具有二阶非完整约束的铰接多刚体系统动力学建模与应用研究
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摘要
无根(无固定基座)铰接多刚体系统与欠驱动铰接多刚体系统的共同特征是系统的控制输入维数少于系统的广义坐标维数,其位形空间约束方程不能满足系统确定运动的控制要求,但由于关节间存在动力耦合作用,因此可基于动力学约束对系统进行控制。基于动力学模型建立的约束方程为二阶微分方程,一般不可积分,因此这两类系统实质上为具有二阶非完整约束的动力系统。本课题针对此类二阶非完整系统的动力学建模进行研究,并基于动力学模型推导出系统的非完整约束方程,从而对多冗余度移动机器人系统、欠驱动柔顺机构及空间机械臂系统的耦合运动进行分析,主要内容如下:
(1)对具有弹性储能关节的欠驱动铰接多刚体系统进行了运动学分析,并基于D’Alembert-Lagrange原理建立了欠驱动系统的动力学模型,为基于二阶非完整约束的多冗余度欠驱动机器人系统进行动力学特性分析与运动控制奠定了基础。
(2)通过在无根铰接多刚体系统与地面参考坐标系间增加动力虚设机构,将此类非完整多刚体系统转化为具有固定基座的欠驱动铰接多刚体系统;基于动力学模型解耦形式得到了系统的二阶非完整约束方程,推导出了虚设关节和机构关节的加速度表达式;提出了机构关节角加速度输出精度指标,对虚设机构的约束特性进行了分析,并讨论了系统结构参数对运动输出的影响。
(3)基于无根铰接多刚体系统动力学虚设机构法,建立弹性欠驱动蛇形机器人蜿蜒运动的动力学模型,推导了被动关节的非完整约束方程;在定义了被动关节耦合运动性能指标的基础上,讨论了运动学、动力学参数及弹性储能元件刚度阻尼特性等因素对弹性欠驱动蛇形机器人运动耦合性能的影响。
(4)以J型仿生足为例提出了一种基于柔顺构件几何形状和刚度分布的伪刚性段划分方法,建立了J型仿生足的伪刚体模型,将柔顺机构等效为了具有弹性储能关节的欠驱动铰接多刚体系统;基于对系统的受力分析及动力学虚设机构法,建立了J型足的动力学模型,并推导出了伪刚体模型等效关节加速度的非完整约束方程;在定义了力/力矩传递性能指标与耦合运动性能指标的基础上,讨论了J型仿生足结构参数变化、末端作用力对其运动性能的影响。
(5)基于动力学虚设机构法,在空间机械臂系统与轨道坐标系间增加动力虚设机构,并基于李群、李代数给出了系统的一、二阶影响系数,建立系统的动力学模型;推导出了机械臂载体加速度的约束方程,定义了载体耦合运动性能指标,讨论了机械臂结构参数变化与主动关节输入对载体耦合运动性能的影响。
(6)基于蛇形机器人样机对实际的无根铰接多刚体系统进行运动轨迹规划控制及实验研究。在分析关节空间机构运动学和蜿蜒步态规划的基础上,对样机驱动电机的耦合进行了力矩分析;通过实验验证了蛇形机器人可实现蜿蜒爬行、转向、抬头等多种运动方式。
The common characteristic of rootless multibody system (without fixed base) and underactuated multibody system is that the quantity of control input is less than that of generalized coordinates. The constraint equations of configuration space can’t satisfy the control request of system certain motions, but due to the dynamic coupling between joints, the dynamic constraints can be applied to the system control. These dynamic constraint equations are second-order differential equations and not integral in general, therefore these two multibody systems are essentially dynamic systems with second-order nonholonomic constraints. The paper investigates the dynamics modeling of this second-order nonholonomic systems, and analyses the coupled motion of redundant mobile robots, underactuated compliant mechanism and space manipulator system based on the nonholonomic constraint equations. The main research contents are as follows:
(1)The kinematics of underactuated aritculated multi-body systems with elastic energy storage joints is analyzed, and a dynamic model of underactuated system is built based on D'Alembert-Lagrange principle. They provide the foundations for the analysis of dynamic characteristics and the motion control of the high redundancy underactuated robots with nonholonomic constraints.
