Localization, Mapping, and SLAM using Python

When it comes to autonomous robots, the process of localization uses data from sensors to determine their behaviours and responses. Sensors in the system provide data inputs to the robot regarding the environment, following which it implements an algorithm to determine its upcoming behaviours. It is important to understand how vehicles and robots navigate their environment through localization.

This week will cover

• Methods of performing localization (With the example of the self-driving car)
• Different sensors used for localization (LiDAR, RADAR, GNSS, INS, wheel encoders)
• Sensing models for sensors used in practice that increase the presence of uncertain results in imperfect models
• Downloading Python and Jupyter notebook
• NumPy and matplotlib

As events that autonomous robots may encounter are not always predicted, the probability theory is considered to work through uncertainties in the environment. By applying algorithms in probability theory, all possible outcomes can be calculated. It is important to understand the basic concepts of probability theory, and the different functions and algorithms employed in determining possible outcomes.

This week will cover

• Error sources: limitations of sensing - deterministic vs. non-deterministic
• Augmented odometry model with error
• Deviations because of error additions
• Error propagation in IMU
• Concepts such as random variable, random vectors, density function, joint density, marginal density, conditional independence
• Probability Density Function (PDF), gaussian, multivariate gaussian
• Variance and covariance
• Random variables in robotics state estimation
• Probability distribution

Probabilistic modelling takes the effect of random events into consideration to predict the occurrence of possible future outcomes. In robotics, Bayesian filtering is used for determining the possibilities of multiple perceptions to let the robot understand its relative position and orientation. It is important to understand how probabilistic modelling and Bayesian filtering work in the context of robotics.

This week will cover

• Probabilistic generative laws
• Definitions for state and environment
• Concepts of belief, posterior
• Probabilistic models for perception and state transition
• Bayesian filter, Markov assumption
• Kalman filters and Particle filters: Introduction

The Kalman filter works to reduce the overall error covariance and uncertainty by combining all the uncertainties in terms of the robot’s state and sensor measurements. It is essential in localization, trajectory tracking, identifying parameters, positioning, and the control of robots. It is important to understand how the Kalman filter works in the automation of robots.

This week will cover

• Kalman filter and its derivation from Bayes filter
• Kalman Gain (with an example)
• Kalman filter assumptions and optimality

The extended Kalman filter is applied for non-linear systems, while the Kalman filter is used for linear systems. By using the extended variant of the Kalman filter, limitations from using the Kalman filter alone can be overcome. The unscented Kalman filter is a non-linear Kalman filter. It is important to understand the different Kalman filters and when they are used.

This week will cover

• Limitations of Kalman filter
• Variants that overcome the limitations
• Jacobians in Extended Kalman filter

Particle filter localization, also called Monte Carlo Localization, is an algorithm implemented for localization. This algorithm predicts the position of the robot as it works its way through the environment by using a series of samples/particles. It is important to understand the implications of particle filter localization in the automation of robots.

This week will cover

• Map-based localization
• Derivation of particle filter from the Bayes filter
• PF handling non-linearity
• Properties of particle filter

Multi-sensor fusion is the means by which data from multiple sensors or sources are integrated to reduce the uncertainty of information from individual sources. This allows for accurate estimations of an autonomous robot’s location, position, and orientation. There are different methods and algorithms used in multi-sensor fusion, such as Kalman filtering and extended Kalman filtering. It is important to understand the algorithms used to combine data from multiple sensors.

This week will cover

• Loosely coupled and tightly coupled techniques in Extended Kalman filtering
• Extension of state vector to accept multiple inputs

Autonomous robots and vehicles develop maps of their surroundings through mapping. In this process, sensors are used to gather information about the surrounding environment, and create a map with it. Mapping is a concept central to the development of autonomous vehicles and robots, making it imperative for learners to understand the process of map generation.

This week will cover

• Map generation process from the perspective of self-driving car

SLAM (Simultaneous localization and mapping) is implemented for autonomous robots and vehicles to develop a map and localize the subject on that map. It programs the autonomous subject to navigate the environment on its own through localization and mapping. While localization uses input data from sensors to determine behaviours, mapping uses information from the sensors to develop a map for the subject to understand its positioning and orientation.

This week will cover

• Explanation of how SLAM problems resemble chicken and egg proble
• Explanation of simplest SLAM implementation - EFF, SLAM, and loop closure

Graph SLAM takes information regarding the locations of the autonomous robot as initial and relative motion constraints to provide the future probabilities of its movement. It is important to understand how graph-based SLAM works in the development of a robot’s position and orientation.

This week will cover

• Difference between offline SLAM and online SLAM
• Motivate graph based modeling of SLAM problem 
• Explanation of mathematical formulation of Graph SLAM
• Explanation of how Graph SLAM can be used offline to generate a map of environment

FastSLAM is an algorithm that combines extended Kalman filters and particle filters to recursively predict full posterior distribution across the landmark locations and robot pose. It is important to understand how the FastSLAM algorithm works, and the mathematical derivations involved.

This week will cover 

• Particle filter based SLAM
• Mathematical derivation and comparison with three SLAM techniques

 SLAM is used in mobile robotics to build and update the map of the environment that the robot has not explored by using sensors that get inputs from the surroundings. There are also other applications of SLAM. It is important to understand SLAM in the context of the Robotic Operating System (ROS).

This week will cover

• Explanation of factor graph and pose graph formulations of SLAM problem
• Explanation of how camera is used as sensing source in SLAM
• Example of factor graph implementation on drone fitted with downward facing camera
• ROS - what it is and important concepts (Publisher, subscriber, topics, message)