CN112208793B - Intelligent jumping method for controlling momentum-driven robot - Google Patents
Intelligent jumping method for controlling momentum-driven robot Download PDFInfo
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Abstract
The invention discloses an intelligent jumping method for controlling a momentum-driven robot, and belongs to the field of control of deep space exploration robots. The invention designs the take-off process by utilizing the momentum wheel brake mechanism of the robot, and the take-off process is divided into four stages of trial jump, soaring, accelerated take-off and flying to enable the momentum-driven robot to finish jumping, and the take-off process of the momentum-driven robot is clear and convenient to control by combining the characteristics of the four stages, so that the accuracy of a landing point is improved; establishing a jumping behavior dynamic model of the momentum-driven robot in a weak gravitational field environment; the method comprises the steps of finding out the relation between environmental parameters and motion parameters at the end of a trial jump stage by using a machine learning algorithm, establishing the relation between a jump moment parameter and a jump track parameter by using the machine learning algorithm under the condition that the environmental parameters are known, enabling the momentum-driven robot to have the capability of sensing external environmental parameters and adapting to a complex environment, and designing a jump parameter and planning the momentum wheel rotating speed based on the environmental parameters to enable the jump distance and the flying height to be controllable.
Description
Technical Field
The invention relates to a momentum-driven robot and an intelligent jumping method thereof, belonging to the field of control of deep space exploration robots.
Background
Since the beginning of the united states and the soviet union started the lunar exploration program in 1958, various types of deep space exploration activities were successively developed in developed countries and the major astronautics of the world. In recent years, in order to face the difficulties of small star size, weak gravitational environment, complex topography and the like faced by the small planet surface landing detection, the small momentum-driven robot is paid much attention due to the advantages of small volume, simple structure, flexible deployment, capability of redeploying in a jumping mode and the like. Although JAXA minor planet jump type detector MINERVA successfully lands and finishes jump redeployment, the detector cannot realize control on jump distance and flight time and attitude control in a jump process, and the problems of randomness, low photographing imaging quality and the like in a detection process are caused. At present, the problems of intelligent planning and control of jumping distance and flying height, a jumping process and the like of a momentum-driven robot are not researched thoroughly, and environmental parameter identification and robot motion control under the condition of unknown complex environment or environmental conditions are difficult to research.
Disclosure of Invention
The invention discloses an intelligent jumping method for controlling a momentum-driven robot, which aims to solve the technical problems that: through the intelligent planning and control of the jumping distance and the flying height of the momentum-driven robot and the deep analysis of the jumping process and the establishment of the relation between the environmental parameters and the motion of the momentum-driven robot by using a machine learning algorithm, the momentum-driven robot has the capability of sensing the external environmental parameters and adapting to the complex environment, and the jumping parameter is designed based on the environmental parameters to plan the rotating speed of the momentum wheel so as to control the jumping distance and the flying height.
The purpose of the invention is realized by the following technical scheme.
The invention discloses an intelligent jumping method for controlling a momentum-driven robot, wherein the momentum-driven robot is a momentum-driven robot with a spherical frustum-shaped symmetrical structure, a jumping-off process is designed by utilizing a momentum wheel brake mechanism of the momentum-driven robot, and the jumping-off process comprises four stages of trial jumping, accelerated jumping and flying to enable the momentum-driven robot to finish jumping; establishing a jumping behavior dynamic model of the momentum-driven robot in a weak gravitational field environment; under the dynamic model, a machine learning algorithm is utilized to find the relation between the environmental parameters and the motion parameters at the end of the trial jump stage, the machine learning algorithm is utilized to establish the relation between the jump moment parameters and the jump track parameters under the condition that the environmental parameters are known, so that the momentum-driven robot has the capability of sensing the external environmental parameters and adapting to the complex environment, and the jump parameters are designed based on the environmental parameters to plan the rotation speed of the momentum wheel so as to control the jump distance and the flying height.
The invention discloses an intelligent jumping method for controlling a momentum-driven robot, wherein the momentum-driven robot is a momentum-driven robot with a spherical frustum-shaped symmetrical structure, antennae are distributed on the periphery of a momentum-driven robot body, and the tail ends of the antennae use flexible parts to buffer the vibration impact of small planet surfaces on the body structure in jumping and collision processes; the momentum wheel is arranged in the body and used as a driving system of the robot, and the motor is used for controlling the momentum wheel to generate control torque required in a jumping process and an attitude control process.
The invention discloses an intelligent jumping method for controlling a momentum-driven robot, which comprises the following steps:
step one, in a weak gravitational field environment, after the momentum wheel completes the deceleration braking operation, the momentum-driven robot tends to roll forward under the action of momentum exchange, and then the momentum-driven robot has the condition of completing jumping. Designing a take-off strategy by utilizing a self momentum wheel brake mechanism: the takeoff strategy divides the takeoff process into four stages of trial jump, flight, accelerated takeoff and flight; the momentum wheel slowly accelerates to store momentum, and a trial jump stage is carried out when the inclination angle is smaller than or equal to a jump-off angle; after leaving the ground, when the inclination angle is larger than the takeoff angle and smaller than or equal to the flight angle, the flight stage is carried out, and the inclination angle is finally controlled to be close to the flight angle; then the momentum-driven robot falls, and when the momentum-driven robot reaches the height of applying the maximum moment, the acceleration jump stage is carried out; and entering a flight stage after the takeoff is finished.
Under the environment of a weak gravitational field, the momentum-driven robot is in contact with the surface of the asteroid to collide, and the jumping is completed by means of the braking mechanism of the momentum-driven robot and the elastic deformation between the momentum-driven robot and the surface of the asteroid. After the momentum wheel finishes the deceleration brake operation, moment can be applied to the momentum-driven robot due to the momentum exchange effect, the momentum-driven robot will have the tendency of rolling forward under the moment effect, the tendency makes the invasion depth of the feeler and the contact surface increase, makes the elastic deformation of the contact surface increase, and then makes the supporting force that the momentum-driven robot obtained increase. When the vertical component of the supporting force is larger than the gravity, the momentum-driven robot generates vertical upward acceleration to enable the contact point to be separated from the surface of the asteroid, and then the momentum-driven robot has the condition of finishing jumping. Designing a take-off strategy by utilizing a self momentum wheel brake mechanism, wherein the take-off strategy is used for taking offThe process is divided into four stages of trial jump, flight, accelerated takeoff and flight. The method comprises the following steps that a connecting line of projections of antennae of the momentum-driven robot on a horizontal plane is a symmetrical regular even polygon, and the side length of the regular even polygon is defined as an equivalent side length l; defining an inclination angle eta, which is an included angle between a connecting line of the contact point O and the mass center of the momentum-driven robot and the ground; take-off control time t0The end time of the take-off phase; the takeoff angle alpha is the maximum value of the trial jump stage eta; the soaring angle beta is the maximum value of the eta angle in the motor stalling process in the soaring stage; the height chi of the maximum applied moment is a mark quantity of the momentum-driven robot entering an acceleration takeoff stage. Firstly, slowly accelerating a momentum wheel to store momentum; then, in a trial jump stage, applying torque to drive the robot to rotate until the inclination angle eta is increased to a jump starting angle alpha, and driving the robot to leave the ground by momentum to enter an emptying stage; then, the momentum drives the robot to continue rotating to enable the inclination angle eta to continue increasing, and finally the inclination angle eta is controlled to be close to the flight angle beta; then, the momentum-driven robot falls down, when the height from the surface of the minor planet to the nearest antenna is larger than x, the acceleration jump stage is started, and the momentum wheel brake provides instantaneous large torque to drive the momentum-driven robot to finish acceleration jump; and finally, in a flight phase, the momentum-driven robot is kept in a required attitude by controlling the rotating speed of the momentum wheel.
