A control and adjustment method for a dual-motor propulsion system

Abstract

The present invention relates to the technical field of motor speed regulation, and in particular to a control and regulation method for a dual-motor propulsion system. The method obtains a command-compliant balance value at a corresponding moment according to the difference in angular velocity data of the diagonally distributed main motors of a quad-rotor drone at each moment; determines the suspected rotation center when the quad-rotor drone executes a rotation command, uses the command-compliant balance value of the suspected rotation center at the corresponding moment to adjust the corresponding suspected rotation center to obtain the actual rotation center, and then obtains the initial centrifugal force of the main motor when the quad-rotor drone executes the rotation command, and combines the command-compliant balance values ​​of all quad-rotor drones at all moments in a test time period to control and regulate the auxiliary motor of a quad-rotor drone using a dual-motor propulsion system. The present invention effectively improves the accuracy of control and regulation of the dual-motor propulsion system, and increases the attitude stability and heading control accuracy of the drone when performing a rotation action.

Description

Technical Field

[0001] The present invention relates to the technical field of motor speed regulation, and in particular to a control and regulation method for a dual-motor propulsion system. Background Art

[0002] A dual-motor propulsion system refers to a system that uses two electric motors to provide power. The dual-motor propulsion system is applied to quad-rotor drones, which means that each rotor of the drone has two electric motors to provide thrust, thereby controlling the flight of the drone. Centrifugal force is generated when the quad-rotor drone is rotated, resulting in errors in the rotation control of the drone. Therefore, the dual-motor propulsion system of the quad-rotor drone needs to be controlled and adjusted.

[0003] Each rotor of a quadcopter drone that uses a dual-motor propulsion system has a main motor and an auxiliary motor. The main motor is usually used to provide thrust for the drone, and the auxiliary motor is used to perform feedforward compensation for the centrifugal force generated when the main motor is rotated to control the quadcopter drone. The dual-motor propulsion system of the quadcopter drone can be controlled and adjusted to achieve the purpose of precise control of the drone.

[0004] Due to the influence of factors such as wind and sand in the environment, the rotational movement of the quadrotor drone around a specific point, namely the preset rotation center, is not standard, resulting in a deviation between the actual rotation center of the quadrotor drone and the position of the preset rotation center. There is an error in the rotation radius determined based on the preset rotation center, which makes the centrifugal force generated by the main motor during rotation control inaccurate, and thus the accuracy of control and adjustment of the dual-motor propulsion system is low. Summary of the invention

[0005] In order to solve the technical problem that the actual rotation center of the UAV rotating motion is different from the preset rotation center, resulting in low accuracy in the control and adjustment of the dual-motor propulsion system, the purpose of the present invention is to provide a control and adjustment method for the dual-motor propulsion system, and the technical solution adopted is as follows:

[0006] The present invention proposes a control and regulation method for a dual-motor propulsion system, the method comprising:

[0007] Obtain the angular velocity data of the main motors of several quad-rotor drones using a dual-motor propulsion system that execute the same rotation command at each moment during the test period;

[0008] According to the difference in angular velocity data of the diagonally distributed main motors of each quad-rotor drone at each moment and the angular velocity data of the main motors at each moment, a command-compliant balance value at each moment when each quad-rotor drone executes a rotation command is obtained;

[0009] Obtaining a suspected rotation center when each quadrotor drone executes a rotation instruction; adjusting the corresponding suspected rotation center using the instruction-compliant balance value at the corresponding moment of the suspected rotation center to obtain the actual rotation center when each quadrotor drone executes the rotation instruction, and obtaining the initial centrifugal force of the main motor of each quadrotor drone when the quadrotor drone executes the rotation instruction based on the actual rotation center;

[0010] According to the command-compliant balance value and the initial centrifugal force at all times during the test period of the quadrotor drone, the auxiliary motor of the quadrotor drone using a dual-motor propulsion system is controlled and adjusted.

[0011] Further, the method of obtaining the balance value that meets the command at each moment when each quad-rotor drone executes the rotation command according to the difference in angular velocity data of the diagonally distributed main motors of each quad-rotor drone at each moment and the angular velocity data of the main motors at each moment includes:

[0012] According to the difference in angular velocity data of the diagonally distributed main motors of each quad-rotor drone at each moment, the rotation speed symmetry value of each quad-rotor drone at each moment when executing a rotation instruction is obtained;

[0013] The preset angular velocity data of each main motor of the quad-rotor drone is set when the quad-rotor drone executes a rotation instruction; according to the difference between the angular velocity data of the main motor of each quad-rotor drone at each moment and the preset angular velocity data, as well as the rotation speed symmetry value, the balance value that conforms to the instruction at each moment when each quad-rotor drone executes the rotation instruction is obtained.

[0014] Furthermore, the obtaining of the rotation speed symmetry value at each moment when each quad-rotor drone executes the rotation instruction includes:

[0015] The two main motors of each quadrotor drone are diagonally distributed to form a diagonal motor pair; each quadrotor drone has two diagonal motor pairs;

[0016] The absolute value of the difference between the angular velocity data of the two main motors in each diagonal motor pair of each quadrotor drone at each moment is used as the angular velocity difference value of the corresponding diagonal motor pair at each moment;

[0017] The cumulative sum of the angular velocity difference values ​​of all diagonal motor pairs of each quad-rotor drone is negatively correlated and normalized to obtain the rotation speed symmetry value at each moment when each quad-rotor drone executes the rotation instruction.

[0018] Furthermore, the step of obtaining the balance value that complies with the instruction at each moment when each quad-rotor drone executes the rotation instruction includes:

[0019] Select two adjacent main motors from the main motors of each quadrotor drone as analysis motors;

[0020] The sum of the absolute values ​​of the differences between the angular velocity data of the same analysis motor of each quad-rotor drone at each moment and the preset angular velocity data is accumulated as the command compliance value at each moment when each quad-rotor drone executes the rotation command;

[0021] According to the instruction conformity value and the rotational speed symmetry value, the instruction conformity balance value at each moment when each quad-rotor drone executes the rotation instruction is obtained; the instruction conformity value and the instruction conformity balance value are negatively correlated, and the rotational speed symmetry value and the instruction conformity balance value are positively correlated.

