/robotics_notes

Notes on robotics, mainly (arm) manipulation robotics: kinematics, dynamics, trajectory generation, control.

Notes on Robotics

Notes on robotics, mainly (arm) manipulation robotics: kinematics, dynamics, trajectory generation, control. I made these notes as a possible script for my students.

Some of the used resources:

The notes were done using Notability for iPad.

Each topic has its own PDF:

  1. Spatial Descriptions and Transformation Matrices for Robotic Manipulators (Videos 1, 2, 3; Craig 2)

    • Position vector
    • Orientation/Rotation matrix
    • Frames = Coordinate Systems
    • Transformations
    • Rotation Matrices
    • Compositions of transformations
    • Inverse Transformation matrix
    • Example: Compositions

  2. Rotation: Euler Angles & Co. (Videos 4, 5; Craig 2)

    • Fixed Angle representation
    • Euler Angle representation (moving)
    • Comparing rotation representations
    • Example: Find Euler angles
    • Angle-axis representation
    • Unit Quaternions = Euler parameters
    • Rodrigues' Formula
    • Exponential Representation of Rotations

  3. Direct (Forward) Kinematics (Videos 6, 7, 8, 9; Craig 3)

    • Links and joints
    • Conventions for fixing frames to joints
    • Denavit-Hartenberg (DH) representation for describing direct kinematics
    • DH Parameters example
    • Frames with standard names
    • DH parameters of the URe-s

  4. Inverse Kinematics (Craig 4)

    • Solvability issues
    • Example with a planar manipulator
    • Repeatability and Accuracy

  5. Jacobians (Videos 10, 11, 12, 13; Craig 5)

    • Linear and angular velocities: time-varying position and orientation
    • Velocity of Rigid Bodies
    • Notes on the Angular Velocity
    • Velocity Propagation from Link to Link
    • The Jacobian Matrix
    • The Frame of the Jacobian
    • Singularities
    • Calculating the Jacobian
      • Partial differentiation method
      • Velocity propagation method
    • Static Forces in Manipulators
    • Computation of forces and torques necessary at the joints to support a force at the endeffector using the Jacobian
    • Cartesian Transformation of Velocities and STatic Forces

  6. Dynamics (Craig 6)

    • Acceleration of a Rigid Body
    • Mass Distribution
    • Newton-Euler Equations of Motion
    • Iterative Newton-Euler Dynamic Formulation: Obtain Joint Torques Necessary for Joint Motion (Inverse Dynamics)
    • An Example of Closed-Form Dynamic Equations
    • The Structure of a Manipulator's Dynamic Equations
      • The State-Space Equation
      • The Configuration-Space Equation
    • Lagrangian Formulation for Manipulator Dynamics
    • Manipulator Dynamics in Cartesian Space
    • Inclusion of Other Effects
    • Dynamics Simulation: Forward Dynamics

  7. Trajectory Generation (Craig 7)

    • Path Generation with Joint Schemes
      • Cubic Polynomials of Joint Values with Via Points
      • Linear Functions with Parabolic Blends
    • Path Generation with Cartesian Schemes
      • Cartesian Straight-Line Motion
      • Problems with Cartesian Paths
    • Path Generation at Run-Time

  8. Mechanism Design (Craig 8)

    • Basing the Design on Task Requirements
    • Kinematic Configuration
    • Quantitative Measures of Workspace Attributes
    • Actuation Schemes
    • Stiffness and Deflections
    • Actuators and Sensors

  9. Linear control of manipulators (Craig 9)

    • Feedback and Closed-Loop Control
    • Second-Order Linear Systems
      • Laplace
      • Solving the second-order linear system
    • Control of Second-Order Systems
      • Position Regulation Control
    • Control-Law Partitioning
    • Trajectory-Following Control
    • Disturbance Rejection
      • Steady State Error
      • PID Control
    • Continuous vs. Discrete Time Control
    • Modeling and Control of a Single Joint
    • Architecture of an Industrial-Robot Controller

  10. Nonlinear control of manipulators (Craig 10, TBD.)

  11. Force control of manipulators (Craig 11, TBD.)

Mikel Sagardia, 2021.
No guarantees.