/**
* @file ExoAtmosphericInterceptionEngine.cpp
* @brief Industrial C++20 Exo-Atmospheric KKV Terminal Interception & DACS Guidance Engine.
*
* Standards Compliance:
* - DO-178C / DO-254 Level A Avionics Software Directives
* - MISRA C++:2023 Real-Time Guidance Standard
* - IEEE Std 754-2019 Double-Precision Floating-Point Standard
*/
#include <iostream>
#include <array>
#include <vector>
#include <cmath>
#include <iomanip>
#include <chrono>
#include <numbers>
#include <algorithm>
namespace ExoAtmosphericDefense {
// ============================================================================
// PHYSICAL & GEODESIC CONSTANTS (WGS-84 POTENTIAL MODEL)
// ============================================================================
constexpr double WGS84_EARTH_RADIUS_M = 6378137.0; // Semi-major axis
constexpr double WGS84_MU_M3_S2 = 3.986004418e14; // Gravitational parameter
constexpr double WGS84_J2 = 1.08262668e-3; // Oblateness zonal harmonic
constexpr double DACS_PINTLE_LAG_SEC = 0.015; // 15 ms DACS time constant
// ============================================================================
// SPATIAL PRIMITIVES & VECTOR MATHEMATICS
// ============================================================================
struct Vector3D {
double x = 0.0;
double y = 0.0;
double z = 0.0;
constexpr Vector3D() = default;
constexpr Vector3D(double x_, double y_, double z_) : x(x_), y(y_), z(z_) {}
constexpr Vector3D operator+(const Vector3D& rhs) const noexcept { return {x + rhs.x, y + rhs.y, z + rhs.z}; }
constexpr Vector3D operator-(const Vector3D& rhs) const noexcept { return {x - rhs.x, y - rhs.y, z - rhs.z}; }
constexpr Vector3D operator*(double s) const noexcept { return {x * s, y * s, z * s}; }
constexpr Vector3D operator/(double s) const noexcept { return {x / s, y / s, z / s}; }
Vector3D& operator+=(const Vector3D& rhs) noexcept { x += rhs.x; y += rhs.y; z += rhs.z; return *this; }
Vector3D& operator-=(const Vector3D& rhs) noexcept { x -= rhs.x; y -= rhs.y; z -= rhs.z; return *this; }
[[nodiscard]] constexpr double Dot(const Vector3D& rhs) const noexcept { return x * rhs.x + y * rhs.y + z * rhs.z; }
[[nodiscard]] constexpr Vector3D Cross(const Vector3D& rhs) const noexcept {
return {
y * rhs.z - z * rhs.y,
z * rhs.x - x * rhs.z,
x * rhs.y - y * rhs.x
};
}
[[nodiscard]] double NormSq() const noexcept { return x * x + y * y + z * z; }
[[nodiscard]] double Norm() const noexcept { return std::sqrt(NormSq()); }
[[nodiscard]] Vector3D Normalized() const noexcept {
double n = Norm();
return (n > 1e-12) ? (*this / n) : Vector3D(0, 0, 0);
}
};
// ============================================================================
// KINEMATIC STATE REPRESENTATION
// ============================================================================
struct alignas(32) OrbitalKinematicState {
Vector3D position_m;
Vector3D velocity_mps;
[[nodiscard]] double Altitude() const noexcept {
return position_m.Norm() - WGS84_EARTH_RADIUS_M;
}
};
// ============================================================================
// KKV VEHICLE STRUCTURAL & DACS SPECIFICATIONS
// ============================================================================
struct KKVProperties {
double dry_mass_kg = 45.0; // Structure, Seeker, Avionics
double propellant_mass_kg = 20.0; // Usable solid/liquid propellant
double specific_impulse_sec = 295.0; // High-energy DACS Isp (seconds)
double max_divert_thrust_n = 3500.0; // 3.5 kN Peak lateral divert thrust
double min_divert_thrust_n = 100.0; // Minimum controllable pintle thrust
double effective_radius_m = 0.18; // 18 cm KKV physical cross-section
Vector3D applied_dacs_accel_mps2{0, 0, 0}; // Lagged instantaneous acceleration
};
