CN116909199B - A control method for reconfigurable drones based on link configuration - Google Patents
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Abstract
本发明公开了一种基于连杆配置的可重构无人机的控制方法,可重构无人机包括重构控制器、设置在姿态环的BSTSMC控制器以及与BSTSMC控制器连接的扩张状态观测器;控制方法包括:重构控制器根据接收的重构信号对可重构无人机进行重构;扩张状态观测器获取重构后的可重构无人机的姿态变化信息,并根据姿态变化信息对可重构无人机的姿态进行实时补偿;BSTSMC控制器获取实时补偿后的姿态控制信号,根据姿态控制信号对可重构无人机的姿态进行实时调节。在可重构无人机物理属性时变,存在模型不确定性以及外部扰动的情况下可以对扰动进行实时估计并补偿,以实现在飞行时同步变形可以保持可靠的飞行性能。
The invention discloses a control method for a reconfigurable unmanned aerial vehicle based on link configuration. The reconfigurable unmanned aerial vehicle includes a reconfiguration controller, a BSTSMC controller arranged in an attitude ring, and an expansion state connected to the BSTSMC controller. observer; the control method includes: the reconstruction controller reconstructs the reconfigurable UAV according to the received reconstruction signal; the expanded state observer obtains the attitude change information of the reconstructed reconfigurable UAV, and The attitude change information compensates the attitude of the reconfigurable UAV in real time; the BSTSMC controller obtains the real-time compensated attitude control signal and adjusts the attitude of the reconfigurable UAV in real time based on the attitude control signal. In the case of time-varying physical properties of the reconfigurable UAV and the presence of model uncertainty and external disturbances, the disturbances can be estimated and compensated in real time to achieve synchronous deformation during flight and maintain reliable flight performance.
Description
技术领域Technical Field
本发明属于无人机控制技术领域,尤其涉及一种基于连杆配置的可重构无人机的控制方法。The present invention belongs to the technical field of unmanned aerial vehicle control, and in particular relates to a control method of a reconfigurable unmanned aerial vehicle based on connecting rod configuration.
背景技术Background Art
可重构无人机在飞行中可以重构自身形态以适应所处环境,从而拓展其应用范围,而自身形态的改变会很大程度上影响无人机的属性参数,对无人机姿态造成较大干扰,对于旋翼无人机这类欠驱动系统,姿态的干扰也会体现在位置上,这时无人机会进入短暂的失稳状态,这并不满足实际应用中平稳控制的要求,为了减弱无人机重构时的姿态干扰,研究者们提出了很多改进的控制算法,大部分文献为时变的参数设计自适应律进行估计,将其实时补偿到基于模型推导的非线性控制率中,这种方法虽然有效的减弱了重构造成的干扰,但是自适应律的引入加大了该控制方法对模型精度的依赖,并且所针对的干扰源较为单一,这并不利于控制算法的普适性。Reconfigurable UAVs can reconfigure their own shapes during flight to adapt to the environment, thereby expanding their scope of application. The change in their own shape will greatly affect the attribute parameters of the UAV and cause great interference to the UAV's attitude. For under-actuated systems such as rotorcraft UAVs, the interference of attitude will also be reflected in the position. At this time, the UAV will enter a short-term unstable state, which does not meet the requirements of stable control in practical applications. In order to reduce the attitude interference during UAV reconstruction, researchers have proposed many improved control algorithms. Most of the literature estimates the time-varying parameters by designing adaptive laws and compensates them in real time to the nonlinear control rate derived from the model. Although this method effectively reduces the interference caused by reconstruction, the introduction of the adaptive law increases the control method's dependence on the model accuracy, and the interference source targeted is relatively single, which is not conducive to the universality of the control algorithm.
发明内容Summary of the invention
本发明提供一种基于连杆配置的可重构无人机的控制方法,用于解决可重构无人机在飞行过程中进行重构会产生较大的姿态干扰的技术问题。The present invention provides a control method for a reconfigurable UAV based on a connecting rod configuration, which is used to solve the technical problem that a large attitude interference may be generated when the reconfigurable UAV is reconfigured during flight.