(2)Through adding the dynamic nominal mechanism between the rootless aritculated multi-body system and the ground reference frame, such nonholonomic multi-body system is converted into underactuated articulated multi-body system with fixed base; the second-order nonholonomic constraint equations of the system and the acceleration expressions of nominal and actual joints are derived based on the decoupling form of the dynamic model; based on the definition of joint angular acceleration output precision indices, the constraint characteristic of the nominal mechanism is analyzed and the influence of system parameters on the output is discussed.
(3)Based on the dynamic nominal mechanism method, the dynamic model of the serpentine locomotion of elastic underactuated snake-like robot is built, and the nonholonomic constraint equations of passive joints are derived; based on the definition of the performance indices for describing the coupling motion of passive joint, the effect of kinematics, dynamics parameters and the stiffness and damping characteristics of elastic energy storage element and other factors on coupling characteristic of the elastic underactuated snake-like robot are discussed.
(4)Taking the J-type bionic foot as an example, the pseudo-rigid-segments partition method is proposed based on the geometrical shape and stiffness distribution of compliant components, and the J-type foot pseudo-rigid-body modeling is built; therefore, the compliant mechanism is equivalent to a underactuated articulated multi-body system with elastic energy storage joints; based on force analysis and dynamics nominal mechanism method, the dynamic modeling of J-foot is established, and the nonholonomic constraint equations of the equivalent joint acceleration of pseudo-rigid body model is derived; on the basis of the definition of the performance indices of force/torque transmission and the coupling action, the effect of the structure parameters of the J-type foot and the end force on locomotion characteristic is discussed.
(5)Based on the dynamic nominal mechanism method, the dynamic nominal mechanisms between the space manipulator system and orbit coordinate are added, and the first and second order effect coefficients of the system are given based on Lie group, Lie algebra, the dynamic model is built; the acceleration constraint equations of the carrier are derived, the coupling motion performance indices are defined, and the effect of the arm structural parameters on the carrier coupling motion performance is discussed
(6)Based on the snake-like robot prototype, motion path planning control and experiments researches of a actual rootless multibody system are investigated; the coupling torque of servomotors of the prototype is analyzed based on the analysis of spatial linkage mechanism kinematics and serpentine crawling path planning; the experiments confirm that the robot is of ability to realize several motion modes, including lateral undulation, left and right turning motions, and uplifting head.
(1)对具有弹性储能关节的欠驱动铰接多刚体系统进行了运动学分析,并基于D’Alembert-Lagrange原理建立了欠驱动系统的动力学模型,为基于二阶非完整约束的多冗余度欠驱动机器人系统进行动力学特性分析与运动控制奠定了基础。
(2)通过在无根铰接多刚体系统与地面参考坐标系间增加动力虚设机构,将此类非完整多刚体系统转化为具有固定基座的欠驱动铰接多刚体系统;基于动力学模型解耦形式得到了系统的二阶非完整约束方程,推导出了虚设关节和机构关节的加速度表达式;提出了机构关节角加速度输出精度指标,对虚设机构的约束特性进行了分析,并讨论了系统结构参数对运动输出的影响。
(3)基于无根铰接多刚体系统动力学虚设机构法,建立弹性欠驱动蛇形机器人蜿蜒运动的动力学模型,推导了被动关节的非完整约束方程;在定义了被动关节耦合运动性能指标的基础上,讨论了运动学、动力学参数及弹性储能元件刚度阻尼特性等因素对弹性欠驱动蛇形机器人运动耦合性能的影响。
(4)以J型仿生足为例提出了一种基于柔顺构件几何形状和刚度分布的伪刚性段划分方法,建立了J型仿生足的伪刚体模型,将柔顺机构等效为了具有弹性储能关节的欠驱动铰接多刚体系统;基于对系统的受力分析及动力学虚设机构法,建立了J型足的动力学模型,并推导出了伪刚体模型等效关节加速度的非完整约束方程;在定义了力/力矩传递性能指标与耦合运动性能指标的基础上,讨论了J型仿生足结构参数变化、末端作用力对其运动性能的影响。
(5)基于动力学虚设机构法,在空间机械臂系统与轨道坐标系间增加动力虚设机构,并基于李群、李代数给出了系统的一、二阶影响系数,建立系统的动力学模型;推导出了机械臂载体加速度的约束方程,定义了载体耦合运动性能指标,讨论了机械臂结构参数变化与主动关节输入对载体耦合运动性能的影响。
(6)基于蛇形机器人样机对实际的无根铰接多刚体系统进行运动轨迹规划控制及实验研究。在分析关节空间机构运动学和蜿蜒步态规划的基础上,对样机驱动电机的耦合进行了力矩分析;通过实验验证了蛇形机器人可实现蜿蜒爬行、转向、抬头等多种运动方式。
