Lecture

Jacobian - Explicit Form

This module presents the explicit form of the Jacobian matrix, crucial for robotic motion analysis. Key topics discussed include:

  • Jacobian Jv and Jw components
  • Jacobian in different frames, including frame {0}
  • Case studies using the Scheinman Arm
  • Understanding kinematic singularities and their implications

This knowledge is vital for designing effective control systems for robots.


Course Lectures
  • Course Overview
    Oussama Khatib

    This module provides an overview of the course, including the historical context of robotics and its various applications across industries. You will also learn about related courses offered at Stanford and the overall structure of the course including:

    • Lecture and reading schedules
    • Manipulator kinematics and dynamics
    • Manipulator control and force control
    • Advanced robotics topics
  • Spatial Descriptions
    Oussama Khatib

    This module explores spatial descriptions essential for robotics, including:

    • Generalized and operational coordinates
    • Rotation matrices and their applications
    • Homogeneous transformations
    • Examples illustrating translations and operators

    Understanding these concepts is crucial for modeling robots in various environments.

  • This module dives into the interpretations of homogeneous transforms in robotics. Key topics include:

    • Compound transformations
    • Spatial descriptions and their significance
    • Various rotation representations including Euler angles
    • Examples demonstrating singularities and Euler parameters

    These foundational concepts enable students to understand complex robot movements.

  • Manipulator Kinematics
    Oussama Khatib

    This module focuses on manipulator kinematics, which is essential for understanding how robotic arms operate. Key components covered include:

    • Link descriptions and connections
    • Denavit-Hartenberg parameters and their applications
    • Examples illustrating the DH table and forward kinematics

    Students will learn to analyze and design robotic systems effectively.

  • This module provides a summary of frame attachment concepts in manipulator design. Students will engage with:

    • An example involving the RPRR manipulator
    • The Stanford Scheinman Arm and its DH table
    • Forward kinematics and T-matrices for the Scheinman Arm
    • Final results and their implications in robotics

    This knowledge is critical for understanding how robots maintain their position and orientation.

  • Instantaneous Kinematics
    Oussama Khatib

    This module introduces instantaneous kinematics, focusing on the Jacobian matrix and its applications. Key points include:

    • Direct differentiation for calculating Jacobians
    • Examples using the Scheinman Arm to illustrate concepts
    • Position representations and the cross product operator
    • Velocity propagation and its significance in control

    Students will gain insights into how robots achieve instantaneous motion.

  • Jacobian - Explicit Form
    Oussama Khatib

    This module presents the explicit form of the Jacobian matrix, crucial for robotic motion analysis. Key topics discussed include:

    • Jacobian Jv and Jw components
    • Jacobian in different frames, including frame {0}
    • Case studies using the Scheinman Arm
    • Understanding kinematic singularities and their implications

    This knowledge is vital for designing effective control systems for robots.

  • Scheinman Arm - Demo
    Oussama Khatib

    This module features a demonstration of the Scheinman Arm, showcasing practical applications of kinematics. Key elements include:

    • Understanding kinematic singularities through examples
    • Puma simulation to illustrate control concepts
    • Resolved rate motion control and its applications
    • Exploring angular and linear velocities/forces, along with their duality
    • Virtual work principles in robotic systems

    The practical insights gained here are crucial for real-world robot applications.

  • This module features a guest lecture by Gregory Hager, focusing on the intersection of robotics and computer vision. Key topics include:

    • Overview of computer vision technologies
    • Computational stereo and stereo-based reconstruction methods
    • Disparity maps and SIFT feature selection techniques
    • Challenges in tracking and face stabilization

    This lecture provides insights into how vision systems enhance robotic capabilities.

  • This module features a guest lecture by Krasimir Kolarov, focusing on trajectory generation in robotic systems. Key concepts discussed include:

    • Basic problems associated with trajectory generation
    • Cartesian planning and cubic polynomial methods
    • Finding via point velocities and linear interpolation
    • Higher order polynomial techniques
    • Trajectory planning in the presence of obstacles

    This lecture highlights the intricacies of motion planning for effective robotic operation.

  • Joint Space Dynamics
    Oussama Khatib

    This module covers joint space dynamics, crucial for understanding the forces and motions involved in robotic systems. Key topics include:

    • Newton-Euler algorithm for dynamic analysis
    • Understanding inertia tensors with examples
    • Newton-Euler equations and their applications
    • Lagrange equations as an alternative approach
    • Equations of motion in robotics

    Students will gain a comprehensive understanding of dynamic behavior in robots.

  • Lagrange Equations
    Oussama Khatib

    This module focuses on Lagrange equations, a fundamental aspect of robotic dynamics. Key topics include:

    • Formulation of equations of motion
    • Understanding kinetic energy in robotic systems
    • Explicit forms of motion equations
    • Centrifugal and Coriolis forces and their significance
    • Christoffel symbols and mass matrix formulations

    This knowledge is essential for advanced control and dynamic modeling in robotics.

  • Control - Overview
    Oussama Khatib

    This module provides an overview of control systems in robotics, focusing on different types of control techniques. Key discussions include:

    • Joint space control and its applications
    • Resolved motion rate control strategies
    • Understanding natural and dissipative systems
    • Examples highlighting passive system stability

    Students will learn how to design effective control systems for robotic applications.

  • PD Control
    Oussama Khatib

    This module focuses on PD control techniques, essential for effective motion control in robotics. Key topics include:

    • Control partitioning for improved performance
    • Motion control strategies and disturbance rejection
    • Understanding steady-state error and PID control
    • Effective inertia concepts in control systems

    Students will learn how to implement PD control for efficient robotic motion.

  • Manipulator Control
    Oussama Khatib

    This module examines manipulator control techniques, building on previous knowledge to enhance task-oriented control. Key areas of focus include:

    • PD control stability and its implications
    • Task-oriented control strategies
    • Equations of motion for task-oriented applications
    • Operational space dynamics and their significance
    • Nonlinear dynamic decoupling for improved tracking

    Students will develop skills necessary for advanced control in robotic applications.

  • Compliance
    Oussama Khatib

    This module addresses compliance and force control in robotics, essential for safe and effective robot interactions. Key topics include:

    • Understanding compliance in robotic systems
    • Dynamics and task description for force control
    • A historical perspective on robotics
    • Stanford's human-safe robots and their designs
    • Multi-contact whole-body control considerations

    Students will learn how to implement safe and compliant control strategies in robotics.