本发明提供一种基于连杆配置的可重构无人机的控制方法,所述可重构无人机包括重构控制器、设置在姿态环的BSTSMC控制器以及与所述BSTSMC控制器连接的扩张状态观测器;所述控制方法包括:The present invention provides a control method for a reconfigurable UAV based on a link configuration, wherein the reconfigurable UAV comprises a reconfiguration controller, a BSTSMC controller arranged in an attitude loop, and an extended state observer connected to the BSTSMC controller; the control method comprises:
重构控制器根据接收的重构信号对所述可重构无人机进行重构,其中,当某一机臂变形时,所述可重构无人机的最小限制角度的表达式为: ,The reconfiguration controller reconfigures the reconfigurable UAV according to the received reconfiguration signal, wherein when a certain arm is deformed, the expression of the minimum limiting angle of the reconfigurable UAV is: ,
当相邻的两个机臂组合变形以及任意三个或全部机臂进行变形时,所述可重构无人机的最大限制角度的表达式为:,When two adjacent arms are deformed in combination and any three or all arms are deformed, the expression of the maximum limit angle of the reconfigurable UAV is: ,
式中,、分别为无人机重构时机臂旋转的最小限制角度和最大限制角度,为连杆与电机的连接点到桨叶根部的距离,为旋翼直径,为机体对角长度,为机臂长度;In the formula, , are the minimum and maximum limit angles of the arm rotation during the reconstruction of the UAV, is the distance from the connection point between the connecting rod and the motor to the root of the blade, is the rotor diameter, is the diagonal length of the body, is the length of the machine arm;
扩张状态观测器获取重构后的所述可重构无人机的姿态变化信息,并根据所述姿态变化信息对所述可重构无人机的姿态进行实时补偿;The extended state observer obtains the attitude change information of the reconfigurable UAV after reconstruction, and performs real-time compensation on the attitude of the reconfigurable UAV according to the attitude change information;
BSTSMC控制器获取实时补偿后的姿态控制信号,根据所述姿态控制信号对所述可重构无人机的姿态进行实时调节,所述BSTSMC控制器的表达式为:The BSTSMC controller obtains the attitude control signal after real-time compensation, and adjusts the attitude of the reconfigurable UAV in real time according to the attitude control signal. The expression of the BSTSMC controller is:
, ,
式中,为总控制量,为基于反步法的控制量,为超螺旋控制算法的控制量,为一组可调增益,为扩张状态观测器观测到的各通道总扰动,为期望值和反馈值的误差,为期望值,为误差微分增益,为误差的微分,为滑模面增益,为滑模面,为超螺旋系数,为符号函数,为超螺旋系数,为当前运行时间。In the formula, is the total control quantity, is the control quantity based on the backstepping method, is the control quantity of the superhelix control algorithm, is a set of adjustable gains, is the total disturbance of each channel observed by the extended state observer, is the error between the expected value and the feedback value, is the expected value, is the error differential gain, is the differential of the error, is the sliding surface gain, is the sliding surface, is the superhelical coefficient, is the symbolic function, is the superhelical coefficient, The current running time.
进一步地,当对角的两个机臂组合变形时,所述可重构无人机的最大限制角度的表达式为:Furthermore, when the two diagonal arms are combined and deformed, the expression of the maximum limit angle of the reconfigurable UAV is:
。 .
进一步地,其中,所述扩张状态观测器的表达式为:Furthermore, the expression of the extended state observer is:
, ,
式中,为第时刻跟踪误差,为第时刻滚转通道的跟踪反馈量,为第时刻滚转通道的跟踪反馈量,为第时刻无人机滚转角,为观测器步长,为第时刻滚转通道的跟踪反馈量的微分,为第时刻滚转通道的跟踪反馈量的微分,为第时刻滚转通道的扰动观测量,为第时刻滚转通道的扰动观测量,、、均为观测器可调增益,为系数是0.5时的非线性函数,为输出反馈增益,为第时刻滚转通道的控制器输出量,为系数是0.25时的非线性函数;In the formula, For the Tracking error at any time, For the The tracking feedback amount of the momentary roll channel, For the The tracking feedback amount of the momentary roll channel, For the The rolling angle of the drone at the moment, is the observer step size, For the The differential of the tracking feedback amount of the moment roll channel, For the The differential of the tracking feedback amount of the moment roll channel, For the The disturbance observation of the moment rolling channel, For the The disturbance observation of the moment rolling channel, , , are the observer adjustable gains, is a nonlinear function with a coefficient of 0.5, is the output feedback gain, For the The controller output of the momentary roll channel, is a nonlinear function with a coefficient of 0.25;
, ,
式中,为系数是时的非线性函数,为自变量,为极小值,为符号函数。In the formula, The coefficient is The nonlinear function of is the independent variable, is the minimum value, is a symbolic function.
进一步地,所述姿态变化信息包括重心变化量和惯量变化量。Furthermore, the posture change information includes a change in center of gravity and a change in inertia.
进一步地,假设可重构无人机在重构前的几何中心为原点,则可重构无人机的重心变化量的表达式为:Furthermore, assuming that the geometric center of the reconfigurable UAV before reconstruction is the origin, the expression of the change in the center of gravity of the reconfigurable UAV is:
, ,
式中,为重心偏移量,为机身与舵机质量,为机身重心到坐标原点的矢量,为机臂、转子和旋翼的总力偶,为机臂质量,为电机质量,为旋翼质量,为第个机臂重心到坐标原点的矢量,为第个电机重心到坐标原点的矢量,为第个旋翼重心到坐标原点的矢量。In the formula, is the center of gravity offset, is the mass of the fuselage and servo, is the vector from the center of gravity of the fuselage to the origin of the coordinate system, is the total couple of the arm, rotor and rotor, is the mass of the arm, is the motor mass, is the rotor mass, For the The vector from the center of gravity of the arm to the origin of the coordinate system, For the The vector from the motor center of gravity to the coordinate origin, For the The vector from the rotor center of gravity to the coordinate origin.
进一步地,可重构无人机的机臂的惯量变化量的表达式为:Furthermore, the expression of the inertia change of the arm of the reconfigurable UAV is:
, ,
式中,为第1个机臂和第3个机臂重构后的惯量,为绕y轴旋转矩阵,为机臂不重构时的惯量,为绕y轴旋转矩阵的转置,为第2个机臂和第4个机臂重构后的惯量,为绕x轴旋转矩阵,为绕x轴旋转矩阵的转置;In the formula, is the reconstructed inertia of the first and third arms, is the rotation matrix around the y axis, is the inertia of the arm when it is not reconstructed, is the transpose of the rotation matrix around the y-axis, is the reconstructed inertia of the second and fourth arms, is the rotation matrix around the x-axis, is the transpose of the rotation matrix around the x-axis;
其中,,in, ,
式中,为第2个机臂和第4个机臂的旋转角的余弦值,为第2个机臂和第4个机臂旋转角的正弦值;In the formula, is the cosine value of the rotation angle of the second and fourth arms, is the sine value of the rotation angle of the second and fourth arms;
, ,
式中,为第1个机臂和第3个机臂的旋转角的余弦值,为第1个机臂和第3个机臂的旋转角的正弦值。In the formula, is the cosine value of the rotation angle of the first and third arms, is the sine of the rotation angle of the first and third arms.