And step two, under the weak gravitational field environment, establishing a hopping behavior dynamic model of the momentum-driven robot by using a Hertz collision model and a Karnopp friction model.
Establishing a minor planet inertial coordinate system fe(Oexeyeze) The origin being the centroid of the little planet, OexeThe axis pointing in the direction of the axis of least inertia, O, of the little planetezeThe axis pointing in the direction of the axis of rotation of the little planet, OeyeThe shaft constitutes a right-hand system; momentum-driven robot body coordinate system fu(Ouxuyuzu) The origin is located at the centroid, Ouxu、OuyuAnd OuzuThe three shafts are fixed on the body to form a right-hand system; momentum wheel mounting coordinate system fd(Odxdydzd) With origin at the geometric center of the momentum wheel, OdxdThe shaft is along the rotation axis of the momentum wheel, OdydShaft and OdzdThe shafts are mutually perpendicular in a rotating plane to form a right-hand system; momentum wheel rotating coordinate system fw(Owxwywzw) Connected fixedly to the momentum wheel fwRelative to fdIs Ω.
Obtaining the expression in the coordinate system f according to the theorem of moment of momentumuThe rotational kinetic equation of the lower momentum-driven robot is
In the formula: a. the1、B1、C1Is a coefficient matrix; omegadIs a vector array of the angular velocity of the momentum-driven robot relative to the inertial system;
is omegadA cross-product matrix of; v. ofdIs a vector array of the momentum-driven robot centroid velocity;
is omegad、vdA derivative of (a); a. theuwiIs the ith flywheel fwTo fuThe coordinate transformation matrix of (2); a. thewuiIs AuwiThe transposed matrix of (2); i iswiIs the moment of inertia of the ith flywheel; omegaiIs the rotational angular velocity of the ith flywheel;
is omegaiA derivative of (a); i isdIs the moment of inertia of the momentum-driven robot; m iswiIs the mass of the ith flywheel; m is the mass of the momentum-driven robot;
is a momentum-driven robot body to the bodyA cross-multiplication matrix of the static moment of the coordinate system;
is a cross-multiplication matrix from the momentum-driven robot centroid to the ith flywheel centroid vector array; r isuf1The vector array of the connecting vector of the momentum-driven robot centroid and the contact collision point; r isuf2The vector array of the connecting vector of the center of mass and the center of gravity of the momentum-driven robot is formed;
and
is ruf1And ruf2A cross-product matrix of; fnAnd FfThe vector array of the supporting force and the friction force suffered by the momentum-driven robot; g is the vector array of the momentum-driven robot subjected to gravity.
According to the momentum theorem, the description in the coordinate system f is obtained by sortinguThe translational kinetic equation of the lower momentum driving robot is
In the formula: a. the2、B2、C2Is a coefficient matrix; omegadIs a vector array of the angular velocity of the momentum-driven robot relative to the inertial system;
is omegadA cross-product matrix of; v. ofdIs a vector array of the momentum-driven robot centroid velocity;
is omegad、vdA derivative of (a); fnAnd FfThe vector array of the supporting force and the friction force suffered by the momentum-driven robot; g is a vector array of the momentum-driven robot subjected to gravity; m iswiIs the mass of the ith flywheel;m is the mass of the momentum-driven robot;
is a cross-multiplication matrix from the momentum-driven robot centroid to the ith flywheel centroid vector array; suThe static moment of the body coordinate system of the momentum-driven robot body is obtained;
is SuCross-product matrix of (a).
The small celestial body has small mass and volume, and the small celestial body is irregular in shape, so that an irregular weak gravitational field is presented nearby the small celestial body. Therefore, it is necessary to describe the weak gravitational field environment in which the momentum-driven robot takes off the jump. And describing the weak gravitational field environment where the momentum-driven robot is located by using a spherical harmonic coefficient method. Simplifying the asteroid with irregular shape and mass into an ellipsoid, and expanding the ellipsoid by using a spherical harmonic coefficient method to obtain the gravitational potential function of the target asteroid as
In the formula: pn,m(sin φ) is an associated Legendre polynomial, Cn,mAnd Sn,mFor the spherical harmonic coefficients of the gravitational field model, θ and φ are the longitude and latitude of the landing site of the probe, respectively, n and m are the order and number of times of the gravitational field model, respectively, R0Is the reference radius of the target asteroid, R is the distance from the detector to the centroid of the asteroid, and G is the universal gravitation constant.
The momentum-driven robot completes take-off mainly by means of elastic deformation between the momentum-driven robot and the surface of the asteroid. Support force F generated by collision of feeler of momentum-driven robot with contact surface of asteroidnEquivalent to a continuous contact force model. The continuous contact force model considers factors such as deformation, displacement, stress and acting time of an object in the collision process, the collision process is described by using an equivalent spring damping model, and the spring contact force is generally determined according to the Hertz law. The normal contact force contacting the impact point during impact can be described as
In the formula: fnIs a vector array of supporting forces to which the momentum-driven robot is subjected; k is a contact stiffness coefficient, C is a damping coefficient, and an environment parameter value K, C is obtained through a neural network algorithm; ri、Ei、νiRespectively the curvature radius, the elastic modulus and the Poisson ratio of the two contact surfaces; e is the coefficient of restitution; v. of0Is the initial relative velocity of the point of impact; r iscoIs a vector array of the connecting radial diameters of the initial intrusion point of the antenna and the surface contact point of the minor planet,
is rcoThe derivative of (c).
