Lecture 9 : Localisation

What is the difference between guidance and navigation?

Guidance = directing motion ("where am I going?"); Navigation = ascertaining position and planning/following a route ("where am I?" and "how do I get there?")

What are the two broad categories of robot localisation strategies?

1. External positioning (uses infrastructure/signals from outside the robot); 2. On-board positioning (uses sensors carried by the robot itself)

What does exteroceptive sensing mean?

Using external cues (e.g. GPS, WiFi beacons) to determine position — as opposed to relying solely on internal sensors

Limitation of exteroceptive sensing → why on-board positioning is needed

External systems may lack accuracy, require infrastructure that doesn't exist in new/disaster areas, or have security vulnerabilities — so robots must track position without external cues

Name 5 localisation technologies from the lecture

IMU, LIDAR, Computer Vision (e.g. QR codes), Ultra-Wide-Band (UWB), GPS / Radio frequency (WiFi/Bluetooth)

IMU → what it measures and key limitation

Accelerometer + gyroscope; fast, strong anti-interference — but errors accumulate over time (drift)

LIDAR advantages for localisation

2D or 3D information; works in dark environments; no modification of the environment required

UWB → key properties

Uses narrow-band pulses; high speed; high time-resolution — one of the most accurate indoor positioning technologies

VLC (Visible Light Communication) → advantage and limitation

Low cost, no interference with radio communications — but requires line-of-sight

GPS → how does it work?

Receiver measures signal travel time from ≥3 satellites; calculates distance via trilateration; network of ≥24 satellites at ~20,200 km altitude

How many satellites are needed for 2D vs 3D GPS positioning?

2D (latitude + longitude) = 3 satellites; 3D (latitude + longitude + altitude) = 4+ satellites (also needed to sync receiver clock)

GPS accuracy and key limitation

~2m at best outdoors; worse in urban environments; does not work indoors; can be power hungry

What is differential GPS?

Using a fixed reference station to correct atmospheric errors and improve GPS accuracy

Indoor external positioning method 1: WiFi/Bluetooth beacons — methods used

'In-range', signal drop-off (attenuation), or triangulation (like GPS) — accuracy is limited

Indoor external positioning method 2: iGPS

Uses rotating laser transmitters and sensors on the robot to measure angle/timing; enables high-accuracy indoor positioning

What is odometry?

Using data from motion sensors (e.g. wheel encoders, IMU) to estimate change in position (pose) over time, relative to a starting location

Etymology of "odometry"

From Greek: 'odos' = route + 'metron' = measure

What sensors does the TurtleBot3-Waffle use for odometry?

IMU (gyroscope, accelerometer, compass) + wheel encoders

What is dead reckoning?

Deducing position by estimating speed (relative to a stationary object or dead object thrown overboard) plus a bearing — no external reference needed

What is path integration?

The method animals use for dead reckoning — continuously updating estimated position by integrating distance and direction of travel over time

Dead reckoning path integration formula

x(t) = x(t-1) + Δx; y(t) = y(t-1) + Δy; where Δx = d·cos(θ), Δy = d·sin(θ)

In path integration, what do d and θ represent?

d = distance travelled in one step; θ = heading/orientation angle

Dead reckoning example: robot at (0,0) moves 2m East (θ=0). What is the new position?

Δx = 2·cos(0) = 2; Δy = 2·sin(0) = 0 → new position = (2, 0)

Why do errors accumulate in dead reckoning?

Each step adds small errors (ε) in both distance (εd) and orientation (εθ); these compound over many steps

Error formula for dead reckoning with noise

Δx = (d + εd)·sin(θ + εθ); Δy = (d + εd)·cos(θ + εθ); errors from wheel slip and sensor interference accumulate

Two main causes of odometry error

1. Wheel slip (gives false distance reading); 2. Sensor interference (e.g. magnetic interference causing noisy compass/gyro readings)

Dead reckoning error scale across applications

Ranges from millimetres (CNC machining) to kilometres (UAVs) depending on the system and duration of travel

Odometry Euclidean accumulated error formula

e = √((x_meas − x_true)² + (y_meas − y_true)²)

Odometry worked example: at waypoint 1, perfect reading d=3m, θ=−90°. What are Δx and Δy?

Δx = 3·cos(−90°) = 0; Δy = 3·sin(−90°) = −3.0 → position (0, −3)

Odometry worked example: noisy reading d=3.1m, θ=−90°. What is the error at waypoint 1?

Δx = 0, Δy = 3.1·sin(−90°) = −3.1 → position (0, −3.1); error = √(0² + 0.1²) = 0.1 m

Odometry worked example: noisy reading d=3m, θ=−98°. What is the error at waypoint 1?

Δx = 3·cos(−98°) = −0.42; Δy = 3·sin(−98°) = −2.97 → error = √(0.42² + 0.03²) ≈ 0.42 m

What was the accumulated Euclidean error after 4 waypoints with noisy distance readings?

