Robotics 3 - Manipulators

From @VergilOP

Lecture 3 - Manipulators

Learning Objectives

Objectives:

1. Introduction to Manipulators
2. Manipulators and joints

Robotic Manipulators 机械臂

Benefits in repetitive operation:

• Increase volume / capacity 增加容量
• Improve quality and consistency 改进质量
• Untouched by human hand 不能人手触碰
• Reduce wastage 减少浪费
• “Up skilling” of work force 技能提升

A Return On Investment(ROI 回报率) study would be performed to quatify these factors and justify the investment in a bespoke robotics solution

joints 关节

• Different types of joints
  • Revolute Joint 旋转关节
    • 绕固定轴旋转，自由度(DOF)为1
  • Prismatic Joint 伸缩关节
    • 可以沿直线滑动，自由度(DOF)为1
  • Cylindrical Joint 圆柱关节
  • Spherical Joint 球形关节
  • Universal Joint 万向关节

Manipulators 机械臂

• Different types of manipulator:
  • Cartesian PPP 笛卡尔型
    • 三个线性关节，适合直线运动
  • Cylindrical RPP 圆柱型
    • 适合具有圆柱形工作空间的任务
  • Spherical RRP 球型
    • 适合球型工作空间
  • Articulated RRR 关节型
    • 更加灵活，常用于需要复杂运动的任务中
  • SCARA, RRP (Selective Compliance Assembly Robot Arm 选择顺应性装配机械手臂)

  

• Links

  • n moving link(s) n个活动连杆
  • 1 fixed link 固定基座
• joints
  • Revolute (1 DOF)
  • Prismatic (1 DOF)
• Position Parameters 位置参数
  • Position parameters describe the full configuration of the system

n links -> 9n parameters (3 vectors: Each vector has 3 parameters)

Generalised coordinates: A set of independent configuration parameters **Degreee of Freedom**: Number of generalised coordinates

• We need 6 DOF to have access to all space
  • 3 DOF: Position 位置
  • 3 DOF: Orientation 姿态

Revolute and prismatic joints have 1 DOF

• Generalised coordinates 广义坐标

  • A set of independent configuration parameters 独立参数

  • Each rigid body(刚体) needs 6 parameters to be described

    • 3 positions
    • 3 orientations

  • For n rigid body, we need 6n parameters

  • Constrains myst be applied:

    • Each joint has 1DOF, so 5 constrains will be introduced

    n moving links -> 6n parameters
    n joints -> 5n constrains
    n DOF
    This is for manipulator with fixed base

• End effectors configuration 末端执行器配置

  • End effector is the last rigid-body and it has all the freedom from previous links

  • A set of parameters describing position and orientation of the end effector: $(x_1, x_2, x_3, … , x_m)$ with respect to {0}

    $O_{n+1}$: is operational coordinates(task coordinates)

  • A set of $x_1, x_2, x_3, … , x_{m_o}$ of $m_o$ independent configuration parameters

  • $m_o$ is number of DOF of the end effector, max 6 DOF 末端执行器自由度最高为6

• End effector, Joint coordination 末端执行器，关节坐标

  • Joint space (configuration space) is the space that a manipulator is represented as a point.
  • (x,y) is a vector for position of end effector $\alpha$ defines orientation(angle) of end effector
  • Defines: operational coordinates -> operational space

• Redundancy 冗余

  • A manipulator is Redundant if \(n>m\) n number of DOF of the manipulator
    m number of DOF of the end effector(operational space)
    Degreee of Redundancy: n - m

冗余（Redundancy）：

• 定义：
  • 当机械臂的自由度数$n$大于末端执行器所需控制的自由度数$m$*时，称该机械臂是*冗余的。
  • 数学表达式： n>mn > mn>m
• 参数说明：
  • $n$：机械臂的自由度数量，即关节的数量。
  • $m$：末端执行器在操作空间中的自由度数量，最大为6。
• 冗余度：
  • 冗余度 = $n - m$。
  • 表示机械臂拥有的额外自由度数量。

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冗余机械臂的优势：

• 避障能力：
  • 由于有额外的自由度，机械臂可以在完成主要任务的同时避开工作空间中的障碍物。
• 灵活性：
  • 可以实现更优化的运动，例如最小化能量消耗、避免奇异点或优化机械臂的姿态。
• 多任务处理：
  • 能够同时满足多个次要任务的要求，例如保持特定的姿态或力。