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机器人动力学

This topic details the different elements, properties, and equations of rigid body robot dynamics.机器人动力学are the relationship between the forces acting on a robot and the resulting motion of the robot. In Robotics System Toolbox™, manipulator dynamics information is contained within a刚性木板对象为运动学和动力学计算指定刚体，固定点和惯性参数。

Note

要使用Dynamics对象函数，您必须设置DataFormat属性刚性木板反对"row"或者"column". These setting accept inputs and return outputs as row or column vectors, respectively, for relevant robotics calculations, such as robot configurations or joint torques.

Dynamics Properties

使用机器人动力学时，请使用这些属性指定操纵器机器人的各个物体的信息rigidBodyobjects:

Mass- 刚体的质量为千克。
CenterOfMass— Center of mass position of the rigid body, specified as a vector of the form[x y z]. The vector describes the location of the center of mass of the rigid body, relative to the body frame, in meters. ThecenterOfMassobject function uses these rigid body property values when computing the center of mass of a robot.
Inertia- 刚体的惯性，被指定为形式的向量[Ixx Iyy Izz Iyz Ixz Ixy]. The vector is relative to the body frame in kilogram square meters. The inertia tensor is a positive definite matrix of the form:

The first three elements of theInertiavector are the moment of inertia, which are the diagonal elements of the inertia tensor. The last three elements are the product of inertia, which are the off-diagonal elements of the inertia tensor.

有关与整个操纵器机器人模型相关的信息，请指定这些信息刚性木板object properties:

重力- 机器人经历的引力加速度，指定为[x y z]vector in m/s². By default, there is no gravitational acceleration.
DataFormat— The input and output data format for the kinematics and dynamics functions, specified as"struct","row", or"column".

Dynamics Equations

机械手刚体动力学are governed by this equation:

$\frac{d}{d t} [\begin{matrix} q \\ \dot{q} \end{matrix}] = [\begin{matrix} \dot{q} \\ M {(q)}^{- 1} (- C (q, \dot{q}) \dot{q} - G (q) - J {(q)}^{T} F_{E x t} + τ) \end{matrix}]$

also written as:

$M (q) \ddot{q} = - C (q, \dot{q}) \dot{q} - G (q) - J {(q)}^{T} F_{E x t} + τ$

where:

$M (q)$ — is a joint-space mass matrix based on the current robot configuration. Calculate this matrix by using themassMatrix对象功能。
$C (q, \dot{q})$ - 是科里奥利的术语，乘以 $\dot{q}$ to calculate the velocity product. Calculate the velocity product by using by the速度生产对象功能。
$G (q)$ — is the gravity torques and forces required for all joints to maintain their positions in the specified gravity重力. Calculate the gravity torque by using thegravityTorque对象功能。
$J (q)$ — is the geometric Jacobian for the specified joint configuration. Calculate the geometric Jacobian by using thegeometricJacobian对象功能。
$F_{E x t}$ — is a matrix of the external forces applied to the rigid body. Generate external forces by using theexternalForce对象功能。
$τ$ — are the joint torques and forces applied directly as a vector to each joint.
$q, \dot{q}, \ddot{q}$ — are the joint configuration, joint velocities, and joint accelerations, respectively, as individual vectors. For revolute joints, specify values in radians, rad/s, and rad/s², respectively. For prismatic joints, specify in meters, m/s, and m/s².

To compute the dynamics directly, use theforwardDynamics对象功能。The function calculates the joint accelerations for the specified combinations of the above inputs.

要达到一系列动作，请使用inverseDynamics对象功能。该函数计算实现指定配置，速度，加速度和外部力所需的关节扭矩。