Robot Path Planning

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Robot Path Planning

• CONTENTS
• 1. Introduction
• 2. Interpolation

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Robot Path Planning

• 1. Introduction
• The user specifies goal points. There is an issue
  about the intermediate points.
• Goal points are converted to joint points -gt
  joint scheme, so the issue becomes to determine
  the intermediate angles given two angles as well
  as their time stamps (see Figure 1.
• Criterion of determining these intermediate
  angles is smoothness of eth motion.
• 2. Joint space schemes

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• Given the initial and end goal points, there are
  different ways to interpolate, see Figure 1.

Figure 1
Rotary motor
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• Cubic polynomials
• There are at least four conditions to constrain
  the interpolation
• (1)
• (2)
• (3)
• (4)

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• These four constraints can be satisfied by a
  polynomial of at least third degree. A cubic has
  the form
• (5)

We can get the velocity and acceleration
expression for the above equation (5). We can
determine the coefficients as follows
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(6)
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• Example A single-link robot with a rotary joint
  is motionless at

It is desired to move the joint in a smooth
manner to
in 3 seconds. Find the coefficients of a cubic
which
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• accomplishes this motion and brings the
  manipulator to rest at the goal.
• Solution can be found by plugging into the
  equations for the coefficients, we can find

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Figure 2 shows the position Velocity Acceleratio
n
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Figure 2
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• Cubic polynomials for a path with via points
• In this case

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• Cubic polynomials for a path with via points

In this case, the condition about velocity has
been changed see the previous slides The four
coefficients can be found (to be filled in the
classroom
(7)
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Figure 3
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Figure 4
Constant Velocity Improvement

• Linear function with parabolic blends

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Change slope