进一步地,所述重构控制器的表达式为:Furthermore, the expression of the reconstruction controller is:
, ,
式中,为第个机臂的转动角速度,为第个独立变形通道的增益,为第个机臂的期望角度,为第个机臂的当前角度。In the formula, For the The angular velocity of the arm, For the Gain of independent deformation channels, For the The desired angle of the arm, For the The current angle of the arm.
本申请的基于连杆配置的可重构无人机的控制方法,采用BSTSMC控制器以及与所述BSTSMC控制器连接的扩张状态观测器的串级控制框架,该控制框架降低了对模型精度的依赖性,在可重构无人机物理属性时变,存在模型不确定性以及外部扰动的情况下可以对扰动进行实时估计并补偿,以实现在飞行时同步变形可以保持可靠的飞行性能。The control method of the reconfigurable UAV based on the link configuration of the present application adopts a cascade control framework of a BSTSMC controller and an extended state observer connected to the BSTSMC controller. The control framework reduces the dependence on model accuracy. When the physical properties of the reconfigurable UAV vary with time and there are model uncertainties and external disturbances, the disturbance can be estimated and compensated in real time to achieve synchronous deformation during flight and maintain reliable flight performance.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
为了更清楚地说明本发明实施例的技术方案,下面将对实施例描述中所需要使用的附图作一简单地介绍,显而易见地,下面描述中的附图是本发明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其他的附图。In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.
图1为本发明一实施例提供的一种基于连杆配置的可重构无人机的控制方法的流程图;FIG1 is a flow chart of a control method of a reconfigurable UAV based on a link configuration provided by an embodiment of the present invention;
图2为本发明一实施例提供一个具体实施例的可重构无人机尺寸的定义与限制图;FIG2 is a diagram showing the definition and limitation of the size of a reconfigurable drone according to a specific embodiment of the present invention;
图3为本发明一实施例提供一个具体实施例的重构控制仿真图;FIG3 is a simulation diagram of a reconstruction control of a specific embodiment provided by an embodiment of the present invention;
图4为本发明一实施例提供一个具体实施例的轨迹跟踪仿真图;FIG4 is a trajectory tracking simulation diagram of a specific embodiment provided by an embodiment of the present invention;
图5为本发明一实施例提供一个具体实施例的位置控制响应图;FIG5 is a position control response diagram of a specific embodiment provided by an embodiment of the present invention;
图6为本发明一实施例提供一个具体实施例的姿态控制响应图;FIG6 is a posture control response diagram of a specific embodiment provided in one embodiment of the present invention;
图7为本发明一实施例提供一个具体实施例的重构时位置干扰应对图;FIG. 7 is a diagram of coping with position interference during reconstruction according to a specific embodiment of the present invention;
图8为本发明一实施例提供一个具体实施例的重构时姿态干扰应对图。FIG8 is a diagram of coping with posture interference during reconstruction according to a specific embodiment of the present invention.
具体实施方式DETAILED DESCRIPTION
为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
请参阅图1,其示出了本申请的一种基于连杆配置的可重构无人机的控制方法的流程图。可重构无人机包括重构控制器、设置在姿态环的BSTSMC控制器以及与所述BSTSMC控制器连接的扩张状态观测器。Please refer to Figure 1, which shows a flow chart of a control method of a reconfigurable UAV based on a link configuration of the present application. The reconfigurable UAV includes a reconfiguration controller, a BSTSMC controller arranged in an attitude loop, and an extended state observer connected to the BSTSMC controller.
如图1所示,基于连杆配置的可重构无人机的控制方法具体包括以下步骤:As shown in FIG1 , the control method of the reconfigurable UAV based on the link configuration specifically includes the following steps:
步骤S101,重构控制器根据接收的重构信号对所述可重构无人机进行重构。Step S101: a reconstruction controller reconstructs the reconfigurable UAV according to a received reconstruction signal.
在本步骤中,重构控制器的表达式为:In this step, the expression of the reconstructed controller is:
, ,
式中,为第个机臂的转动角速度,为第个独立变形通道的增益,为第个机臂的期望角度,为第个机臂的当前角度。In the formula, For the The angular velocity of the arm, For the Gain of independent deformation channels, For the The desired angle of the arm, For the The current angle of the arm.
具体地,采用四个无刷电机为无人机提供推力,四个伺服电机与机体固连分别驱动四个机臂独立运动,构建了模块化的可重构无人机。Specifically, four brushless motors are used to provide thrust for the drone, and four servo motors are fixed to the body to drive the four arms to move independently, thus building a modular reconfigurable drone.
