仿马四足机器人机构分析与步态研究
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摘要
四足机器人具有较强的承载能力、机动性和适应特殊地形的能力,在许多行业有着广泛的应用前景。本文以仿马四足机器人的机构和步态为研究对象,分析和制作了六自由度小型仿马四足机器人,建立了四足机器人一般步态的时间顺序分析模型和对称步态变换模型,然后利用庞加莱映射研究了四足机器人和关节型腿机构的被动跳跃步态,对四足机器人从步行到跳跃开展了基础研究。
本文首先参考马的结构设计了一种四足机器人的结构模型,然后对该模型进行了运动学和动力学分析,得到了四足机器人机体和各关节间的运动关系以及系统的拉格朗日方程。然后根据步行仿真和移动效率的仿真,设定了四足机器人的结构参数,制作了实验用小型四足机器人系统。
其次,基于四足动物腿部动作的时间顺序,提出了采用五个参数来描述四足机器人一般步态分析的时间序列,经过归一化处理,建立了一个步态周期内的常用对称步态和非对称步态的时间顺序模型。基于该模型建立了对称步态变换的分析模型,证明了在等速等占空系数以及等速等步态周期的对称步态之间需要一个变换步态。实验结果表明四足机器人能够实现稳定的步态变换行走。
接着,采用拉格朗日法推导了四足机器人被动跳跃步态中各运动相的动力学方程,并根据跳跃步态特征给出了基于事件的运动相转换方程。利用被动跳跃步态周期性特点,合理降维定义了四足机器人被动跳跃步态的庞加莱映射,运用牛顿迭代法获得了庞加莱映射的某个固定点。此固定点作为初始条件对各运动相动力学方程进行了数值积分,得到了被动跳跃步态的周期性运动曲线,证明了四足机器人在某个初始条件下能够实现稳定的被动跳跃步态。
然后,针对隔离地面冲击的需要设计一种由连杆和线性拉伸弹簧组成的关节型腿机构,利用最小二乘法将该被动缓冲型腿机构的等效刚度表示为由三次非线性刚度和线性刚度组成的分段非线性刚度。建立了缓冲过程的力学模型,通过数值计算,在并联最优阻尼比的情况下,该腿机构能够获得很小的缓冲系数。最后,采用相同的方法得到了关节型腿机构等效质量弹簧倒立摆被动跳跃步态的周期性运动曲线,证明了该腿机构在某个初始条件下能够实现稳定的被动跳跃步态。
With good performance in capacity, mobility and versatility, quadruped robot can be applied in many fields. This dissertation studies the structure and gaits of quadruped robot imitating a horse, presents the timing sequence analysis models of common gaits as well as the transition model between symmetric gaits, builds up a mini-quadruped imitating a horse, and carries out a gait transition experiment. It also studies the passive bounding gait of the quadruped and the articulated leg with Poincarémap, and conducts a basic research on quadruped from walk to bounding.
Firstly, a structural model of a quadruped robot is designed according to a horse, and then kinematic and dynamic analyses of the model are conducted. Thus the relationship between body and limbs as well as the system Lagrange equation is achieved. The structural variables are laid out according to walking simulation and energy consumption simulation during locomotion. A mini-quadruped robot is built up for the experiment.
Secondly, on the basis of the timing sequence of quadruped’s limbs movements, a timing sequence analysis model on common gaits in quadruped is presented with five variables. The timing sequence of common gaits in a stride cycle is achieved after being standardized, and then the gait transition analysis model is established. This dissertation proves that the gait transition between symmetrical gaits with the same duty factor or stride cycle can be completed in one stride cycle under a constant speed. The result of the experiment shows that the quadruped can perform the steady gait transition.
Thirdly, the dynamic equations of the quadruped in the phases of bounding gait are derived with Lagrange method, and the transition equations between phases are presented according to the characteristic of bound gait. The Poincarémap of the quadruped bound gait is defined with reasonable dimensional reduction according to the characteristics of the periodic cycle. A fix point of Poincarémap is figured out with Newton-Raphson method. With the fixed point as initial condition, the dynamic equations are integrated numerically with Matlab, and the periodic motion curves are achieved. It is proved that quadruped robot can realize steady passive bound gait with a suitable initial condition.
Fourthly, an articulated leg mechanism, consisting of links, a linear tension spring, which is used to isolate the ground impact on legged robot is presented. The equivalent stiffness of the leg mechanism is expressed in piecewise as a cubic stiffness and a linear stiffness through least-squares procedure. The mechanic model of buffering is built up, and it is calculated with numeric method. The result shows that when the leg mechanism connects to an optimal damping ratio in parallel, it can achieve a small buffer coefficient.
