Robot localization is the process of estimating a robot’s pose within a known map.
A robot’s pose consists of three variables:
x: position along the horizontal axis.
y: position along the vertical axis.
θ: orientation, or the direction the robot is facing.
We can represent its pose as:
x=xyθ
Because sensors and robot movements are noisy, the robot usually cannot know its exact pose immediately. Instead, it uses a probabilistic algorithm to estimate its pose and update that estimate as new sensor measurements arrive.
2. Four common localization algorithms
1. Extended Kalman Filter (EKF) Localization
Estimates the robot's pose using a Gaussian probability distribution. It handles nonlinear motion and measurement models through linear approximations.
2. Markov Localization
Maintains a probability distribution over possible robot poses and updates it using motion and sensor information.
3. Grid Localization
Divides the map into discrete cells and tracks the probability that the robot occupies each possible position and orientation. It is commonly associated with histogram filters.
4. Monte Carlo Localization (MCL)
Uses a collection of weighted particles, each representing a possible robot pose. Particles are updated and resampled as the robot receives new measurements.
The lesson focuses on EKF localization and Monte Carlo localization.
3. The three localization problems
1. Position Tracking (Local Localization)
The initial pose is known.
The robot estimates its pose as it moves.
Uncertainty typically remains concentrated around its estimated location, although it can grow over time.
2. Global Localization
The initial pose is unknown.
The robot must determine where it is on the map.
It may initially consider many possible locations and orientations.
3. The Kidnapped Robot Problem
The robot can suddenly be moved to a different location without being informed.
Its previous pose estimate may become incorrect.
It must recover by identifying its new pose from sensor measurements and the map.
4. EKF vs. MCL: the key difference
Feature
EKF Localization
Monte Carlo Localization
Representation
Gaussian distribution
Set of particles
Pose hypotheses
Usually one central estimate with covariance
Many possible poses
Best suited for
Approximately unimodal uncertainty
Complex or multimodal uncertainty
Main limitation
Can struggle with nonlinearities and multiple distinct pose hypotheses
Requires enough particles and computational resources
Both algorithms combine information about robot movement with sensor measurements to improve the pose estimate.