The common characteristic of rootless multibody system (without fixed base) and underactuated multibody system is that the quantity of control input is less than that of generalized coordinates. The constraint equations of configuration space can’t satisfy the control request of system certain motions, but due to the dynamic coupling between joints, the dynamic constraints can be applied to the system control. These dynamic constraint equations are second-order differential equations and not integral in general, therefore these two multibody systems are essentially dynamic systems with second-order nonholonomic constraints. The paper investigates the dynamics modeling of this second-order nonholonomic systems, and analyses the coupled motion of redundant mobile robots, underactuated compliant mechanism and space manipulator system based on the nonholonomic constraint equations. The main research contents are as follows:
(1)The kinematics of underactuated aritculated multi-body systems with elastic energy storage joints is analyzed, and a dynamic model of underactuated system is built based on D'Alembert-Lagrange principle. They provide the foundations for the analysis of dynamic characteristics and the motion control of the high redundancy underactuated robots with nonholonomic constraints.
(2)Through adding the dynamic nominal mechanism between the rootless aritculated multi-body system and the ground reference frame, such nonholonomic multi-body system is converted into underactuated articulated multi-body system with fixed base; the second-order nonholonomic constraint equations of the system and the acceleration expressions of nominal and actual joints are derived based on the decoupling form of the dynamic model; based on the definition of joint angular acceleration output precision indices, the constraint characteristic of the nominal mechanism is analyzed and the influence of system parameters on the output is discussed.
(3)Based on the dynamic nominal mechanism method, the dynamic model of the serpentine locomotion of elastic underactuated snake-like robot is built, and the nonholonomic constraint equations of passive joints are derived; based on the definition of the performance indices for describing the coupling motion of passive joint, the effect of kinematics, dynamics parameters and the stiffness and damping characteristics of elastic energy storage element and other factors on coupling characteristic of the elastic underactuated snake-like robot are discussed.
(4)Taking the J-type bionic foot as an example, the pseudo-rigid-segments partition method is proposed based on the geometrical shape and stiffness distribution of compliant components, and the J-type foot pseudo-rigid-body modeling is built; therefore, the compliant mechanism is equivalent to a underactuated articulated multi-body system with elastic energy storage joints; based on force analysis and dynamics nominal mechanism method, the dynamic modeling of J-foot is established, and the nonholonomic constraint equations of the equivalent joint acceleration of pseudo-rigid body model is derived; on the basis of the definition of the performance indices of force/torque transmission and the coupling action, the effect of the structure parameters of the J-type foot and the end force on locomotion characteristic is discussed.
(5)Based on the dynamic nominal mechanism method, the dynamic nominal mechanisms between the space manipulator system and orbit coordinate are added, and the first and second order effect coefficients of the system are given based on Lie group, Lie algebra, the dynamic model is built; the acceleration constraint equations of the carrier are derived, the coupling motion performance indices are defined, and the effect of the arm structural parameters on the carrier coupling motion performance is discussed
(6)Based on the snake-like robot prototype, motion path planning control and experiments researches of a actual rootless multibody system are investigated; the coupling torque of servomotors of the prototype is analyzed based on the analysis of spatial linkage mechanism kinematics and serpentine crawling path planning; the experiments confirm that the robot is of ability to realize several motion modes, including lateral undulation, left and right turning motions, and uplifting head.
引文
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