Finally, in the same way, the periodic motion curves of the spring load inverted pendulum equivalent to the articulated leg are achieved. It is proved that the articulated leg can realize steady passive bound gait with a suitable initial condition.
本文首先参考马的结构设计了一种四足机器人的结构模型,然后对该模型进行了运动学和动力学分析,得到了四足机器人机体和各关节间的运动关系以及系统的拉格朗日方程。然后根据步行仿真和移动效率的仿真,设定了四足机器人的结构参数,制作了实验用小型四足机器人系统。
其次,基于四足动物腿部动作的时间顺序,提出了采用五个参数来描述四足机器人一般步态分析的时间序列,经过归一化处理,建立了一个步态周期内的常用对称步态和非对称步态的时间顺序模型。基于该模型建立了对称步态变换的分析模型,证明了在等速等占空系数以及等速等步态周期的对称步态之间需要一个变换步态。实验结果表明四足机器人能够实现稳定的步态变换行走。
接着,采用拉格朗日法推导了四足机器人被动跳跃步态中各运动相的动力学方程,并根据跳跃步态特征给出了基于事件的运动相转换方程。利用被动跳跃步态周期性特点,合理降维定义了四足机器人被动跳跃步态的庞加莱映射,运用牛顿迭代法获得了庞加莱映射的某个固定点。此固定点作为初始条件对各运动相动力学方程进行了数值积分,得到了被动跳跃步态的周期性运动曲线,证明了四足机器人在某个初始条件下能够实现稳定的被动跳跃步态。
然后,针对隔离地面冲击的需要设计一种由连杆和线性拉伸弹簧组成的关节型腿机构,利用最小二乘法将该被动缓冲型腿机构的等效刚度表示为由三次非线性刚度和线性刚度组成的分段非线性刚度。建立了缓冲过程的力学模型,通过数值计算,在并联最优阻尼比的情况下,该腿机构能够获得很小的缓冲系数。最后,采用相同的方法得到了关节型腿机构等效质量弹簧倒立摆被动跳跃步态的周期性运动曲线,证明了该腿机构在某个初始条件下能够实现稳定的被动跳跃步态。
With good performance in capacity, mobility and versatility, quadruped robot can be applied in many fields. This dissertation studies the structure and gaits of quadruped robot imitating a horse, presents the timing sequence analysis models of common gaits as well as the transition model between symmetric gaits, builds up a mini-quadruped imitating a horse, and carries out a gait transition experiment. It also studies the passive bounding gait of the quadruped and the articulated leg with Poincarémap, and conducts a basic research on quadruped from walk to bounding.
Firstly, a structural model of a quadruped robot is designed according to a horse, and then kinematic and dynamic analyses of the model are conducted. Thus the relationship between body and limbs as well as the system Lagrange equation is achieved. The structural variables are laid out according to walking simulation and energy consumption simulation during locomotion. A mini-quadruped robot is built up for the experiment.
Secondly, on the basis of the timing sequence of quadruped’s limbs movements, a timing sequence analysis model on common gaits in quadruped is presented with five variables. The timing sequence of common gaits in a stride cycle is achieved after being standardized, and then the gait transition analysis model is established. This dissertation proves that the gait transition between symmetrical gaits with the same duty factor or stride cycle can be completed in one stride cycle under a constant speed. The result of the experiment shows that the quadruped can perform the steady gait transition.
Thirdly, the dynamic equations of the quadruped in the phases of bounding gait are derived with Lagrange method, and the transition equations between phases are presented according to the characteristic of bound gait. The Poincarémap of the quadruped bound gait is defined with reasonable dimensional reduction according to the characteristics of the periodic cycle. A fix point of Poincarémap is figured out with Newton-Raphson method. With the fixed point as initial condition, the dynamic equations are integrated numerically with Matlab, and the periodic motion curves are achieved. It is proved that quadruped robot can realize steady passive bound gait with a suitable initial condition.
Fourthly, an articulated leg mechanism, consisting of links, a linear tension spring, which is used to isolate the ground impact on legged robot is presented. The equivalent stiffness of the leg mechanism is expressed in piecewise as a cubic stiffness and a linear stiffness through least-squares procedure. The mechanic model of buffering is built up, and it is calculated with numeric method. The result shows that when the leg mechanism connects to an optimal damping ratio in parallel, it can achieve a small buffer coefficient.
Finally, in the same way, the periodic motion curves of the spring load inverted pendulum equivalent to the articulated leg are achieved. It is proved that the articulated leg can realize steady passive bound gait with a suitable initial condition.
引文
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