Robotic arm robot-use Matlab Robotic ToolBox to establish a four-axis robot arm model and realize motion control simulation

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In order to realize the motion trajectory planning of the robotic arm, and at the same time to learn more about the theory of robotics and apply it to time, I use Robotic ToolBox to build a four-axis robot model and realize motion control simulation, and record and share it.

Physical four-axis robotic arm

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Robotic ToolBox Robotic Arm Modeling

1. Create a DH table for the robotic arm

Here I choose standard DH parameters for modeling, and the meaning of each parameter is shown in the figure: What
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needs to be noted is:

When determining the axis, the Z-axis is the rotation axis of the connecting rod joint (here, the rotation axis of the steering gear), and the X-axis is the common vertical of the Z-axis of the current joint and the Z-axis of the next joint (going up one by one) Line (here is the parallel line of the robot arm lever).

Establish a robotic arm coordinate system

Coordinate system establishment method:
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The robot arm coordinate system establishment is shown in the figure:

Establish DH table according to coordinate system

The first thing that needs to be done is to create a DH table for the robotic arm :

i	a (unit: m)	alpha
1	0	pi/2 (z1 rotates 90° around x1 to z2)
2	0.105	0
3	0.09	0
4	0.04	0

2. Code modeling

%% 机械臂建模
% 定义各个连杆以及关节类型，默认为转动关节
%           theta      d        a        alpha
L1=Link([       0       0      0     pi/2 ], 'standard'); % [四个DH参数], options
L2=Link([    0         0       0.105       0], 'standard');
L3=Link([     0           0  0.09      0], 'standard');
L4=Link([     0        0   0.04     0], 'standard');

robot=SerialLink([L1,L2,L3,L4]); % 将四个连杆组成机械臂
robot.name='4DOF Robotic Arm';
robot.display();
view(3); % 解决robot.teach()和plot的索引超出报错
robot.teach();
robot.plot([0 pi/2 0 0]);

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Kinematics simulation of robotic arm

1. Positive kinematics simulation

Given the rotation angle of each joint, the robot can realize motion control.

clc;
clear;
%% 机械臂建模
% 定义各个连杆以及关节类型，默认为转动关节
%          theta      d       a      alpha
L1=Link([     0       0        0      pi/2], 'standard'); % [四个DH参数], options
L2=Link([     0       0      0.105     0], 'standard');
L3=Link([     0       0      0.09      0], 'standard');
L4=Link([     0       0      0.04      0], 'standard');
b=isrevolute(L1);
robot=SerialLink([L1,L2,L3,L4],'name','Irvingao Arm'); % 将四个连杆组成机械臂
robot.name='4DOF Robotic Arm';
robot.display();

%% 轨迹规划
% 初始值及目标值
init_ang=[0 0 0 0];
targ_ang=[0, -pi/6, -pi/5, pi/6];
step=200;

[q,qd,qdd]=jtraj(init_ang,targ_ang,step); %关节空间规划轨迹，得到机器人末端运动的[位置，速度，加速度]
T0=robot.fkine(init_ang); % 正运动学解算
Tf=robot.fkine(targ_ang);
subplot(2,4,3); i=1:4; plot(q(:,i)); title("位置"); grid on;
subplot(2,4,4); i=1:4; plot(qd(:,i)); title("速度"); grid on;
subplot(2,4,7); i=1:4; plot(qdd(:,i)); title("加速度"); grid on;

Tc=ctraj(T0,Tf,step); % 笛卡尔空间规划轨迹，得到机器人末端运动的变换矩阵
Tjtraj=transl(Tc);
subplot(2,4,8); plot2(Tjtraj, 'r');
title('p1到p2直线轨迹'); grid on;
subplot(2,4,[1,2,5,6]);
plot3(Tjtraj(:,1),Tjtraj(:,2),Tjtraj(:,3),"b"); grid on;
hold on;
view(3); % 解决robot.teach()和plot的索引超出报错
qq=robot.ikine(Tc, 'q0',[0 0 0 0], 'mask',[1 1 1 1 0 0]); % 逆解算
robot.plot(qq);

The motion effects of the robotic arm are as follows:

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2. Inverse kinematics simulation

Here we define the coordinates of the target point for our convenience, so we change the unit of a to m.

%% 机械臂建模
% 定义各个连杆以及关节类型，默认为转动关节
%          theta      d       a      alpha
L1=Link([     0       0        0      pi/2], 'standard'); % [四个DH参数], options
L2=Link([     0       0      10.5     0], 'standard');
L3=Link([     0       0      9      0], 'standard');
L4=Link([     0       0      4      0], 'standard');

b=isrevolute(L1);
robot=SerialLink([L1,L2,L3,L4],'name','Irvingao Arm'); % 将四个连杆组成机械臂
robot.name='4DOF Robotic Arm';
robot.display();
view(3);
robot.teach();
robot.plot([0 pi/2 0 0]);

Reference article: