CN112757299A - Method and device for acquiring centroid trajectory, robot and storage medium - Google Patents

Method and device for acquiring centroid trajectory, robot and storage medium Download PDF

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CN112757299A
CN112757299A CN202011611800.9A CN202011611800A CN112757299A CN 112757299 A CN112757299 A CN 112757299A CN 202011611800 A CN202011611800 A CN 202011611800A CN 112757299 A CN112757299 A CN 112757299A
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matrix
robot
centroid
variable
preset
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CN112757299B (en
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冷晓琨
常琳
何治成
白学林
柯真东
王松
吴雨璁
黄贤贤
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Leju Shenzhen Robotics Co Ltd
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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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • 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

The application provides a method and a device for acquiring a centroid trajectory, a robot and a storage medium, wherein the method comprises the following steps: the method comprises the steps of constructing an optimized variable according to N mass center variables of the robot in N control periods and the acceleration change rate of the N mass centers, obtaining a coefficient matrix for solving a zero moment point track according to the optimized variable and a first preset matrix, obtaining an expression matrix of a cost function of the robot according to the coefficient matrix for solving the zero moment point track and an expected zero moment point track, obtaining an equality constraint condition of the mass center of the robot, and carrying out constraint solution on the optimized variable according to the equality constraint condition and the expression matrix of the cost function to obtain the mass center track of the robot. In the method, the equality constraint condition is adopted to carry out constraint solution on the optimization variables, so that the cost function constructed by solving the zero moment point track and the expected zero moment point track is minimum, and the centroid track corresponding to the zero moment point track in any shape can be obtained through solution.

Description

Method and device for acquiring centroid trajectory, robot and storage medium
Technical Field
The application relates to the technical field of robot control, in particular to a method and a device for acquiring a centroid trajectory, a robot and a storage medium.
Background
At present, when planning a walking track, an existing humanoid robot generally uses a linear inverted pendulum model, manually designates a foot-drop Point sequence, interpolates according to the foot-drop Point sequence to obtain a Zero Moment Point (ZMP) track, solves according to the ZMP track to obtain a centroid track, plans according to the foot-drop Point sequence to obtain a foot-end track, and then controls the robot to reach a target Point according to the ZMP track, the centroid track and the foot-end track.
In the prior art, the centroid trajectory is usually solved by solving a linear inverted pendulum differential equation to obtain an analytic solution of the centroid position and the centroid position, however, the solving method requires that the ZMP trajectory is a regular multi-segment line, so that the centroid trajectory corresponding to the ZMP trajectory in any shape cannot be solved.
Disclosure of Invention
The present application aims to provide a method, an apparatus, a robot, and a storage medium for acquiring a centroid trajectory, which are used to acquire a centroid trajectory corresponding to a ZMP trajectory of an arbitrary shape, in view of the above-mentioned deficiencies in the prior art.
In order to achieve the above purpose, the technical solutions adopted in the embodiments of the present application are as follows:
in a first aspect, an embodiment of the present application provides a method for acquiring a centroid trajectory, where the method includes:
constructing an optimized variable according to N mass center variables of the robot in N control periods and the acceleration change rate of the N mass centers, wherein N is the number of the control periods, and is greater than or equal to 2;
obtaining a coefficient matrix for solving a zero moment point track according to the optimized variable and a first preset matrix, wherein elements in the first preset matrix are obtained by calculation according to a first relation matrix between a centroid variable of the robot in a kth control period and a position of a zero moment point of the kth control period, and k is less than or equal to N-1 and is greater than or equal to 1;
obtaining an expression matrix of a cost function of the robot according to the coefficient matrix of the solved zero moment point track and the expected zero moment point track;
obtaining an equality constraint condition of the center of mass of the robot, wherein the equality constraint condition is used for carrying out equality constraint on the optimized variable and a second preset matrix, and elements in the second preset matrix are obtained by calculation according to a second relation matrix between the center of mass variable of the robot in the kth control period and the center of mass variable of the (k + 1) th control period;
and carrying out constraint solution on the optimization variables according to the equality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
In an alternative embodiment, the equality constraint is obtained by:
establishing a second relation matrix of a mass center variable of the robot in the kth control period and a mass center variable of the robot in the (k + 1) th control period by adopting a linear inverted pendulum model;
constructing a second preset matrix according to the first parameter and the second parameter in the second relation matrix, wherein elements in the second preset matrix are determined according to the first parameter and the second parameter;
and constructing the equality constraint condition according to the optimization variable and the second preset matrix.
In an optional embodiment, the performing a constraint solution on the optimization variable according to the equation constraint condition and the expression matrix of the cost function to obtain the centroid trajectory of the robot includes:
obtaining inequality constraint conditions of the center of mass of the robot, wherein the inequality constraint conditions are used for presetting an identity matrixThe power and the optimization variable are subjected to inequality constraint, and the preset power is (4N +3)2；
And carrying out constraint solution on the optimization variables according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
In an alternative embodiment, the inequality constraint is obtained by:
constructing a first matrix according to a preset minimum value of a mass center variable of the robot and a preset minimum value of an acceleration change rate of the mass center;
constructing a second matrix according to a preset maximum value of a mass center variable of the robot and a preset maximum value of an acceleration change rate of the mass center;
obtaining the product of the preset power of the unit matrix and the optimization variable;
and constructing the inequality constraint condition according to the first matrix, the second matrix and the product.