The surface of the asteroid is uneven, and the tangential friction force F applied to the momentum-driven robot by the asteroid surface in the take-off processf. According to the designed take-off process, the tangential friction force assists in completing the take-off of the momentum-driven robot, so that a tangential friction force model in the collision process needs to be established. Tangential frictional force FfIs calculated by the formula
In the formula: ffIs the contact friction force, FnIs positive pressure of the contact surface, FeIs the other external force to which the body is subjected,
is FeUnit vector of (1), FsIs the magnitude of the maximum static friction force, mu is the coefficient of kinetic friction, fvIs the coefficient of the viscous friction of the,
is a vector of the unit relative velocity of motion,
is the speed transition tolerance.
The permanent magnet synchronous motor is used for realizing the accurate control of the momentum wheel so that the momentum-driven robot can complete the tasks of jumping action, attitude control and the like. By using idThe vector control strategy of 0 requires the minimum stator current and low loss. Only the influence of friction nonlinearity on the system is considered, and the LuGre friction model is used for describing the nonlinearity. The LuGre friction model is expressed as
In the formula: fmIs the friction torque established by LuGre friction; beta is a0、β1、β2The friction force parameters respectively represent the rigidity coefficient, the damping coefficient and the viscosity coefficient of two contact surfaces;
is a non-linear function, representing the effect of different frictions; fsIs the coulomb friction value; thetasIs the Stribeck effective stress value; fcIs the speed value of the Stribeck effect; the physical meaning of the z-state is the average stiffness of the friction between two interacting surfaces.
The momentum-driven robot can complete the jumping actions and attitude control of four stages of trial jump, flight, accelerated takeoff and flight, and needs precise motor control. And the motor obtains the expected angular velocity according to the integral of the expected angular acceleration of the system, and tracks the actual angular velocity through a servo system. The actual angular velocity is input to the system dynamics by an actual angular acceleration obtained by a finite time differentiator. The differential precision is ensured by using a finite time convergence differentiator based on the singular perturbation technology, although the differentiator has a sharp point in the tracking process in the initial stage, the differentiator can be rapidly matched with an ideal differential value along with the increase of time, and the form of the differentiator is designed according to the characteristics of the system
In the formula: x is the number of1、x2、x3Is the angular velocity, angular acceleration, first derivative of angular acceleration,
is x1、x2、x3The derivative of (c).
And substituting the established gravitational field model formula (3), Hertz collision model formula (4), Karnopp friction model formula (5) and LuGre friction model formula (6) into the formulas (1) and (2) to obtain a jumping collision behavior dynamics model of the momentum-driven robot.
And step three, driving the momentum-driven robot to take off according to the take-off strategy designed in the step one and the momentum-driven robot jump behavior dynamic model established in the step two, wherein the take-off process comprises the processes of trial jump, flight, accelerated take-off and flight in the take-off strategy.
And fourthly, identifying the environmental parameters by using a machine learning algorithm, establishing a relation between the environmental parameters and the momentum-driven robot, enabling the momentum-driven robot to have the capability of sensing external environmental parameters and adapting to a complex environment, and designing jump parameters based on the environmental parameters to enable the jump distance and the flying height of the momentum-driven robot to be controllable.
Because the surface topography of the asteroid cannot be accurately mastered, the working condition of the momentum-driven robot is complex and changeable, and the robot has the capabilities of sensing environmental parameters and adapting to a complex environment by identifying the environmental parameters and intelligently controlling the motion by considering complex environmental factors through machine learning. After the environmental parameters are identified, corresponding jump parameters are selected according to different environmental parameter values. Obtaining the functional relation between the environmental parameter K, C and the speed V at the end of the trial jump stage, the included angle theta between the speed and the horizontal plane and the height h through training a neural network, namely
And eliminating data of more than two times of jumping of the momentum-driven robot and data of too small jumping distance and height of the momentum-driven robot due to improper parameters to obtain a large number of environmental parameter values. And (3) training a neural network by using the data to obtain the relation between the neural network and V, theta and h in the formula (8), wherein the learning result is used as a basis for distinguishing the environmental parameters in the trial jump stage of the momentum-driven robot. After the momentum-driven robot identifies the environmental parameters K and C, a jump parameter T is selected through a machine learning algorithmeAlpha and beta, so that the power-driven robot can obtain the expected flight height and jump distance once per jump. T in the course of actual jumpeIs preset, and therefore can be considered to be at TeThe jumping process is a fixed value. Establishing a jump moment parameter TeAlpha, beta and a jump track parameter H, L, and realizes multiple jumps from a starting point to an end point through momentum distribution, so that the flight height and the jump distance are controllable. Establishing TeThe functional relationships between α and β and H, L are as follows
Preferably, the momentum-driven robot is of a spherical table-shaped symmetrical structure, eight antennae are distributed on two sides of the spherical table respectively, and flexible parts are used at the tail ends of the antennae to buffer the vibration impact of small planet surfaces on the body structure in the jumping and collision processes; three momentum wheels which are orthogonally arranged inside are used as a driving system of the robot, and control torque required in the jumping process and the attitude control process is generated through motor control.
When eight antennae are distributed on two sides of the table respectively, in the step one, the connecting line of the horizontal plane projection of the antennae of the momentum-driven robot is a symmetrical regular octagon.
Has the advantages that:
1. the invention discloses an intelligent jumping method for controlling a momentum-driven robot, which utilizes a momentum wheel brake mechanism of the intelligent jumping method to firstly innovatively design a jumping strategy: the takeoff strategy divides the takeoff process into four stages of trial jump, flight, accelerated takeoff and flight; the momentum wheel slowly accelerates to store momentum, and a trial jump stage is carried out when the inclination angle is smaller than or equal to a jump-off angle; after leaving the ground, when the inclination angle is larger than the takeoff angle and smaller than or equal to the flight angle, the flight stage is carried out, and the inclination angle is finally controlled to be close to the flight angle; then the momentum-driven robot falls, and when the momentum-driven robot reaches the height of applying the maximum moment, the acceleration jump stage is carried out; and entering a flight stage after the takeoff is finished. Through the jumping strategy, jumping is realized by means of friction and collision with the surfaces of the asteroids, the jumping process is divided into four stages of trial jumping, accelerated jumping and flying, the characteristics of the four stages are described respectively, the jumping process of the momentum-driven robot is clear and convenient to control by combining the characteristics of the four stages, and the accuracy of the landing point is improved.
2. The invention discloses an intelligent jumping method for controlling a momentum-driven robot, which comprises the steps of establishing a dynamic model of jumping behavior of the momentum-driven robot by utilizing a Hertz collision model and a Karnopp friction model in a weak gravitational field environment, driving the momentum-driven robot to jump by combining a jump-out strategy designed by beneficial effect 1, wherein the jump-out process comprises trial jump, vacation, accelerated jump-out and flight processes in the jump-out strategy, identifying environmental parameters by using a machine learning algorithm on the basis, establishing a relation between the environmental parameters and the momentum-driven robot motion, enabling the momentum-driven robot to have the capability of sensing external environmental parameters and adapting to a complex environment, designing jumping parameters based on the environmental parameters to enable the jumping distance and the vacation height of the momentum-driven robot to be controllable, enabling the precision of a landing point of the momentum-driven robot to be within 0.35m, and enabling the precision of a highest jumping point to be within 0.2m, the attitude stabilization precision is within 0.5 degrees.
