This website houses notes from my studies at the University of Liverpool. If you see any errors or issues, please do open an issue on this site's GitHub.
This is where we model the world as a 2D or 3D array. We can then store the probability that we are in any one location in this array. Piecewise Constant Representation Markov localisation utilised a probability distribution across all states: Represented as $\text{Bel}(x_t)$ for each $x_t$. We can model...
This is also known as local path planning. The goal is to avoid obstacles without the use of a map. This is implemented as a subsumption behaviour, second to the main task. Bug Algorithms These are simple obstacle avoidance algorithms that assume: The robo has only local knowledge and the...
Gain-Offset Correction This determines the contrast in an image. We may have to re-scale images in a video to ensure all images in a sequence have similar brightness and contrast. This correction fixes two issues of image sensors: Gain - A multiplicative error in the output. Offset - An additive...
Types of Navigation Global Navigation This is about deciding how to get from some start point to a goal point: The robot plans in some sense. This plan consists of a series of waypoints. Local Navigation This is about obstacle avoidance: We can use sensors to ensure that we don’t...
Common knowledge relates to multiple agents knowing the same thing about each-other: People drive on the left because we know that other people know to drive on the left. Definition of Common Knowledge We can use $E$ to denote that “everybody knows”: $E\phi$ means $K_a\phi\wedge K_b\phi\wedge\ldots$ Fixed Point Definition A...
Features correspond to artefacts in the environment.: These may be obstacles that we need to avoid. Can also be beacons that aid in localisation. There are several formas a feature might take but it will depend on: What sensors the robot has. What features can be extracted. Map Once we...
Filtering Filtering is a neighbourhood operation: The output pixel is a function of neighbourhood pixels. Linear Filtering The output pixel is a linear combination of input pixels. We use a mask that contains weights to be assigned to each pixel: The operation is applies to every pixel by sliding the...
This is the process of using landmarks to reduce the uncertainty of a robot’s location. We start with some distribution across all states: This includes heading as well as position. This is typically uniform if the initial robot position is unknown. This means that we don’t know where we are....
We can also use the following models to localise a robot: Map Matching (sonar, laser) Generate small, local maps from sensor data and match local maps against a global model. Scan Matching (laser) Map is represented by scan endpoints, match scan into this map. Beacons (sonar, laser, vision) Extract features...
The correspondence of: Reflexivity and truthfulness Transitivity and positive introspection Euclidity and negative introspection This proof system is known as $S5$. Truthfulness Knowledge is truthful, therefore: \[\square\phi\implies\phi\] This axiom corresponds to reflexivity. This means that there is an arrow from each world to itself (for each agent). Positive Introspection Generally...