In an optional embodiment, the performing a constraint solution on the optimization variable according to the equality constraint condition, the inequality constraint condition, and the expression matrix of the cost function to obtain the centroid trajectory of the robot includes:
and carrying out minimum value constraint solving on the optimized variable according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
In an optional embodiment, the obtaining a coefficient matrix for solving a zero moment point trajectory according to the optimized variable and a first preset matrix includes:
establishing a first relation matrix between a mass center variable of the robot in a kth control period and a position of a zero moment point of the kth control period by adopting a linear inverted pendulum model;
constructing the first preset matrix according to the parameters in the first relation matrix, wherein the elements in the first preset matrix are determined according to the parameters in the first relation matrix;
and acquiring a coefficient matrix of the solved zero moment point track according to the product of the first preset matrix and the optimization variable.
In an optional embodiment, after the constrained solution is performed on the optimization variable according to the equation constraint condition and the expression matrix of the cost function, and a centroid trajectory of the robot is obtained, the method further includes:
and controlling the robot to move according to the centroid track of the robot.
In a second aspect, another embodiment of the present application provides an apparatus for acquiring a centroid trajectory, the apparatus including:
the construction module is used for constructing an optimized variable according to N mass center variables of the robot in N control periods and the acceleration change rate of the N mass centers, wherein N is the number of the control periods, and is greater than or equal to 2;
an obtaining module, configured to obtain a coefficient matrix for solving a zero moment point trajectory according to the optimized variable and a first preset matrix, where elements in the first preset matrix are obtained through calculation according to a first relation matrix between a centroid variable of the robot in a kth control cycle and a position of a zero moment point in the kth control cycle, where k is less than or equal to N-1 and greater than or equal to 1, obtain an expression matrix of a cost function of the robot according to the coefficient matrix for solving the zero moment point trajectory and an expected zero moment point trajectory, and obtain an equality constraint condition of the centroid of the robot, where the equality constraint condition is used to perform equality constraint on the optimized variable and the first preset matrix;
and the solving module is used for carrying out constraint solving on the optimization variables according to the equality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
In an optional embodiment, the building module is further configured to:
establishing a second relation matrix of a mass center variable of the robot in the kth control period and a mass center variable of the robot in the (k + 1) th control period by adopting a linear inverted pendulum model;
constructing a second preset matrix according to the first parameter and the second parameter in the second relation matrix, wherein elements in the second preset matrix are determined according to the first parameter and the second parameter;
and constructing the equality constraint condition according to the optimization variable and the second preset matrix.
In an optional implementation manner, the solving module is specifically configured to:
obtaining inequality constraint conditions of the center of mass of the robot, wherein the inequality constraint conditions are used for carrying out inequality constraint on a preset power of a unit matrix and the optimization variables, and the preset power is (4N +3)2；
And carrying out constraint solution on the optimization variables according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
In an optional embodiment, the building module is further configured to:
constructing a first matrix according to a preset minimum value of a mass center variable of the robot and a preset minimum value of an acceleration degree change rate of the mass center, and constructing a second matrix according to a preset maximum value of the mass center variable of the robot and a preset maximum value of the acceleration degree change rate of the mass center;
the obtaining module is further used for obtaining the product of the preset power of the unit matrix and the optimization variable;
the constructing module is further configured to construct the inequality constraint condition according to the first matrix, the second matrix, and the product.
In an optional implementation manner, the solving module is specifically configured to:
and carrying out minimum value constraint solving on the optimized variable according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
In an optional implementation manner, the obtaining module is specifically configured to:
establishing a first relation matrix between a mass center variable of the robot in a kth control period and a position of a zero moment point of the kth control period by adopting a linear inverted pendulum model;
constructing the first preset matrix according to the parameters in the first relation matrix, wherein the elements in the first preset matrix are determined according to the parameters in the first relation matrix;
and acquiring a coefficient matrix of the solved zero moment point track according to the product of the first preset matrix and the optimization variable.
In an optional embodiment, the method further comprises:
and the control module is used for controlling the robot to move according to the centroid track of the robot.
In a third aspect, another embodiment of the present application provides a robot controller, including: a controller, a memory and a bus, the memory storing machine readable instructions executable by the controller, the controller and the memory communicating via the bus when the robot controller is operating, the controller executing the machine readable instructions to perform the method according to any of the first aspect.
In a fourth aspect, another embodiment of the present application provides a storage medium having a computer program stored thereon, where the computer program is executed by a controller to perform the method according to any one of the above first aspects.
The application provides a method and a device for acquiring a centroid trajectory, a robot and a storage medium, wherein the method comprises the following steps: the method comprises the steps of constructing an optimized variable according to N mass center variables of the robot in N control periods and the acceleration change rate of the N mass centers, obtaining a coefficient matrix for solving a zero moment point track according to the optimized variable and a first preset matrix, obtaining an expression matrix of a cost function of the robot according to the coefficient matrix for solving the zero moment point track and an expected zero moment point track, obtaining an equality constraint condition of the mass center of the robot, and carrying out constraint solution on the optimized variable according to the equality constraint condition and the expression matrix of the cost function to obtain the mass center track of the robot. In the method, the equality constraint condition is adopted to carry out constraint solution on the optimization variables, so that the cost function constructed by solving the zero moment point track and the expected zero moment point track is minimum, and the centroid track corresponding to the zero moment point track in any shape can be obtained through solution.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained from the drawings without inventive effort.