0.585 m (distance noise only) vs 0.253 m (orientation noise only) — both worsen over more steps

What is optical flow?

The pattern of apparent motion of objects in a visual scene caused by camera/robot movement — enables 'direct perception' of movement

What is the 'point of expansion' in optical flow?

The point in the image from which all motion vectors radiate outwards — indicates the direction the camera/robot is heading

What is visual odometry?

Using optical flow (pixel velocities) and the Image Jacobian to estimate camera/robot velocity and track position

Image Jacobian — what does it relate?

Pixel velocity [u̇, v̇] to camera velocities (translational: cx, cy, cz) and rotational velocities (ωx, ωy, ωz)

Full Image Jacobian equation (structure)

[u̇; v̇] = J(u,v,Z) · [cx; cy; cz; ωx; ωy; ωz]; J contains terms involving focal length f̂, pixel coords u,v, and depth Z

For a UAV at fixed height, what simplification applies to the Image Jacobian?

cz = 0 (no vertical camera motion), simplifying the Jacobian to a 2×4 matrix

Simplified visual odometry equations for drone (no rotation)

cx = Z(Juω − u̇) / f̂; cy = Z(Jvω − v̇) / f̂; where ω clusters angular velocity terms

Visual odometry worked example: pixel at [u,v]=[0,0], Z=100cm, f=10mm (100px/mm), camera moves left at 5cm/s. What is [u̇, v̇]?

u̇ = 50 px/s; v̇ = 0 px/s (camera moving left shifts image right → positive u̇)

Visual odometry worked example: given u̇=50, what camera velocity is recovered?

cx = −Z·u̇/f̂ = −1·50/1000 = −0.05 m/s; cy = 0 — correctly recovers the original leftward motion

How does a gyro help visual odometry?

Angular velocities (ω) measured by gyroscope are substituted into visual odometry equations to isolate translational camera velocity

Animal dead reckoning: which animal is used as an example and why?

The Cataglyphis desert ant — navigates km-long foraging paths and returns directly home using path integration (step-counting + polarised-light compass)

Comparison: GPS vs WiFi indoor accuracy

GPS: ~2m best case; WiFi: ~2.31m — both are relatively poor for precise indoor robot tasks

Most accurate indoor positioning technologies (from review table)

RFID: <0.01m; UWB: <0.1m; LIDAR: <0.025m — best accuracy with tradeoffs in cost/complexity

IMU indoor accuracy and main disadvantage

~0.2m accuracy; low cost; but suffers from accumulated error (drift) — needs fusion with other sensors

LIDAR advantages vs disadvantages for indoor positioning

Advantages: <0.025m accuracy, no env. modification, strong stability; Disadvantages: high hardware and computational cost, affected by glass objects

Computer vision indoor accuracy and disadvantages

~0.09m; no env. modification needed; but affected by lighting, high algorithmic requirements, weak feature environments

What sensor fusion approach improves outdoor odometry?

Combining LPS (local positioning), odometer, inclinometer, gyroscope, anemometer, and thermistor through a sensor fusion module → drives motion controller

Outdoor high-accuracy odometry example: robotic golf mower accuracy

Position accuracy: 3.1 cm RMS; orientation accuracy: 0.23° RMS (using LPS + sensor fusion)

Modern commercial outdoor robot example: Luba Mini 2 AWD mower — key localisation features

Tri-camera AI vision + NetRTK → centimetre-precise operation; 4WD; AI obstacle avoidance (>2.5×2.5cm)

What is NetRTK and why is it relevant?

Network Real-Time Kinematic — a form of differential GPS using network corrections; enables cm-level outdoor positioning

What is the exam trap regarding GPS and triangulation?

GPS uses trilateration (distance from multiple satellites), not triangulation (angles). The lecture uses the word 'triangulation' loosely — understand the distinction.

Exam trap: does more satellites always mean better GPS?

More satellites improve accuracy and allow 3D positioning — 3 = 2D only; 4+ = 3D + clock sync. But atmospheric conditions still limit precision.

Exam trap: can odometry alone reliably localise a robot over long distances?

No — errors accumulate with each step (wheel slip, sensor noise), making long-distance dead reckoning increasingly inaccurate without corrections

Why is path integration described as the animal equivalent of dead reckoning?

Animals like ants continuously integrate distance and direction signals (step counts + polarised light) to maintain a home vector — same mathematical principle as robot path integration

What does the worked odometry example demonstrate about orientation error vs distance error?

Orientation error (0.253m over 4 waypoints) can be less damaging than distance error (0.585m) — but both accumulate; in practice both exist simultaneously

Summary: what topics does Lecture 9 cover?

Localisation strategies; external positioning (GPS, indoor); on-board positioning; odometry; dead reckoning; path integration; optical flow; visual odometry; accuracy outdoors/indoors