CN115533915B - An active contact detection and control method for aerial working robots in uncertain environments - Google Patents
An active contact detection and control method for aerial working robots in uncertain environments Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
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- B—PERFORMING OPERATIONS; TRANSPORTING
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- B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
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Abstract
本发明公开了一种不确定环境下空中作业机器人主动接触检测控制方法，包括构建与环境主动接触检测的空中作业机器人系统并进行动力学建模分析；设计额外弯矩估计器估计接触交互力/力矩；引入二阶弹簧‑质量‑阻尼模型建立理想接触力与空中作业机器人位置之间的动态关系，进而设计基于时变刚度系数的力跟踪阻抗控制策略，得出计算修正后的位置命令轨迹；根据修正后的位置命令轨迹、命令姿态、空中作业机器人的动力学模型和额外弯矩估计器设计空中作业机器人位姿控制率表达式，得到空中机器人位姿控制率；结合空中作业机器人系统中的转子转速与推力/转矩之间的转换表达式得到转子转速，以使空中作业机器人完成不确定环境下的主动接触检测任务。
The invention discloses an active contact detection control method for an aerial working robot in an uncertain environment, comprising constructing an aerial working robot system for active contact detection with an environment and performing dynamic modeling analysis; designing an extra bending moment estimator to estimate the contact interaction force/torque; introducing a second-order spring-mass-damper model to establish a dynamic relationship between an ideal contact force and a position of the aerial working robot, and then designing a force tracking impedance control strategy based on a time-varying stiffness coefficient to obtain a position command trajectory after calculation and correction; designing an aerial working robot posture control rate expression according to the corrected position command trajectory, a command posture, a dynamic model of the aerial working robot and an extra bending moment estimator to obtain the aerial robot posture control rate; and combining a rotor speed in the aerial working robot system with a conversion expression between thrust/torque to obtain a rotor speed, so that the aerial working robot can complete the active contact detection task in the uncertain environment.
Description
Technical Field
The invention belongs to the technical field of aerial working robots, and particularly relates to an active contact detection control method of an aerial working robot in an uncertain environment.
Background
In the past, aerial robots were considered to lack active work capabilities, primarily for passive monitoring tasks. With the progress of the air robot technology, the research field of the air robot is gradually expanded to realize the active contact detection operation with the environment. This new type of aerial robotic system for aerial contact detection is commonly referred to as an aerial work robot, and has attracted the search of numerous researchers. Aerial work robots have many potential applications, such as inspecting infrastructure of bridges or manufacturing plants, touch detection tasks to press emergency switches in industrial accidents, and maintenance work in places where it is difficult to reach. In fact, research challenges include system stability and adjustment of the required contact force throughout the interaction. In order to meet the demands of aerial work robots for infrastructure inspection and maintenance tasks, there is a need to develop an active contact detection capability for aerial work robots with uncertain environments.
Disclosure of Invention
The invention provides an active contact detection control method for an aerial working robot in an uncertain environment, aiming at solving the technical problem of active contact detection between the aerial working robot and the uncertain environment in the background technology.
The technical scheme adopted for solving the technical problems is as follows:
An active contact detection control method of an aerial working robot in an uncertain environment comprises the following steps:
S100, constructing an aerial work robot system actively contacted with the environment for detection, and carrying out dynamic modeling analysis on the aerial work robot system to obtain a dynamic model of the aerial work robot;
S200, obtaining a conversion expression between expected rolling and pitch angle and rotor rotating speed and thrust/torque in an aerial working robot system according to generalized input in a dynamic model of the aerial working robot;
s300, designing an additional bending moment estimator to estimate contact interaction force/moment;
s400, introducing a second-order spring-mass-damping model to establish a dynamic relation between an ideal contact force and the position of the aerial work robot, and further designing a force tracking impedance control strategy based on a time-varying stiffness coefficient to obtain a position command track after calculation and correction;
s500, obtaining a command gesture according to the expected rolling and pitch angle, obtaining a state error according to the corrected position command track and the command gesture, and designing a gesture control rate expression of the aerial work robot according to the state error, a dynamic model of the aerial work robot and an additional bending moment estimator to obtain a gesture control rate of the aerial work robot;
and S600, obtaining the rotor rotating speed according to the pose control rate of the aerial robot and a conversion expression between the rotor rotating speed and the thrust/torque in the aerial work robot system, so that the aerial work robot can complete the active contact detection task under the uncertain environment.
