Range sensors: ultrasonic, infrared, time-of-flight and lidar

Before a robot can avoid an obstacle, build a map or pick up a box, it needs to know how far away things are. Range sensors answer that question directly, and they are the backbone of mobile robot navigation. They all work on one of two principles: measuring how long an emitted pulse takes to come back (time of flight), or measuring the geometry of a reflected beam (triangulation). This lesson covers the main families, from the $3 ultrasonic module on a student robot to the spinning and solid-state lidars on autonomous vehicles, and develops the calculations needed to choose and place them. Lesson 5 covers cameras and radar, which can also measure range.

Time of flight: the basic idea

An active range sensor emits a pulse of sound or light, and the echo returns after a round trip. The range is half the round-trip distance:

The wave speed v sets everything else. Sound travels at about 343 m/s in air at 20 °C, so echoes take milliseconds and can be timed with simple electronics. Light travels at 299,792 km/s, so a 1 cm range resolution requires timing to about 67 picoseconds, which needs specialized detectors and electronics. That difference explains why ultrasonic sensors are cheap and slow, and lidars expensive and fast.

Ultrasonic sensors

An ultrasonic rangefinder sends a short burst at around 40 kHz from a piezoelectric transducer and listens for the echo. They are inexpensive, work regardless of color or transparency (they see glass doors that fool optical sensors), and are widely used for parking sensors, bin-level measurement and low-speed obstacle detection. Their limitations come from the physics of sound. The beam is wide, typically a cone of 15° to 30°, so the sensor reports the nearest object anywhere in the cone, not what lies straight ahead. Smooth surfaces at a glancing angle reflect the sound away like a mirror, so a wall seen obliquely can be invisible (specular reflection). Soft materials such as foam and fabric absorb sound. Several sensors firing at once hear each other's echoes (crosstalk), so they must be scheduled. And the speed of sound depends on temperature, rising by about 0.6 m/s per degree Celsius.

The wide beam also sets a lateral uncertainty. At range r with half-angle \( \alpha \), the echo could come from anywhere in a patch of width \( 2r\tan\alpha \). At 2 m with a 15° half-angle, that patch is about 1.07 m wide, which is why occupancy-grid mapping (ROB-340) models ultrasonic readings as arcs rather than points.

Infrared triangulation and optical time-of-flight sensors

Small infrared range sensors come in two kinds. Triangulation sensors project an infrared spot and measure where its reflection lands on a position-sensitive detector a short distance away; as the target gets closer, the spot moves across the detector. The relationship is nonlinear, accuracy falls off quickly with distance, and most such sensors have a minimum range below which the readings fold back. They are compact and cheap but have largely been replaced by single-point optical time-of-flight (ToF) chips.

An optical ToF chip contains a tiny infrared laser (a VCSEL) and an array of single-photon avalanche diodes (SPADs) that time individual returning photons. Statistical histograms of many photon arrival times give range with millimeter-to-centimeter precision out to several meters, in a package a few millimeters across. Some versions report a small grid of zones, such as 8 × 8, giving a coarse depth image. They are now common on robot vacuum cleaners, drones (for altitude hold over the ground) and grippers. Their main weaknesses are strong sunlight, which floods the detector with background photons and reduces range, and very dark or shiny targets.

Lidar

Lidar (light detection and ranging) is time of flight with a narrow laser beam and a scanning mechanism, building up hundreds of thousands of range measurements per second. Two-dimensional scanners sweep a single beam in a plane and are standard on indoor mobile robots and automated guided vehicles; three-dimensional lidars add vertical coverage with multiple beams, typically 16 to 128 channels, or with a scanning pattern, and produce point clouds of the surroundings. Most lidars use near-infrared light at 905 nm, where silicon detectors are cheap, or at 1550 nm, where eye-safety limits permit much higher pulse energies and so longer range, at the cost of more expensive detectors.

