Graduate Seminar in Robotics


Overview

The home work assignments will deal with a simplified 3 degree-of-freedom robot. The different tasks will span from the kinematic modeling (HW1) to  trajectory generation, modeling and simulation of the robot dynamics and  finally the control design for the robot performing a typical  pick-and-place operation as indicated in the figure below.

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Home Work Assignment 1—Kinematics

Due: May 17, 2006

Problem 1.1 : Provide kinematic modeling  of the  3DOF robotic pick-and-place operation  indicated in the figure below. The modeling should comprise kinematics using two different coordinate representations—e.g., modeling via the Denavit-Hartenberg-parameterization, homogeneous coordinates, twists, screws, quaternions, exponential coordinates.  You need to write functions for the forward and inverse kinematics for the manipulator. Your solution to be presented should include graphical and algebraic representations


Problem 1.2:
This part is related to a new proposed calibration method, which might show up later in the course. We are using the same 3 DOF robot as in Problem 1.1. Assume that you have a stationary laser pointer mounted in the work cell and a 2D-sensor attached to the robot TCP (tool center point). From the sensor we get (x,y)-coordinates corresponding to where the laser beam intersects the sensor plane.

(a)
Make a simulation model of the sensor (virtual sensor);"input parameters": laser pointer (location and orientation in world coordinate frame), mounting of sensor (sensor frame with respect to robot TCP) and robot joint angles (use the robot kinematics from Problem1.1) with output (x,y)-coordinates in sensor frame.
(b) 
Make a  Matlab/Simulink-simulation of the feedback connection from the sensor to move the robot so that the laser beam  intersection will move to intersect at the origin of the sensor (from some initial position). You may allow a large sensor area. 


Assume that  the robot joints are decoupled and individually position controlled with the transfer functions G(s)=1/(0.1s+1) from angle reference to angle. Discuss how to use the Jacobian mapping and how the limited number of degrees-of-freedom affect and restrict the task solution.


Home Work Assignment 2—Kinematic Calibration


Utgående från 3 DOF-modellen för roboten i hemuppgiften:

Vi vill undersöka en ny föreslagen kalibreringsmetod. (Här kommer vi inte att skatta några parametrar utan enbart titta på de kinematiska sambanden utifrån antaganden om att alla parametrar är kända).

Antag att man har en laserpekare fast placerad i rummet riktad mot en
tvådimensionell sensor placerad på robothanden. Från sensorn får man ut XY-koordinater var laserstrålen träffar sensorn.

Inför en lämplig placeing av laserpekare/stråle samt någon transformation från robotens TCP (Tool Center Point) till sensorns baskoordinatsystem.

Gör en simuleringsmodell av sensorn:
inparametrar:
    laserpekarens placering och riktning
    robotens tre ledvinklar
    transf. robot TCP ->
utsignal: (x,y) (sensor koordinater)


Gör en enkel Matlab/Simulink-simulering av återkoppling från sensorn för att flytta roboten så att laserpunkten centreras på sensorn (från given    initialposition av roboten).

Antag att varje led på roboten, oberoende av varandra, kan anses ha överföringsfunktionen  1/(0.1s+1)   från vinkel_referens till vinkel.


Home Work Assignment 3—Robot Dynamics and Control

Provide modeling and simulation of the robotic pick-and-place operation  indicated in the figure above. The modeling should comprise
The simulation should represent the pick-and-place operation using any simulation environment you might want such as