# Blog

## What is PRM path planning? ## What is PRM in robotics?

A probabilistic roadmap (PRM) is a network graph of possible paths in a given map based on free and occupied spaces. The mobileRobotPRM object randomly generates nodes and creates connections between these nodes based on the PRM algorithm parameters.

## Is PRM probabilistically complete?

Given certain relatively weak conditions on the shape of the free space, PRM is provably probabilistically complete, meaning that as the number of sampled points increases without bound, the probability that the algorithm will not find a path if one exists approaches zero.

## What is RRT algorithm?

A rapidly exploring random tree (RRT) is an algorithm designed to efficiently search nonconvex, high-dimensional spaces by randomly building a space-filling tree.

## HOW DOES A * search work?

Description. A* is an informed search algorithm, or a best-first search, meaning that it is formulated in terms of weighted graphs: starting from a specific starting node of a graph, it aims to find a path to the given goal node having the smallest cost (least distance travelled, shortest time, etc.).  ### What is configuration space topology?

In mathematics, a configuration space is a construction closely related to state spaces or phase spaces in physics. ... In mathematics, they are used to describe assignments of a collection of points to positions in a topological space.

### Why is RRT not optimal?

RRTs are not asymptotically optimal because the existing state graph biases future expansion. RRT* overcomes this by introducing incremental rewiring of the graph. New states are not only added to a tree, but also considered as replacement parents for existing nearby states in the tree.Nov 28, 2014

### Is RRT complete?

Surprisingly, it is not completely obvious under what conditions RRT is probabilistically complete, especially when using forward propagation of con- trols for the kinodynamic case.Sep 19, 2018

### WHY A * is optimal?

A* search is optimal if the heuristic is admissible. Admissible makes that whichever node you expand, it makes sure that the current estimate is always smaller than the optimal, so path about to expand maintains a chance to find the optimal path.Dec 13, 2019

### What is A * and AO * algorithm?

An AO* algorithm represents an AND-OR graph algorithm that is used to find more than one solution by ANDing more than one branch. ... A* algorithm is an OR Graph Algorithm while AO* is an AND-OR Graph Algorithm. A* algorithm cost function include f' = g' + h' while AO* algorithm cost function is simply f' = h'.

### WHY A * is admissible?

A* is admissible if it uses an admissible heuristic, and h(goal) = 0. (h(n) is smaller than h*(n)), then A* is guaranteed to find an optimal solution. i.e., f(n) is non-decreasing along any path. Theorem: If h(n) is consistent, f along any path is non-decreasing.

### What is the difference between workspace and configuration space?

Configuration Space: All the possible values of 'theta1' and 'theta2' it can take. Workspace: The physical volume it can cover. That in this case, is a circle with the radius that is the sum of the link lengths of 2 arms (It obviously cannot go beyond that).

### What do u mean by phase space?

In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. ... It is the outer product of direct space and reciprocal space.

### What is manifold configuration?

In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system. ... This manifold is called the configuration manifold of the system.