[0022] Furthermore, obtaining the suspected rotation center of each quadrotor drone when executing the rotation instruction includes:

[0023] Select a number of analysis moments from the test time period; obtain the position point of each quadcopter at each analysis moment when executing the rotation command;

[0024] Performing curve fitting on the position points at the analysis time when each quad-rotor drone executes a rotation command to obtain a motion trajectory line; obtaining a perpendicular line of the position points at each analysis time on the motion trajectory line, and recording it as the analysis line at the corresponding analysis time;

[0025] The intersection of the analysis lines at all analysis moments when each quad-rotor drone executes a rotation instruction is recorded as the suspected rotation center when each quad-rotor drone executes a rotation instruction.

[0026] Furthermore, the method for obtaining the actual rotation center of each quad-rotor drone when executing a rotation instruction includes:

[0027] For each suspected rotation center when the quad-rotor drone executes a rotation command, the analysis time corresponding to the analysis line passing through each suspected rotation center is recorded as the target time corresponding to the suspected rotation center; according to the command-compliant balance value of all target times of each suspected rotation center when each quad-rotor drone executes a rotation command, and the abnormality degree of the suspected rotation center, the rotation radius contribution value of each suspected rotation center is obtained;

[0028] Based on the rotation radius contribution values ​​of all suspected rotation centers when each quadrotor drone executes a rotation command, the rotation radius contribution value of each suspected rotation center is normalized to obtain the contribution weight of each suspected rotation center; the values ​​of each dimension of all suspected rotation centers are weighted and summed according to the contribution weight, and the result of the weighted summation of each dimension is used as the value of each dimension of the actual rotation center when each quadrotor drone executes a rotation command.

[0029] Further, the obtaining of the rotation radius contribution value of the suspected rotation center includes:

[0030] The average of the command-compliant balance values ​​at all target moments of each suspected rotation center when each quadrotor drone executes a rotation command is used as the command-compliant concentrated value of the corresponding suspected rotation center; the LOF value of each suspected rotation center when each quadrotor drone executes a rotation command is obtained by using a local anomaly factor algorithm;

[0031] According to the instruction set value and the LOF value, the rotation radius contribution value of each suspected rotation center when each quadrotor drone executes the rotation command is obtained; the instruction set value and the rotation radius contribution value are positively correlated, and the LOF value and the rotation radius contribution value are negatively correlated.

[0032] Further, the controlling and adjusting of the auxiliary motor of the quad-rotor drone using a dual-motor propulsion system according to the command-compliant balance value and the initial centrifugal force at all times of the quad-rotor drone during the test period includes:

[0033] According to the command-compliant balance values ​​and the initial centrifugal force of all quad-rotor drones at all times during the test period, the comprehensive centrifugal force of the main motor when the quad-rotor drone executes the rotation command is obtained;

[0034] Based on the comprehensive centrifugal force, the MPC algorithm is used to control and adjust the auxiliary motor of the quad-rotor drone using a dual-motor propulsion system.

[0035] Furthermore, the method of obtaining the comprehensive centrifugal force of the main motor when the quad-rotor drone executes the rotation instruction includes:

[0036] The average of the command-compliant balance values ​​of each quadrotor drone at all times during the test period is used as the system balance value of each quadrotor drone executing the rotation command;

[0037] Based on the system balance value of all quadrotor drones, the system balance value of each quadrotor drone is normalized to obtain the balance weight of each quadrotor drone; according to the balance weight, the initial centrifugal forces of all quadrotor drones are weighted and summed to obtain the comprehensive centrifugal force of the main motor when the quadrotor drone executes a rotation command.

[0038] Furthermore, the obtaining of the initial centrifugal force of the main motor of each quad-rotor drone when executing the rotation instruction based on the actual rotation center includes:

[0039] The distance between the initial position of each quadrotor drone when executing the rotation instruction and the actual rotation center is used as the rotation radius of each quadrotor drone when executing the rotation instruction;

[0040] The two endpoints of the motion trajectory line corresponding to each quadrotor drone are respectively connected to the actual rotation center to obtain two reference line segments of each quadrotor drone; the ratio of the angle between the two reference line segments to the duration of the test time period is used as the reference angular velocity of each quadrotor drone;

[0041] The mass of the quad-rotor drone is obtained, and the initial centrifugal force of the main motor of each quad-rotor drone when executing a rotation instruction is obtained by combining the rotation radius and the reference angular velocity.

[0042] The present invention has the following beneficial effects:

[0043] In an embodiment of the present invention, due to interference from factors such as wind during the flight of a drone, the rotation speeds of the diagonally distributed main motors of the quadrotor drone are different during flight and the rotation speeds of the main motors deviate from the standard rotation speed. Combined with the differences in angular velocity data of the diagonally distributed main motors of the quadrotor drone at each moment and the angular velocity data of the main motors at each moment, the degree to which the flight state of the quadrotor drone conforms to the ideal flight state when executing a rotation instruction is analyzed to obtain a command-compliant balance value. Since the rotational motion of the drone is not standard due to interference from factors such as wind, there are multiple suspected rotation centers in the rotational motion of the drone. The command-compliant balance value presents the accuracy of the information of the drone at each moment. The suspected rotation center is adjusted using the command-compliant balance value to obtain the obtained The actual rotation center is more accurate, and thus the initial centrifugal force generated when each quadrotor drone executes a rotation command is more accurate; the accuracy of the information of the drone at each moment is presented in accordance with the command balance value, and it is used to determine the contribution of the initial centrifugal force of the main motor to the final centrifugal force when each quadrotor drone executes a rotation command, so that the centrifugal force generated by the quadrotor drone when executing the rotation command is finally determined to be more in line with the actual situation and accurate; the final centrifugal force generated when the quadrotor drone executes the rotation command is used to control and adjust the auxiliary motor of the quadrotor drone, so that the auxiliary motor compensates for the centrifugal force generated by the rotation of the main motor, so that the drone can maintain attitude stability and heading control accuracy when performing a rotation action, thereby improving the flight stability of the drone in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0045] Figure 1A flowchart of a control and adjustment method for a dual-motor propulsion system provided by one embodiment of the present invention;

[0046] Figure 2 A schematic diagram of a quad-rotor drone using a dual-motor propulsion system provided by one embodiment of the present invention;

[0047] Figure 3 A flowchart of a method for obtaining a command balance value according to an embodiment of the present invention;

[0048] Figure 4 A system structure diagram of a control and regulation system for a dual-motor propulsion system provided by one embodiment of the present invention;

[0049] Figure 5 A schematic diagram of a computer device for a control and adjustment device for a dual-motor propulsion system provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following is a detailed description of the control and adjustment method for a dual-motor propulsion system proposed by the present invention, its specific implementation method, structure, features and effects, in combination with the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics in one or more embodiments may be combined in any suitable form.