Fig. 1 is a first flowchart illustrating a method for acquiring a centroid trajectory according to an embodiment of the present application;
fig. 2 is a schematic flowchart illustrating a second method for acquiring a centroid trajectory according to an embodiment of the present application;
fig. 3 is a schematic flowchart illustrating a third method for acquiring a centroid trajectory according to an embodiment of the present application;
fig. 4 is a flowchart illustrating a fourth method for acquiring a centroid trajectory according to an embodiment of the present application;
fig. 5 is a schematic structural diagram illustrating an apparatus for acquiring a centroid trajectory according to an embodiment of the present application;
fig. 6 shows a schematic structural diagram of a robot controller provided in an embodiment of the present application.
Detailed Description
In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it should be understood that the drawings in the present application are for illustrative and descriptive purposes only and are not used to limit the scope of protection of the present application. Additionally, it should be understood that the schematic drawings are not necessarily drawn to scale. The flowcharts used in this application illustrate operations implemented according to some embodiments of the present application. It should be understood that the operations of the flow diagrams may be performed out of order, and steps without logical context may be performed in reverse order or simultaneously. One skilled in the art, under the guidance of this application, may add one or more other operations to, or remove one or more operations from, the flowchart.
In addition, the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.
It should be noted that in the embodiments of the present application, the term "comprising" is used to indicate the presence of the features stated hereinafter, but does not exclude the addition of further features.
Before describing the technical solutions of the present application, the technical terms related to the present application will be explained first.
Zero Moment Point (Zero Moment Point, ZMP): the zero moment point ZMP is an important index for judging the dynamic stable motion of the humanoid robot, and the robot can walk stably when the ZMP falls in the range of the sole.
Center of mass: refers to an imaginary point on the matter system where the mass is considered to be concentrated, typically the center point of the object.
In the existing method for solving the centroid trajectory, the analytic solutions of the centroid position and the centroid speed are obtained by solving the differential equation of the linear inverted pendulum, however, the method has high requirements on the precision of the initial value of the centroid position and the initial value of the centroid speed, has high requirements on the precision of the trajectory of a zero moment point, is easy to fail in solving, and has unstable solving results. In addition, this solution requires that the ZMP trajectory be a regular polyline, and therefore, a centroid trajectory corresponding to a ZMP of an arbitrary shape cannot be solved.
Based on the above, the method for acquiring the centroid trajectory is provided, and the equation constraint condition is adopted to carry out constraint solution on the optimization variables, so that the cost function constructed by the solution zero moment point trajectory and the expected zero moment point trajectory is minimum, the centroid trajectory corresponding to the zero moment point trajectory in any shape can be obtained through solution, the solution failure is not easy to occur, and the solution result is stable.
The following describes the method for acquiring the centroid trajectory provided by the present application in detail with reference to several specific embodiments.
Fig. 1 is a schematic flow chart of a method for acquiring a centroid trajectory according to an embodiment of the present application, where an execution main body of the embodiment may be a robot, for example, a robot controller. As shown in fig. 1, the method may include:
s101, constructing an optimized variable according to N mass center variables of the robot in N control periods and the acceleration change rate of the N mass centers.
The center of mass of the robot may be the center of mass of the robot, e.g. may be the center point of the robot. The centroid variables may include centroid position, centroid velocity, centroid acceleration.
The centroid trajectory of the robot may be divided into N control cycles, the duration of each control cycle may be 5 seconds or 6 seconds, and may be specifically selected according to an operation to be performed by the robot, which is not particularly limited in this embodiment.
The acceleration rate, which is a rate of change of the acceleration of the center of mass of the robot, may be a function related to the duration of the control period. The acceleration rates of the N centroids may be respective corresponding acceleration rates for the N control periods.
In the embodiment, the acceleration changes of the robot in the N center of mass variables and the N center of mass in the N control cycles are obtained, and then the optimization variable is constructed according to the center of mass variables and the acceleration change rate of the center of mass of the robot. As an example, a 4N +3 dimensional optimization variable may be constructed according to N centroid variables of the robot in N control cycles and the acceleration change rates of the N centroids.
Each of the N centroid variables may be a centroid matrix composed of a centroid position, a centroid velocity, and a centroid acceleration, and as an example, a transposed matrix of the N centroid matrices is obtained, and the N transposed matrices and the acceleration change rates of the N centroids are spliced to construct an optimized variable.
Wherein N centroid variables are respectively denoted as x1、x2…xNThe transpose matrixes corresponding to the N centroid variables are respectively recorded as
Figure BDA0002874845740000081
The acceleration change rates of N centroids are respectively recorded as u1、u2…uNThen the robot's optimization vector Y may be:
Figure BDA0002874845740000082
the optimized vector may be a 4N +3 dimensional vector.
S102, obtaining a coefficient matrix for solving the zero moment point track according to the optimization variable and the first preset matrix.
The elements in the first preset matrix are obtained by calculation according to a first relation matrix between the centroid variable of the robot in the kth control period and the position of the zero moment point of the kth control period, wherein the first relation matrix between the centroid variable of the kth control period and the position of the zero moment point of the kth control period can be obtained by adopting a linear inverted pendulum model.
Wherein k is less than or equal to N-1 and greater than or equal to 1.
In this embodiment, the product of the optimization variable and the first preset matrix may be used as a coefficient matrix for solving the zero moment point trajectory.
S103, obtaining an expression matrix of a cost function of the robot according to the coefficient matrix of the solved zero moment point track and the expected zero moment point track.
The cost function is a function constructed by a solution zero moment point track and an expected zero moment point track of the robot, the expected zero moment point track is a zero moment point track of the robot which is expected to be planned, and a coefficient matrix of the solution zero moment point track is a coefficient matrix of the zero moment point track obtained by solution when the robot plans a walking track, wherein the obtaining mode of the coefficient matrix of the solution zero moment point track is similar to that of the prior art, and is not repeated here.
