[Matlab six-degree-of-freedom robot] Detailed steps to establish the improved DH parameters (modified Denavit-Hartenberg)

recent update

【Main line】

$kinematics$

• Build a robot model
• Correct solution of kinematics
• Construction of workspace based on Monte Carlo Method

$Kinetics(to\; beadded)$

【Supplementary explanation】

• Understanding of Flexible Workspaces and Accessible Workspaces
• Detailed establishment steps of modified DH parameters (modified Denavit-Hartenberg)
• Questions about parameterization of rotation (Euler angles, attitude angles, quaternions)
• The Explanation of Double Variable Function atan2(x,y)

Supplementary Note

Understanding of Flexible Workspaces and Accessible Workspaces

foreword

This paper studies the joint variable $q_i$relation to the position and extent of the end effector, an introduction toImproved DH parameter tableBased on the establishment of DH rules, the following algorithm is summarized, which can be used to derive the forward kinematics of any robot (manipulator).

---

The following is the text of this article

text

Detailed steps to establish DH parameter table

The DH convention defines the forward kinematic equations of a manipulator, that is, the mapping from joint variables to end-effector positions and poses.

Step 1: Locate and mark the joint axis $z_0,\cdot \cdot \cdot ,z_{n-1}$
Step 2: Establish a reference coordinate system, the origin can be set at $z_0$any point on the axis. Reasonably choose $x_0$axis and $y_0$axes, forming a right-handed coordinate system.
For $i=1,\cdot \cdot \cdot ,n-1$ , repeat step$3$ to step$5$
Step 3:Locate the origin$o_i$，Use $z_i$轴和$z_{i-1}$The common normals of the axes intersect at $z_i$, like $z_i$Sum $z_{i-1}$mutual relationship, general $o_i$located at this intersection. if $z_i$Sum $z_{i-1}$Parallel, forward $o_i$The axes are positioned at $z_i$any position on the axis.
Step 4: Along $z_{i-1}$和$z_i$common normal direction and pass through $o_i$set $x_i$axis; or when $z_{i-1}$和$z_i$zi $z_{i-1}—z_i$The direction of the plane normal is set to $x_i$axis
step 5: set $y_i$Axis, forming a right-handed coordinate system
Step 6: Establish the coordinate system of the end effector $o_n{x}_n{y}_n{z}_n$. Suppose the $n$ joints are rotational joints, set$z_n=a$ and parallel to$z_{n-1}$. z_ $z_n$Axes set the proper origin $o_n$, usually preferentially placed in the center of the gripper, or at the tip of any tool the robot arm might be carrying. Put $y_n=s$ is set in the closing direction of the gripper, and set$x_n=n$ , namely$s\times a$ . If the tool is not a simple gripper, set the appropriate$x_n$和$y_n$Form a right-handed coordinate system.
Step 7: Create a DH parameter $a_i$、$d_i$、$a_i$、$i_i$list of.
$a_i=$ from$x_i$Sum $z_{i-1}$Axis intersection to origin $o_i$The line segment along $x_i$axis distance.
$d_i=$ fromoi$o_{i-1}$to $x_i$Sum $z_{i-1}$The line segment at the intersection of the axes is along $z_{i-1}$axis distance. if joint $i$ is a translational joint, then$d_i$is the independent variable of the joint.
$a_i=$ xi$x_i$axis measured from $z_{i-1}$to $z_i$angle.
$i_i=$ zi$z_{i-1}$axis measured from $x_{i-1}$to $x_i$Angle. if joint $i$ is a rotating joint, then$i_i$is the joint variable.
Step 8: Substitute the above parameters into the formula $A_i=Ro{t}_{z,i_i}Tran{s}_{z,d_i}Tran{s}_{x,a_i}Ro{t}_{x,a_i}$, get the homogeneous transformation matrix $A_i$.
Step 9: Solve for $T_n^0=A_1\cdot \cdot \cdot A_n$. This gives the position and orientation coordinates of the tool frame relative to the base frame.

Summarize

The above is the content of this article. This article studies the joint variable $q_i$and the relationship between the position and range of the end effector, introduces theImproved DH parameter tableThe establishment of, and based on the DH rule, summarizes the algorithm, used to derive the forward kinematics of any robot (manipulator).

references

Robot Modeling and Control