[0051] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0052] The following is a detailed description of a control and regulation method for a dual-motor propulsion system provided by the present invention in conjunction with the accompanying drawings.

[0053] Embodiment 1:

[0054] The present invention proposes a control and regulation method for a dual-motor propulsion system, see Figure 1 , which shows a flow chart of steps of a control and adjustment method for a dual-motor propulsion system provided by an embodiment of the present invention, the method comprising:

[0055] Step S1: Obtain the angular velocity data of the main motors of several quad-rotor drones using a dual-motor propulsion system that execute the same rotation instruction at each moment during a test period.

[0056] Specifically, each rotor of a quad-rotor drone using a dual-motor propulsion system is equipped with two motors, the motor at the upper position of the two motors is the main motor, and the motor at the lower position is the auxiliary motor. Figure 2 A schematic diagram of a quad-rotor drone using a dual-motor propulsion system provided by an embodiment of the present invention is shown in FIG. Figure 2 As shown, Figure 2 In the figure, 1 represents the first rotor, 2 represents the second rotor, 3 represents the third rotor, and 4 represents the fourth rotor; the first rotor 1 includes: a main motor 5 and an auxiliary motor 6, and the motor distribution of other rotors is the same as that of the first rotor 1; the diagonally distributed main motors of the quadrotor UAV include: the main motors in the first rotor 1 and the third rotor 3, and the main motors in the second rotor 2 and the fourth rotor 4.

[0057] The principle of a quadrotor drone executing a rotation command is as follows: increase the rotation speed of a pair of diagonally distributed main motors (such as the main motors in the second rotor 2 and the fourth rotor 4), and reduce the rotation speed of another pair of diagonally distributed main motors (such as the main motors in the first rotor 1 and the third rotor 3), so that the counter-torque of the second rotor 2 and the fourth rotor 4 on the fuselage is greater than the counter-torque of the first rotor 1 and the third rotor 3 on the fuselage, thereby causing the fuselage to rotate under the action of the unbalanced counter-torque, thereby realizing the yaw rotation motion of the drone.

[0058] When a single-motor-driven drone rotates, centrifugal force is generated. Due to its limited hardware resources, it cannot meet the needs of real-time processing of high-precision centrifugal force compensation, resulting in deviations in the control accuracy of the drone. Therefore, this solution uses the auxiliary motor of each rotor to perform feedforward compensation on the centrifugal force generated when the main motor is rotating, and then uses the Model Predictive Control (MPC) algorithm of feedforward control to provide more precise control and reduce delays, thereby improving the flight stability of the drone in complex environments.

[0059] A gyroscope is installed at the main motor position of each rotor of the quadcopter drone, and a positioning device such as the Global Positioning System (GPS) is installed on the drone body. The gyroscope is used to measure the angular velocity data of the main motor when it rotates, and the positioning device is used to measure the position of the drone. Select several quadcopter drones with equal mass and dual-motor propulsion systems, control these drones to execute the same rotation command, and collect the angular velocity data and position points of each main motor of each drone at each moment during the test period.

[0060] In this embodiment, the frequency of the gyroscope collecting data is 60 Hz, the frequency of the positioning device collecting data is 1 Hz, and the duration of the test period is 60 seconds, which can be set by the implementer according to the specific situation. It should be noted that the duration of the test period needs to be less than the time required for the drone to rotate once when executing the rotation command.

[0061] Step S2: According to the difference in angular velocity data of the diagonally distributed main motors of each quad-rotor drone at each moment, and the angular velocity data of the main motors at each moment, obtain the command-compliant balance value at each moment when each quad-rotor drone executes a rotation command.

[0062] Ideally, the speed of the diagonally distributed main motors of a quadcopter should remain consistent during flight, and the speed of the main motors should be close to the preset speed of the corresponding motors; however, in actual situations, the size and direction of the wind in the environment will affect the operation of the motors, causing the speed of the main motors to deviate, thereby generating an unbalanced torque, which results in inaccurate centrifugal force of the main motors when the quadcopter executes a rotation command. Therefore, based on the difference in angular velocity data of the diagonally distributed main motors of the quadcopter at each moment, and the difference between the angular velocity data of the main motors at each moment and the preset speed, the degree to which the flight state of the quadcopter when executing a rotation command conforms to the ideal flight state is analyzed, and the balance value that conforms to the command is obtained.

[0063] See also Figure 3 , which shows a flowchart of a method for obtaining an instruction balance value provided by an embodiment of the present invention, the method comprising:

[0064] Step S210: According to the difference in angular velocity data of the diagonally distributed main motors of each quad-rotor drone at each moment, the rotational speed symmetry value of each quad-rotor drone at each moment when executing the rotation instruction is obtained.

[0065] If the angular velocities of the diagonally distributed main motors of the quadcopter are different when executing the rotation command, an unbalanced torque will be generated, causing the drone to rotate and fly unsteadily. Therefore, in order to ensure the balance of the drone and the accuracy of attitude control, the speed of the diagonally distributed main motors of the quadcopter should be kept consistent to avoid unbalanced torque.

[0066] Preferably, in some possible implementation modes of the embodiments of the present invention, the method for obtaining the rotational speed symmetry value includes: a diagonal motor pair is formed by two main motors diagonally distributed in each quadrotor drone; each quadrotor drone has two diagonal motor pairs; the absolute value of the difference in angular velocity data of the two main motors in each diagonal motor pair of each quadrotor drone at each moment is used as the angular velocity difference value of the corresponding diagonal motor pair at each moment; the cumulative sum of the angular velocity difference values ​​of all diagonal motor pairs of each quadrotor drone is negatively correlated and normalized to obtain the rotational speed symmetry value of each quadrotor drone at each moment when executing a rotation command.