可重构无人机的最终重构形态由四个独立的机臂变形情况组合而成,每个机臂的变形原理相同,下面以其中一个机臂为例进行说明,如图2所示的平行四边形,为了方面表达,将所有机械构件抽象为线段进行说明,线段代表连杆,线段代表机臂,线段代表机体,线段代表电机以及旋翼,为每个单独旋翼产生的推力矢量。在图2中的为变形之后的状态,其中与之间的运动为主动运动,依靠舵机驱动,其余运动均为在平行四边形的约束下的被动运动,可以看出,采用本申请提出的这种平行连杆结构可以保证的方向始终与平行,即垂直机体水平面。The final reconfigured shape of the reconfigurable drone is composed of the deformation of four independent arms. The deformation principle of each arm is the same. The following takes one of the arms as an example to illustrate the parallelogram shown in Figure 2. In order to facilitate expression, all mechanical components are abstracted as line segments for illustration. Represents connecting rod, line segment Represents the arm, line segment Represents the body, line segment Represents the motor and rotor, The thrust vector generated for each individual rotor. for The state after deformation, where and The movement between is active movement, driven by the steering gear, and the rest of the movement is passive movement under the constraint of the parallelogram. It can be seen that the parallel connecting rod structure proposed in this application can ensure The direction is always Parallel means perpendicular to the horizontal plane of the aircraft.
单个机臂进行变形时,以机体水平面为零度,向下为负,第个机臂的当前角度为;多个机臂进行组合变形时,会发生旋翼与连杆或旋翼之间的重叠,对组合变形时的情况进行分析,对旋转角度做以下限制。When a single arm is deformed, the horizontal plane of the body is zero degrees, downward is negative, and the The current angle of the arm for When multiple arms are combined and deformed, overlap between the rotor and the connecting rod or the rotor will occur. The situation during the combined deformation is analyzed and the following restrictions are imposed on the rotation angle.
机臂旋转角度的最小值限制发生在机臂向下旋转的过程中,达到一定角度时,桨叶会与连杆发生重叠,当某一机臂变形时,可重构无人机的最小限制角度的表达式为:The minimum limit of the arm rotation angle occurs when the arm rotates downward. When a certain angle is reached, the blades will overlap with the connecting rod. When a certain arm is deformed, the expression of the minimum limit angle of the reconfigurable drone is:
, ,
式中,为无人机重构时机臂旋转的最小限制角度,为连杆与电机的连接点到桨叶根部的距离,为旋翼直径。In the formula, The minimum limit angle of arm rotation when reconstructing the drone, is the distance from the connection point between the connecting rod and the motor to the root of the blade, is the rotor diameter.
在分析最大限制角度时,分三种组合变形情况:When analyzing the maximum limiting angle, there are three combined deformation situations:
1)对角的两个机臂组合变形时,需要满足以下关系:1) When the two diagonal arms are combined and deformed, the following relationship needs to be satisfied:
, ,
式中,为无人机轴距,为机体对角长度;In the formula, is the wheelbase of the drone, is the diagonal length of the body;
若螺旋桨满足,则最大限制角度与机体各构建尺寸有关,If the propeller meets , then the maximum limit angle is related to the dimensions of each body.
可重构无人机的最大限制角度的表达式为:The expression of the maximum limiting angle of the reconfigurable UAV is:
, ,
2)相邻两个机臂组合变形时,添加限制条件为:,2) When two adjacent arms are deformed in combination, the added restriction conditions are: ,
则可重构无人机的最大限制角度的表达式为:Then the expression of the maximum limiting angle of the reconstructible drone is:
, ,
3)任意三个或全部机臂进行变形时,添加限制条件为:3) When any three or all arms are deformed, add the following restrictions:
, ,
则可重构无人机的最大限制角度的表达式为:Then the expression of the maximum limiting angle of the reconstructible drone is:
, ,
式中,为无人机重构时机臂旋转的最大限制角度,为旋翼直径,为机体对角长度,为机臂长度。In the formula, The maximum limit angle of arm rotation when reconstructing the drone, is the rotor diameter, is the diagonal length of the body, is the arm length.
基于以上分析得出的限制,提出可重构无人机的变形范围最大最小轴距为:Based on the limitations obtained from the above analysis, the maximum and minimum wheelbase of the deformation range of the reconfigurable UAV is proposed to be:
, ,
式中,为无人机最大轴距,为无人机最小轴距。In the formula, is the maximum wheelbase of the drone, The minimum wheelbase of the drone.
步骤S102,扩张状态观测器获取重构后的所述可重构无人机的姿态变化信息,并根据所述姿态变化信息对所述可重构无人机的姿态进行实时补偿。Step S102: The extended state observer obtains the attitude change information of the reconfigurable UAV after the reconstruction, and performs real-time compensation on the attitude of the reconfigurable UAV according to the attitude change information.
为描述可重构无人机姿态,在地面上任选一点o作为原点,X轴指向地球表面任意一个方向,Z轴沿着铅直方向指向天空,Y轴在水平面内与X轴垂直,指向通过右手法则来确定。To describe the attitude of the reconfigurable drone, a point o is randomly selected on the ground as the origin. The X-axis points to any direction on the earth's surface, the Z-axis points to the sky along the vertical direction, and the Y-axis is perpendicular to the X-axis in the horizontal plane. The direction is determined by the right-hand rule.
机体坐标系原点o位于可重构无人机姿态的质心处,x轴在可重构无人机姿态的对称平面内,并且平行于可重构无人机姿态的设计轴线,指向可重构无人机姿态的机头前方,y轴垂直于机身对称平面,并指向可重构无人机姿态的机身左方,z轴过o点并与xoy平面垂直,指向可重构无人机姿态上方。The origin o of the body coordinate system is located at the center of mass of the reconfigurable UAV posture. The x-axis is in the symmetry plane of the reconfigurable UAV posture and is parallel to the design axis of the reconfigurable UAV posture, pointing to the front of the nose of the reconfigurable UAV posture. The y-axis is perpendicular to the symmetry plane of the fuselage and points to the left of the fuselage of the reconfigurable UAV posture. The z-axis passes through point o and is perpendicular to the xoy plane, pointing to the top of the reconfigurable UAV posture.