It should be noted that, each control cycle of the robot in the N control cycles has a solved zero moment point trajectory and an expected zero moment point trajectory, and then, for each control cycle, an expression matrix of a cost function of the robot in each control cycle may be obtained according to a difference between a coefficient matrix of the solved zero moment point trajectory and the expected zero moment point trajectory.
And S104, acquiring an equality constraint condition of the center of mass of the robot.
The equality constraint condition is used for carrying out equality constraint on an optimized variable of the robot and a second preset matrix, and elements in the second preset matrix are obtained by calculation according to a second relation matrix of the robot between a centroid variable of a kth control period and a centroid variable of a (k + 1) th control period, wherein the equality constraint can be carried out on the product of the optimized variable of the robot and the second preset matrix, the left side of an equality is equal to 0, and the right side of the equality is equal to the product of the optimized variable and the second preset matrix.
It should be noted that the centroid variable of the kth control cycle may be the centroid variable of the robot at the beginning of the kth control cycle, for example, the duration of the control cycle is 5 seconds, then the centroid variable of the kth control cycle may be the centroid variable of the robot at the kth 5 seconds, and similarly, the centroid variable of the (k + 1) th control cycle may be the centroid variable of the robot at the beginning of the (k + 1) th control cycle.
And S105, carrying out constraint solution on the optimized variable according to the equality constraint condition and the expression matrix of the cost function, and obtaining the centroid track of the robot.
According to the equality constraint condition and the expression matrix of the cost function, the optimized variable is constrained and solved, namely under the condition of meeting the equality constraint condition, the optimized variable can be constrained and solved to obtain the centroid track of the robot, specifically, under the condition of meeting the equality constraint condition, the expression matrix of the cost function can approach 0 infinitely, namely the cost function constructed by solving the zero moment point track and the expected zero moment point track is minimized, and the optimized variable is constrained and solved to obtain the centroid track of the robot.
The centroid trajectory is composed of a plurality of discrete points, namely, the centroid trajectory of the robot can be determined according to the centroid position of each control cycle, the equality constraint condition is used for carrying out equality constraint on an optimization variable and a second preset matrix of the robot, the optimization variable is a variable constructed according to the centroid variable of the robot and the acceleration change rate of the centroid, the centroid variable comprises the centroid position, then, the optimization variable is subjected to constraint solution according to the equality constraint condition and the expression matrix of the cost function, the centroid position of each control cycle, namely, the discrete points of the centroid trajectory can be obtained, and then, the centroid trajectory of the robot can be obtained according to the discrete points of the centroid trajectory.
It should be noted that, the solved zero moment point trajectory and the expected zero moment point trajectory are respectively composed of a plurality of discrete points, that is, in this embodiment, discrete points based on the zero moment point trajectory can solve discrete points of the centroid trajectory of the robot, so that a centroid trajectory corresponding to a continuously or discontinuously solved zero moment point trajectory of any shape, such as a solved zero moment point trajectory after being compensated by a dynamic model, can be solved.
In an optional embodiment, after step S105, the method may further include:
and controlling the robot to move according to the centroid track of the robot.
After the centroid trajectory of the robot is obtained by solving in the present embodiment, the robot may be controlled to move according to the centroid trajectory of the robot to reach the target location, and specifically, the robot may be controlled to move to the target location according to the foot end trajectory of the robot obtained by solving, the zero moment point trajectory obtained by solving, and the centroid trajectory of the robot. The stability of the barycenter track of the robot obtained by solving in the mode of the embodiment is high, and the stable control of the robot is facilitated.
The method for obtaining the centroid trajectory in this embodiment includes constructing an optimized variable according to N centroid variables of a robot in N control cycles and acceleration change rates of the N centroids, obtaining a coefficient matrix for solving a zero moment point trajectory according to the optimized variable and a first preset matrix, obtaining an expression matrix of a cost function of the robot according to the coefficient matrix for solving the zero moment point trajectory and an expected zero moment point trajectory, obtaining an equality constraint condition of the centroid of the robot, and performing constraint solution on the optimized variable according to the equality constraint condition and the expression matrix of the cost function to obtain the centroid trajectory of the robot. In the method, the equality constraint condition is adopted to carry out constraint solution on the optimization variables, so that the cost function constructed by solving the zero moment point track and the expected zero moment point track is minimum, and the centroid track corresponding to the zero moment point track in any shape can be obtained through solution.
Fig. 2 shows a flow diagram of a second method for acquiring a centroid trajectory according to the embodiment of the present application, and as shown in fig. 2, the equality constraint is obtained through the following steps:
s201, establishing a second relation matrix of a center-of-mass variable of the robot in the kth control period and a center-of-mass variable of the k +1 th control period by adopting a linear inverted pendulum model.
The second relation matrix is used for representing the relation between the centroid variable of the robot in the kth control period and the centroid variable of the kth +1 control period.
By adopting a linear inverted pendulum model, a second-order differential equation can be used for describing the relation between the centroid track and the zero moment point track, and the following formula is referred to:
Figure BDA0002874845740000111
x is the locus of the center of mass,
Figure BDA0002874845740000112
is the acceleration of mass center, p is the position of zero moment point, and g is the acceleration of gravityAnd the degree, z, is the distance from the center of mass of the robot to the ground, and is assumed to be unchanged during the walking process of the robot.