Lidars are classified by how they scan. Mechanical spinning lidars rotate the whole emitter and detector assembly to give a 360° view. Solid-state and semi-solid-state lidars steer the beam with MEMS mirrors, optical phased arrays or flash illumination of the whole scene at once; they have fewer moving parts and lower cost but usually a limited field of view, such as 120° × 25°, so a vehicle needs several. Some newer lidars use frequency-modulated continuous wave (FMCW) detection, which measures range from a frequency shift and also gives the radial velocity of each point directly through the Doppler effect.

Angular resolution and point density

A lidar's usefulness for detecting small or distant objects depends on how far apart its beams are when they reach the target. Adjacent beams separated by angle \( \Delta\theta \) are spaced about \( r\,\Delta\theta \) apart at range r (with \( \Delta\theta \) in radians). The number of points an object returns is roughly its size divided by that spacing in each direction.

import math
def points_on_target(r, width, height, dh_deg, dv_deg):
    sh = r * math.radians(dh_deg); sv = r * math.radians(dv_deg)
    return max(1, round(width / sh)) * max(0, round(height / sv)), sh, sv
for r in (10, 30, 60, 120):
    n, sh, sv = points_on_target(r, 0.5, 1.7, 0.2, 1.0)
    print(f"range {r:4d} m  spacing {sh:5.2f} m x {sv:5.2f} m  ~{n:3d} points on a 0.5 x 1.7 m target")

range   10 m  spacing  0.03 m x  0.17 m  ~140 points on a 0.5 x 1.7 m target
range   30 m  spacing  0.10 m x  0.52 m  ~ 15 points on a 0.5 x 1.7 m target
range   60 m  spacing  0.21 m x  1.05 m  ~  4 points on a 0.5 x 1.7 m target
range  120 m  spacing  0.42 m x  2.09 m  ~  1 points on a 0.5 x 1.7 m target

Data volume follows from the same numbers. A 64-channel lidar at 0.2° horizontal resolution and 10 Hz produces \( 64 \times 1800 \times 10 = 1.15 \) million points per second; at around 16 bytes per point that is about 18 MB/s, a figure to keep in mind when sizing a robot's computer and network (ROB-110 discussed bandwidth on ROS 2 topics).

Things that fool range sensors

Every range sensor has characteristic failure modes, and robust robots are designed around them. Optical sensors see through glass or receive a reflection from it, and may report the wall behind a glass door or a phantom robot in a mirror. Black, wet or very shiny surfaces return little light. Rain, fog, snow, dust and steam scatter laser light and produce clutter points near the sensor; Canadian and northern US winters are a serious test for outdoor lidars, and spray from other vehicles can blind them. Multipath, in which the signal bounces off two surfaces before returning, produces points that appear behind real surfaces. Sunlight raises the noise floor of every optical sensor. And sensors of the same type can interfere: two robots with identical lidars or ultrasonic modules may detect each other's pulses, which manufacturers counter with coding and randomized timing.

No single range sensor covers every case. A typical warehouse robot combines a safety-rated 2-D lidar near the floor, a 3-D camera for overhanging shelves and a few ultrasonic or optical ToF sensors for glass and close-range blind spots. Choosing that combination for a specific robot is part of the capstone in lesson 12.

Laser safety

Every lidar and ToF sensor contains a laser, and laser products are classified by the accessible emission they can produce. Class 1 is safe under all reasonably foreseeable conditions, and almost all robot lidars are designed to be Class 1 so that people can look into them; Class 1M is safe unless viewed through magnifying optics; higher classes (2, 3R, 3B and 4) need labels, controls and, for the highest classes, trained operators. The classification scheme comes from the international standard IEC 60825-1.

In the United States, laser products are regulated by the FDA's Center for Devices and Radiological Health under 21 CFR 1040.10 and 1040.11. Under FDA Laser Notice No. 56 (2019), manufacturers may instead conform to IEC 60825-1 Ed. 3 for classification and labeling, and most robot lidars are certified this way. Manufacturers of laser products must file reports with the FDA. If you integrate a lidar into a robot, keep the manufacturer's classification valid: do not open the housing, change the optics or run it outside its specified conditions, and follow OSHA guidance and ANSI Z136.1 where workers use higher-class lasers.