机体坐标系到地面坐标系的旋转矩阵通过左乘基本旋转矩阵得到,计算简化结果如下:The rotation matrix from the body coordinate system to the ground coordinate system is obtained by left-multiplying the basic rotation matrix. The simplified calculation result is as follows:
, ,
式中,为无人机旋转矩阵,为无人机俯仰角,为无人机滚转角, 为无人机偏航角;In the formula, is the drone rotation matrix, is the pitch angle of the drone, is the roll angle of the drone, is the yaw angle of the drone;
即,机体坐标系与地面坐标系的转换关系为:That is, the conversion relationship between the body coordinate system and the ground coordinate system is:
, ,
式中,为某点在地面坐标系中的表示,为某点在机体坐标系中的表示。In the formula, is the representation of a point in the ground coordinate system, is the representation of a point in the body coordinate system.
根据牛顿欧拉方程建立可重构无人机六自由度数学模型,其中位置三自由度模型在地面坐标系表示,姿态三自由度模型在机体坐标系表示。A six-degree-of-freedom mathematical model of a reconfigurable UAV is established based on the Newton-Euler equations, in which the position three-degree-of-freedom model is represented in the ground coordinate system, and the attitude three-degree-of-freedom model is represented in the body coordinate system.
, ,
式中,为无人机质量,为无人机加速度,为无人机的惯性矩阵,为无人机角加速度,为无人机角速度,为旋翼产生的升力,为无人机的重力,为飞行过程中的阻力,为重构造成的扰动,为外部扰动的总和,为旋翼产生的升力矩,为空气阻力对旋翼产生的反力矩,为陀螺力矩,为重构产生的重力矩;In the formula, For drone quality, is the acceleration of the drone, is the inertia matrix of the UAV, is the angular acceleration of the drone, is the angular velocity of the drone, is the lift generated by the rotor, is the gravity of the drone, is the resistance during flight, The disturbance caused by reconstruction, is the sum of external disturbances, is the lift moment generated by the rotor, is the reaction torque generated by air resistance on the rotor, is the gyroscopic torque, The gravitational moment generated for the reconstruction;
可重构无人机的惯性矩阵在变形过程中会发生变化,可重构无人机的惯性矩阵的表达式为:The inertia matrix of the reconfigurable UAV will change during the deformation process. The expression of the inertia matrix of the reconfigurable UAV is:
, ,
式中,为无人机x轴惯量,为无人机y轴惯量,为无人机z轴惯量;In the formula, is the x-axis inertia of the drone, is the y-axis inertia of the drone, is the z-axis inertia of the drone;
空气阻力对旋翼产生的反力矩为:The reaction torque generated by air resistance on the rotor is:
, ,
式中,为反扭力矩系数,为第旋翼的转速;In the formula, is the anti-torque coefficient, For the Rotor speed;
陀螺力矩为:The gyroscopic torque is:
, ,
式中,为转子转动惯量,为无人机绕y轴角速度,为第1旋翼的转速,为第2旋翼的转速,为第3旋翼的转速,为第4旋翼的转速,为无人机绕x轴角速度;In the formula, is the rotor moment of inertia, is the angular velocity of the drone around the y-axis, is the rotation speed of the first rotor, is the rotation speed of the second rotor, is the rotation speed of the third rotor, is the rotation speed of the 4th rotor, is the angular velocity of the drone around the x-axis;
重构产生的重力矩如下:The reconstructed gravity moment is as follows:
, ,
式中,为重心偏移量,为旋转矩阵,为无人机的重力;In the formula, is the center of gravity offset, is the rotation matrix, is the gravity of the drone;
由旋翼产生的力和力矩与旋翼转速之间的关系如下:The forces and moments generated by the rotor are related to the rotor speed as follows:
, ,
式中,为旋翼产生的升力,为旋翼产生的升力矩,为升力,,为升力系数,当可重构无人机重构时是一个时变矩阵,代表控制分配矩阵,表达式如下:In the formula, is the lift generated by the rotor, is the lift moment generated by the rotor, For lift, , is the lift coefficient, when the reconfigurable UAV is reconfigured is a time-varying matrix representing the control allocation matrix, expressed as follows:
, ,
式中,为反扭力矩系数,为第个机臂的等效力臂,。In the formula, is the anti-torque coefficient, For the The equivalent arm of the machine arm, .