Firstly, the formula is converted into a matrix form to obtain a second relation matrix:
xk+1＝Apxk+bpuk
wherein,
Figure BDA0002874845740000113
x (k deltat) is the centroid position for the kth control cycle,
Figure BDA0002874845740000114
the centroid velocity for the kth control period,
Figure BDA0002874845740000115
the centroid acceleration of the kth control period is shown, and Δ t is the duration of the control period.
uk＝u(kΔt)，ukThe acceleration change rate of the center of mass of the robot in the k control period.
xk+1The centroid variable of the robot in the (k + 1) th control period is shown.
S202, constructing a first preset matrix according to the first parameter and the second parameter in the second relation matrix.
And S203, constructing an equality constraint condition according to the optimized variable and the second preset matrix.
Wherein the first parameter in the second relation matrix may be a coefficient of a centroid variable of the robot in the kth control cycle, i.e. xkHas a coefficient ofPThe second parameter in the second relation matrix may be a coefficient of the acceleration change rate of the robot in the k-th control period, i.e. ukCoefficient of (b)P。
A second preset matrix can be constructed according to the first parameter and the second parameter in the second relation matrix, and the elements in the second preset matrix are according to the first parameter APAnd a second parameter bPDetermining, as an example, a second predetermined matrix is denoted Aeq。
Figure BDA0002874845740000121
The constraint condition of the equation is constructed according to the optimized variable and the second preset matrix, for example, let the left side of the equation be beq，beq＝[0,0,0…0]TLet equation right be the product of the optimized variable and the second predetermined matrix, i.e. beq＝AeqY, namely, an equality constraint is constructed.
Wherein A iseqThe values of other elements not shown are all 0.
The method for acquiring the centroid trajectory in the embodiment includes the steps of constructing an optimized variable according to N centroid variables of a robot in N control periods and acceleration change rates of the N centroids, establishing a second relation matrix of the centroid variable of the robot in a kth control period and the centroid variable of a kth +1 control period by adopting a linear inverted pendulum model, constructing a second preset matrix according to a first parameter and a second parameter in the second relation matrix, determining elements in the second preset matrix according to the first parameter and the second parameter, and constructing an equality constraint condition according to the optimized variable and the second preset matrix. By the method, the equality constraint condition of the cost function can be constructed, and the constraint solution of the optimization variable based on the equality constraint condition is convenient to carry out subsequently.
In an alternative implementation, the equality constraint condition and the inequality constraint condition may be used to jointly perform constraint solution on the optimization variables, which is described below with reference to the embodiment of fig. 3. Fig. 3 shows a third schematic flowchart of the method for acquiring the centroid trajectory according to the embodiment of the present application, and as shown in fig. 3, step S103 may include:
and S1031, obtaining inequality constraint conditions of the center of mass of the robot.
The inequality constraint condition is used for carrying out inequality constraint on a preset power and an optimized variable of the unit matrix, and the preset power is (4N +3)2。
The inequality constraint on the preset power of the unit matrix and the optimization variable may be an inequality constraint on a product of the preset power of the unit matrix and the optimization variable on a maximum value of the centroid variable and a minimum value of the centroid variable, that is, a product of the preset power of the unit matrix and the optimization variable is greater than the minimum value of the centroid variable and less than the maximum value of the centroid variable. Since the trajectory of the center of mass of the robot is composed of a plurality of discrete points, i.e. the trajectory of the center of mass of the robot can be determined from the center of mass position, wherein the center of mass variable comprises the center of mass position.
The diagonal elements in the unit matrix are all 1, the other elements are all 0, and N is the number of control periods.
And (3) carrying out constraint solving on the cost function by taking the equality constraint condition and the inequality constraint condition of the centroid of the robot as consideration factors, so that the accuracy of the obtained centroid track of the robot is higher.
In an alternative embodiment, the inequality constraint is obtained by:
constructing a first matrix according to a preset minimum value of a mass center variable of the robot and a preset minimum value of an acceleration change rate of the mass center;
and constructing a second matrix according to the preset maximum value of the mass center variable of the robot and the preset maximum value of the acceleration change rate of the mass center.
Obtaining the product of the preset power of the unit matrix and the optimization variable;
and constructing inequality constraint conditions according to the first matrix, the second matrix and the product.
The preset minimum value of the robot center of mass variable can be determined according to the minimum value of each element in the center of mass variable, and the minimum value of each element in the center of mass variable comprises: the minimum value of barycenter position, the minimum value of barycenter speed, the minimum value of barycenter acceleration, similarly, the preset maximum value of the barycenter variable of the robot can be determined according to the maximum value of each element in the barycenter variable, and the maximum value of each element in the barycenter variable includes: the maximum value of the centroid position, the maximum value of the centroid speed and the maximum value of the centroid acceleration.
The preset maximum value of the centroid variable and the preset maximum value of the centroid variable may be selected according to actual situations, which is not particularly limited in this embodiment.
Similarly, the preset minimum value of the acceleration rate of the centroid and the preset maximum value of the acceleration rate of the centroid may be selected according to actual situations, which is not particularly limited in this embodiment.
And then, calculating the product of the preset power of the identity matrix and the optimization variable, and constructing an inequality constraint condition according to the first matrix, the second matrix and the product.
As an example, the preset minimum value of the robot's center of mass variable is denoted xminThe preset minimum value of the acceleration change rate of the centroid is recorded as uminThen, a first matrix L constructed according to the preset minimum value of the centroid variable of the robot and the preset minimum value of the acceleration change rate of the centroid may be recorded as:
L＝[xmin…xmin umin…umin]
the dimension of the first matrix L may be determined by the dimension of the inequality constraint condition, and the dimension of the first matrix L is not particularly limited in this embodiment.