Drawings
Fig. 1 is a schematic view of a momentum-driven robot with a symmetrical structure in a table shape designed by the present invention, wherein fig. 1a is a three-dimensional perspective view of the momentum-driven robot, and fig. 1b is a cross-sectional view thereof;
FIG. 2 is a schematic diagram of the rolling motion and the jumping motion of the momentum-driven robot of the present invention;
FIG. 3 is a schematic diagram of the jumping process of the momentum-driven robot of the present invention;
FIG. 4 is a diagram of four coordinate systems established for the momentum-driven robot according to the present invention;
FIG. 5 illustrates an ideal motion trajectory and an actual motion trajectory of the momentum-driven robot according to the present invention;
FIG. 6 is a graph illustrating the error values of yaw angle and yaw rate of the momentum-driven robot of the present invention;
fig. 7 is a flowchart of an intelligent jumping method for controlling a momentum-driven robot according to the present disclosure.
Detailed Description
In the intelligent jumping method for controlling a momentum-driven robot disclosed in this embodiment, the momentum-driven robot is a momentum-driven robot with a spherical frustum-shaped symmetrical structure, as shown in fig. 1, antennae are distributed around a momentum-driven robot body, and flexible components are used at the tail ends of the antennae to buffer the vibration impact of the small planet surface on the body structure in the jumping and collision processes; the momentum wheel is arranged in the body and used as a driving system of the robot, and the motor is used for controlling the momentum wheel to generate control torque required in a jumping process and an attitude control process.
As shown in fig. 7, the intelligent jumping method for controlling a momentum-driven robot disclosed in this embodiment includes the following steps:
step one, in a weak gravitational field environment, after the momentum wheel completes the deceleration braking operation, the momentum-driven robot tends to roll forward under the action of momentum exchange, and then the momentum-driven robot has the condition of completing jumping. As shown in fig. 2 and 3, the takeoff strategy is designed by using the own momentum wheel brake mechanism: the takeoff strategy divides the takeoff process into four stages of trial jump, flight, accelerated takeoff and flight; the momentum wheel slowly accelerates to store momentum, and a trial jump stage is carried out when the inclination angle is smaller than or equal to a jump-off angle; after leaving the ground, when the inclination angle is larger than the takeoff angle and smaller than or equal to the flight angle, the flight stage is carried out, and the inclination angle is finally controlled to be close to the flight angle; then the momentum-driven robot falls, and when the momentum-driven robot reaches the height of applying the maximum moment, the acceleration jump stage is carried out; and entering a flight stage after the takeoff is finished.
Under the environment of a weak gravitational field, the momentum-driven robot is in contact with the surface of the asteroid to collide, and the jumping is completed by means of the braking mechanism of the momentum-driven robot and the elastic deformation between the momentum-driven robot and the surface of the asteroid. After the momentum wheel finishes the deceleration brake operation, moment can be applied to the momentum-driven robot due to the momentum exchange effect, the momentum-driven robot will have the tendency of rolling forward under the moment effect, the tendency makes the invasion depth of the feeler and the contact surface increase, makes the elastic deformation of the contact surface increase, and then makes the supporting force that the momentum-driven robot obtained increase. When the vertical component of the supporting force is larger than the gravity, the momentum-driven robot generates vertical upward acceleration to enable the contact point to be separated from the surface of the asteroid, and then the momentum-driven robot has the condition of finishing jumping. A take-off strategy is designed by utilizing a momentum wheel brake mechanism of the self, and the take-off strategy divides the take-off process into four stages of trial jump, soaring, accelerated take-off and flying. The method comprises the following steps that a connecting line of projections of antennae of the momentum-driven robot on a horizontal plane is a symmetrical regular even polygon, and the side length of the regular even polygon is defined as an equivalent side length l; defining an inclination angle eta, which is an included angle between a connecting line of the contact point O and the mass center of the momentum-driven robot and the ground; take-off control time t0The end time of the take-off phase; the takeoff angle alpha is the maximum value of the trial jump stage eta; the soaring angle beta is the maximum value of the eta angle in the motor stalling process in the soaring stage; the height chi of the maximum applied moment is a mark quantity of the momentum-driven robot entering an acceleration takeoff stage. Firstly, slowly accelerating a momentum wheel to store momentum; then, in a trial jump stage, applying torque to drive the robot to rotate until the inclination angle eta is increased to a jump starting angle alpha, and driving the robot to leave the ground by momentum to enter an emptying stage; then, the momentum drives the robot to continue rotating to enable the inclination angle eta to continue increasing, and finally the inclination angle eta is controlled to be close to the flight angle beta; then, the momentum-driven robot falls down, when the height from the surface of the minor planet to the nearest antenna is larger than x, the acceleration jump stage is started, and the momentum wheel brake provides instantaneous large torque to drive the momentum-driven robot to finish acceleration jump; and finally, in a flight phase, the momentum-driven robot is kept in a required attitude by controlling the rotating speed of the momentum wheel.
And step two, under the weak gravitational field environment, establishing a hopping behavior dynamic model of the momentum-driven robot by using a Hertz collision model and a Karnopp friction model.
Establishing a minor planet inertial coordinate system fe(Oexeyeze) The origin being the centroid of the little planet, OexeThe axis pointing in the direction of the axis of least inertia, O, of the little planetezeThe axis pointing in the direction of the axis of rotation of the little planet, OeyeThe shaft constitutes a right-hand system; momentum-driven robot body coordinate system fu(Ouxuyuzu) The origin is located at the centroid, Ouxu、OuyuAnd OuzuThe three shafts are fixed on the body to form a right-hand system; momentum wheel mounting coordinate system fd(Odxdydzd) With origin at the geometric center of the momentum wheel, OdxdThe shaft is along the rotation axis of the momentum wheel, OdydShaft and OdzdThe shafts are mutually perpendicular in a rotating plane to form a right-hand system; momentum wheel rotating coordinate system fw(Owxwywzw) Connected fixedly to the momentum wheel fwRelative to fdIs Ω.