定义控制输入如下:Define the control input as follows:
, ,
式中,为高度控制量,为横滚通道控制量,为俯仰通道控制量,为偏航通道控制量;In the formula, For high control, is the roll channel control quantity, is the pitch channel control quantity, is the yaw channel control quantity;
将可重构无人机的六自由度动力学模型改写为:The six-degree-of-freedom dynamics model of the reconfigurable UAV is rewritten as:
, ,
式中,为x位置二阶导,为y位置二阶导,为无人机滚转角二阶导,为无人机俯仰角二阶导,为无人机偏航角二阶导,为空气阻力系数,为偏航角,为x位置一阶导,为无人机质量,为无人机俯仰角,为x位置通道重构扰动,为x位置通道外部总扰动,为y位置一阶导,为y位置通道重构扰动,为y位置通道外部总扰动,为重力加速度,为高度通道一阶导,为高度通道重构扰动,为高度通道外部总扰动,为无人机俯仰角一阶导,为无人机偏航角一阶导,为无人机y轴惯量,为无人机z轴惯量,为无人机x轴惯量,为横滚通道控制量,为转子惯量,为四个旋翼转速差,为横滚角通道重构扰动,为横滚角通道外部总干扰,为无人机滚转角一阶导,为俯仰通道控制量,为俯仰角重构扰动,为俯仰角外部总扰动,为偏航角重构扰动,为偏航通道控制量,为偏航角外部总扰动。In the formula, is the second-order derivative of the x position, is the second-order derivative of the y position, is the second-order derivative of the UAV roll angle, is the second-order derivative of the UAV pitch angle, is the second-order derivative of the UAV yaw angle, is the air resistance coefficient, is the yaw angle, is the first-order derivative of the x position, For drone quality, is the pitch angle of the drone, Reconstruct the perturbation for the x-position channel, is the total external disturbance of the x-position channel, is the first-order derivative of the y position, Reconstruct the perturbation for the y position channel, is the total external disturbance of the y position channel, is the acceleration due to gravity, is the first-order derivative of the height channel, is the height channel reconstruction perturbation, is the total external disturbance of the height channel, is the first-order derivative of the UAV pitch angle, is the first-order derivative of the UAV yaw angle, is the y-axis inertia of the drone, is the UAV z-axis inertia, is the x-axis inertia of the drone, is the roll channel control quantity, is the rotor inertia, is the speed difference of the four rotors, Reconstruct the disturbance for the roll angle channel, is the total external interference of the roll angle channel, is the first-order derivative of the UAV roll angle, is the pitch channel control quantity, Reconstruct the disturbance for the pitch angle, is the total external disturbance of the pitch angle, Reconstruct the disturbance for the yaw angle, is the yaw channel control quantity, is the total external disturbance of the yaw angle.
需要说明的是,可重构无人机包括机体、电源、飞控、四个舵机、四个机臂、四个电机和四个旋翼,其中电源、飞控、舵机与机体固定连接,将重构无人机视为机身长宽为,机身高为的长方体,将机臂视为机臂长、机臂宽、机臂高分别为、、的长方体,将电机和旋翼分别视为电机半径为,电机高为和旋翼半径为,旋翼高为的圆柱姿态变化信息包括重心变化量和惯量变化量。It should be noted that the reconfigurable drone includes a fuselage, a power supply, a flight control system, four steering gears, four arms, four motors and four rotors, of which the power supply, flight control system and steering gear are fixedly connected to the fuselage. The reconfigurable drone is regarded as a fuselage with a length and width of , the fuselage height is The arm is a rectangular parallelepiped, and the arm length, arm width, and arm height are respectively , , The motor and rotor are considered as a rectangular block with a motor radius of , the motor height is and the rotor radius is , rotor height is The cylinder posture change information includes the change in center of gravity and the change in inertia.
假设可重构无人机在重构前的几何中心为原点,则可重构无人机的重心变化量的表达式为:Assuming that the geometric center of the reconfigurable UAV before reconstruction is the origin, the expression of the change in the center of gravity of the reconfigurable UAV is:
, ,
式中,为重心偏移量,为机身与舵机质量,为机身重心到坐标原点的矢量,为机臂、转子和旋翼的总力偶,为机臂质量,为电机质量,为旋翼质量,为第个机臂重心到坐标原点的矢量,为第个电机重心到坐标原点的矢量,为第个旋翼重心到坐标原点的矢量。In the formula, is the center of gravity offset, is the mass of the fuselage and servo, is the vector from the center of gravity of the fuselage to the origin of the coordinate system, is the total couple of the arm, rotor and rotor, is the mass of the arm, is the motor mass, is the rotor mass, For the The vector from the center of gravity of the arm to the origin of the coordinate system, For the The vector from the motor center of gravity to the coordinate origin, For the The vector from the rotor center of gravity to the coordinate origin.
运用平行轴定理计算可重构无人机的转动惯量。具体地,计算各部分转动惯量的表达式为:The moment of inertia of the reconfigurable UAV is calculated using the parallel axis theorem. Specifically, the expression for calculating the moment of inertia of each part is:
, ,
式中,为无人机重构前机体惯量,为无人机重构前机臂惯量,为无人机重构前转子惯量,为无人机重构前旋翼惯量,为机身与舵机质量,为机臂质量,为电机质量,为旋翼质量;In the formula, Reconstruct the front body inertia for the drone, Reconstruct the front arm inertia for the drone, Reconstructing the front rotor inertia for the drone, Reconstructing the front rotor inertia for drones, is the mass of the fuselage and servo, is the mass of the arm, is the motor mass, is the rotor mass;
在变形过程中,惯量需要重新计算,其中圆柱的惯量不发生变化,机体固连于坐标系,所以其惯量也不会变化,下面引入旋转矩阵表示可重构无人机的机臂的惯量变化量,惯量变化量的表达式为:During the deformation process, the inertia needs to be recalculated. The inertia of the cylinder does not change. The body is fixed to the coordinate system, so its inertia will not change. The following introduces the rotation matrix to represent the change in inertia of the arm of the reconfigurable drone. The expression of the change in inertia is:
, ,
式中,为第1个机臂和第3个机臂重构后的惯量,为绕y轴旋转矩阵,为机臂不重构时的惯量,为绕y轴旋转矩阵的转置,为第2个机臂和第4个机臂重构后的惯量,为绕x轴旋转矩阵,为绕x轴旋转矩阵的转置;In the formula, is the reconstructed inertia of the first and third arms, is the rotation matrix around the y axis, is the inertia of the arm when it is not reconstructed, is the transpose of the rotation matrix around the y-axis, is the reconstructed inertia of the second and fourth arms, is the rotation matrix around the x-axis, is the transpose of the rotation matrix around the x-axis;
其中,,in, ,
式中,为第2个机臂和第4个机臂的旋转角的余弦值,为第2个机臂和第4个机臂旋转角的正弦值;In the formula, is the cosine value of the rotation angle of the second and fourth arms, is the sine value of the rotation angle of the second and fourth arms;
, ,
式中,为第1个机臂和第3个机臂的旋转角的余弦值,为第1个机臂和第3个机臂的旋转角的正弦值。In the formula, is the cosine value of the rotation angle of the first and third arms, is the sine of the rotation angle of the first and third arms.
