Page 130 - Innovations in Intelligent Machines

Evolution-based Dynamic Path Planning for Autonomous Vehicles 121
v
σ is a given parameter specifying the bound of the uncertainty in the velocity.
j
In the model presented here, each site is assumed to maintain constant
velocity at all times. Therefore, the expected velocity of site j while t q ∈
(t k ,t N ] is given by
˜ E ˜ E (9)
˙ z (q)= ˙z (k)
j
j
As a result, the dynamic propagation of the expected position of site j is
given by
˜ E
E
E
˜ z (q +1) = ˜z (q)+ ˙z (k)∆t (10)
j j j
for all q ∈{k, k +1,...,N − 1} and ∆t = t q+1 − t q . The dynamic equation of
x
the uncertainty radius σ is given by
j
x
v
x
σ (q +1) = σ (q)+ σ (k)∆t (11)
j j j
The dynamic propagation of the expected value of the state of task i, i ∈
{1, 2,... ,N T }, is described by

˜ i
F
F
˜ V
˜ x (q +1) = ˜x (q) 1 − B (q +1)ξ (q)η V (12)
υ
i
i
˜ i
where B is the probability that the path of vehicle v intersects the target
υ
location z G associated with task i during the time t q <t ≤ t q+1 . The details
i
˜ i
of how to compute B are given in Section 3. η V is the effectiveness of the
υ
vehicle in performing the task. Using the Equations 3 to 12, we can compute
the expected values of all states at time t q ∈ (t k ,t N ].
˜
To formulate the planner’s objective function, we define a variable R i (q)
as the task score the vehicle will have at time t q as a result of executing task
i. This task score is used as a measure of success of the mission. The expected
task score of task i for q ∈{1, 2,... ,N} is given by
˜
˜
˜
F
F
F

R i (q +1) = R i (q)+ α (q) ˜x (q) − ˜x (q +1) ; R i (0) = 0 (13)
i
i
i
Substituting Equation 12 into Equation 13, we obtain

˜
˜
˜ i
˜ V
F
F
R i (q +1) = R i (q)+ α (q)(˜x (q) B (q +1)ξ (q)η V (14)
i
υ
i
F
where α (q) is the score weighting factor for task i. It can either be a constant
i
or a time dependent function. This function is used to define a time window
requirement for the vehicle to execute each task.
, the goal of the planner is to find a path that
At any time t k <t s p
maximizes the predicted total score obtained by completing each task while
<t ≤ t N .The
minimizing the predicted operation cost during the time t s p
objective function can be written as
N T

˜
˜

˜
˜
J = R i (N) − R i (s p ) − C(Q(s p )) (15)
i=1