AI Consulting and Training Club, Bahria Town Lahore

Category: Courses

  • Robot Dynamics and Control – Robotics Theory

    Robot Dynamics and Control: A 4-Month Self-Study Course

    Syllabus

    Course Description

    This comprehensive 4-month self-study course, “Robot Dynamics and Control,” is designed for motivated beginners and intermediate learners eager to delve into the fundamental principles governing robot motion and manipulation. From understanding how robots move in space to controlling their actions with precision, this course bridges the gap between theoretical concepts and practical applications. We will explore the mathematics of robot kinematics and dynamics, delve into various control strategies, and equip you with the knowledge to analyze, design, and implement effective control systems for a wide range of robotic platforms. Through engaging lessons, clear explanations, and hands-on programming examples, you will build a solid foundation in this critical field, preparing you for advanced studies or practical robotics development.

    Primary Learning Objectives

    Upon successful completion of this course, you will be able to:

    • Understand and apply the principles of forward and inverse kinematics for robotic manipulators.
    • Formulate and analyze the dynamic equations of motion for robotic systems.
    • Implement various control strategies, including PID control, for trajectory tracking and force control.
    • Develop basic robot simulations and visualize kinematic and dynamic behaviors.
    • Analyze the stability and performance of robot control systems.
    • Apply theoretical knowledge to practical robotic control problems using programming examples.

    Necessary Materials

    • Computer: A desktop or laptop capable of running simulation software.
    • Software:
      • Python 3 (Anaconda distribution recommended)
      • SymPy (for symbolic mathematics)
      • NumPy and SciPy (for numerical operations)
      • Matplotlib (for plotting and visualization)
      • PyBullet or CoppeliaSim (for robot simulation)
    • Textbook (Recommended, not mandatory): Robot Modeling and Control by Mark W. Spong, Seth Hutchinson, and M. Vidyasagar.
    • Internet Access: For accessing online resources, documentation, and supplementary materials.

    Course Content

    Week 1-2: Foundations of Robot Kinematics

    Lesson 1: Introduction to Robotics and Coordinate Frames
    • Learning Objectives:
      • Define what a robot is and differentiate between different types of robots.
      • Understand the necessity of coordinate frames in robotics.
      • Learn to represent points and vectors in different coordinate frames.
    • Key Vocabulary:
      • Robot: An autonomous or semi-autonomous machine designed to perform tasks.
      • Manipulator: A robotic arm or system designed for manipulation.
      • End-Effector: The tool or gripper attached to the end of a robotic arm.
      • Joints: Connections between rigid bodies (links) in a robot, allowing relative motion.
      • Degrees of Freedom (DoF): The number of independent parameters that define the configuration of a mechanical system.
      • Coordinate Frame: A system used to define the position and orientation of objects in space.
    • Content:Robotics is a fascinating field that blends mechanics, electronics, and computer science to create intelligent machines. Before we dive into how robots move, we need a common language to describe their position and orientation in space. This is where coordinate frames come in. Imagine describing the location of a book on a shelf. You might say “third shelf, five books from the left.” This is essentially using a local coordinate frame. In robotics, we use Cartesian coordinate systems (X, Y, Z axes) to precisely define locations.

      We’ll start by understanding how to represent a point in 2D and 3D space using coordinates. Then, we’ll introduce the concept of multiple coordinate frames: a fixed “world” frame and frames attached to each part of the robot (links and joints). The ability to describe how one frame relates to another is crucial for understanding robot motion. We’ll touch upon basic vector operations and how they translate between different coordinate systems.