根据平行轴定理有惯量计算式为:According to the parallel axis theorem, the inertia calculation formula is:
, ,
式中,为无人机重构后惯量,为机体惯量,为机身与舵机质量,为机身重心到坐标原点的矢量,为重心偏移量,为第个机臂的惯量,为机臂质量,为第个机臂重心到坐标原点的矢量,为转子惯量,为电机质量,为第个电机重心到坐标原点的矢量,为旋翼的惯量,为旋翼质量,为第个旋翼到坐标原点的矢量;In the formula, Reconstruct the inertia of the drone. is the body inertia, is the mass of the fuselage and servo, is the vector from the center of gravity of the fuselage to the origin of the coordinate system, is the center of gravity offset, For the The inertia of the arm, is the mass of the arm, For the The vector from the center of gravity of the arm to the origin of the coordinate system, is the rotor inertia, is the motor mass, For the The vector from the motor center of gravity to the coordinate origin, is the inertia of the rotor, is the rotor mass, For the The vector from the rotor to the origin of the coordinate system;
可重构无人机进行变形时,其每个机臂的等效力臂也会发生变化,对变形过程进行分析发现,等效力臂的变化有两个方面,一方面是机臂变形导致旋翼到坐标原点的水平距离变化,可以表示为:When the reconfigurable UAV is deformed, the equivalent arm force of each arm will also change. Analysis of the deformation process shows that there are two aspects of the change in the equivalent arm force. On the one hand, the deformation of the arm causes the horizontal distance from the rotor to the origin of the coordinate system to change, which can be expressed as:
, ,
式中,为第个等效力臂不考虑重心偏移的长度,为机臂长度,为第个机臂的当前角度,为机体长度;In the formula, For the The length of the equivalent force arm without considering the center of gravity offset is is the arm length, For the The current angle of the arm, is the length of the body;
另一方面是因为可重构无人机变形导致的中心的偏移,假设此时的重心为,则每个机臂的等效力臂如下表示:On the other hand, due to the displacement of the center caused by the deformation of the reconfigurable drone, it is assumed that the center of gravity is , then the equivalent force arm of each arm is expressed as follows:
, ,
式中,为第个等效力臂,为重心偏移x轴分量,为重心偏移y轴分量,为重心偏移Z轴分量;In the formula, For the Equivalent force arm, is the x-axis component of the center of gravity offset, is the y-axis component of the center of gravity offset, The Z-axis component of the center of gravity offset;
其中,所述扩张状态观测器的表达式为:The expression of the extended state observer is:
, ,
式中,为第时刻跟踪误差,为第时刻滚转通道的跟踪反馈量,为第时刻滚转通道的跟踪反馈量,为第时刻无人机滚转角,为观测器步长,为第时刻滚转通道的跟踪反馈量的微分,为第时刻滚转通道的跟踪反馈量的微分,为第时刻滚转通道的扰动观测量,为第时刻滚转通道的扰动观测量,、、均为观测器可调增益,为系数是0.5时的非线性函数,为输出反馈增益,为第时刻滚转通道的控制器输出量,为系数是0.25时的非线性函数;In the formula, For the Tracking error at any time, For the The tracking feedback amount of the momentary roll channel, For the The tracking feedback amount of the momentary roll channel, For the The rolling angle of the drone at the moment, is the observer step size, For the The differential of the tracking feedback amount of the moment roll channel, For the The differential of the tracking feedback amount of the moment roll channel, For the The disturbance observation of the moment rolling channel, For the The disturbance observation of the moment rolling channel, , , are the observer adjustable gains, is a nonlinear function with a coefficient of 0.5, is the output feedback gain, For the The controller output of the momentary roll channel, is a nonlinear function with a coefficient of 0.25;
, ,
式中,为系数是时的非线性函数,为自变量,为极小值,为符号函数。In the formula, The coefficient is The nonlinear function of is the independent variable, is the minimum value, is a symbolic function.
步骤S103,BSTSMC控制器获取实时补偿后的姿态控制信号,根据所述姿态控制信号对所述可重构无人机的姿态进行实时调节。Step S103: the BSTSMC controller obtains the attitude control signal after real-time compensation, and adjusts the attitude of the reconfigurable UAV in real time according to the attitude control signal.
