매니퓰레이터

자율시스템설계 중간 정리

3-4문제

🔷URDF

• Unified Robotics Description Format

로봇 모델을 표현하기 위한 xml 파일로, link와 joint 등의 조합으로 로봇을 표현한다.

예시

<robot name="testbot">

  <!-- 로봇 본체 -->
  <link name="base_link">
    <visual>
      <geometry>
        <box size="0.5 0.4 0.1"/>
      </geometry>
      <origin xyz="0 0 0.05"/>
      <material>
        <color rgba="0.5 0.5 0.5 1.0"/>
      </material>
    </visual>
    <collision>
      <origin xyz="0 0 0.05"/>
      <geometry>
        <box size="0.5 0.4 0.1"/>
      </geometry>
    </collision>
    <inertial>
      <mass value="5.0"/>
      <origin xyz="0 0 0.05"/>
      <inertia ixx="0.1" ixy="0" ixz="0" iyy="0.1" iyz="0" izz="0.1"/>
    </inertial>
  </link>

  <!-- 바퀴 4개 -->
  <link name="wheel_front_left">
    <visual>
      <geometry>
        <cylinder radius="0.05" length="0.02"/>
      </geometry>
      <origin xyz="0 0 0" rpy="1.5708 0 0"/>
      <material>
        <color rgba="0 0 0 1"/>
      </material>
    </visual>
    <collision>
      <origin xyz="0 0 0" rpy="1.5708 0 0"/>
      <geometry>
        <cylinder radius="0.05" length="0.02"/>
      </geometry>
    </collision>
    <inertial>
      <mass value="0.5"/>
      <origin xyz="0 0 0"/>
      <inertia ixx="0.001" ixy="0.0" ixz="0.0"
               iyy="0.001" iyz="0.0"
               izz="0.001"/>
    </inertial>
  </link>

  <link name="wheel_front_right">
    <visual>
      <geometry>
        <cylinder radius="0.05" length="0.02"/>
      </geometry>
      <origin xyz="0 0 0" rpy="1.5708 0 0"/>
      <material>
        <color rgba="0 0 0 1"/>
      </material>
    </visual>
    <collision>
      <origin xyz="0 0 0" rpy="1.5708 0 0"/>
      <geometry>
        <cylinder radius="0.05" length="0.02"/>
      </geometry>
    </collision>
    <inertial>
      <mass value="0.5"/>
      <origin xyz="0 0 0"/>
      <inertia ixx="0.001" ixy="0.0" ixz="0.0"
               iyy="0.001" iyz="0.0"
               izz="0.001"/>
    </inertial>
  </link>

  <link name="wheel_back_left">
    <visual>
      <geometry>
        <cylinder radius="0.05" length="0.02"/>
      </geometry>
      <origin xyz="0 0 0" rpy="1.5708 0 0"/>
      <material>
        <color rgba="0 0 0 1"/>
      </material>
    </visual>
    <collision>
      <origin xyz="0 0 0" rpy="1.5708 0 0"/>
      <geometry>
        <cylinder radius="0.05" length="0.02"/>
      </geometry>
    </collision>
    <inertial>
      <mass value="0.5"/>
      <origin xyz="0 0 0"/>
      <inertia ixx="0.001" ixy="0.0" ixz="0.0"
               iyy="0.001" iyz="0.0"
               izz="0.001"/>
    </inertial>
  </link>

  <link name="wheel_back_right">
    <visual>
      <geometry>
        <cylinder radius="0.05" length="0.02"/>
      </geometry>
      <origin xyz="0 0 0" rpy="1.5708 0 0"/>
      <material>
        <color rgba="0 0 0 1"/>
      </material>
    </visual>
    <collision>
      <origin xyz="0 0 0" rpy="1.5708 0 0"/>
      <geometry>
        <cylinder radius="0.05" length="0.02"/>
      </geometry>
    </collision>
    <inertial>
      <mass value="0.5"/>
      <origin xyz="0 0 0"/>
      <inertia ixx="0.001" ixy="0.0" ixz="0.0"
               iyy="0.001" iyz="0.0"
               izz="0.001"/>
    </inertial>
  </link>

