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Robot Localization (Episode 104) | The Robot Doctor

  Classroom Resource Information  

Title:

 Robot Localization (Episode 104) | The Robot Doctor

URL:

 https://aptv.pbslearningmedia.org/resource/episode-104-robot-localization-video/the-robot-doctor/

Content Source:

 PBS
Type: Audio/Video

Overview:

Explore how a robot keeps track of its position as it moves, and how to update that position with math using ranges to known landmarks, in this 14-minute episode. The goal of this video series is to teach the basics of Robotics: the what, why, and how—with examples—and to provide take-home problems to solve.

How do robots determine their location? In this lesson we will explore a three-step process to find the position by 1) finding at least 3 nearby landmarks with known positions 2) determine the robot's range to each landmark using onboard sensors and 3) calculate the intersection point of the 3 range circles to find the robot's position.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Geometry with Data Analysis
6. Derive the equation of a circle of given center and radius using the Pythagorean Theorem.

a. Given the endpoints of the diameter of a circle, use the midpoint formula to find its center and then use the Pythagorean Theorem to find its equation.

b. Derive the distance formula from the Pythagorean Theorem.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given the center (h,k) and radius (r) of a circle,
  • Explain and justify that every point on the circle is a combination of a horizontal and vertical shift from the center with a length equal to the radius.
  • Create a right triangle from the center of a circle to a general point on the circle, and show that the legs of the right triangle are the absolute values of x-h and y-k, and the hypotenuse is r, then apply Pythagorean theorem to show that r2 = (x - h)2 + (y - k)2.


Given the endpoint of the diameter of the circle,
  • Find the center of the circle using the midpoint formula, and write the equation of the circle in standard form using the Pythagorean Theorem.
  • Analyze distance in the coordinate plane and use distance to relate points and lines.
  • Calculate the distance between two points using the Pythagorean Theorem.
  • Generalize methods for determining the distance between two coordinate points.
  • Derive the distance formula using a right triangle and the Pythagorean Theorem.
Teacher Vocabulary:
  • Pythagorean theorem
  • Radius
  • Translation
Knowledge:
Students know:
  • Key features of a circle.
  • The Pythagorean Theorem, Midpoint Formula, Distance Formula.
Skills:
Students are able to:
  • Create a right triangle in a circle using the horizontal and vertical shifts from the center as the legs and the radius of the circle as the hypotenuse.
  • Write the equation of the circle in standard form when given the endpoints of the diameter of a circle, using the midpoint formula to find the circle's center, and then use the Pythagorean Theorem to find the equation of the circle.
  • Find the distance between two points when using the Pythagorean Theorem and use that process to create the Distance Formula.
Understanding:
Students understand that:
  • Circles represent a fixed distance in all directions in a plane from a given point, and a right triangle may be created to show the relationship of the horizontal and vertical shift to the distance,
  • Circles written in standard form are useful for recognizing the center and radius of a circle.
  • The distance formula and Pythagorean Theorem can both be used to find length measurements of segments (or sides of a geometric figure)
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
GEO.6.1: Define radius, diameter, midpoint and Pythagorean Theorem.
GEO.6.2: Apply the Pythagorean Theorem to find the distance from the center to a point on the circle.
GEO.6.3: Derive the equation of a circle given the center and the radius.
GEO.6.4: Use the midpoint formula to find the center of a circle based on the endpoints of the diameter.

Prior Knowledge Skills:
  • Identify parts of a circle.
  • Recall how to find circumference of a circle.
  • Recall the meaning of a radius and diameter.
  • Identify all types of angles.
  • Recognize the attributes of a circle.
  • Identify and label parts of a circle.
  • Define diameter, radius, circumference, area of a circle, and formula.
Alabama Alternate Achievement Standards
AAS Standard:
M.G.AAS.9.6 Using real-world models (Ex. Pizza or Pie) on a coordinate grid, determine the length of the radius.

Tags: distance, localization, mapping, range, robot
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

This resource contains the following resources:

 Episode 4 Robot Localization       
The Robot Doctor Episode 4 Activity Guide
The Robot Doctor Localization Map
The Robot Doctor Note to Teachers
  This resource provided by:  
Author: Kristy Lacks
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