    • Hands-on Example:
      • Write a Python script to define 2D and 3D points.
      • Represent a vector in a given coordinate frame.
      • Practice transforming coordinates of a point from one 2D frame to another using simple translations and rotations (e.g., if frame B is shifted by (5,2) relative to frame A, and a point is at (1,1) in frame B, what are its coordinates in frame A?).
    Lesson 2: Homogeneous Transformation Matrices
    • Learning Objectives:
      • Understand the concept of homogeneous transformation matrices.
      • Perform basic translations and rotations using transformation matrices.
      • Combine multiple transformations to represent complex movements.
    • Key Vocabulary:
      • Rotation Matrix: A matrix that describes the orientation of one coordinate frame with respect to another.
      • Translation Vector: A vector that describes the position of the origin of one coordinate frame with respect to another.
      • Homogeneous Transformation Matrix: A 4×4 matrix that combines rotation and translation into a single representation.
      • Pose: The position and orientation of a rigid body in space.
    • Content:While representing rotations and translations separately is possible, it quickly becomes cumbersome for multi-link robots. Homogeneous transformation matrices provide an elegant solution by combining both rotation and translation into a single 4×4 matrix. This allows us to perform sequences of transformations (e.g., rotating then translating, or translating then rotating) through simple matrix multiplication.

      We will learn how to construct these matrices for pure translations along an axis and pure rotations about an axis. The real power of homogeneous transformations comes when we chain them together. If you know the transformation from frame A to B, and from B to C, you can find the transformation from A to C by multiplying the individual transformation matrices. This forms the backbone of forward kinematics.

    • Hands-on Example:
      • Implement Python functions to generate 2D and 3D homogeneous transformation matrices for given rotations (e.g., around X, Y, Z axes) and translations.
      • Given two coordinate frames and a point in the second frame, calculate the point’s coordinates in the first frame using a single homogeneous transformation.
      • Chain two transformation matrices to find the combined transformation and verify with a simple example (e.g., rotate by 90 degrees around Z, then translate by (1,0,0)).

    Week 3-4: Forward Kinematics

    Lesson 3: Denavit-Hartenberg (DH) Parameters
    • Learning Objectives:
      • Understand the concept and significance of Denavit-Hartenberg (DH) parameters.
      • Learn the rules for assigning coordinate frames to robot links using DH parameters.
      • Extract DH parameters from simple robot arm configurations.
    • Key Vocabulary:
      • DH Parameters: A standardized set of four parameters (a, α, d, θ) that describe the geometric relationship between two adjacent links in a robotic arm.
      • Link: A rigid body in a robotic manipulator.
      • Joint Axis: The axis around which a joint rotates or along which it translates.
    • Content:To systematically describe the kinematics of a multi-link robot, we need a standardized approach. Denavit-Hartenberg (DH) parameters provide just that. They offer a convention for assigning coordinate frames to each link of a robot manipulator, ensuring a unique and unambiguous description of its geometry. There are four parameters for each link-joint pair: a (link length), alpha (link twist), d (joint offset), and theta (joint angle).

      We will go through the step-by-step rules for assigning these frames and extracting the DH parameters from a given robot arm schematic. This can be a bit tricky initially, but with practice, it becomes intuitive. The key is to consistently follow the established rules to ensure correctness.

    • Hands-on Example:
      • Given simple 2R (two revolute joints) or 3R planar manipulators, practice assigning DH frames and deriving the corresponding DH parameters.
      • Verify your understanding by drawing the frames and parameters on paper for a simple robot.
    Lesson 4: Forward Kinematics Equation Derivation
    • Learning Objectives:
      • Derive the forward kinematics equations for a given robot arm using DH parameters.
      • Implement forward kinematics calculations in Python.
      • Understand the relationship between joint variables and end-effector pose.
    • Key Vocabulary:
      • Forward Kinematics: The process of calculating the end-effector’s pose (position and orientation) given the joint variables (angles or displacements).
      • Joint Variables: The independent parameters that describe the configuration of a robot (e.g., joint angles for revolute joints, joint displacements for prismatic joints).
    • Content:Once we have the DH parameters for each link, we can derive the forward kinematics equations. Each pair of adjacent links and their associated DH parameters allow us to define a homogeneous transformation matrix between their respective coordinate frames. By multiplying these individual transformation matrices in sequence, we can find the overall