Preferably, S100 includes:
S110, constructing an aerial work robot system for actively detecting contact with the environment, wherein the aerial work robot interaction system comprises a four-rotor unmanned aerial vehicle and a rigidly-installed contact tool;
s120, using Newton-Euler equation method, the dynamic model of the aerial working robot is described as follows:
wherein, AndThe position of the mass center of the aerial working robot under the world inertial coordinate system and the angular velocity of the mass center of the aerial working robot under the machine body coordinate system are respectively,Representing an entity set, m u is the total mass of the aerial working robot,Denoted as rotation matrix from body coordinate system to world inertial coordinate system, j=diag (I φ,Iθ,Iψ) is inertial matrix, where I φ,Iθ,Iψ is inertial constant, g is denoted as gravitational constant, e 3＝[0,0,1]T, operator "x" denotes cross; Total lift for an aerial work robot, where T i, i=1,..4 represents lift per rotor; A manual moment vector for an aerial working machine; And Is the external force and moment generated on the mass center of the aerial working robot by the force and moment applied to the tool by the external environment;
S130, defining the attitude phi B＝[φ,θ,ψ]T of the aerial working robot and the angular speed under the world inertial coordinate system Euler angle change rateThe conversion relationship with ω B is:
wherein,
Substituting formula (2) and its time derivative calculation into formula (1) can result in the following kinetic model:
wherein, Representing an inertia matrix of the device,Is a Kelvin and centrifugal matrix, wherein S (·) represents a skewed symmetric matrix operator,Is the time differential of Q (phi B), and
Step S140 definition of variablesThe kinetic model of the aerial work robot may be represented in the form of a matrix as follows:
wherein, Representing a positive definite inertia matrix of the device,For the terms of the coriolis and centrifuge,Is a gravity vector, u= [ (TR Be3)T,(Q(ΦB)TMB)T]T is a generalized input,Is the additional force/moment acting on the mass center of the aerial work robot, and can be expressed as:
wherein, Representing the interaction forces/moments between the environment and the tool tip,Is the end position of the tool under the machine body coordinate system;
Preferably, S200 includes:
Step S210, calculating expected rolling and pitch angles by using generalized inputs u (1), u (2) and u (3) in a dynamic model of the aerial work robot in view of underactuated characteristics of the aerial work robot, wherein the expected rolling and pitch angles are as follows:
wherein phi d,θd,ψd represents the desired roll, pitch, yaw angles respectively, AndRepresenting the trigonometric functions cos (ψ d) and sin (ψ d)ψd representing the desired yaw angle, respectively;
step S220, as the rotor rotates to generate lift force and moment, the conversion expression between the rotor rotating speed and the thrust force/torque in the aerial working robot system is obtained according to the generalized input in the dynamic model of the aerial working robot, wherein the conversion expression is as follows:
Wherein Ω i, i=1,..4 is rotor speed, c T and c M are noted as lift and moment coefficients, d represents the wheelbase length of the aerial work robot.
Preferably, S300 includes:
Step S310, constructing an additional bending moment estimator intermediate auxiliary variable as follows:
wherein, Representing the estimated value of W B, a being the normal number gain of the estimator;
Step S320, irrespective of the linear acceleration information measurement, by constructing the lyapunov function, the differential form of the intermediate auxiliary variable of the estimator is designed as follows:
step S330, designing an additional bending moment estimator according to the formulas (8) and (9) to obtain the following steps:
Preferably, S400 includes:
Step S410, considering an environment model with linear stiffness of k e, the contact force can be expressed as:
wherein x e represents the x-direction position when the tool is just touching the target without external force being applied;
Step S420, defining an x-direction force error according to the contact force of formula (11) as follows:
wherein, Is the x-direction desired contact force in the body coordinate, where f E,d is the desired force in the end tool coordinate system,
Step S430, simulating the uncertain environment behavior of human hand contact, and defining a force tracking impedance control strategy with a time-varying stiffness coefficient in a general one-dimensional direction as follows:
wherein, m d,bd is a number of the following components, The mass, damping, stiffness coefficients of the impedance model are respectively represented, the correction x dc is defined as x dc＝xd-xc, where x d is the desired position calculated by the off-line trajectory generator, x c is the corrected commanded position trajectory, k p and k v are respectively the normal PD control gains, and k 0 is the impedance model initial stiffness.
