This script implements the RLV re-entry trajectory problem using evolutionary approach.
Output maps generated by the script.
Implemented RLV re-entry trajectory optimization problem as published on the paper
Reentry Trajectory Optimization : Evolutionary Approach
[ https://arc.aiaa.org/doi/10.2514/6.2002-5466 ]
The main aim is to control the flight path of the vehicle throughout the reentry phase with safety bounds.
To meet the objective, the states r, V , γ , φ , θ , ψ are considered, with their dynamics given by the following equations and with α as a control variable.
where
r is the radial distance from the center of the Earth to the vehicle,
V is the earth relative velocity,
Ωe is the earth angular speed,
γ is the flight path angle,
σ is the bank angle,
ψ is the heading angle,
m is the mass of the vehicle,
g is the acceleration due to gravity,
φ and θ are the latitude and longitude respectively.
The guidance command is supposed to guide the vehicle through the flight corridor, dictated by the following path constraints:
- Heat flux constraint, q < 18.5 W/cm^2
- Dynamic pressure, Q < 45 kPa
For the simulations, the initial state vector corresponding to the reentry point is assumed to be [ h0 V0 γ0 φ0 θ0 ψ0 ] = [150000,1500,0,0,0,0]
L and D represents the aerodynamic lift and drag forces acting on the vehicle whose expressions are given by
L = (1/2) * ρ * V^2 * CL * Sref
D = (1/2) * ρ * V^2 * CD * Sref
Note that L and D are functions of the angle of attack α through the dependence
of the drag and lift coefficients CD and CL on α.
CL = CL0 + CLα * α
CD = CD0 + k * CL^2
Sref represents the aerodynamic reference area and CL, CD are the aerodynamic coefficients calculated by a two-dimensional table look up with angle of attack and mach number as the independent variables.
Genetic algorithm is used as an optimization tool for this implementation using the library DEAP [ https://deap.readthedocs.io/en/master/ ].
Weighted sum cost function approach is used and multiple objectives are weighted and summed together to create a composite objective function. Optimization of this composite objective results in the optimization of individual objective functions.
The integration of equations of motion is carried out at 1s interval upto 300s.
If your processor is slow, increase time step value mentioned in [endtime = 300; t_step = 1;] as t_step = 10
The problem is discretized into 300 steps [t1,t2,..t300] where we have to determine control vector U[α] so as to satisfy constraints.
The initial values of state vectors are specified. In the present study, cross range optimization is not carried out and as such σ = 0 is assumed.
Script is written with python (Version: 3.6) on linux. Additional modules required :
- numpy (tested with Version: 1.18.4 )
- matplotlib (tested with Version: 2.1.1 )
- scipy (tested with Version: 0.19.1 )
- DEAP (tested with Version: 1.3)
- Verify and install required modules
- run
python rlv_trajectory_optimizer.py.
- [06Sep2022]
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