[0067] It should be noted that the two diagonal motor pairs of the quadcopter are: Figure 2 As shown, the main motors in the first rotor 1 and the third rotor 3 constitute a first diagonal motor pair, and the main motors in the second rotor 2 and the fourth rotor 4 constitute a second diagonal motor pair.

[0068] In a specific implementation of the embodiment of the present invention, the rotational speed symmetry value is expressed by the formula:

[0069]

[0070] Wherein, W is the symmetric value of the rotation speed at each moment when each quadrotor drone executes a rotation command; A is the total number of diagonal motor pairs of each quadrotor drone, and in this embodiment, A is 2; The angular velocity data of the first main motor of the a-th diagonal motor pair of each quadrotor drone at each moment; The angular velocity data of the second main motor of the a-th diagonal motor pair of each quadrotor drone at each moment; is the angular velocity difference value of the a-th diagonal motor pair of each quadrotor drone at each moment; is the absolute value function; exp is the exponential function with a natural constant as the base.

[0071] It should be noted that, when the rotation speed symmetry value W is larger, it means that the flight state of the quadrotor drone executing the rotation command is closer to the ideal flight state.

[0072] Step S220: setting the preset angular velocity data of each main motor when the quad-rotor drone executes a rotation instruction; obtaining the balance value that complies with the instruction at each moment when each quad-rotor drone executes a rotation instruction based on the difference between the angular velocity data of the main motor of each quad-rotor drone at each moment and the preset angular velocity data, as well as the rotational speed symmetry value.

[0073] Preferably, in some possible implementation modes of the embodiments of the present invention, the method for obtaining the instruction-compliant balance value includes: randomly selecting two adjacent main motors from the main motors of each quadrotor drone as analysis motors; taking the cumulative sum of the absolute values ​​of the difference between the angular velocity data and the preset angular velocity data of the same analysis motor of each quadrotor drone at each moment as the instruction compliance value at each moment when each quadrotor drone executes a rotation instruction; according to the instruction compliance value and the speed symmetry value, obtaining the instruction-compliant balance value at each moment when each quadrotor drone executes the rotation instruction; the instruction compliance value and the instruction compliance balance value are negatively correlated, and the speed symmetry value and the instruction compliance balance value are positively correlated.

[0074] In the process of analyzing whether the flight state of the quadcopter drone meets the ideal flight state, in order to reduce the amount of calculation, only the speeds of any two adjacent main motors of the quadcopter drone are used for analysis. The two adjacent main motors are taken from two diagonal motor pairs, and the speeds of the diagonally distributed main motors of the quadcopter drone should be relatively close. Figure 2 As shown, the adjacent main motors of the quad-rotor drone include: the main motors in the first rotor 1 and the second rotor 2, the main motors in the second rotor 2 and the third rotor 3, the main motors in the third rotor 3 and the fourth rotor 4, and the main motors in the fourth rotor 4 and the first rotor 1 are all two adjacent main motors. Figure 2 The main motors of the first rotor 1 and the second rotor 2 are recorded as analysis motors.

[0075] It should be noted that when the quadrotor drone is flying, the main motor of each rotor has angular velocity preset data, which is the ideal speed of the main motor without being disturbed by the environment. The angular velocity preset data can be obtained from the instruction manual of the quadrotor drone, or can be tested in an environment such as indoors where there is no interference from conditions. It will not be repeated here.

[0076] If the angular velocity data at each moment when each quadcopter executes a rotation instruction is closer to the preset angular velocity data, that is, the smaller the instruction compliance value is, the speed of the main motor of the quadcopter at each moment when executing the rotation instruction is more in line with the ideal flight state. If the speed symmetry value is larger, the flight state of the quadcopter executing the rotation instruction is closer to the ideal flight state. The closer the flight state of the quadcopter executing the rotation instruction is to the ideal flight state, the more balanced the drone flight is, and the larger the instruction compliance balance value is. Therefore, the instruction compliance value is negatively correlated with the instruction compliance balance value, and the speed symmetry value is positively correlated with the instruction compliance balance value.

[0077] In a specific implementation of the embodiment of the present invention, the instruction balance value is expressed by the formula:

[0078]

[0079] Wherein, Z is the balance value that meets the command at each moment when each quad-rotor drone executes the rotation command; B is the total number of analyzed motors of each quad-rotor drone, and B is 2 in this embodiment; The bth analysis of the angular velocity data of the motor at each moment when executing the rotation command for each quadrotor drone; The angular velocity preset data of the bth analyzed motor when executing the rotation command for each quadrotor drone; The command value at each moment when each quadcopter executes the rotation command; is the absolute value function; exp is the exponential function with a natural constant as the base.

[0080] It should be noted that the larger the command balance value is, the better the balance of the drone at each moment when each quadcopter executes the rotation command, and the more accurate the centrifugal force of the quadcopter when it rotates at that moment.

[0081] Step S3: Obtain the suspected rotation center of each quadrotor when executing the rotation command; use the suspected rotation center's balance value that conforms to the command at the corresponding moment to adjust the corresponding suspected rotation center to obtain the actual rotation center of each quadrotor when executing the rotation command, and obtain the initial centrifugal force of the main motor of each quadrotor when executing the rotation command based on the actual rotation center.

[0082] In the process of determining the centrifugal force generated when the quadcopter executes a rotation command, it is necessary to obtain the rotation radius of the drone when it executes the rotation command. The focus of the rotation radius is the rotation center. The steps for obtaining the initial centrifugal force of the main motor of each quadcopter when it executes a rotation command are as follows:

[0083] The method for obtaining the suspected rotation center when each quadrotor drone executes a rotation command is as follows:

[0084] The execution of a rotation command by a quadrotor drone usually refers to the drone rotating around a specific point. However, due to interference from factors such as wind in the environment, the rotation movement of the quadrotor drone is not standard, which results in multiple suspected rotation centers in the rotation movement of the quadrotor drone.