Preferably, S500 includes:
Step S510, calculating a command attitude phi B,c according to the expected roll and pitch angle of the formula (6), and defining a position error e p＝p-pc and an attitude error according to the command attitude phi B,c and the corrected position command trajectory x c The state error is obtained according to the position error and the attitude error as follows:
e=q-qc (15)
wherein, And is also provided withpc＝[xc,yc,zc]T。
Step S520 defines the boundary of the error vector by using the performance function ρ k (t):
wherein, Delta k is a positive constant and the performance function is defined as follows:
Wherein the normal numbers ρ ∞,k and l k are the final boundary and convergence speed of the error, respectively;
step S530, mapping the constrained space state error to the unconstrained space through an equivalent transfer function, and defining a transformation with predefined performance specification error as follows:
Wherein ε k is the kth element of the transfer error ε= [ ε 1,…,ε6]T;
step S540, constructing the following terminal sliding die surface to stabilize the variable epsilon in a limited time:
Wherein sigma and For a normal number, satisfy σ >0 and,Wherein sgn (&) and | I, I respectively represent standard sign functions and euclidean norms;
step S550 of defining The following assumptions are given:
wherein β is an unknown normal number;
step S560, designing the following pose control rate of the aerial work robot by combining the additional bending moment estimator (10):
Wherein K 0 is a positive-diagonal matrix, Represents an estimated value of beta, lambda and b are positive constants,Is a diagonal matrix.
The method can ensure safe and reliable contact detection behavior of the aerial working robot under the condition of no need of a force/moment sensor, and has the advantages of robust interaction capability, safety and reliability and low cost.
Drawings
FIG. 1 is a flow chart of an active contact detection control method for an aerial working robot in an uncertain environment according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a method for controlling active contact detection of an aerial working robot in an uncertain environment according to an embodiment of the present invention;
FIG. 3 is an algorithm block diagram of an active contact detection control method for an aerial work robot in an uncertain environment in accordance with an embodiment of the present invention;
FIG. 4 is a diagram of an xyz-direction position tracking trajectory of an aerial work robot in a simulation in accordance with an embodiment of the present invention;
FIG. 5 is a diagram of an aerial work robot gesture tracking trajectory in a simulation in an embodiment of the present invention;
FIG. 6 is a schematic diagram of xyz-direction position tracking error with predefined performance in simulation for an aerial work robot in an embodiment of the present invention;
FIG. 7 is a schematic diagram of attitude tracking errors for an aerial work robot having predefined performance in simulation in an embodiment of the present invention;
FIG. 8 is a schematic diagram of a force trace of an aerial work robot in a simulation in accordance with an embodiment of the present invention.
Detailed Description
In order to make the technical scheme of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings.
In one embodiment, as shown in fig. 1 to 3, a method for controlling active contact detection of an aerial working robot in an uncertain environment includes the following steps:
S100, constructing an aerial working robot system actively contacted with the environment for detection, and carrying out dynamic modeling analysis on the aerial working robot system to obtain a dynamic model of the aerial working robot.
