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LiDAR

Time of Flight (TOF)

Lidar (Light Detection and Ranging) sensors operate by rotating and emitting laser beams often referred to as lidar-rays to scan and map their surrounding environment. This rotational movement allows the sensor to cover a wide Field of View (FoV), capturing detailed spatial information essential for applications like autonomous robotics, navigation, and environmental mapping. Lidar operates on these basic principles:

  1. Rays of Light are dispersed from the Lidar Sensor.
  2. The Rays of Light will reflect off objects returning to the lidar, distance measured with the Time of Flight equation.

Time Of Flight Equation:

\(d = \frac{ct}{2}\)
  • d is the distance calculated.
  • c is the speed of light constant, representing the velocity of light.

  • t is the time the lidar ray took to return.

  • 0.5 appears in the equation representing the intial and returning trajcetory of the laser.

Lidar properties
Basic LiDAR principles

While the distance is important, we must also consider something called the seperation angle. As the angle between our lidar rays will play a role in determining how accurate our readings will be.

Angle Separation:

\( \theta = \frac{\text{Field of View (FOV)}}{\text{Number of scans per rotation}} \)

Angle Seperation is the angle between fired lidar-rays. It is a critical parameter that influences the sensor's ability to accurately detect and distinguish between objects within its field of view (FoV).

Calculate the Angle Seperation for 2D Lidar:

  • Field of View (FOV): 270°
  • Number of Scans per Rotation: 1080

Answer Below

\( \theta = \frac{275^\circ}{1080} = 0.25^\circ \text{ per scan} \)

Interpretation: Each laser pulse is emitted 25° apart from the previous one. This high angular resolution allows the Lidar to detect objects with fine angular distinctions, enhancing the detail and accuracy.

An analogy we can use to describe the angle seperation of a lidar is blurryness of an image. The Image below displays what our readings would look if the angle of seperation was large (blurry image) vs small angles of seperation (clear image)

Low vs High Angle Separation
Higher angle of separation leads to decreased resolution

Understanding the Scan Angle (𝜃):

The Scan Angle 𝜃' represents the specific angle at which a particular laser pulse is emitted relative to a reference direction (usually the Lidar's forward-facing direction)

Warning: The Scan Angle 𝜃' is different from the Angle Seperation 𝜃 previously discussed.

Calculating Endpoint Coordinates: Each laser pulse travels outward from the Lidar sensor, reflects off an object, and returns to the sensor. The distance d measured is used to calculate the position of the object in polar coordinates (r, 𝜃) and then converted to Cartesian coordinates (x, y) for mapping purposes. The conversion from polar to Cartesian coordinates is given by:

Cartesian Coordinate Conversion:

\( x = d \times \cos(\theta) \)
\( y = d \times \sin(\theta) \)

Where:

  • d Is the measured distance between the object and the Lidar.
  • 𝜃 The angle at which the lidar-ray was emitted.
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