[0085] In an embodiment of the present invention, a method for obtaining a suspected rotation center is as follows: select a number of analysis moments from a test time period; obtain the position point at each analysis moment when each quadrotor drone executes a rotation command; perform curve fitting on the position point at the analysis moment when each quadrotor drone executes a rotation command to obtain a motion trajectory line; obtain a perpendicular line to the position point at each analysis moment on the motion trajectory line, and record it as the analysis line at the corresponding analysis moment; and record the intersection of the analysis lines at all analysis moments when each quadrotor drone executes a rotation command as the suspected rotation center when each quadrotor drone executes a rotation command.

[0086] Because ideally, the perpendicular lines of all points on the trajectory of rotational motion intersect at the center of rotation, the suspected rotation center of the quadrotor drone when executing the rotation command can be determined by the intersection of the analysis lines of the position points at the analysis time on the motion trajectory.

[0087] It should be noted that, since the frequency of data collection by the gyroscope is greater than the frequency of data collection by the positioning device, the analysis moment is equivalent to selecting several moments at equal intervals from all moments within the test time period. This scheme only considers the centrifugal force generated by the quad-rotor drone when it rotates in the horizontal plane, and determines the position point of the drone in the geodetic coordinate system at each analysis moment through the positioning device; the quad-rotor drone executes the rotation command in the same horizontal plane and does not move in the vertical direction. This embodiment uses the least squares method to perform curve fitting on the position points of all analysis moments when the quad-rotor drone executes the rotation command. Among them, the geodetic coordinate system is a two-dimensional spherical coordinate system, and the least squares method and the geodetic coordinate system are both well-known technologies and will not be introduced here.

[0088] The method for obtaining the initial centrifugal force of the main motor when each quadrotor drone executes a rotation command is as follows:

[0089] The command-compliant balance value reflects the balance of the quadrotor drone at each moment when the quadrotor drone executes a rotation command. The higher the balance of the drone, the greater the contribution of the suspected rotation center determined by the analysis line at the analysis moment to the determination of the actual rotation center. The suspected rotation center is adjusted using the command-compliant balance value at the corresponding moment of the suspected rotation center to determine the actual rotation center.

[0090] Preferably, in some possible implementation methods of the embodiments of the present invention, the method for obtaining the actual rotation center includes: for each suspected rotation center when the quadrotor drone executes a rotation command, the analysis time corresponding to the analysis line passing through each suspected rotation center is recorded as the target time of the corresponding suspected rotation center; according to the command-compliant balance value of all target moments of each suspected rotation center when each quadrotor drone executes the rotation command, and the abnormality of the suspected rotation center, the rotation radius contribution value of each suspected rotation center is obtained; based on the rotation radius contribution values ​​of all suspected rotation centers when each quadrotor drone executes the rotation command, the rotation radius contribution value of each suspected rotation center is normalized to obtain the contribution weight of each suspected rotation center; according to the contribution weight, the values ​​of each dimension of all suspected rotation centers are weighted and summed, and the result of the weighted sum of each dimension is used as the value of each dimension of the actual rotation center of each quadrotor drone when the rotation command is executed.

[0091] The density of other suspected rotation centers within the local range of each suspected rotation center reflects the possibility that each suspected rotation center is the rotation center of the quadrotor drone when executing the rotation command under ideal flight conditions; the command-compliant balance value at the analysis moment corresponding to the analysis line passing through the suspected rotation center reflects the stable flight state of the drone at the analysis moment corresponding to the suspected rotation center. Both factors can show the contribution degree of the suspected rotation center to the determination of the actual rotation center. The two are combined for analysis to obtain the rotation radius contribution value of the suspected rotation center.

[0092] In this embodiment, the method for obtaining the rotation radius contribution value is as follows: the average of the instruction balance values ​​of all target moments of each suspected rotation center when each quad-rotor drone executes a rotation instruction is used as the instruction concentration value corresponding to the suspected rotation center; the LOF value of each suspected rotation center when each quad-rotor drone executes a rotation instruction is obtained by using the local anomaly factor algorithm; according to the instruction concentration value and the LOF value, the rotation radius contribution value of each suspected rotation center when each quad-rotor drone executes a rotation instruction is obtained; the instruction concentration value is positively correlated with the rotation radius contribution value, and the LOF value is negatively correlated with the rotation radius contribution value. Among them, the local anomaly factor algorithm is a well-known technology for those skilled in the art and will not be repeated here.

[0093] If the value in the instruction set that conforms to the suspected rotation center is larger, the contribution of the suspected rotation center to the determination of the actual rotation center is greater. If the LOF value of the suspected rotation center is smaller, the other suspected rotation centers within the local range of the suspected rotation center are denser, indicating that the suspected rotation center is the rotation center of the quadcopter when executing the rotation instruction under ideal flight conditions. The greater the possibility, the greater the contribution of the suspected rotation center to the determination of the actual rotation center. Therefore, the value in the instruction set is positively correlated with the contribution value of the rotation radius, and the LOF value is negatively correlated with the contribution value of the rotation radius. In an embodiment of the present invention, the LOF value of each suspected rotation center is negatively correlated, and the product of the mapping result and the value in the instruction set is used as the contribution value of the rotation radius of each suspected rotation center when each quadcopter executes the rotation instruction.

[0094] In the embodiment of the present invention, the correlation between the LOF value and the value in the instruction set and the rotation radius contribution value can also be constructed through other basic mathematical operations, which are not limited or elaborated here.

[0095] The embodiment uses an exponential function with a natural constant as the base to perform negative correlation mapping. The specific operation is: first take the opposite number of the LOF value, and use the opposite number as the exponent of the exponential function with a natural constant as the base, so as to achieve negative correlation mapping. In other embodiments, the reciprocal of the LOF value can also be taken to achieve negative correlation mapping, which is not limited here.

[0096] Since the suspected rotation center is in a two-dimensional spherical coordinate system, the suspected rotation center has two-dimensional values. The process of a quadcopter executing a rotation command is as follows: first, the drone is raised to a certain height, and then the drone is rotated; the position of the drone before the rotation is recorded as the initial position of the drone when it executes the rotation command. Due to the interference of factors such as wind during the rotation of the drone, the real-time position of the drone may be affected. Using the initial position to calculate the rotation radius can avoid errors caused by interference and improve the stability and accuracy of the calculation. It should be noted that the initial position is equivalent to the starting point of the drone's rotation movement.