In one embodiment, S100 comprises:
S110, constructing an aerial work robot system for actively detecting contact with the environment, wherein the aerial work robot interaction system comprises a four-rotor unmanned aerial vehicle and a rigidly-installed contact tool;
s120, using Newton-Euler equation method, the dynamic model of the aerial working robot is described as follows:
wherein, AndThe position of the mass center of the aerial working robot under the world inertial coordinate system and the angular velocity of the mass center of the aerial working robot under the machine body coordinate system are respectively,Representing an entity set, m u is the total mass of the aerial working robot,Denoted as rotation matrix from body coordinate system to world inertial coordinate system, j=diag (I φ,Iθ,Iψ) is inertial matrix, where I φ,Iθ,Iψ is inertial constant, g is denoted as gravitational constant, e 3＝[0,0,1]T, operator "x" denotes cross; Total lift for an aerial work robot, where T i, i=1,..4 represents lift per rotor; A manual moment vector for an aerial working machine; And Is the external force and moment generated on the mass center of the aerial working robot by the force and moment applied to the tool by the external environment;
S130, defining the attitude phi B＝[φ,θ,ψ]T of the aerial working robot and the angular speed under the world inertial coordinate system Euler angle change rateThe conversion relationship with ω B is:
wherein,
Substituting formula (2) and its time derivative calculation into formula (1) can result in the following kinetic model:
wherein, Representing an inertia matrix of the device,Is a Kelvin and centrifugal matrix, wherein S (·) represents a skewed symmetric matrix operator,Is the time differential of Q (phi B), and
Step S140 definition of variablesThe kinetic model of the aerial work robot may be represented in the form of a matrix as follows:
wherein, Representing a positive definite inertia matrix of the device,For the terms of the coriolis and centrifuge,Is a gravity vector, u= [ (TR Be3)T,(Q(ΦB)TMB)T]T is a generalized input,Is the additional force/moment acting on the mass center of the aerial work robot, and can be expressed as:
wherein, Representing the interaction forces/moments between the environment and the tool tip,Is the end position of the tool in the machine body coordinate system.
And S200, obtaining a conversion expression between the expected rolling and pitching angle and the rotor rotating speed and the thrust/torque in the aerial working robot system according to the generalized input in the dynamic model of the aerial working robot.
In one embodiment, S200 includes:
Step S210, calculating expected rolling and pitch angles by using generalized inputs u (1), u (2) and u (3) in a dynamic model of the aerial work robot in view of underactuated characteristics of the aerial work robot, wherein the expected rolling and pitch angles are as follows:
wherein phi d,θd,ψd represents the desired roll, pitch, yaw angles respectively, AndRepresenting the trigonometric functions cos (ψ d) and sin (ψ d), respectively;
step S220, as the rotor rotates to generate lift force and moment, the conversion expression between the rotor rotating speed and the thrust force/torque in the aerial working robot system is obtained according to the generalized input in the dynamic model of the aerial working robot, wherein the conversion expression is as follows:
Wherein Ω i, i=1,..4 is rotor speed, c T and c M are noted as lift and moment coefficients, d represents the wheelbase length of the aerial work robot.
And S300, designing an additional bending moment estimator to estimate the contact interaction force/moment.
In one embodiment, S300 includes:
Step S310, constructing an additional bending moment estimator intermediate auxiliary variable as follows:
wherein, Representing the estimated value of W B, a being the normal number gain of the estimator;
Step S320, irrespective of the linear acceleration information measurement, by constructing the lyapunov function, the differential form of the intermediate auxiliary variable of the estimator is designed as follows:
step S330, designing an additional bending moment estimator according to the formulas (8) and (9) to obtain the following steps:
S400, a second-order spring-mass-damping model is introduced to establish a dynamic relation between ideal contact force and the position of the aerial work robot, and then a force tracking impedance control strategy based on a time-varying stiffness coefficient is designed to obtain a position command track after calculation and correction.
In one embodiment, S400 includes:
Step S410, considering an environment model with linear stiffness of k e, the contact force can be expressed as:
wherein x e represents the x-direction position when the tool is just touching the target without external force being applied;
Step S420, defining an x-direction force error according to the contact force of formula (11) as follows:
wherein, Is the x-direction desired contact force in the body coordinate, where f E,d is the desired force in the end tool coordinate system,
Step S430, simulating the uncertain environment behavior of human hand contact, and defining a force tracking impedance control strategy with a time-varying stiffness coefficient in a general one-dimensional direction as follows:
wherein, m d,bd is a number of the following components, The mass, damping, stiffness coefficients of the impedance model are respectively represented, the correction x dc is defined as x dc＝xd-xc, where x d is the desired position calculated by the off-line trajectory generator, x c is the corrected commanded position trajectory, k p and k v are respectively the normal PD control gains, and k 0 is the impedance model initial stiffness.