Obtaining the expression in the coordinate system f according to the theorem of moment of momentumuThe rotational kinetic equation of the lower momentum-driven robot is
In the formula: a. the1、B1、C1Is a coefficient matrix; omegadIs a vector array of the angular velocity of the momentum-driven robot relative to the inertial system;
is omegadA cross-product matrix of; v. ofdIs a vector array of the momentum-driven robot centroid velocity;
is omegad、vdA derivative of (a); a. theuwiIs the ith flywheel fwTo fuThe coordinate transformation matrix of (2); a. thewuiIs AuwiThe transposed matrix of (2); i iswiIs the moment of inertia of the ith flywheel; omegaiIs the rotational angular velocity of the ith flywheel;
is omegaiA derivative of (a); i isdIs the moment of inertia of the momentum-driven robot; m iswiIs the mass of the ith flywheel; m is the mass of the momentum-driven robot;
the method is characterized in that the method is a cross multiplication matrix of the static moment of a body coordinate system of the momentum-driven robot body;
is a cross-multiplication matrix from the momentum-driven robot centroid to the ith flywheel centroid vector array; r isuf1The vector array of the connecting vector of the momentum-driven robot centroid and the contact collision point; r isuf2The vector array of the connecting vector of the center of mass and the center of gravity of the momentum-driven robot is formed;
and
is ruf1And ruf2A cross-product matrix of; fnAnd FfThe vector array of the supporting force and the friction force suffered by the momentum-driven robot; g is the vector array of the momentum-driven robot subjected to gravity.
According to the momentum theorem, the description in the coordinate system f is obtained by sortinguThe translational kinetic equation of the lower momentum driving robot is
In the formula: a. the2、B2、C2Is a coefficient matrix; omegadIs a vector array of the angular velocity of the momentum-driven robot relative to the inertial system;
is omegadA cross-product matrix of; v. ofdIs a vector array of the momentum-driven robot centroid velocity;
is omegad、vdA derivative of (a); fnAnd FfThe vector array of the supporting force and the friction force suffered by the momentum-driven robot; g is a vector array of the momentum-driven robot subjected to gravity; m iswiIs the mass of the ith flywheel; m is the mass of the momentum-driven robot;
is a cross-multiplication matrix from the momentum-driven robot centroid to the ith flywheel centroid vector array; suThe static moment of the body coordinate system of the momentum-driven robot body is obtained;
is SuCross-product matrix of (a).
The small celestial body has small mass and volume, and the small celestial body is irregular in shape, so that an irregular weak gravitational field is presented nearby the small celestial body. Therefore, it is necessary to describe the weak gravitational field environment in which the momentum-driven robot takes off the jump. And describing the weak gravitational field environment where the momentum-driven robot is located by using a spherical harmonic coefficient method. Simplifying the asteroid with irregular shape and mass into an ellipsoid, and expanding the ellipsoid by using a spherical harmonic coefficient method to obtain the gravitational potential function of the target asteroid as
In the formula: pn,m(sin φ) is an associated Legendre polynomial,Cn,mand Sn,mFor the spherical harmonic coefficients of the gravitational field model, θ and φ are the longitude and latitude of the landing site of the probe, respectively, n and m are the order and number of times of the gravitational field model, respectively, R0Is the reference radius of the target asteroid, R is the distance from the detector to the centroid of the asteroid, and G is the universal gravitation constant.
The momentum-driven robot completes take-off mainly by means of elastic deformation between the momentum-driven robot and the surface of the asteroid. Support force F generated by collision of feeler of momentum-driven robot with contact surface of asteroidnEquivalent to a continuous contact force model. The continuous contact force model considers factors such as deformation, displacement, stress and acting time of an object in the collision process, the collision process is described by using an equivalent spring damping model, and the spring contact force is generally determined according to the Hertz law. The normal contact force contacting the impact point during impact can be described as
In the formula: fnIs a vector array of supporting forces to which the momentum-driven robot is subjected; k is a contact stiffness coefficient, C is a damping coefficient, and an environment parameter value K, C is obtained through a neural network algorithm; ri、Ei、νiRespectively the curvature radius, the elastic modulus and the Poisson ratio of the two contact surfaces; e is the coefficient of restitution; v. of0Is the initial relative velocity of the point of impact; r iscoIs a vector array of the connecting radial diameters of the initial intrusion point of the antenna and the surface contact point of the minor planet,
is rcoThe derivative of (c).
The surface of the asteroid is uneven, and the tangential friction force F applied to the momentum-driven robot by the asteroid surface in the take-off processf. According to the designed take-off process, the tangential friction force assists in completing the take-off of the momentum-driven robot, so that a tangential friction force model in the collision process needs to be established. Tangential frictional force FfIs calculated by the formula
In the formula: ffIs the contact friction force, FnIs positive pressure of the contact surface, FeIs the other external force to which the body is subjected,
is FeUnit vector of (1), FsIs the magnitude of the maximum static friction force, mu is the coefficient of kinetic friction, fvIs the coefficient of the viscous friction of the,
is a vector of the unit relative velocity of motion,
is the speed transition tolerance.
The permanent magnet synchronous motor is used for realizing the accurate control of the momentum wheel so that the momentum-driven robot can complete the tasks of jumping action, attitude control and the like. By using idThe vector control strategy of 0 requires the minimum stator current and low loss. Only the influence of friction nonlinearity on the system is considered, and the LuGre friction model is used for describing the nonlinearity. The LuGre friction model is expressed as
In the formula: fmIs the friction torque established by LuGre friction; beta is a0、β1、β2The friction force parameters respectively represent the rigidity coefficient, the damping coefficient and the viscosity coefficient of two contact surfaces;
is a non-linear function, representing the effect of different frictions; fsIs the coulomb friction value; thetasIs the Stribeck effective stress value; fcIs the speed value of the Stribeck effect; in the z stateThe physical meaning is the average stiffness of the friction between two interacting surfaces.
The momentum-driven robot can complete the jumping actions and attitude control of four stages of trial jump, flight, accelerated takeoff and flight, and needs precise motor control. And the motor obtains the expected angular velocity according to the integral of the expected angular acceleration of the system, and tracks the actual angular velocity through a servo system. The actual angular velocity is input to the system dynamics by an actual angular acceleration obtained by a finite time differentiator. The differential precision is ensured by using a finite time convergence differentiator based on the singular perturbation technology, although the differentiator has a sharp point in the tracking process in the initial stage, the differentiator can be rapidly matched with an ideal differential value along with the increase of time, and the form of the differentiator is designed according to the characteristics of the system
In the formula: x is the number of1、x2、x3Is the angular velocity, angular acceleration, first derivative of angular acceleration,
is x1、x2、x3Derivative of (2)
And substituting the established gravitational field model formula (3), Hertz collision model formula (4), Karnopp friction model formula (5) and LuGre friction model formula (6) into the formulas (1) and (2) to obtain a jumping collision behavior dynamics model of the momentum-driven robot.