[0097] The distance between the initial position of each quad-rotor drone when executing the rotation instruction and the actual rotation center is used as the rotation radius of each quad-rotor drone when executing the rotation instruction. In a specific implementation of the embodiment of the present invention, the rotation radius of the quad-rotor drone when executing the rotation instruction is expressed by the formula:

[0098]

[0099] Where r is the rotation radius of each quadrotor when executing a rotation command; E is the total number of suspected rotation centers when each quadrotor executes a rotation command; The contribution value of the rotation radius of the cth suspected rotation center when each quadrotor drone executes a rotation command; The contribution value of the rotation radius of the kth suspected rotation center when each quadrotor drone executes the rotation command; The contribution weight of the cth suspected rotation center when each quadrotor drone executes a rotation command; The value of the first dimension of the cth suspected rotation center when each quadrotor drone executes a rotation command; The value of the second dimension of the cth suspected rotation center when each quadrotor drone executes the rotation command; The value of the first dimension of the initial position when each quadrotor drone executes a rotation command; The value of the second dimension of the initial position when each quadrotor executes a rotation command.

[0100] It should be noted that It is the actual rotation center of a quadrotor drone when executing a rotation command.

[0101] Connect the two endpoints of the motion trajectory line corresponding to each quad-rotor drone with the actual rotation center to obtain two reference line segments of each quad-rotor drone; take the ratio of the angle between the two reference line segments and the duration of the test period as the reference angular velocity of each quad-rotor drone; obtain the mass of the quad-rotor drone, combine the rotation radius and the reference angular velocity, and obtain the initial centrifugal force of the main motor of each quad-rotor drone when executing the rotation command. The initial centrifugal force is expressed by the formula:

[0102]

[0103] Where F is the initial centrifugal force of the main motor when each quadrotor drone executes a rotation command; m is the mass of the quadrotor drone; is the reference angular velocity of each quad-rotor drone; r is the rotation radius of each quad-rotor drone when executing a rotation instruction. The calculation formula of the centrifugal force is a well-known technology and will not be repeated here.

[0104] It should be noted that the angle between the two reference line segments of the quadrotor drone is the angle between the reference line segment at one end point of the motion trajectory of the quadrotor drone and the reference line segment at the other end point along the direction of the motion trajectory, and the duration of the test time period needs to be less than the time required for the drone to rotate once when executing the rotation command. The value range of the angle between the two reference line segments of the quadrotor drone is .

[0105] Step S4: According to the command-compliant balance value and the initial centrifugal force of the quad-rotor drone at all times during the test period, the auxiliary motor of the quad-rotor drone using the dual-motor propulsion system is controlled and adjusted.

[0106] When the drone system is stable, the vibration and turbulence generated during the rotation process will be minimized, and the air flow will be more uniform, reducing the impact of aerodynamics on the rotation process. At this time, the centrifugal force measurement during rotation will be closer to the actual value, and the aerodynamic disturbance will be smaller. The command balance value reflects the degree to which the flight state of the drone executing the rotation command conforms to the ideal flight state, and then determines the contribution of the initial centrifugal force at the corresponding moment of the command balance value to the comprehensive centrifugal force. The comprehensive centrifugal force of the main motor of the quadrotor drone when the quadrotor drone executes the rotation command is determined by combining the relevant information of all quadrotors.

[0107] Preferably, in some possible implementation modes of the embodiments of the present invention, the method for obtaining the comprehensive centrifugal force includes: taking the average of the command-compliant balance values ​​of each quadrotor drone at all times during the test time period as the system balance value of each quadrotor drone executing a rotation command; normalizing the system balance value of each quadrotor drone based on the system balance value of all quadrotors to obtain a balance weight; and weightedly summing the initial centrifugal forces of all quadrotors according to the balance weight to obtain the comprehensive centrifugal force of the main motor when the quadrotor drone executes a rotation command.

[0108] When a quad-rotor drone executes a rotation command, the balance error will accumulate over time, affecting the stability of the drone and the accuracy of the mission. Therefore, it is necessary to ensure the system stability of the quad-rotor drone at all times during the test period. The command-compliant balance value represents the degree to which the flight state of the drone at a single moment conforms to the ideal flight state. The larger the system balance value, the more accurate the data generated during the execution of the rotation command by each quad-rotor drone, that is, the initial centrifugal force, and the greater the contribution of the initial centrifugal force to the comprehensive centrifugal force.

[0109] In a specific implementation of the embodiment of the present invention, the comprehensive centrifugal force is expressed by the formula:

[0110]

[0111] In the formula, is the comprehensive centrifugal force of the main motor when the quadrotor drone executes the rotation command; N is the total number of quadrotor drones executing the rotation command; The system balance value for executing the rotation command for the nth quadrotor drone; The system balance value for the vth quadrotor drone to execute the rotation command; is the balance weight of the nth quadrotor drone; The initial centrifugal force of the main motor when the nth quadrotor drone executes the rotation command.

[0112] Based on the comprehensive centrifugal force, the MPC algorithm is used to control and adjust the auxiliary motor of the quadrotor drone using a dual-motor propulsion system. The specific contents are as follows:

[0113] First, a feedforward controller is designed to adjust the thrust of the auxiliary motor based on the comprehensive centrifugal force of the main motor when the quad-rotor drone executes the rotation command, so that the torque generated by the auxiliary motor can compensate for the comprehensive centrifugal force generated by the main motor. Secondly, an MPC model is established, and the mechanical model and feedforward controller of the quad-rotor drone are integrated into the MPC model, and the constraints of the control input and state variables are defined: the control input is the comprehensive centrifugal force of the main motor when the quad-rotor drone executes the rotation command, and the constraints are the maximum speed and thrust range of the motor; the MPC wear resistance is used for real-time prediction and optimization to generate the minimization objective function of the control input, that is, the attitude error, and the control input generated by the MPC model is used for the dual-motor propulsion system of the quad-rotor drone to ensure the precise control of the drone's rotation action. Then, the feedforward controller and the MPC model are integrated into the control system of the drone to ensure that the two can work together, test the system performance in actual flight, and debug and optimize according to actual conditions. Finally, the parameters in the feedforward controller and the MPC model are adjusted according to the test results to ensure the robustness and stability of the system of the quad-rotor drone under different flight conditions. Among them, the MPC algorithm is a well-known technology for those skilled in the art and will not be repeated here.