S500, obtaining a command gesture according to the expected rolling and pitch angle, obtaining a state error according to the corrected position command track and the command gesture, and designing an aerial operation robot pose control rate expression according to the state error, a dynamic model of the aerial operation robot and an additional bending moment estimator to obtain the aerial operation robot pose control rate.
In one embodiment, S500 includes:
Step S510, calculating a command attitude phi B,c according to the expected roll and pitch angle of the formula (6), and defining a position error e p＝p-pc and an attitude error according to the command attitude phi B,c and the corrected position command trajectory x c The state error is obtained according to the position error and the attitude error as follows:
e=q-qc (15)
wherein, And is also provided withpc＝[xc,yc,zc]T。
Step S520 defines the boundary of the error vector by using the performance function ρ k (t):
wherein, Delta k is a positive constant and the performance function is defined as follows:
Wherein the normal numbers ρ ∞,k and l k are the final boundary and convergence speed of the error, respectively;
step S530, mapping the constrained space state error to the unconstrained space through an equivalent transfer function, and defining a transformation with predefined performance specification error as follows:
Wherein ε k is the kth element of the transfer error ε= [ ε 1,…,ε6]T;
step S540, constructing the following terminal sliding die surface to stabilize the variable epsilon in a limited time:
Wherein sigma and For a normal number, satisfy σ >0 and Wherein sgn (&) and | I, I respectively represent standard sign functions and euclidean norms;
step S550 of defining The following assumptions are given:
wherein β is an unknown normal number;
step S560, designing the following pose control rate of the aerial work robot by combining the additional bending moment estimator (10):
Wherein K 0 is a positive-diagonal matrix, Represents an estimated value of beta, lambda and b are positive constants,Is a diagonal matrix.
And S600, obtaining the rotor rotating speed according to the pose control rate of the aerial robot and a conversion expression between the rotor rotating speed and the thrust/torque in the aerial work robot system, so that the aerial work robot can complete the active contact detection task under the uncertain environment.
In the embodiment of the invention, the quadrotor unmanned aerial vehicle is provided with a rigidly connected tool, and in order to obtain position feedback in an environment where a GPS cannot be used, a monocular camera with the resolution of 640 multiplied by 480 which is arranged on the aerial working robot is adopted for calculating the relative position between the aerial working robot and the tag. Parameters of the aerial working robot are set to be m u＝0.85kg,J＝diag(0.0820,0.0845,0.1377)kg·m2,g＝9.81kg·m/s2, an additional bending moment estimator parameter is selected to be a=6, an initial value of an auxiliary variable gamma of the estimator is set to be gamma (0) =0 6×1, an impedance control parameter is set to be m d＝0.85,bd＝30,k0＝50,kp＝1.5,kv =0.1, and predefined performance parameters in the pose controller are set to be: I k = 0.5, ρ 0,k＝1.0,ρ∞,k = 0.15 for k = 1,2,3, ρ 0,k＝1.5,ρ∞,k = 0.5 for k = 4,5,6, controller parameters are selected to be σ = 1, K0=diag(8,3,3,1,2,1),λ=0.001,b=2;The initial value of (1) is set as
The desired position trajectory is set as:
the desired yaw angle is always zero, the desired contact force is set to:
The environmental model stiffness coefficient k e is set to suddenly change from 100N/m to 200N/m at t=25s and to suddenly change from 200N/m to 100N/m at t=65s. In the initial state, the aerial work robot hovers at point p (0) = [0.4, -0.3,1.2] T m.
Fig. 4-8 show graphs of xyz-direction position tracking trajectories of an aerial working robot in the simulation, fig. 5 shows graphs of gesture tracking trajectories of an aerial working robot in the simulation, and it can be seen that the aerial working robot in the simulation has good convergence speed and tracking accuracy, fig. 6 shows graphs of xyz-direction position tracking errors of the aerial working robot in the simulation, fig. 7 shows graphs of gesture tracking errors of the aerial working robot in the simulation, all state errors of the system are always within predefined performance boundaries in transient and steady-state phases, and steady-state errors are always smaller than final boundaries of performance functions, fig. 8 shows graphs of force tracking trajectories of the aerial working robot in the simulation, and an additional bending moment estimator can obtain good estimation effect on required contact force with severe changes, so that an active contact detection task with an environment is completed, interaction force has obvious influence at t=25 s and t=65 s, because when the environmental rigidity k e suddenly changes, the contact force of a tool is still stable until the position of the tool is reached.