And step three, driving the momentum-driven robot to take off according to the take-off strategy designed in the step one and the momentum-driven robot jump behavior dynamic model established in the step two, wherein the take-off process comprises the processes of trial jump, flight, accelerated take-off and flight in the take-off strategy.
And fourthly, identifying the environmental parameters by using a machine learning algorithm, establishing a relation between the environmental parameters and the momentum-driven robot, enabling the momentum-driven robot to have the capability of sensing external environmental parameters and adapting to a complex environment, and designing jump parameters based on the environmental parameters to enable the jump distance and the flying height of the momentum-driven robot to be controllable.
Because the surface topography of the asteroid cannot be accurately mastered, the working condition of the momentum-driven robot is complex and changeable, and the robot has the capabilities of sensing environmental parameters and adapting to a complex environment by identifying the environmental parameters and intelligently controlling the motion by considering complex environmental factors through machine learning. After the environmental parameters are identified, corresponding jump parameters are selected according to different environmental parameter values. Obtaining the functional relation between the environmental parameter K, C and the speed V at the end of the trial jump stage, the included angle theta between the speed and the horizontal plane and the height h through training a neural network, namely
And eliminating data of more than two times of jumping of the momentum-driven robot and data of too small jumping distance and height of the momentum-driven robot due to improper parameters to obtain a large number of environmental parameter values. And (3) training a neural network by using the data to obtain the relation between the neural network and V, theta and h in the formula (8), wherein the learning result is used as a basis for distinguishing the environmental parameters in the trial jump stage of the momentum-driven robot. After the momentum-driven robot identifies the environmental parameters K and C, a jump parameter T is selected through a machine learning algorithmeAlpha and beta, so that the power-driven robot can obtain the expected flight height and jump distance once per jump. T in the course of actual jumpeIs preset, and therefore can be considered to be at TeThe jumping process is a fixed value. Establishing a jump moment parameter TeAlpha, beta and a jump track parameter H, L, and realizes multiple jumps from a starting point to an end point through momentum distribution, so that the flight height and the jump distance are controllable. Establishing TeThe functional relationships between α and β and H, L are as follows
Designing a continuous hopping task on the surface of the asteroid, determining hopping parameters according to the environmental parameter identification result, and driving the robot to complete hopping through four stages of trial hopping, soaring, accelerated takeoff and flying. And (4) given the coordinates of the point B of the destination point, the momentum-driven robot reaches the destination point B from the departure point A through a plurality of jumps. The attitude of the momentum-driven robot is described by using an Euler angle, and after the momentum-driven robot takes off, an attitude control moment is generated to keep the momentum-driven robot in a certain specific attitude to execute a fixed-point photographing task, so that the range of an observation task is enlarged. The three momentum wheels respectively and independently control the postures of the pitching axis, the yawing axis and the rolling axis. The attitude control laws of the two have similarity, wherein the attitude control law of the yaw axis direction controlled by one momentum wheel is
In the formula: l is the equivalent side length, psi is the yaw angle of the momentum-driven robot,
yaw rate, y, for momentum-driven robotsminFor the y coordinate of the antenna nearest to the surface of the asteroid, mod is the remainder of the solution, and sgn is the sign function.
Under the environment of a weak gravitational field, the momentum-driven robot obtains the environment parameters of the robot through a machine learning algorithm after a plurality of trial jumps. Given environment parameter K-119000N/m3/2，C＝106N/(m·s-1) After a plurality of test jumps, the value of the obtained environmental parameter is K104702N/m3/2、C＝103.8N/(m·s-1). The target position of the jumping task given momentum-driven robot is a point B of an x-y plane, and the coordinates are (20, -18) m.
The momentum-driven robot finally reaches the destination point B through four jumps. The x-y coordinates of the actual arrival at destination point B are (20.5404, -17.2605) m. And respectively giving the ideal jumping point coordinate, the ideal highest point coordinate and the ideal landing point coordinate of each jump. And giving an ideal jumping track of each jumping, wherein the ideal track is formed by two sections of parabolas which take the z axis where the highest point of the ideal jumping is located as a symmetry axis and respectively pass through an ideal jumping point and an ideal landing point. Fig. 5 shows an ideal motion trajectory and an actual motion trajectory of the momentum-driven robot, in which an ideal curve and an actual curve are marked, and a starting point, a highest point and a landing point of each jump of the momentum-driven robot are marked. The numbers 1, 2, 3, 4 are the jump order of four jumps of the momentum-driven robot. The error of the momentum-driven robot jumping the highest point is within 0.2m, the error of landing is within 0.35m, and the precision can meet the fixed-point photographing and redeployment tasks of asteroid detection. The momentum-driven robot needs to adjust the attitude in the air during each jump to complete the shooting task, and fig. 6 shows the yaw rate error and the yaw angle error during the continuous jump of the momentum-driven robot. The yaw angles given in the four-jump process are respectively 42 degrees, 144 degrees, 85 degrees and 113 degrees, the yaw angle control error of the momentum-driven robot in the flight process is within 0.5 degree, and the precision can meet the shooting task of the momentum-driven robot. The momentum-driven robot can be impacted greatly at the moment of landing, so that the attitude angular velocity of the momentum-driven robot changes suddenly, the sudden change lasts for about 0.1s, and disappears after the momentum-driven robot lands stably.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. An intelligent jumping method for controlling a momentum-driven robot is characterized in that antennae are distributed around a momentum-driven robot body, and flexible parts are used at the tail ends of the antennae to buffer the vibration impact of small planet surfaces on the body structure in jumping and collision processes; a momentum wheel is arranged in the body and used as a driving system of the robot, and the momentum wheel is controlled by a motor to generate control torque required in a jumping process and an attitude control process;
the method is characterized in that: comprises the following steps of (a) carrying out,
step one, in a weak gravitational field environment, after a momentum wheel finishes the operation of deceleration and braking, the momentum-driven robot tends to roll forward under the action of momentum exchange, so that the momentum-driven robot has the condition of finishing jumping; designing a take-off strategy by utilizing a self momentum wheel brake mechanism: the takeoff strategy divides the takeoff process into four stages of trial jump, flight, accelerated takeoff and flight; the momentum wheel slowly accelerates to store momentum, and a trial jump stage is carried out when the inclination angle is smaller than or equal to a jump-off angle; after leaving the ground, when the inclination angle is larger than the takeoff angle and smaller than or equal to the flight angle, the flight stage is carried out, and the inclination angle is finally controlled to be close to the flight angle; then the momentum-driven robot falls, and when the momentum-driven robot reaches the height of applying the maximum moment, the acceleration jump stage is carried out; entering a flight stage after the takeoff is finished;
step two, under the environment of a weak gravitational field, establishing a hopping behavior dynamic model of the momentum-driven robot by using a Hertz collision model and a Karnopp friction model;
thirdly, driving the momentum-driven robot to take off according to the take-off strategy designed in the first step and the momentum-driven robot jump behavior dynamic model established in the second step, wherein the take-off process comprises trial jump, flight, accelerated take-off and flight processes in the take-off strategy;
and fourthly, identifying the environmental parameters by using a machine learning algorithm, establishing a relation between the environmental parameters and the momentum-driven robot, enabling the momentum-driven robot to have the capability of sensing external environmental parameters and adapting to a complex environment, and designing jump parameters based on the environmental parameters to enable the jump distance and the flying height of the momentum-driven robot to be controllable.