[0114] At this point, the drone can maintain better attitude stability and heading control when performing rotational movements, improving flight performance and reliability, and making the drone's rotation smoother and in line with the expected trajectory.

[0115] So far, the present invention is completed.

[0116] Embodiment 2:

[0117] The present invention proposes a control and regulation system for a dual-motor propulsion system, see Figure 4 , which shows a system structure diagram of a control and regulation system for a dual-motor propulsion system provided by an embodiment of the present invention, the system comprising:

[0118] The data acquisition module 510 is used to obtain the angular velocity data of the main motors of several quad-rotor drones using a dual-motor propulsion system that execute the same rotation instruction at each moment in a test period;

[0119] The instruction compliance analysis module 520 is used to obtain the instruction compliance balance value at each moment when each quad-rotor drone executes the rotation instruction according to the difference of the angular velocity data of the diagonally distributed main motors of each quad-rotor drone at each moment and the angular velocity data of the main motors at each moment;

[0120] The centrifugal force analysis module 530 is used to obtain the suspected rotation center of each quadrotor drone when executing the rotation command; adjust the corresponding suspected rotation center by using the instruction-compliant balance value at the corresponding moment of the suspected rotation center to obtain the actual rotation center of each quadrotor drone when executing the rotation command, and obtain the initial centrifugal force of the main motor of each quadrotor drone when executing the rotation command based on the actual rotation center;

[0121] The control and adjustment module 540 is used to control and adjust the auxiliary motor of the quad-rotor drone using a dual-motor propulsion system according to the command-compliant balance value and the initial centrifugal force of the quad-rotor drone at all times during the test period.

[0122] It should be noted that: the device provided in the above embodiment is only illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the computer device is divided into different functional modules to complete all or part of the functions described above. In addition, the control and adjustment system for a dual-motor propulsion system provided in the above embodiment and the control and adjustment method embodiment for a dual-motor propulsion system belong to the same concept. The specific implementation process is detailed in the method embodiment and will not be repeated here.

[0123] Embodiment 3:

[0124] Figure 5 A schematic diagram of a computer device for a control and regulation device for a dual-motor propulsion system provided by an embodiment of the present invention. For example, Figure 5 As shown, the computer device includes: a memory 601, a processor 602, and a computer program 603 stored in the memory 601 and running on the processor 602, wherein when the processor 602 executes the computer program 603, the computer device can execute any one of the control and adjustment methods for the dual-motor propulsion system introduced above.

[0125] In addition, an embodiment of the present application also protects a device, which may include a memory and a processor, wherein the memory stores executable program code, and the processor is used to call and execute the executable program code to execute a control and adjustment method for a dual-motor propulsion system provided in an embodiment of the present application.

[0126] In this embodiment, the functional modules of the device can be divided according to the above method example. For example, each functional module can be corresponded, or two or more functions can be integrated into one processing module. The above integrated module can be implemented in the form of hardware. It should be noted that the division of modules in this embodiment is schematic and is only a logical function division. There may be other division methods in actual implementation.

[0127] It should be understood that the device provided in this embodiment is used to execute the above-mentioned control and adjustment method for a dual-motor propulsion system, and thus can achieve the same effect as the above-mentioned implementation method.

[0128] In the case of an integrated unit, the device may include a processing module and a storage module. When the device is applied to a device, the processing module may be used to control and manage the actions of the device. The storage module may be used to support the device to execute mutual program codes, etc.

[0129] The processing module may be a processor or a controller, which may implement or execute various exemplary logic blocks, modules and circuits included in the disclosure of this application. The processor may also be a combination that implements computing functions, such as a combination of one or more microprocessors, a combination of digital signal processing (DSP) and a microprocessor, etc. The storage module may be a memory.

[0130] It should be noted that the sequence of the above embodiments of the present invention is only for description and does not represent the advantages and disadvantages of the embodiments. The processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0131] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

