So, here is the link to the paper I am talking about: pdf
Group:
Robust Robotics Group from MIT
Samuel Prentice and Nicholas Roy are the authors
Contribution:
Planning in belief space can be done efficiently for linear Gaussian systems using a factored form of the covariance matrix.
Intuition:
The idea of the paper is simple and yet awesome! To explain it I will take a simple example. Lets say you want to drive from point A to point B in a city and you have continuous GPS signal available. There are multiple ways to get from A to B but the catch is the GPS signal is accurate to millimeters(open spaces?) in some places but not so accurate at other places(surrounded by tall buildings?). Given this information you are to plan a route and execute it. Your basic gut will tell you to pick the route where the GPS information is more accurate even though the route is longer but at the same time you would not mind lapses in the GPS signal occasionally. So, how do you capture this mathematically? That is exactly what this paper solves and its uber cool!!
Figures:
The figure below captures the essence of the paper. In the figure(a) you sample means from a space( note an inherent assumption is made that it is easy to classify a mean position to be free or classified as an obstacle) and in figure(b) you add edges to nearest points and then pick the shortest path to reach the goal. In figure(c) after sampling the means you also estimate the covariance matrices at each position(covariance is the inverse of information matrix so the smaller the norm of the covariance the more certain you are about the position) and you pick the path that maximizes the certainty or minimizes the covariance upon reaching the goal(instead of the shortest path picked by the PRM algorithm).
Previous Techniques:
Prior to this paper people used a technique called PRM - Probabilistic roadmap algorithm. Since your current position is not accurately determined you have an estimate of your current position. In PRM the planner uses only the mean and not the covariance where as in BRM you also incorporate additional statistics such as the covariance. So, in actuality you are doing nothing but increase the state space of your PRM configuration. But, this also complicates things on how to compute the covariances at various mean positions given the starting position. That is the latter part of the paper using lemmas and theorems but the intuition again is that they facator the covariance matrix and achieve this somehow. ( not important to understand the idea! ).
Gory details:
Control theory to factorize the covariance matrix..
Future Work according to authors:
This paper only takes the kinematic motion planning into consideration but they plan to extend it to kinodynamic planning.
My ideas on future work:
Group:
Robust Robotics Group from MIT
Samuel Prentice and Nicholas Roy are the authors
Contribution:
Planning in belief space can be done efficiently for linear Gaussian systems using a factored form of the covariance matrix.
Intuition:
The idea of the paper is simple and yet awesome! To explain it I will take a simple example. Lets say you want to drive from point A to point B in a city and you have continuous GPS signal available. There are multiple ways to get from A to B but the catch is the GPS signal is accurate to millimeters(open spaces?) in some places but not so accurate at other places(surrounded by tall buildings?). Given this information you are to plan a route and execute it. Your basic gut will tell you to pick the route where the GPS information is more accurate even though the route is longer but at the same time you would not mind lapses in the GPS signal occasionally. So, how do you capture this mathematically? That is exactly what this paper solves and its uber cool!!
Figures:
The figure below captures the essence of the paper. In the figure(a) you sample means from a space( note an inherent assumption is made that it is easy to classify a mean position to be free or classified as an obstacle) and in figure(b) you add edges to nearest points and then pick the shortest path to reach the goal. In figure(c) after sampling the means you also estimate the covariance matrices at each position(covariance is the inverse of information matrix so the smaller the norm of the covariance the more certain you are about the position) and you pick the path that maximizes the certainty or minimizes the covariance upon reaching the goal(instead of the shortest path picked by the PRM algorithm).
Previous Techniques:
Prior to this paper people used a technique called PRM - Probabilistic roadmap algorithm. Since your current position is not accurately determined you have an estimate of your current position. In PRM the planner uses only the mean and not the covariance where as in BRM you also incorporate additional statistics such as the covariance. So, in actuality you are doing nothing but increase the state space of your PRM configuration. But, this also complicates things on how to compute the covariances at various mean positions given the starting position. That is the latter part of the paper using lemmas and theorems but the intuition again is that they facator the covariance matrix and achieve this somehow. ( not important to understand the idea! ).
Gory details:
Control theory to factorize the covariance matrix..
Future Work according to authors:
This paper only takes the kinematic motion planning into consideration but they plan to extend it to kinodynamic planning.
My ideas on future work:
Can we combine this with D*lite and new search techniques to get better planning algorithm?
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