2. An intelligent hopping method for controlling a momentum-driven robot as claimed in claim 1, wherein: the first implementation method comprises the following steps of,
under the environment of a weak gravitational field, the momentum-driven robot is in contact with the surface of the asteroid to collide, and the jumping is completed by means of the braking mechanism of the momentum-driven robot and the elastic deformation between the momentum-driven robot and the surface of the asteroid; when the momentum wheel is finishedAfter the deceleration brake operation, due to the momentum exchange effect, an action moment is applied to the momentum-driven robot, under the action of the moment, the momentum-driven robot tends to roll forward, the invasion depth of an antenna and a contact surface is increased due to the tendency, the elastic deformation of the contact surface is increased, and the supporting force obtained by the momentum-driven robot is increased; when the vertical component of the supporting force is larger than the gravity, the momentum-driven robot generates vertical upward acceleration to enable the contact point to be separated from the surface of the asteroid, and then the momentum-driven robot has the condition of finishing jumping; designing a take-off strategy by utilizing a self momentum wheel brake mechanism, wherein the take-off strategy divides the take-off process into four stages of trial jump, soaring, accelerated take-off and flying; the method comprises the following steps that a connecting line of projections of antennae of the momentum-driven robot on a horizontal plane is a symmetrical regular even polygon, and the side length of the regular even polygon is defined as an equivalent side length l; defining an inclination angle eta, which is an included angle between a connecting line of the contact point O and the mass center of the momentum-driven robot and the ground; take-off control time t0The end time of the take-off phase; the takeoff angle alpha is the maximum value of the trial jump stage eta; the soaring angle beta is the maximum value of the eta angle in the motor stalling process in the soaring stage; the height chi of the maximum applied moment is a mark quantity of the momentum-driven robot entering an accelerated take-off stage; firstly, slowly accelerating a momentum wheel to store momentum; then, in a trial jump stage, applying torque to drive the robot to rotate until the inclination angle eta is increased to a jump starting angle alpha, and driving the robot to leave the ground by momentum to enter an emptying stage; then, the momentum drives the robot to continue rotating to enable the inclination angle eta to continue increasing, and finally the inclination angle eta is controlled to be close to the flight angle beta; then, the momentum-driven robot falls down, when the height from the surface of the minor planet to the nearest antenna is larger than x, the acceleration jump stage is started, and the momentum wheel brake provides instantaneous large torque to drive the momentum-driven robot to finish acceleration jump; and finally, in a flight phase, the momentum-driven robot is kept in a required attitude by controlling the rotating speed of the momentum wheel.
3. An intelligent hopping method for controlling a momentum-driven robot as claimed in claim 2, wherein: the second step is realized by the method that,
establishing a minor planet inertial coordinate system fe(Oexeyeze) The origin being the centroid of the little planet, OexeThe axis pointing in the direction of the axis of least inertia, O, of the little planetezeThe axis pointing in the direction of the axis of rotation of the little planet, OeyeThe shaft constitutes a right-hand system; momentum-driven robot body coordinate system fu(Ouxuyuzu) The origin is located at the centroid, Ouxu、OuyuAnd OuzuThe three shafts are fixed on the body to form a right-hand system; momentum wheel mounting coordinate system fd(Odxdydzd) With origin at the geometric center of the momentum wheel, OdxdThe shaft is along the rotation axis of the momentum wheel, OdydShaft and OdzdThe shafts are mutually perpendicular in a rotating plane to form a right-hand system; momentum wheel rotating coordinate system fw(Owxwywzw) Connected fixedly to the momentum wheel fwRelative to fdThe rotational angular velocity of (3) is Ω;
obtaining the expression in the coordinate system f according to the theorem of moment of momentumuThe rotational kinetic equation of the lower momentum-driven robot is
In the formula: a. the1、B1、C1Is a coefficient matrix; omegadIs a vector array of the angular velocity of the momentum-driven robot relative to the inertial system;
is omegadA cross-product matrix of; v. ofdIs a vector array of the momentum-driven robot centroid velocity;
is omegad、vdDerivative of (2)；AuwiIs the ith flywheel fwTo fuThe coordinate transformation matrix of (2); a. thewuiIs AuwiThe transposed matrix of (2); i iswiIs the moment of inertia of the ith flywheel; omegaiIs the rotational angular velocity of the ith flywheel;
is omegaiA derivative of (a); i isdIs the moment of inertia of the momentum-driven robot; m iswiIs the mass of the ith flywheel; m is the mass of the momentum-driven robot;
the method is characterized in that the method is a cross multiplication matrix of the static moment of a body coordinate system of the momentum-driven robot body;
is a cross-multiplication matrix from the momentum-driven robot centroid to the ith flywheel centroid vector array; r isuf1The vector array of the connecting vector of the momentum-driven robot centroid and the contact collision point; r isuf2The vector array of the connecting vector of the center of mass and the center of gravity of the momentum-driven robot is formed;
and
is ruf1And ruf2A cross-product matrix of; fnAnd FfThe vector array of the supporting force and the friction force suffered by the momentum-driven robot; g is a vector array of the momentum-driven robot subjected to gravity;
according to the momentum theorem, the description in the coordinate system f is obtained by sortinguThe translational kinetic equation of the lower momentum driving robot is
In the formula: a. the2、B2、C2Is a coefficient matrix; omegadIs a vector array of the angular velocity of the momentum-driven robot relative to the inertial system;
is omegadA cross-product matrix of; v. ofdIs a vector array of the momentum-driven robot centroid velocity;
is omegad、vdA derivative of (a); fnAnd FfThe vector array of the supporting force and the friction force suffered by the momentum-driven robot; g is a vector array of the momentum-driven robot subjected to gravity; m iswiIs the mass of the ith flywheel; m is the mass of the momentum-driven robot;
is a cross-multiplication matrix from the momentum-driven robot centroid to the ith flywheel centroid vector array; suThe static moment of the body coordinate system of the momentum-driven robot body is obtained;
is SuA cross-product matrix of;
the small celestial body is small in mass and volume, and irregular in shape causes an irregular weak gravitational field to be formed nearby the small celestial body; therefore, the weak gravitational field environment in which the momentum-driven robot is in the take-off process needs to be described; describing a weak gravitational field environment where the momentum-driven robot is located by using a spherical harmonic coefficient method; simplifying the asteroid with irregular shape and mass into an ellipsoid, and expanding the ellipsoid by using a spherical harmonic coefficient method to obtain the gravitational potential function of the target asteroid as
In the formula: pn,m(sin φ) is an associative Legendre polynomialFormula (II) Cn,mAnd Sn,mAs the spherical harmonic coefficient of the gravitational field model, τ and φ are the longitude and latitude of the landing site of the detector, respectively, n and m are the order and number of times of the gravitational field model, respectively, R0The reference radius of the target asteroid, R is the distance from the detector to the centroid of the asteroid, and G is a universal gravitation constant;