Similarly, the preset maximum value of the robot's centroid variable is denoted xmaxThe preset maximum value of the acceleration change rate of the centroid is recorded as umaxThen, a second matrix U constructed according to the preset maximum value of the centroid variable of the robot and the preset maximum value of the acceleration change rate of the centroid may be recorded as:
U＝[xmax…xmaxumax…umax]
the dimension of the second matrix U may be the same as the dimension of the first matrix L, and is determined by the dimension of the inequality constraint condition.
The identity matrix is denoted as I, and the predetermined power of the identity matrix is denoted as
Figure BDA0002874845740000141
Predetermined power of unit matrix
Figure BDA0002874845740000142
Product A with an optimization variable YineqRecording as follows:
Figure BDA0002874845740000143
according to the first matrix, the second matrix and the preset power of the unit matrix, the constructed inequality constraint strip can be written as:
L＜Aineq＜U
and S1032, carrying out constraint solution on the optimization variables according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function, and obtaining the centroid track of the robot.
The robot centroid trajectory is composed of a plurality of discrete points, namely, according to the centroid position of each control cycle, the robot centroid trajectory can be determined, since the equality constraint condition is used for equality constraint on the optimized variable and the second preset matrix of the robot, the inequality constraint is used for inequality constraint on the preset power of the unit matrix and the optimized variable, the optimized variable is a variable constructed according to the barycenter variable of the robot and the acceleration change rate of the barycenter, the barycenter variable comprises the position of the barycenter, then according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function, the optimization variables are constrained and solved, so that a cost function constructed by solving the zero moment point track and the expected zero moment point track is minimum to obtain the position of the center of mass of each control period, namely discrete points of the centroid trajectory, and then the centroid trajectory of the robot is obtained according to the discrete points of the centroid trajectory.
In an optional embodiment, step S1032 may include:
and carrying out minimum value constraint solving on the optimized variable according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
The expression matrix of the cost function is an expression matrix constructed by a coefficient matrix for solving the zero moment point track and an expected zero moment point track of the robot, and can be, for example, a difference value between the coefficient matrix for solving the zero moment point track and the expected zero moment point track, that is, the difference value between the coefficient matrix for solving the zero moment point track and the expected zero moment point track is minimized as much as possible under the condition of satisfying equality constraint conditions and inequality constraint conditions, that is, the cost function constructed by solving the zero moment point track and the expected zero moment point track is minimized, so that the solved centroid track is beneficial to the stable control of the robot.
As another example, for each control cycle, the coefficient matrix of the expected zero moment point trajectory is denoted as bcmpSolving the zero moment point trajectory and recording as ZcmpThe norm of the difference between the coefficient matrix of the zero moment point trajectory and the expected zero moment point trajectory in each control period can be obtained, and the square of the norm is taken as an expression matrix of the cost function of the robot and can be recorded as: i Zcmp-bcmp||2。
Wherein, bcmp＝[p0 p1… pN]T，p0Expected zero moment point trajectory for the 1 st control cycle, p1Expected zero moment point trajectory for the 2 nd control cycle, pNIs the expected zero moment point track of the Nth control period.
That is, Zcmp-bcmpCan then be constrained according to the equationeq＝AeqY sum inequality constraint L<Aineq<U, to cost function | | Zcmp-bcmp||2Performing minimum constraint solution, namely satisfying equality constraint condition beq＝AeqY sum inequality constraint L<Aineq<In the case of U, min | | | Z is obtainedcmp-bcmp||2To obtain the centroid trajectory of the robot.
Alternatively, Zcmp＝AcmpY。
The method for acquiring the centroid trajectory acquires inequality constraint conditions of the centroid of the robot, and performs constraint solution on the optimization variables according to the equality constraint conditions, the inequality constraint conditions and the expression matrix of the cost function to acquire the centroid trajectory of the robot. In this embodiment, the equality constraint condition and the inequality constraint condition are adopted to solve the optimization variable constraint, so that the cost function constructed by solving the zero moment point trajectory and the expected zero moment point trajectory is minimum, and the centroid trajectory corresponding to the zero moment point trajectory in any shape can be obtained through solving.
In an optional implementation manner, the following describes an obtaining process of the cost function with reference to an embodiment of fig. 4, where fig. 4 shows a flow diagram of a fifth method for obtaining a centroid trajectory provided in the embodiment of the present application, as shown in fig. 4, step S102 may include:
s1021, establishing a first relation matrix between the mass center variable of the robot in the kth control period and the position of the zero moment point of the kth control period by adopting a linear inverted pendulum model.
S1022, constructing a first preset matrix according to the parameters in the first relation matrix.
And S1023, acquiring a coefficient matrix for solving the zero moment point track according to the product of the second preset matrix and the optimization variable.
The first relation matrix is used for representing the relation between the centroid variable of the robot in the kth control period and the position of the zero moment point of the kth control period.
A linear inverted pendulum module is adopted, a second-order differential equation is used for describing the relation between a centroid track and a zero moment point track, and the following formula is referred to:
Figure BDA0002874845740000161
x is the locus of the center of mass,
Figure BDA0002874845740000162
the acceleration of the center of mass, p is the position of a zero moment point, g is the acceleration of gravity, z is the distance from the center of mass of the robot to the ground, and it is assumed that z remains unchanged during the walking process of the robot.
