Questions tagged [probability]

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Implementation of a particle filter algorithm

How do you calculate the likelihood of making an observation ? Does someone have a link to a book or article that explains the math that you need to do to implement a PF algorithm? Conceptually i ...
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25 views

Robot Localization - Motion and Sense Probability

I'm currently taking Udacity's AI for robotics course and came across a question that stumped me. The problem plays on localization probability given uncertainty in our measurement updates. The first ...
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2answers
66 views

Which math books would help in learning SLAM systems? [closed]

Recently I started studying papers on SLAM systems by Durrant-Whyte for my research and I'm finding some difficulties in the math (matrices and probability) that is tackled in these papers. Which ...
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2answers
57 views

Basic question about Markov Localization, probability and belief distribution shift

I am starting in robotics, and reading about Markov Localization, I have one doubt, probably very stupid, but, well, I want to solve it. Let's take the CMU Website example: https://www.cs.cmu.edu/afs/...
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Sampling from guassian distribution for odometry based motion?

I am trying to generate an odometry based motion model as described in the lectures. I have implemented a C++ version of the code. The issue I am having is that when I try to simulate successive ...
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1answer
140 views

How to derive the Time-Update equation of SLAM

I was going through the tutorial on SLAM by Hugh Durrant-Whyte and Tim Bailey† and found this Time-Update equation (equation 4 in the paper): $ P\left(\mathrm{x}_{k},\mathrm{m} | \mathrm{Z}_{0:...
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2answers
29 views

How to calculate the mean of an unsymmetric distribution (Particle Filter)

I'm attempting to implement a variant of Monte Carlo localization in a 2D space with obstacles. While the object is moving around the obstacles the particles flow around the obstacle like in images ...
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1answer
37 views

Can neural network probability directly be used as inverse sensor model?

For my robot i'm using semantic segmentation neural network that assigns to every pixel probability of being "road" (not occupied). By using homography matrix i'm re-projecting image to top-down view. ...
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2answers
95 views

EKF SLAM : Missing older landmarks in new observation

I am a beginner to SLAM and robotics in general and I have been trying to implement SLAM on my GoPiGo3 robot car kit using primarily Chapter 10 from Probabilistic Robotics by Sebastian Thrun as ...
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4answers
134 views

Is Fuzzy logic applicable for robotics research

I found some papers that use fuzzy logic to solve robotics algorithmic problems. But I have recently been told by a few roboticists that fuzzy logic should not be used in robotics because it has ...
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0answers
28 views

Lost on SEIF Slam repeated update landmark

I am working on Sparse Extended Information Slam. I take the reference from Probabilistic Robotics, by Dr.Sebastian Thrun (Chapter 12,page 303). I have some doubt about the implementation of the ...
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2answers
188 views

How should I understand sequential importance resampling in a particle filter?

Suppose I implement a particle filter with $n$ particles. This is a brief description of my understanding of a particle filter. For the first step, I throw out $n$ particles some distance from my ...
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Why does the low variance resampling algorithm for particle filters work?

I am studying and coding particle filters and I am using the Low variance sampling algorithm suggested in the Probabilistic Robotics book. I understand the procedure for the algorithm. A random number ...
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1answer
68 views

Why does a Bayesian Filter require random controls?

As stated in Probabalistic Robotics, the proof for correctness of a Bayesian Filter relies on the fact that $$p(x_{t-1}|z_{1:t-1},\ u_{1:t}) = p(x_{t-1}|z_{1:t-1},\ u_{1:t-1})$$ In order to justify ...
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1answer
338 views

How can we estimate the likelihood field for a particular scan in probabilistic terms?

I am trying to implement a scan matcher using Scan based sensor model but I cant figure out how to estimate likelihood for a particular scan. Is there any implementation available ? Would be thankful ...
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1answer
40 views

$p(m|x_t, u_t, x_{t-1})$ What does Thrun mean with the “map probability”?

Different question from the last one since I still struggle with the concept. In his book "Probabilistic Robotics", Thrun has the following equation: (Context here) (5.49) $p(x_t|u_t,x_{t-1},m) = \...
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0answers
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Probabilistic Robotics: Map-based motion model [closed]

I asked the following question in math.stackexchange, but realized that this might be the more appropriate place to post it: How did Thrun derive the following formula: (Context here) I think that ...
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1answer
149 views

Markov Localization using control as an input

When using Hidden Markov Models in Global Localization problems on the prediction step there is a need to calculate the probability of robot's pose given the actions (control u, odometry): ...
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1answer
401 views

What is the best way to compute the probabilistic belief of a robot equipped with a vision sensor?

I am trying to implement 'belief space' planning for a robot that has a camera as its main sensor. Similar to SLAM, the robot has a map of 3D points, and it localizes by performing 2D-3D matching with ...
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1answer
323 views

Understanding and implementing belief space planning

I am currently working on state estimation/navigation for a system with multiple robots. As of now, what I have is each robot localizing itself with a Kalman filter, given vision based measurements. ...
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3answers
479 views

Addressing the sample impoverishment in particle filter

I have implemented a particle filter algorithm for the state estimation of a mobile robot. There are several external range sensors(transmitters) in the environment which gives information on the ...
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1answer
172 views

Modeling a robot to find its position

The task of the robot is as follows. My robot should catch another robot in the arena, which is trying to escape. The exact position of that robot is sent to my robot at 5Hz. Other than that I can use ...
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1answer
2k views

Low variance resampling algorithm for particle filter

For my particle filter, I decided to try using the low variance resampling algorithm as suggested in Probabilistic Robotics. The algorithm implements systematic resampling while still considering ...
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1answer
135 views

Grid mapping probability calculation algorithmic complexity

I have stumbled upon an equation (http://i.stack.imgur.com/hv64E.png), where the probability of an occupancy grid map cell is calculated. My teacher insists that it's possible to approximate the ...
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1answer
73 views

Non-markovian problems/approaches in robotics

As far as i can tell, the markov assumption is quite ubiquitous in probabilistic methods for robotics and i can see why. The notion that you can summarize all of your robot's previous poses with its ...
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0answers
83 views

Probabilistic Velocity Obstacles

I have been working with the Velocity Obstacles concept. Recently, I came across a probabilistic extension of this and couldn't understand the inner workings. Source: Recursive Probabilistic ...
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1answer
113 views

Laser Beam based model probability in case of single particle

I am trying to calculate likelihood of laser scan($Z$) at give pose($x$) with known map ($m$) using beam based model $P\left(z_t|x_t,m \right)=\prod_{i=1}^{n}P'\left(z_i|x_t,m \right)$ My scan ...