piecewise linear projection operator. For the piecewise-linear projection equation (9), the following numerical algorithm can be used to solve:

e(x^k)＝x^k-F_Ω(x^k-(Qx^k+p)) (10)

x^k+1＝F_Ω(x^k-ρ(x^k)δ(x^k)) (11)

δ(x^k)＝Q^Te(x^k)+Qx^k+p (12)

wherein e represents a calculation error, and δ and ρ represent a specific vector and a constant in the algorithm calculation process respectively; the superscript k denotes the number of iterations and k is 0,1,2, …; i | · | purple wind₂A two-norm representation of a vector; given an initial value x⁰∈R³⁺ⁿThe numerical solution of the piecewise linear projection equation (9) can be obtained through continuous iterative calculation of numerical algorithms (10) - (13). Thereby obtaining the optimal solution of quadratic optimization problems (7) - (8), namely the optimal solution of the speed layer state adjustment schemes (1) - (6) of the three-wheeled omnidirectional mobile robot.

In step S40, according to the above solution result, the lower computer controller will drive the three omni wheels of the mobile platform and the joints of the robot to quickly and accurately adjust the mobile robot from the current state to the desired state, that is: initial state when different planning tasks are performed. Therefore, the three-wheel omnidirectional mobile robot can be regulated automatically in different states, and the complicated process that the three-wheel omnidirectional mobile robot needs to measure the horizontal position and the orientation angle of the mobile platform and the joint angle of the robot for many times when executing different tasks is avoided.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.