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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

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