Robot Localization (Episode 104) | The Robot Doctor

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

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.

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.6

Derive the equation of a circle of given center and radius using the Pythagorean Theorem.

UP:MA19.GDA.6

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)

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD
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