Hobby Robots (Expensive Toys)
According to the NPD Group, a market research firm, sales of robotic and interactive playmates in the United States were $284 million in the 12 months ended in October, 2007, up from $213 million in the previous 12 months. On
Mathematics of Coordinate Transformation
Origin of frame 2 is translated and the axes rotated relative to frame 1.
Mathematical Representations:
Robot arm links rotate and/or translate with respect to a reference coordinate system. By considering a bodyat
Position and Orientation of End Effector
Homogeneous Transformation Matrices Example: Puma 560
Homogeneous Transformation 4 x 4 Matrix Accounts for body Rotation Translation
Columns Specify the directions of the bodys coordinate axes Translation Vector
Ca
Linear transformation which provides the geometric relationship between two coordinate systems: Nx Ny Nz 0 Ox Oy Oz 0 Ax Ay Az 0 Px Py Pz 1
Initial coordinate system X Y Z Final coordinate system N O A
T=
Nx - Cosine of the angle between N and X Ny - Cosi
SOLUTION EVALUATION
To avoid exciting manipulators at their resonant frequency, want
Fsolution
> 10 Fresonance
where Fsolution is the frequency at which the solution is computed. Each solution results in a change in acceleration Impulse loading For serv
VELOCITY AND PATH CONTROL
VELOCITY CONTROL We not only wish to control position and orientation of the hand, but also its velocity
This requires the specication of a velocity vector - 3 linear & 3 rotational motions for the hand which must be related to t
Computation of the Jacobian
Innitesimal rotations obey the rules of vector addition, while nite rotations do not.
Example 2: Consider the two D.O.F. planar arm. 1) 2) Resolve the end point velocity to joint velocities Find singular congurations
Example 3:
Static Force Analysis: Another Role for the Jacobian
Static Force Analysis: Balance of forces and moments Consider forces and moments acting on link i. Arm links are stationary.
Special Case
Exerted on the end effector by an external object
Equivalent Joi
Manipulator Dynamics: Two Degrees-of-freedom
Manipulator Dynamics Objective: Calculate the torques necessary to overcome dynamic effects Consider 2 dimensional example
Based on Lagrangian approach The Lagrangian
Generalized coordinate Torque or force
For
Task Primitives and Programming
Task descriptions Task: Insert pin in block
In order to manipulate objects in space, must consider: OBJ: Object coord frame w.r.t. O F: Coord frame attached to feature dened w.r.t. OBJ G: Posn & Orientation of gripper tip (
Determining Path Trajectories: Interpolation and Spline Functions
The Manipulator Path: Motion between positions Consider series of positions: Posn. 1: (T6)1 x Tool1 = Coord1 x Pos1 Posn. 2: (T6)2 x Tool2 = Coord2 x Pos2 Posn. 3: (T6)3 x Tool3 = Coord3 x
Quintic No Clipping
Case: 3 axes, no clipping
Estimated total time is 3.651 sec Actual total time is 3.656 sec Error in total time is -0.1%
Note: Graphs for other two axes are similar
Cubic No Clipping
Desired Motion: (x,y) = (40, 40)
t = 0.047 sec
Estima
Force Based Control
Denitions
Force = Force and torque
Position= Position and angle
Motion= Translation and rotation
A force feedback algorithm: Takes in * Force and motion commands * Sensed forces and positions Puts out * Motion commands
Two Main Types o
Manipulator Peripherals: The Remote Center Compliance
Remote Center Compliance (RCC)
What is compliance? Producing the proper jiggle to correct for misalignments
Passive compliance:
Compliant stationary xtures
Robot grippers with remote center complianc
Wired Magazine, Issue 14.01- January 2006 The 50 Best Robots Ever By Robert Capps
Quoting from the article,
They're exploring the deep sea and distant planets. They're saving lives in the operating room and on the battlefield. They're transforming fact
Quadruped Robots: BigDog (Boston Dynamics Inc.) http:/www.bostondynamics.com/content/sec.php?section=robotics
Quadruped robot that walks, runs, and climbs on rough terrain and carries heavy loads. Powered by a gasoline engine that drives a hydraulic actu
Predator General Atomics Aeronautical Systems San Diego http:/www.uav.com/home/index.html Wingspan: 48.7 ft. Payload: 450 lb. Range: <400 nautical mi. Ceiling: <25,000 ft. Cost: $4.5 million (2003) was $25 million (1999)
Others: Global Hawk from Northrop
ROBOTICS COURSE NOTES
1981, 1991, 2001, 2009 Max Donath (Incorporates material from many sources) DEPARTMENT OF MECHANICAL ENGINEERING
UNIVERSITY OF MINNESOTA
111 CHURCH ST. S.E. MINNEAPOLIS, MN 55455
Topics: 1. Robotics: An Introduction 2. Manipulator sp