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Robot Path Planning CONTENTS 1. Introduction 2. Interpolation Robot Path Planning 1. Introduction The user specifies goal points. There is an issue about the intermediate points.

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Presentation Transcript
robot path planning
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 -> 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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Robot Path Planning
  • 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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Robot Path Planning

(6)

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Robot Path Planning
  • 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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Robot Path Planning

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

Acceleration

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Figure 2

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Robot Path Planning

Cubic polynomials for a path with via points

In this case

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Robot Path Planning

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

Robot Path Planning

Linear function with parabolic blends

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Robot Path Planning

Change slope

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