the momentum-driven robot finishes take-off mainly by means of elastic deformation between the momentum-driven robot and the surface of the minor planet; support force F generated by collision of feeler of momentum-driven robot with contact surface of asteroidnEquivalent to a continuous contact force model; the continuous contact force model considers deformation, displacement, stress and action time of an object in the collision process, the collision process is described by using an equivalent spring damping model, and the spring contact force is generally determined according to the Hertz law; the normal contact force contacting the impact point during impact is described as
In the formula: fnIs a vector array of supporting forces to which the momentum-driven robot is subjected; k is a contact stiffness coefficient, C is a damping coefficient, and an environment parameter value K, C is obtained through a neural network algorithm; ri、Ei、νiRespectively the curvature radius, the elastic modulus and the Poisson ratio of the two contact surfaces; e is the coefficient of restitution; v. of0Is the initial relative velocity of the point of impact; r iscoIs a vector array of the connecting radial diameters of the initial intrusion point of the antenna and the surface contact point of the minor planet,
is rcoA derivative of (a);
the surface of the asteroid is uneven, and the tangential friction force F applied to the momentum-driven robot by the asteroid surface in the take-off processf(ii) a According to the designed take-off process, the tangential friction force assists in completing the take-off of the momentum-driven robot, so that a tangential friction force model in the collision process needs to be established; tangential frictional force FfIs calculated by the formula
In the formula: feIs the other external force to which the body is subjected,
is FeUnit vector of (1), FsIs the magnitude of the maximum static friction force, mu is the coefficient of kinetic friction, fvIs the coefficient of the viscous friction of the,
is a vector of the unit relative velocity of motion,
is the speed conversion tolerance;
the permanent magnet synchronous motor is utilized to realize the accurate control of the momentum wheel so that the momentum driving robot can complete the jumping action and the attitude control; by using idThe vector control strategy is 0, and the required stator current of the strategy is minimum and the loss is low; only considering the influence of friction nonlinearity on the system, describing the nonlinearity by using a LuGre friction model; the LuGre friction model is expressed as
In the formula: fmIs the friction torque established by LuGre friction; beta is a0、β1、β2The friction force parameters respectively represent the rigidity coefficient, the damping coefficient and the viscosity coefficient of two contact surfaces;
is a non-linear function, representing the effect of different frictions; gsIs the coulomb friction value; thetasIs the Stribeck effective stress value; fcIs of the Stribeck effectA speed value; the physical meaning of the z-state is the average stiffness of the friction between two interacting surfaces;
the momentum-driven robot finishes jumping actions and attitude control in four stages of trial jump, soaring, accelerated takeoff and flying, and needs to be accurately controlled by a motor; the motor obtains an expected angular velocity according to the integral of the expected angular acceleration of the system, and tracks the actual angular velocity through a servo system; the actual angular velocity is used as the input of system dynamics by obtaining the actual angular acceleration through a finite time differentiator; the differential precision is ensured by using a finite time convergence differentiator based on the singular perturbation technology, although the differentiator has a sharp point in the tracking process in the initial stage, the differentiator can be rapidly matched with an ideal differential value along with the increase of time, and the form of the differentiator is designed according to the characteristics of the system
In the formula: x is the number of1、x2、x3Is the angular velocity, angular acceleration, first derivative of angular acceleration,
is x1、x2、x3A derivative of (a);
and substituting the established gravitational field model formula, Hertz collision model formula (4), Karnopp friction model formula (5) and LuGre friction model formula into the formulas (1) and (2) to obtain the jumping collision behavior dynamics model of the momentum-driven robot.
4. An intelligent hopping method for controlling a momentum-driven robot as claimed in claim 3, wherein: the implementation method of the fourth step is that,
because the topography condition of the asteroid surface can not be accurately mastered, the working condition of the momentum-driven robot is complex and changeable, the environment parameter identification is carried out through machine learning, and the intelligent motion control considering the complex environment factors is carried out, so that the robot has the capability of sensing the environment parameters and adapting to the complex environment; after identifying the environmental parameters, selecting corresponding jump parameters according to different environmental parameter values; obtaining the functional relation between the environmental parameter K, C and the speed V at the end of the trial jump stage, the included angle theta between the speed and the horizontal plane and the height h through training a neural network, namely
(K,C)＝f(V,θ,h) (8)
Eliminating data of more than two times of jumping of the momentum-driven robot and data of too small jumping distance and height of the momentum-driven robot due to improper parameters to obtain a large number of environmental parameter values; using the data to train the neural network to obtain the relation between the data and V, theta and h in the formula (7), wherein the learning result is used as a basis for distinguishing environmental parameters in the trial jump stage of the momentum-driven robot; after the momentum-driven robot identifies the environmental parameters K and C, a jump parameter T is selected through a machine learning algorithmeAlpha and beta, so that the power-driven robot can obtain the expected flight height and jump distance once per jump; t in the course of actual jumpeIs preset, and therefore can be considered to be at TeThe value is fixed during jumping; establishing a jump moment parameter TeThe alpha, the beta and the jumping trajectory parameter H, L, and realizes multiple jumps from the starting point to the end point through momentum distribution, so that the flying height and the jumping distance are controllable; establishing TeThe functional relationships between α and β and H, L are as follows
(H,L)＝g(Te,α,β)KC＝const (9)。
5. An intelligent hopping method for controlling a momentum-driven robot as claimed in claim 4, wherein: the momentum-driven robot is of a spherical table-shaped symmetrical structure, eight antennae are distributed on two sides of the spherical table respectively, and flexible parts are used at the tail ends of the antennae to buffer the vibration impact of the small planet surface on the body structure in the jumping and collision processes; three momentum wheels which are orthogonally arranged inside are used as a driving system of the robot, and control torque required in the jumping process and the attitude control process is generated through motor control;
when eight antennae are distributed on two sides of the table respectively, in the step one, the connecting line of the horizontal plane projection of the antennae of the momentum-driven robot is a symmetrical regular octagon.
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