UWE Bristol Engineering showcase 2015

Ji Qiu
BEng (Hons) Electronic Engineering
Project Supervisor
Professor Quan Min Zhu
Application of Hidden Markov Model to Locate Soccer Robots
Introduction
The Hidden Markov Model is a statistical model with unobserved and independent states. This project aims to advance the applicable algorithms by Hidden
Markov Model as a basis for predicting the probabilities in location of soccer robot’s trajectories. Moreover, the algorithm adopts Hidden Markov Model as a
means of estimating and predicting position of soccer robot with given map and sensory data. Finally, computational experiment approach was used to
demonstrate the analytical results with MATLAB simulations.
Rolling-Back Algorithm
As Hidden Markov Model shown in Figure 1, the dynamic process for the
probability in total states can be described as below:
pp 1 tt + ∆tt = ww 1,1 pp 1 tt + ww 2,1 pp 2 tt + ⋯ + ww nn,1 pp nn tt
pp 2 tt + ∆tt = ww 1,2 pp 1 tt + ww 2,2 pp 2 tt + ⋯ + ww nn,2 pp nn tt
…
pp nn tt + ∆tt = ww 1,nn pp 1 tt + ww 2,nn pp 2 tt + ⋯ + ww nn,nn pp nn tt
Where tt (0, 1, 2 … ) is the discrete time index. When tt = 0, pp 1 0 = 1,
pp ii 0 = 0(ii = 2,3, … , nn)
Application in Predicting
Suppose that the original situation is like figure right hand side. Assume that
up move is the direction to goal. That is, the connect probability from
beginning state to up state is the largest one. Generally, left and right
directions are the same value and down direction has the least probability.
Blue and red rectangles mean different teams when the circle one represents
the soccer robot which is analysed carrying the soccer ball. As other robots
are obstacles, blue and red rectangles are unwalkable.
Computational Application
This simulation generally contains three
parts as follows:
• Field specification
• Determine transition probability matrix
• Position prediction
This progress can be organised as an
excellent self-adaptation control system.
The rolling-back algorithm defaults that the
Markov Model discussed here satisfies
homogeneity. But in actual practical
application, the stochastic sequence may
not satisfy the homogeneity. Under this
situation, perhaps overlying the predicting
probabilities of different orders should be
considered together, because these
probabilities may donate to the prediction.
Furthermore, the influences of these
probabilities of different orders on the
prediction can be different in fact. In order
to improve the system, this kind of
considerations should be taken into
account. That is to say, these predicted
results of different orders should be
superimposed with different weighting
factors.
Assume that the probability of initial state of
the system can be represented by a vector PP ss .
After ∆tt = 1 times, the relationship between
PP ss and the expected probability vector
PP ss (tt + 1) = (aa 1 , aa 2 , aa 3 … aa nn ) could be
described as the equation (Rolling-Back
Algorithm)below:
PP tttttttttttttttttttt ∈ PP ss (tt) PP ss tt + 1 = PP ss tt WW mmmmmm
Where WW is a matrix.
• Step 1: Calculate the probability by Hidden Markov Model
Algorithm.
• Step 2: Find the best trajectory by compare these
probabilities above.
• Step 3: The robot could make a decision for next step.
Hence, the available state should be detected again at the
same time and calculate the initial probabilities originally
from present state to next step in expected state.
Figure 3: Example simulation
Figure 1: Markov Chain
Figure 2: Simple example
Project summary
This project adopts a Hidden Markov Model as a basis
for predicting the probabilities in location of soccer
robot’s trajectories, and uses computational
experiment approach to demonstrate the analytical
results with MATLAB simulations.
Project Objectives
• Take critical survey on the up-to-date status of the
relevant research and applications.
• Tailor the theory of Markov chains into a
condensed pack for the problems.
• Select parameter estimation algorithms.
• With MATLAB, design program to implement the
numerical algorithms with initial demonstration
of the computational effectiveness and accuracy.
• Apply the Markov model and its parameter
estimation algorithm to soccer robot’s localisation
for further bench test of the theoretical results.
• Design user friendly manual to run the
demonstration programs.
Project Conclusion
This project has formulated a research problem
(location of soccer robots), proposed a solution
procedure (based on Hidden Markov Model), and
finally used computational experiment approach to
demonstrate the analytical results with MATLAB
simulations. With the research understanding,
Hidden Markov Model has been a very useful
framework to accommodate predicting problems
encountered in many stochastic systems, which its
applications in soccer robot location could promote
many other interesting research issues as well as
increasing the robot intelligence. Once again this is
the beginning stage presented in the paper and
comprehensive future studies have been planned
accordingly.