Compared with the prior art, the invention has the following beneficial effects:
1) The active contact detection control system consists of an additional bending moment estimator, a variable stiffness force tracking impedance control and a pose controller, and can realize stable flying movement and active contact detection behavior of the aerial working robot;
2) Compared to existing solutions, the proposed additional bending moment estimator uses the design concept of minimum sensor conditions, without using acceleration and additional force/moment measurements. Since the measurement of acceleration is often unreliable, this method is relatively suitable for practical applications;
3) Aiming at the problem of uncertain contact environment, the provided stiffness force tracking impedance control strategy can ensure the contact stability and force tracking performance of the aerial working robot;
4) The pre-defined transient/steady state performance and the convergence within a limited time in the active contact detection process are realized by utilizing the knowledge of the pre-determined performance and the terminal sliding mode surface, and the dynamic response speed and the control precision of the aerial working robot system are ensured.
The method for controlling the active contact detection of the aerial working robot in the uncertain environment is described in detail. The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to facilitate an understanding of the core concepts of the invention. It should be noted that it will be apparent to those skilled in the art that various modifications and adaptations of the invention can be made without departing from the principles of the invention and these modifications and adaptations are intended to be within the scope of the invention as defined in the following claims.
Claims (4)
1. An active contact detection control method for an aerial working robot in an uncertain environment is characterized by comprising the following steps:
s100, constructing an aerial operation robot system for actively contacting and detecting the environment, and carrying out dynamic modeling analysis on the aerial operation robot system to obtain a dynamic model of the aerial operation robot;
s200, obtaining a conversion expression between expected rolling and pitch angles and rotor rotating speed and thrust/torque in an aerial working robot system according to generalized input in a dynamic model of the aerial working robot;
S300, designing an additional force/moment estimator to estimate the contact interaction force/moment;
s400, introducing a second-order spring-mass-damping model to establish a dynamic relation between an ideal contact force and the position of the aerial work robot, and further designing a force tracking impedance control strategy based on a time-varying stiffness coefficient to obtain a position command track after calculation and correction;
S500, obtaining a command gesture according to the expected rolling and pitch angle, obtaining a state error according to the corrected position command track and the command gesture, and designing an aerial work robot gesture control rate expression according to the state error, the dynamic model of the aerial work robot and the additional force/moment estimator to obtain an aerial work robot gesture control rate;
S600, obtaining the rotor rotating speed according to the pose control rate of the aerial working robot and a conversion expression between the rotor rotating speed and thrust/torque in the aerial working robot system so as to enable the aerial working robot to complete an active contact detection task in an uncertain environment;
S100 includes:
S110, constructing an aerial work robot system for actively detecting contact with the environment, wherein the aerial work robot interaction system comprises a four-rotor unmanned aerial vehicle and a rigidly-installed contact tool;
s120, using Newton-Euler equation method, the dynamic model of the aerial working robot is described as follows:
wherein, AndThe position of the mass center of the aerial working robot under the world inertial coordinate system and the angular velocity of the mass center of the aerial working robot under the machine body coordinate system are respectively,Representing an entity set, m u is the total mass of the aerial working robot,Denoted as rotation matrix from body coordinate system to world inertial coordinate system, j=diag (I φ,Iθ,Iψ) is inertial matrix, where I φ,Iθ,Iψ is inertial constant, g is denoted as gravitational constant, e 3＝[0,0,1]T, operator "x" denotes cross; Total lift for an aerial work robot, where T i, i=1,..4 represents lift per rotor; A manual moment vector for an aerial working machine; And Is the external force and moment generated on the mass center of the aerial working robot by the force and moment applied to the tool by the external environment;
S130, defining the attitude phi B＝[φ,θ,ψ]T of the aerial working robot and the angular speed under the world inertial coordinate system Euler angle change rateThe conversion relationship with ω B is:
wherein,
Substituting formula (2) and its time derivative calculation into formula (1) can result in the following kinetic model:
