What are some problems with control of robot actions?

1
What are some problems with control of robot
actions?

• Joint play, compounded through N joints.
• Accelerating masses produce vibration, elastic
  deformations in links.
• Torques, stresses transmitted depending on end
  actuator loads.
• Feedback loop creates instabilities.
• Delay between sensing and reaction.

2
Lets look at a simple robot.

• Coordinates to describe position.
• rectangular (x,y,z)
• cylindrical (r,?,z)
• spherical (r,?,?)
•  
• Frames to describe position.
• World coordinate frame
• Object frame
• Want a way to transform from one coordinate
  system to another.
• x to x to x

3
Transform from world frame to body frame.
Hold some object. Examine at it as you transform
it.
Simple rotation Rotation translation
4
Any transformation is a combination of
translation rotation.
Yaw Pitch Role
5
Mathematics of Transformations

• General coordinate transformation from x to x
  is x Bx p , where B is a rotation matrix and
  p is a translation vector
• More conveniently, one can create an augmented
  matrix
•   which allows the above equation to be
  expressed as x A x.
• Coordinate transformations of multilink systems
  are represented as
• x0 A01 A12A23. . .A(n-1)(n)xn

6
Back to our robot problem.

• Two-segment arm with arm lengths L1 L2, and
  stepper -motor control of angles ?1 and ?2.
• End actuator (tip) problem must follow a line.
• Does this problem have a specific solution?
• Try it using two pencils.
• How do you throw a dart?

7
How do you control the rotation motors?

• Trajectory of end actuator
• Getting from point A to B may have multiple
  solutions.
• Sometimes there is no closed-form solution.
• Programming for coordinated motion of each link.
• Do it most efficiently.
• The tip traverses its range at constant height y,
  or with no more variation than ?y.
• How do you control ?1 and ?2 ?

8
There is no closed-form solution to this problem.

• Must use approximations, and accept some minor
  variations in y.
• Moving the arm tip through its maximum range of x
  might have to be accomplished through a sequence
  of program steps.
• Possible approaches
• Program the rates of change of ?1 and ?2 for y
  const. for initial values of ?1 and ?2 . When
  arm tip exceeds ?y, reprogram for new values of
  ?1 and ?2.
• Program the rates of change of ?1 and ?2 at the
  initial point and at some other point for y
  const. Take the average of these two rates, and
  hope that ?y is not exceeded. If it is exceeded,
  reprogram for a shorter distance. Continue
  program segments until the arm tip has traversed
  its range.
• The rate of change of ?1 and ?2 can be changed in
  a programming segment, i.e., the rates of change
  need not be uniform over time. This programming
  strategy incorporates approaches 1) and 2).
  Start with rates of change for the initial values
  of ?1 and ?2 , then add an acceleration component
  so that y const. will also be satisfied at a
  distant position.

9
The derivative shows change of position.

• The position of arm tip is
• x L1 (cos ?1 cos ?2)
• y L1 (sin ?1 sin ?2)
• Arm tip moves by changing ?1 and ?2 as a function
  of time.
• Therefore
• So, as ?1 and ?2 are changed, x and y are
  affected.
• To satisfy y constant, we must have
• So the rates at which ?1 and ?2 are changed
  depend on the values of ?1 and ?2.

10
How do you measures of performance of robot?

• Speed and acceleration
• Resolution
• Working volume
• Accuracy
• Cost

11
The Future of Robotics.

• Robots that can learn.
• Robots with artificial intelligence.
• Robots that make other robots.

12
Will robots take over the world?

• Which decisions can the machine make without
  human supervision?
• May machine-intelligent systems make mistakes (at
  the same level as humans)?
• May intelligent systems gamble when uncertain (as
  humans do)?
• Can (or Should) intelligent systems exhibit
  "personality?
• Can (or Should) intelligent systems express
  "emotion?
• How much information should the machine display
  to the human operator?

HAL - 2001 Space Odyssey
13
Play Robot Constructor

• http//www.channel4.com/science/microsites/R/robot
  s/constructor.html

14
A 2-D binary robot segment

• Example of a 2D robotic link having three
  solenoids to determine geometry.
• All members are linked by pin joints.
• Members A,B,C have two statesin, outcontrolled
  by in-line solenoids.
• The geometry can be represented in terms of three
  binary digits corresponding to the states of ABC,
  e.g., 010 represents A,C in, B out.
• Links can be chained together and controlled by
  sets of three bit codes.

15
How are robots different from automated machinery?

• Machinery is designed to carry out a specific
  task.
• Bottling machine
• Dishwasher
• Paint sprayer
• Robots are designed to carry out a variety of
  tasks
• Pick and place arms
• Mobile robots
• Computer Numerical Control machines
• The lines are becoming blurred.