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  • Advanced Robotic - MAE 263D - Introduction

    Instructor: Jacob Rosen

    Office: Engineering IV Rm. 37-146

    Lab: Bionics Lab - Engineering IV, Rm. 18-111

    E-mail: rosen@seas.ucla.edu

    Office Hrs: Wed 2:00-4:00

    TA: Sepehr Ghassemi

    TA Room: ENG IV 43-147

    Email: sepehrghassemi@ucla.edu

    Office Hrs: Tuesdays 1:30 to 3:30

    Phone: 301 385 8947

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Advanced Robotic - MAE 263D - Introduction

    Summary: 263D. Advanced Robotics. (4) Lecture, four hours; outside study, eight hours.

    Recommended preparation: courses 155, 171A, 263C.

    Motion planning and control of articulated dynamic systems: nonlinear joint control,

    experiments in joint control and multiaxis coordination, multibody dynamics, trajectory

    planning, motion optimization, dynamic performance and manipulator design, kinematic

    redundancies, motion planning of manipulators in space, obstacle avoidance. Letter grading.

    Recommended preparation: courses 155, 171A, 263A, 263C

    Assignments & Grading:

    HW Assignments 20%

    Paper Review 5%

    Midterm Exam (Take Home) 30%

    Final Exam (Take Home) 40%

    Participation 5%

    Class Web Site: http://bionics.seas.ucla.edu/education/classes_index.html

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

    Advanced Robotic - MAE 263D - Introduction

    List of Topics

    Introduction

    Transformations & DH Parameters Review

    Forward Kinematics Serial Manipulators - 6 DOF Robot Review

    Inverse Kinematics Serial Manipulators - 6 DOF Robot Review

    Jacobian Velocity Propagations Method

    Jacobian Force Propagation Method

    Jacobian Time derivative of end effector position & orientation

    Dynamics Inertia Matrix

    Dynamics Euler-Newton Method

    Dynamics Lagrange Method

    Midterm Exam Take Home

    Performance Criteria Manipulability - Optimization (Spherical Robot)

    Forward Kinematics Parallel Manipulators

    Inverse Kinematics Parallel Manipulators

    Redundancy

    Control Feedback Control Introduction

    Control - Feedback Position Control

    Control Feedback Force Control

    Teleoperation

    Haptics

    Final Exam Take Home

  • Description of Positioning Task

    Problem

    Given: The manipulator geometrical

    parameters

    Specify: The position and orientation of

    manipulator

    Solution

    Coordinate system or Frames are attached to the manipulator

    and objects in the environment

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Forward Kinematics

    Problem

    Given: Joint angles and links geometry

    Compute: Position and orientation of the end

    effector relative to the base frame

    Solution

    Kinematic Equations - Linear Transformation (4x4 matrix) which is

    a function of the joint positions (angles & displacements) and

    specifies the EE configuration in the base frame.

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Inverse Kinematics

    Problem

    Given: Position and orientation of the end

    effector relative to the base frame

    Compute: All possible sets of joint angles and

    links geometry which could be

    used to attain the given position and

    orientation of the end effetor

    Solution

    There are three approaches for the solution:

    Analytical Approach - Kinematic Equations - Linear

    Transformation (4x4 matrix) which is a function of the joint

    positions (angles & displacements) and specifies the EE

    configuration in the base frame. This linear transformation

    defines 12 non linear equations A subset of these equations

    are used for obtaining the invers kinematics

    Geometric Approach Projecting the arm configurations on

    specific planes and using geometrical consideration to obtain

    the invers kinematics

    Hybrid Approach - Synthesizing the analytical and the

    geometrical approaches

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Velocity Transformation

    Problem

    Given: Joint angles and velocities and links geometry along

    with the transformation matrixes between the joints

    Compute: The Jacobian matrix that maps between the joint

    velocities in the joint space to the end effector

    velocities in the Cartesian space or the end effector

    space

    Solution There are two approaches to the solution:

    Velocity Propagation - A velocity propagation approach is

    taken in which velocities are propagated stating form the

    stationary base all the way to the end effector. The Jacobian

    is then extracted from the velocities of the end effector as a

    function of the joint velocities.

    Time derivative of the end effector position and

    ordinations The time derivative of the explicit positional

    and orientation is taken given the forward kinematics. The

    Jacobian is then extracted from the velocities of the end

    effector as a function of the joint velocities.

    Notes:

    Spatial Description The matrix is a function of the joint angle.

    Singularities - At certain points, called singularities, this

    mapping is not inevitable and the Jacobian Matrix J loosing its

    rank and therefore this mathematical expression is no longer

    valid.

    )(1 J

    )(J

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Force Transformation

    Given: Joint angles, links geometry, transformation matrixes

    between the joints, along with the external loads

    (forces and moments) typically applied on the end

    effector

    Compute: The transpose Jacobian matrix that maps between the

    external loads (forces and moments) typically applied

    at the end effector space joint torques at the

    joint space

    Solution

    Force/Moment Propagation - A force/moment propagation

    approach is taken in which forces and moments are

    propagated stating form the end effector where they can be

    measured by a F/T sensor attached between the gripper and

    the arm all the way to the base of the arm. The Jacobian

    transposed is then extracted from the joint torques as a

    function of the force/moment applied on the end effector

    Note

    Static or quasi static conditions

    fTJ

    f

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Forward Dynamics

    Problem

    Given: Joint torques and links geometry,

    mass, inertia, friction

    Compute: Angular acceleration of the links

    (solve differential equations)

    Solution

    Dynamic Equations - Newton-Euler method or

    Lagrangian Dynamics

    ),()(),()( FGVM

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Inverse Dynamics

    Problem

    Given: Angular acceleration, velocity and

    angels of the links in addition to the

    links geometry, mass, inertia, friction

    Compute: Joint torques

    Solution

    Dynamic Equations - Newton-Euler method or

    Lagrangian Dynamics

    ),()(),()( FGVM

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Trajectory Generation

    Problem

    Given: Manipulator geometry

    Compute: The trajectory of each joint such that

    the end efferctor move in space

    from point A to Point B

    Solution

    Third order (or higher) polynomial spline

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Position Control

    Problem

    Given: Joint angles (sensor readings) links

    geometry, mass, inertia, friction

    Compute: Joint torques to achieve an end

    effector trajectory

    Solution

    Control Algorithm (PID - Feedback loop, Feed

    forward dynamic control)

    Instructor: Jacob Rosen

    Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  • Force Control

    Problem

    Given: Joint torque or end effector

    Force/torque interaction (sensor

    r