wherein, Representing an inertia matrix of the device,Is a Kelvin and centrifugal matrix, wherein S (·) represents a skewed symmetric matrix operator,Is the time differential of Q (phi B), and
Step S140 definition of variablesThe kinetic model of the aerial work robot may be represented in the form of a matrix as follows:
wherein, Representing a positive definite inertia matrix of the device,For the terms of the coriolis and centrifuge,Is the vector of the force of gravity,For a generalized input,Is the additional force/moment acting on the mass center of the aerial work robot, and can be expressed as:
wherein, Representing the interaction forces/moments between the environment and the tool tip,Is the end position of the tool under the machine body coordinate system;
S300 includes:
Step S310, constructing additional force/moment estimator intermediate auxiliary variables as follows:
wherein, Representing the estimated value of W B, a being the normal number gain of the estimator;
Step S320, irrespective of the linear acceleration information measurement, by constructing the lyapunov function, the differential form of the intermediate auxiliary variable of the estimator is designed as follows:
Step S330, designing an additional force/moment estimator according to the formulas (8) and (9) to obtain the following steps:
2. The method of claim 1, wherein S200 comprises:
step S210, calculating expected rolling and pitch angles by using generalized inputs u (1), u (2) and u (3) in a dynamics model of the aerial work robot in view of underactuated characteristics of the aerial work robot, wherein the expected rolling and pitch angles are as follows:
wherein phi d,θd,ψd represents the desired roll, pitch, yaw angles respectively, AndRepresenting the trigonometric functions cos (ψ d) and sin (ψ d), respectively;
Step S220, generating lifting force and moment by rotor rotation, and obtaining a conversion expression between rotor rotation speed and thrust/torque in the aerial working robot system according to generalized input in a dynamic model of the aerial working robot, wherein the conversion expression is as follows:
Wherein Ω i, i=1,..4 is rotor speed, c T and c M are noted as lift and moment coefficients, d represents the wheelbase length of the aerial work robot.
3. The method of claim 2, wherein S400 comprises:
Step S410, considering an environment model with linear stiffness of k e, the contact force can be expressed as:
wherein x e represents the x-direction position when the tool is just touching the target without external force being applied;
Step S420, defining an x-direction force error according to the contact force of formula (11) as follows:
wherein, Is the x-direction desired contact force in the body coordinate, where f E,d is the desired force in the end tool coordinate system,
Step S430, simulating the uncertain environment behavior of human hand contact, and defining a force tracking impedance control strategy with a time-varying stiffness coefficient in a general one-dimensional direction as follows:
wherein, The mass, damping, stiffness coefficients of the impedance model are respectively represented, the correction x dc is defined as x dc＝xd-xc, where x d is the desired position calculated by the off-line trajectory generator, x c is the corrected commanded position trajectory, k p and k v are respectively the normal PD control gains, and k 0 is the impedance model initial stiffness.
4. A method according to claim 3, wherein S500 comprises:
Step S510, calculating a command attitude phi B,c according to the expected rolling and pitch angle of the formula (6), and defining a position error e p＝p-pc and an attitude error according to the command attitude phi B,c and a corrected position command trajectory x c The state error is obtained according to the position error and the attitude error, and is:
e=q-qc(15)
wherein, And is also provided withpc＝[xc,yc,zc]T;
Step S520 defines the boundary of the error vector by using the performance function ρ k (t):
wherein, Delta k is a positive constant and the performance function is defined as follows:
Wherein the normal numbers ρ ∞,k and l k are the final boundary and convergence speed of the error, respectively;
step S530, mapping the constrained space state error to the unconstrained space through an equivalent transfer function, and defining a transformation with predefined performance specification error as follows:
Wherein ε k is the kth element of the transfer error ε= [ ε 1,…,ε6]T;
step S540, constructing the following terminal sliding die surface to stabilize the variable epsilon in a limited time:
Wherein sigma and For a normal number, satisfy σ >0 andWherein sgn (&) and II are each standard sign functions and euclidean norms;
step S550 of defining The following assumptions are given:
wherein β is an unknown normal number;
Step S560, designing the following pose control rate of the aerial work robot by combining the extra force/moment estimator (10):
Wherein K 0 is a positive-diagonal matrix, Represents an estimated value of beta, lambda and b are positive constants,Is a diagonal matrix.
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