  <!-- 조인트 -->
  <joint name="front_left_wheel_joint" type="continuous">
    <parent link="base_link"/>
    <child link="wheel_front_left"/>
    <origin xyz="0.2  0.15 0.025" rpy="0 0 0"/>
    <axis xyz="0 1 0"/>
  </joint>

  <joint name="front_right_wheel_joint" type="continuous">
    <parent link="base_link"/>
    <child link="wheel_front_right"/>
    <origin xyz="0.2 -0.15 0.025" rpy="0 0 0"/>
    <axis xyz="0 1 0"/>
  </joint>

  <joint name="back_left_wheel_joint" type="continuous">
    <parent link="base_link"/>
    <child link="wheel_back_left"/>
    <origin xyz="-0.2  0.15 0.025" rpy="0 0 0"/>
    <axis xyz="0 1 0"/>
  </joint>

  <joint name="back_right_wheel_joint" type="continuous">
    <parent link="base_link"/>
    <child link="wheel_back_right"/>
    <origin xyz="-0.2 -0.15 0.025" rpy="0 0 0"/>
    <axis xyz="0 1 0"/>
  </joint>

  <!-- Gazebo 플러그인 -->
  <gazebo>
    <plugin name="diff_drive_controller" filename="libgazebo_ros_diff_drive.so">
      <ros>
        <namespace>/</namespace>
        <remapping>cmd_vel:=/cmd_vel</remapping>
      </ros>
      <updateRate>30.0</updateRate>
      <leftJoint>front_left_wheel_joint</leftJoint>
      <rightJoint>front_right_wheel_joint</rightJoint>
      <wheelSeparation>0.3</wheelSeparation>
      <wheelDiameter>0.1</wheelDiameter>
      <wheelAcceleration>1.0</wheelAcceleration>
      <wheelTorque>5.0</wheelTorque>
      <robotBaseFrame>base_link</robotBaseFrame>
    </plugin>
  </gazebo>

</robot>

구성: link, joint, visual, collision, inertial, transmission 등 

Link

• collision 충돌 정의를 위한 형상 구성
• joint로 관절 연결
• visual(외관)
  • geometry, material, origin, 
• inertial: 질량 설정 

Joint

• 두 링크(parent, child)를 이어주는 역할
• 직선, 회전 등등 joint 정의 가능
• DoF: 움직이는 축... 수?

정의 요소

• <origin> 이전 joint에 대한 상대 좌표로 origin 지정?
• <axis> 관절의 축 표현, 어떤 방향으로 움직일지 지정
• <limit> limit 관절의 최대 힘, 구동범위, 최대 속도 지정

 

꼭나오는 문제 Robot Kinematics

🔷Forward Kinematics

주관심사: end effector의 위치(좌표)
task 공간에서 end-effector의 pose를 찾는 것
관절의 각도로부터 좌표를 얻음

$$(x,y)=f(\theta_{1},\theta_{2})$$

rotation matrix + translation matrix (4 x 4 matrix)
rotation과 translation 각 3DoF 

방법 

1. 회전 matrix 찾기(각 축 단위 벡터가 어떻게 됐는지)
2. 단위벡터이기에 정규화 필요(길이 1로 맞추기)
3. 평행이동 시키기 (translation matrix 추가)

여러 관절에의 적용

base부터 $T_{1}, T_{2}, T_{3} \cdots$ 이면 $T_{3}T_{2}T_{1}$

rotation은 순서가 매우 중요함

🔷Inverse Kinematics

주관심사: 관절의 각도
end effector 혹은 관절의 좌표로부터 각도를 얻음

각 관절까지 ?

T1T2T3