[0132] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A control and adjustment method for a dual-motor propulsion system, characterized in that: The method includes: Obtain the angular velocity data of the main motors of several quad-rotor drones using a dual-motor propulsion system that execute the same rotation command at each moment during the test period; According to the difference in angular velocity data of the diagonally distributed main motors of each quad-rotor drone at each moment and the angular velocity data of the main motors at each moment, a command-compliant balance value at each moment when each quad-rotor drone executes a rotation command is obtained; Obtaining a suspected rotation center when each quadrotor drone executes a rotation instruction; adjusting the corresponding suspected rotation center using the instruction-compliant balance value at the corresponding moment of the suspected rotation center to obtain the actual rotation center when each quadrotor drone executes the rotation instruction, and obtaining the initial centrifugal force of the main motor of each quadrotor drone when the quadrotor drone executes the rotation instruction based on the actual rotation center; Controlling and adjusting the auxiliary motor of the quadrotor drone using a dual-motor propulsion system according to the command-compliant balance value and the initial centrifugal force at all times of the quadrotor drone during the test period; The method of obtaining the command-compliant balance value at each moment when each quad-rotor drone executes a rotation command based on the difference in angular velocity data of the diagonally distributed main motors of each quad-rotor drone at each moment and the angular velocity data of the main motors at each moment comprises: According to the difference in angular velocity data of the diagonally distributed main motors of each quad-rotor drone at each moment, the rotation speed symmetry value of each quad-rotor drone at each moment when executing a rotation instruction is obtained; Setting the preset angular velocity data of each main motor when the quad-rotor drone executes the rotation command; obtaining the command-compliant balance value at each moment when each quad-rotor drone executes the rotation command according to the difference between the angular velocity data of the main motor of each quad-rotor drone at each moment and the preset angular velocity data, and the rotation speed symmetry value; The method of obtaining the rotation speed symmetry value at each moment when each quad-rotor drone executes the rotation instruction includes: The two main motors of each quadrotor drone are diagonally distributed to form a diagonal motor pair; each quadrotor drone has two diagonal motor pairs; The absolute value of the difference between the angular velocity data of the two main motors in each diagonal motor pair of each quadrotor drone at each moment is used as the angular velocity difference value of the corresponding diagonal motor pair at each moment; The accumulated sum of the angular velocity difference values ​​of all diagonal motor pairs of each quad-rotor drone is negatively correlated and normalized to obtain a rotation speed symmetry value at each moment when each quad-rotor drone executes a rotation instruction; The speed symmetry value is expressed by the formula: Where W is the symmetric value of the rotation speed at each moment when each quadrotor drone executes a rotation command; A is the total number of diagonal motor pairs of each quadrotor drone; The angular velocity data of the first main motor of the a-th diagonal motor pair of each quadrotor drone at each moment; The angular velocity data of the second main motor of the a-th diagonal motor pair of each quadrotor drone at each moment; is the angular velocity difference value of the a-th diagonal motor pair of each quadrotor drone at each moment; is the absolute value function; exp is the exponential function with a natural constant as the base; The step of obtaining the balance value that meets the command at each moment when each quad-rotor drone executes the rotation command includes: Select two adjacent main motors from the main motors of each quadrotor drone as analysis motors; The sum of the absolute values ​​of the differences between the angular velocity data of the same analysis motor of each quad-rotor drone at each moment and the preset angular velocity data is accumulated as the command compliance value at each moment when each quad-rotor drone executes the rotation command; According to the instruction compliance value and the rotational speed symmetry value, the instruction compliance balance value at each moment when each quad-rotor drone executes the rotation instruction is obtained; the instruction compliance value and the instruction compliance balance value are negatively correlated, and the rotational speed symmetry value and the instruction compliance balance value are positively correlated; The balance value in accordance with the instruction is expressed by the formula: Where Z is the balance value that meets the command at each moment when each quadrotor drone executes the rotation command; B is the total number of analyzed motors of each quadrotor drone; The bth analysis of the angular velocity data of the motor at each moment when executing the rotation command for each quadrotor drone; The angular velocity preset data of the bth analyzed motor when executing the rotation command for each quadrotor drone; The command value at each moment when each quadcopter executes the rotation command; is the absolute value function; exp is the exponential function with a natural constant as the base; The obtaining of the suspected rotation center of each quadrotor drone when executing the rotation instruction includes: Select a number of analysis moments from the test time period; obtain the position point of each quadcopter at each analysis moment when executing the rotation command; Performing curve fitting on the position points at the analysis time when each quad-rotor drone executes a rotation command to obtain a motion trajectory line; obtaining a perpendicular line of the position points at each analysis time on the motion trajectory line, and recording it as the analysis line at the corresponding analysis time; The intersection of the analysis lines at all analysis moments when each quad-rotor drone executes a rotation instruction is recorded as the suspected rotation center when each quad-rotor drone executes a rotation instruction; The method for obtaining the actual rotation center when each quad-rotor drone executes a rotation instruction includes: For each suspected rotation center when the quad-rotor drone executes a rotation command, the analysis time corresponding to the analysis line passing through each suspected rotation center is recorded as the target time corresponding to the suspected rotation center; according to the command-compliant balance value of all target times of each suspected rotation center when each quad-rotor drone executes a rotation command, and the abnormality degree of the suspected rotation center, the rotation radius contribution value of each suspected rotation center is obtained; Based on the rotation radius contribution values ​​of all suspected rotation centers when each quadrotor drone executes a rotation command, the rotation radius contribution value of each suspected rotation center is normalized to obtain a contribution weight of each suspected rotation center; weighted summation is performed on the values ​​of each dimension of all suspected rotation centers according to the contribution weight, and the result of the weighted summation of each dimension is used as the value of each dimension of the actual rotation center when each quadrotor drone executes a rotation command; The obtaining of the rotation radius contribution value of the suspected rotation center includes: The average of the command-compliant balance values ​​at all target moments of each suspected rotation center when each quadrotor drone executes a rotation command is used as the command-compliant concentrated value of the corresponding suspected rotation center; the LOF value of each suspected rotation center when each quadrotor drone executes a rotation command is obtained by using a local anomaly factor algorithm; According to the instruction set value and the LOF value, a rotation radius contribution value of each suspected rotation center when each quadrotor drone executes a rotation instruction is obtained; the instruction set value and the rotation radius contribution value are positively correlated, and the LOF value and the rotation radius contribution value are negatively correlated; The controlling and adjusting of the auxiliary motor of the quad-rotor drone using a dual-motor propulsion system according to the command-compliant balance value and the initial centrifugal force at all times of the quad-rotor drone during the test period includes: According to the command-compliant balance values ​​and the initial centrifugal force of all quad-rotor drones at all times during the test period, the comprehensive centrifugal force of the main motor when the quad-rotor drone executes the rotation command is obtained; Based on the comprehensive centrifugal force, the auxiliary motor of the quad-rotor drone using the dual-motor propulsion system is controlled and adjusted using the MPC algorithm; The method of obtaining the comprehensive centrifugal force of the main motor when the quad-rotor drone executes a rotation instruction includes: The average of the command-compliant balance values ​​of each quadrotor drone at all times during the test period is used as the system balance value of each quadrotor drone executing the rotation command; Based on the system balance value of all quadrotor drones, the system balance value of each quadrotor drone is normalized to obtain the balance weight of each quadrotor drone; according to the balance weight, the initial centrifugal forces of all quadrotor drones are weighted and summed to obtain the comprehensive centrifugal force of the main motor when the quadrotor drone executes a rotation command.

2. A control and adjustment method for a dual-motor propulsion system according to claim 1, characterized in that: The method of obtaining the initial centrifugal force of the main motor of each quad-rotor drone when executing a rotation instruction based on the actual rotation center includes: The distance between the initial position of each quadrotor drone when executing the rotation instruction and the actual rotation center is used as the rotation radius of each quadrotor drone when executing the rotation instruction; The two endpoints of the motion trajectory line corresponding to each quadrotor drone are respectively connected to the actual rotation center to obtain two reference line segments of each quadrotor drone; the ratio of the angle between the two reference line segments to the duration of the test time period is used as the reference angular velocity of each quadrotor drone; The mass of the quad-rotor drone is obtained, and the initial centrifugal force of the main motor of each quad-rotor drone when executing a rotation instruction is obtained by combining the rotation radius and the reference angular velocity.

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