Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Chapter 7 / Missile Trajectory Optimisation
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7.12 Discussion
The guidance module in the missile
simulator provides the building blocks for
PN and CLOS guidance laws. If none are
selected the program invokes on-line
trajectory optimisation. The optimisation
process is latched to the host’s processor
clock to study the effect of limiting the
available processing time. For example if
the next control to be taken by the autopilot
last for 0.5 s re-optimisation of the missile
controls is allowed for precisely this amount
of time. For this to be meaningful the
algorithms must be written efficiently.
Critical parameters must be stored at the
beginning of each cycle in case the reoptimisation
is prematurely terminated.
Because the algorithms are to be executed in
real-time, global optimisation algorithms
currently in favour such as simulated
annealing and shooting methods are
inappropriate. Given the recent increase in
computing capacity some of the simpler
early optimisation techniques have been
selected.
Gradient techniques have proven to be
robust for real-time optimisation given a
reasonable set of initial controls,
Moody [M.12] . Propagating the dynamic
equations using ATPN with the missile
initially pointing at the target providing the
initial trajectory. The optimiser state space
selected to define the missile dynamics was
Cartesian position, speed and direction with
respect to the earth referenced Alignment
frame. The terms in the cost function and
adjoined dynamic constraints can be
weighted depending on target characteristics
providing a more flexible system. Gradient
projection in function-space along the
direction of steepest-descent with an Armijo
univariate search minimising the cost
function is the primary algorithm. If cost
reduction stalls a conjugate directions are
explored using an exact Fibonnacci search. The line search step-length is
doubled, or halved, depending on cost function values to accelerate the
search for a local minimum.
7-20
SELECT INITIAL SET OF
ADMISSIBLE CONTROLS
AND IMPACT TIME
STATE EQUATION
FORWARD
INTEGRATION FROM
CURRENT TO IMPACT
TIME
COST
EVALUATION
IMPACT POINT
ADJOINTS FROM
TRANSVERSALITY
CONDITIONS
BACKWARD
INTEGRATION OF
EULER-LAGRANGE
EQUATIONS
HAMILTONIAN
VARIATION WRT
CONTROLS, STATES
AND ADJOINTS
( GRADIENTS )
GRDIENT SCALING AND
SEARCH DIRECTION
UNIVARIATE SEARCH
AND CONTROL UPDATE
WITHIN ADMISSABLE
REGION
COST
EVALUATION
PRE AND POST
LAUNCH EXIT
CONDITIONS
Figure 7-2
Optimisation Flowchart