在本步骤中,BSTSMC(反步超螺旋滑膜)控制器的表达式为:In this step, the expression of BSTSMC (backstepping super spiral synovial film) controller is:
, ,
式中,为总控制量,为基于反步法的控制量,为超螺旋控制算法的控制量,为一组可调增益,为扩张状态观测器观测到的各通道总扰动,为期望值和反馈值得误差,为期望值,为误差微分增益,为误差的微分,为滑模面增益,为滑模面,为超螺旋系数,为符号函数,为超螺旋系数,为系统运行当前时间。In the formula, is the total control quantity, is the control quantity based on the backstepping method, is the control quantity of the superhelix control algorithm, is a set of adjustable gains, is the total disturbance of each channel observed by the extended state observer, is the error between the expected value and the feedback value, is the expected value, is the error differential gain, is the differential of the error, is the sliding surface gain, is the sliding surface, is the superhelical coefficient, is the symbolic function, is the superhelical coefficient, The current time for the system to run.
具体地,,Specifically, ,
式中,为中间变量;In the formula, is an intermediate variable;
式中,为期望值,为反馈值,为期望值一阶导,为反馈值一阶导,为期望值一阶导,为中间变量。In the formula, is the expected value, is the feedback value, is the first-order derivative of the expected value, is the first-order derivative of the feedback value, is the first-order derivative of the expected value, is an intermediate variable.
在一个具体实施例中,使用simulink搭建了仿真平台对提出的控制算法进行了验证,系统仿真参数如表1。In a specific embodiment, a simulation platform was built using Simulink to verify the proposed control algorithm. The system simulation parameters are shown in Table 1.
, ,
控制器参数如表2,其中三个姿态的ESO参数相同,位置控制器中可以调节控制器响应速度,、、分别为x通道的滑模系数、 y 通道的滑模系数、z通道的滑模系数,可以调节位置控制器的抗扰能力;BSTSMC控制器中可以调节BSTSMC控制器的响应速度,、、分别为通道 、 通道、通道的滑模面增益,、、、、、分别为各自通道超螺旋系数,、、、均为重构控制器增益。The controller parameters are shown in Table 2. The ESO parameters of the three postures are the same. The controller response speed can be adjusted. , , They are the sliding mode coefficients of the x channel, the y channel, and the z channel, respectively. The anti-disturbance capability of the position controller can be adjusted; in the BSTSMC controller The response speed of the BSTSMC controller can be adjusted. , , They are aisle, aisle, The sliding surface gain of the channel, , , , , , are the superhelical coefficients of their respective channels, , , , are the reconstructed controller gains.
, ,
为了验证本申请提出的控制方法对变形产生的扰动能够进行有效处理,进行了轨迹跟踪实验,并且在飞行过程中不断进行重构,设置的期望轨迹如下:In order to verify that the control method proposed in this application can effectively handle the disturbance caused by deformation, a trajectory tracking experiment was carried out, and the desired trajectory was set as follows during the flight:
, ,
式中,为x轴期望值,为y轴期望值,为高度期望值,为当前运行时间;In the formula, is the expected value on the x-axis, is the expected value on the y-axis, High expectations, is the current running time;
重构机构使用比例控制,实验时各个机臂的重构角度如图3所示,轨迹跟踪曲线如图4所示,可以看出实际轨迹很好的跟踪上了期望轨迹,验证了本申请提出的控制器具有较好的轨迹跟踪性能。The reconstruction mechanism uses proportional control. The reconstruction angles of each arm during the experiment are shown in Figure 3, and the trajectory tracking curve is shown in Figure 4. It can be seen that the actual trajectory tracks the expected trajectory very well, verifying that the controller proposed in this application has good trajectory tracking performance.
为了验证本申请提出的控制器的响应速度,本文分别做了位置响应与姿态响应实验,实验结果如图5和图6所示,控制器在 内达到稳态,可以看出本申请提出的控制方案具有较好的控制响应速度。In order to verify the response speed of the controller proposed in this application, this paper conducted position response and posture response experiments respectively. The experimental results are shown in Figures 5 and 6. It reaches a steady state within 10 seconds, which shows that the control scheme proposed in this application has a good control response speed.
本申请按照图3中的重构方案进行了重构抗扰实验,在第 时按照顺序将四个机臂重构到,位置偏差如图7,可以看出位置偏差很小,并且在很短的时间内恢复稳态,通过前文建立的无人机模型可以发现位置偏差是由姿态偏差引起的。姿态偏差如图8,图中可以看出,在可重构无人机进行重构时,姿态的偏差在以内,说明本申请提出的控制方案针对可重构无人机重构造成的干扰具有较好的处理性能,进一步验证了本申请提出的控制器对于可重构无人机具有较好的控制效果。This application conducted a reconstruction anti-interference experiment according to the reconstruction scheme in Figure 3. Reconstruct the four arms in order , the position deviation is shown in Figure 7. It can be seen that the position deviation is very small and returns to steady state in a very short time. Through the drone model established in the previous article, it can be found that the position deviation is caused by the attitude deviation. The attitude deviation is shown in Figure 8. It can be seen from the figure that when the reconfigurable drone is reconfigured, the attitude deviation is This indicates that the control scheme proposed in this application has good processing performance for the interference caused by the reconstruction of the reconfigurable UAV, which further verifies that the controller proposed in this application has good control effect on the reconfigurable UAV.
最后应说明的是:以上实施例仅用以说明本发明的技术方案,而非对其限制;尽管参照前述实施例对本发明进行了详细的说明,本领域的普通技术人员应当理解:其依然可以对前述各实施例所记载的技术方案进行修改,或者对其中部分技术特征进行等同替换;而这些修改或者替换,并不使相应技术方案的本质脱离本发明各实施例技术方案的精神和范围。Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.
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