Converting the formula into a matrix form to obtain a first relation matrix:
pk＝Cpxk
wherein p isk＝p(kΔt)，pkThe position of the robot at the zero moment point of the kth control cycle.
Figure BDA0002874845740000163
x (k deltat) is the centroid position for the kth control cycle,
Figure BDA0002874845740000164
the centroid velocity for the kth control period,
Figure BDA0002874845740000165
the centroid acceleration of the kth control period is shown, and Δ t is the duration of the control period.
The parameters in the first relation matrix may be coefficients of the centroid position of the robot at the kth control cycle, i.e. xkCoefficient of (A) is CP。
Constructing a first preset matrix according to the parameters in the first relation matrix, wherein the elements of the first preset matrix are composed of the parameters C in the first relation matrixPDetermining, as an example, a first predetermined matrix AcmpRecording as follows:
Figure BDA0002874845740000171
it should be noted that the first predetermined matrix acmpMay include N + 1CPWherein A iscmpThe values of other elements not shown are all 0.
Then, the product of the first preset matrix and the optimization variable can be used as a coefficient matrix for solving the zero moment point trajectory, and can be written as: a. thecmpY。
The method for acquiring the centroid trajectory in the embodiment adopts a linear inverted pendulum model, establishes a first relation matrix between a centroid variable of a robot in a kth control period and a position of a zero moment point of the kth control period, constructs a first preset matrix according to parameters in the first relation matrix, and acquires a coefficient matrix for solving the zero moment point trajectory according to the first preset matrix and an optimization variable. Thereby obtaining a coefficient matrix for solving the zero moment point track.
Fig. 5 shows a schematic structural diagram of an apparatus for acquiring a centroid trajectory provided in an embodiment of the present application, where the apparatus 50 for acquiring a centroid trajectory may be integrated in a robot controller through software and/or hardware. As shown in fig. 5, the centroid trajectory acquiring device 50 includes:
a constructing module 501, configured to construct an optimized variable according to N centroid variables of the robot in N control cycles and an acceleration change rate of the N centroids, where N is the number of the control cycles, and is greater than or equal to 2;
an obtaining module 502, configured to obtain, according to the optimized variable and a first preset matrix, a coefficient matrix for solving a zero moment point trajectory, where elements in the first preset matrix are obtained by calculation according to a first relationship matrix between a centroid variable of the robot in a kth control cycle and a position of a zero moment point in the kth control cycle, where k is less than or equal to N-1 and greater than or equal to 1, obtain, according to the coefficient matrix for solving the zero moment point trajectory and an expected zero moment point trajectory, an expression matrix of a cost function of the robot, and obtain an equality constraint condition of the centroid of the robot, where the equality constraint condition is used to perform equality constraint on the optimized variable and the first preset matrix;
and a solving module 503, configured to perform constraint solving on the optimized variable according to the equation constraint condition and the expression matrix of the cost function, so as to obtain a centroid trajectory of the robot.
In an optional implementation manner, the building module 501 is further configured to:
establishing a second relation matrix of a mass center variable of the robot in the kth control period and a mass center variable of the robot in the (k + 1) th control period by adopting a linear inverted pendulum model;
constructing a second preset matrix according to the first parameter and the second parameter in the second relation matrix, wherein elements in the second preset matrix are determined according to the first parameter and the second parameter;
and constructing the equality constraint condition according to the optimization variable and the second preset matrix.
In an optional implementation manner, the solving module 503 is specifically configured to:
obtaining inequality constraint conditions of the center of mass of the robot, wherein the inequality constraint conditions are used for carrying out inequality constraint on a preset power of a unit matrix and the optimization variables, and the preset power is (4N +3)2；
And carrying out constraint solution on the optimization variables according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
In an optional implementation manner, the building module 501 is further configured to:
constructing a first matrix according to a preset minimum value of a mass center variable of the robot and a preset minimum value of an acceleration degree change rate of the mass center, and constructing a second matrix according to a preset maximum value of the mass center variable of the robot and a preset maximum value of the acceleration degree change rate of the mass center;
an obtaining module 502, further configured to obtain a product of a preset power of the identity matrix and the optimization variable;
the constructing module 501 is further configured to construct the inequality constraint condition according to the first matrix, the second matrix, and the product.
In an optional implementation manner, the solving module 503 is specifically configured to:
and carrying out minimum value constraint solving on the optimized variable according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
In an optional implementation manner, the obtaining module 502 is specifically configured to:
establishing a first relation matrix between a mass center variable of the robot in a kth control period and a position of a zero moment point of the kth control period by adopting a linear inverted pendulum model;
constructing the first preset matrix according to the parameters in the first relation matrix, wherein the elements in the first preset matrix are determined according to the parameters in the first relation matrix;
and acquiring a coefficient matrix of the solved zero moment point track according to the product of the first preset matrix and the optimization variable.
In an optional embodiment, the method further comprises:
and the control module 504 is used for controlling the robot to move according to the centroid track of the robot.
The implementation process and the implementation principle of the device for acquiring a centroid trajectory in this embodiment are similar to the method for acquiring a centroid trajectory in the above method embodiment, and are not described herein again.
Fig. 6 shows a schematic structural diagram of a robot provided in an embodiment of the present application, and as shown in fig. 6, a robot 60 includes: a controller 601, a memory 602 and a bus 603, wherein the memory 602 stores machine-readable instructions executable by the controller 601, when the robot 60 runs, the controller 601 communicates with the memory 602 through the bus 603, and the controller 601 executes the machine-readable instructions to perform the above-mentioned method embodiments.
