Azali Saudi and Jumat Sulaiman
Autonomous Vehicle Navigation Using Harmonic Functions via Modified Arithmetic Mean Iterative Method
101 - 107
2019
13
4
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10010273
https://publications.waset.org/vol/148
World Academy of Science, Engineering and Technology
Harmonic functions are solutions to Laplace’s equation
that are known to have an advantage as a global approach in providing
the potential values for autonomous vehicle navigation. However,
the computation for obtaining harmonic functions is often too slow
particularly when it involves very large environment. This paper
presents a twostage iterative method namely Modified Arithmetic
Mean (MAM) method for solving 2D Laplace’s equation. Once
the harmonic functions are obtained, the standard Gradient Descent
Search (GDS) is performed for path finding of an autonomous vehicle
from arbitrary initial position to the specified goal position. Details
of the MAM method are discussed. Several simulations of vehicle
navigation with path planning in a static known indoor environment
were conducted to verify the efficiency of the MAM method. The
generated paths obtained from the simulations are presented. The
performance of the MAM method in computing harmonic functions
in 2D environment to solve path planning problem for an autonomous
vehicle navigation is also provided.
Open Science Index 148, 2019