Another embodiment of the present application provides a storage medium, on which a computer program is stored, the computer program being executed by a controller to perform the above method embodiments.
It can be clearly understood by those skilled in the art that, for convenience and brevity of description, the specific working processes of the system and the apparatus described above may refer to corresponding processes in the method embodiments, and are not described in detail in this application. In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. The above-described apparatus embodiments are merely illustrative, and for example, the division of the modules is merely a logical division, and there may be other divisions in actual implementation, and for example, a plurality of modules or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or modules through some communication interfaces, and may be in an electrical, mechanical or other form.
In addition, functional units in the embodiments of the present application may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application.

Claims (10)

1. A method for acquiring a centroid trajectory is characterized by comprising the following steps:
constructing an optimized variable according to N mass center variables of the robot in N control cycles and the acceleration change rate of the N mass centers, wherein N is the number of the control cycles, and is greater than or equal to 2;
obtaining a coefficient matrix for solving a zero moment point track according to the optimized variable and a first preset matrix, wherein elements in the first preset matrix are obtained by calculation according to a first relation matrix between a centroid variable of the robot in a kth control period and a position of a zero moment point of the kth control period, and k is less than or equal to N-1 and is greater than or equal to 1;
obtaining an expression matrix of a cost function of the robot according to the coefficient matrix of the solved zero moment point track and the expected zero moment point track;
obtaining an equality constraint condition of the center of mass of the robot, wherein the equality constraint condition is used for carrying out equality constraint on the optimized variable and a second preset matrix, and elements in the second preset matrix are obtained by calculation according to a second relation matrix between the center of mass variable of the robot in the kth control period and the center of mass variable of the (k + 1) th control period;
and carrying out constraint solution on the optimization variables according to the equality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
2. The method of claim 1, wherein the equality constraint is obtained by:
establishing a second relation matrix of a mass center variable of the robot in the kth control period and a mass center variable of the robot in the (k + 1) th control period by adopting a linear inverted pendulum model;
constructing a second preset matrix according to the first parameter and the second parameter in the second relation matrix, wherein elements in the second preset matrix are determined according to the first parameter and the second parameter;
and constructing the equality constraint condition according to the optimization variable and the second preset matrix.
3. The method of claim 1, wherein the constrained solving of the optimization variables according to the equation constraint condition and the expression matrix of the cost function to obtain the centroid trajectory of the robot comprises:
obtaining inequality constraint conditions of the center of mass of the robot, wherein the inequality constraint conditions are used for presetting times of an identity matrixThe power and the optimization variable are subjected to inequality constraint, and the preset power is (4N +3)2；
And carrying out constraint solution on the optimization variables according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
4. A method according to claim 3, characterized in that said inequality constraints are obtained by:
constructing a first matrix according to a preset minimum value of a mass center variable of the robot and a preset minimum value of an acceleration change rate of the mass center;
constructing a second matrix according to a preset maximum value of a mass center variable of the robot and a preset maximum value of an acceleration change rate of the mass center;
obtaining the product of the preset power of the unit matrix and the optimization variable;
and constructing the inequality constraint condition according to the first matrix, the second matrix and the product.
5. The method according to claim 3, wherein the constrained solving of the optimization variables according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid trajectory of the robot comprises:
and carrying out minimum value constraint solving on the optimized variable according to the equality constraint condition, the inequality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
6. The method according to claim 1, wherein obtaining a coefficient matrix for solving the zero moment point trajectory according to the optimization variable and a first preset matrix comprises:
establishing a first relation matrix between a mass center variable of the robot in a kth control period and a position of a zero moment point of the kth control period by adopting a linear inverted pendulum model;
constructing the first preset matrix according to the parameters in the first relation matrix, wherein the elements in the first preset matrix are determined according to the parameters in the first relation matrix;
and acquiring a coefficient matrix of the solved zero moment point track according to the product of the first preset matrix and the optimization variable.
7. The method according to any one of claims 1-6, wherein after the constrained solution of the optimization variables according to the equality constraint and the expression matrix of the cost function to obtain the centroid trajectory of the robot, the method further comprises:
and controlling the robot to move according to the centroid track of the robot.
8. An apparatus for acquiring a centroid trajectory, comprising:
the construction module is used for constructing an optimized variable according to N mass center variables of the robot in N control periods and the acceleration change rate of the N mass centers, wherein N is the number of the control periods, and is greater than or equal to 2;
an obtaining module, configured to obtain a coefficient matrix for solving a zero moment point trajectory according to the optimized variable and a first preset matrix, where elements in the first preset matrix are obtained through calculation according to a first relation matrix between a centroid variable of the robot in a kth control cycle and a position of a zero moment point in the kth control cycle, where k is less than or equal to N-1 and greater than or equal to 1, obtain an expression matrix of a cost function of the robot according to the coefficient matrix for solving the zero moment point trajectory and an expected zero moment point trajectory, and obtain an equality constraint condition of the centroid of the robot, where the equality constraint condition is used to perform equality constraint on the optimized variable and the first preset matrix;
and the solving module is used for carrying out constraint solving on the optimization variables according to the equality constraint condition and the expression matrix of the cost function to obtain the centroid track of the robot.
9. A robot, comprising: a controller, a memory and a bus, the memory storing machine-readable instructions executable by the controller, the controller and the memory communicating over the bus when the robotic controller is operating, the controller executing the machine-readable instructions to perform the method of any of claims 1-7.
10. A storage medium, characterized in that the storage medium has stored thereon a computer program which, when being executed by a controller, performs the method according to any one of claims 1-7.
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