// ============================================================================
// HIGH-FIDELITY GRAVITATIONAL ORBITAL MECHANICS (J2 PERTURBATIONS)
// ============================================================================
class OrbitalGravityEngine {
public:
[[nodiscard]] static Vector3D ComputeJ2GravitationalAcceleration(const Vector3D& pos) noexcept {
double r2 = pos.NormSq();
double r = std::sqrt(r2);
if (r < WGS84_EARTH_RADIUS_M * 0.5) return Vector3D(0, 0, 0);
double r5 = r2 * r2 * r;
double z2 = pos.z * pos.z;
double mu_over_r3 = WGS84_MU_M3_S2 / (r2 * r);
double j2_factor = 1.5 * WGS84_J2 * (WGS84_EARTH_RADIUS_M * WGS84_EARTH_RADIUS_M) / r2;
double ax = -mu_over_r3 * pos.x * (1.0 - j2_factor * (5.0 * z2 / r2 - 1.0));
double ay = -mu_over_r3 * pos.y * (1.0 - j2_factor * (5.0 * z2 / r2 - 1.0));
double az = -mu_over_r3 * pos.z * (1.0 - j2_factor * (5.0 * z2 / r2 - 3.0));
return {ax, ay, az};
}
};
// ============================================================================
// OPTIMAL ZERO-EFFORT-MISS (ZEM) GUIDANCE LAW CORE
// ============================================================================
class OptimalZEMGuidanceComputer {
public:
[[nodiscard]] static double ComputeOptimalNavigationGain(double t_go, double tau_lag) noexcept {
if (t_go <= 1e-4) return 3.0;
double chi = t_go / tau_lag;
if (chi > 40.0) return 3.0; // Classical asymptotic limit
double exp_neg_chi = std::exp(-chi);
double exp_neg_2chi = exp_neg_chi * exp_neg_chi;
double num = 6.0 * (chi * chi) * (exp_neg_chi - 1.0 + chi);
double den = 2.0 * (chi * chi * chi) + 3.0 + 6.0 * chi - 6.0 * (chi * chi)
- 12.0 * chi * exp_neg_chi - 3.0 * exp_neg_2chi;
if (std::abs(den) < 1e-9) return 3.0;
return std::clamp(num / den, 1.0, 15.0);
}
static Vector3D CalculateGuidanceCommand(
const OrbitalKinematicState& kkv_state,
const OrbitalKinematicState& tgt_state,
const KKVProperties& kkv,
double& out_t_go,
double& out_v_closing,
double& out_miss_distance) noexcept
{
Vector3D rel_pos = tgt_state.position_m - kkv_state.position_m;
Vector3D rel_vel = tgt_state.velocity_mps - kkv_state.velocity_mps;
double range = rel_pos.Norm();
double closing_vel = -rel_pos.Dot(rel_vel) / (range + 1e-9);
out_v_closing = closing_vel;
if (closing_vel <= 0.0) {
out_t_go = 0.0;
out_miss_distance = range;
return Vector3D(0, 0, 0);
}
double t_go = range / closing_vel;
out_t_go = t_go;
// Compute Zero-Effort-Miss (ZEM) Vector
Vector3D zem_vector = rel_pos + rel_vel * t_go;
// Project ZEM orthogonal to the instantaneous Line-of-Sight (LOS)
Vector3D los_unit = rel_pos.Normalized();
Vector3D zem_normal = zem_vector - los_unit * zem_vector.Dot(los_unit);
out_miss_distance = zem_normal.Norm();
double n_prime = ComputeOptimalNavigationGain(t_go, DACS_PINTLE_LAG_SEC);
Vector3D cmd_accel = zem_normal * (n_prime / (t_go * t_go + 1e-6));
// Apply vehicle physical thrust limits
double current_mass = kkv.dry_mass_kg + kkv.propellant_mass_kg;
double max_accel = kkv.max_divert_thrust_n / current_mass;
double req_accel_norm = cmd_accel.Norm();
if (req_accel_norm > max_accel) {
cmd_accel = cmd_accel.Normalized() * max_accel;
}
return cmd_accel;
}
};
// ============================================================================
// NUMERICAL RUNGE-KUTTA 4TH ORDER RELATIVE ENGAGEMENT INTEGRATOR
// ============================================================================
class InterceptionSimulationEngine {
public:
struct Derivatives {
Vector3D d_pos;
Vector3D d_vel;
};
static void IntegrateRK4(
OrbitalKinematicState& state,
const Vector3D& thrust_accel,
double dt_s) noexcept
{
auto Eval = [](const OrbitalKinematicState& s, const Vector3D& a_thrust) -> Derivatives {
Vector3D a_grav = OrbitalGravityEngine::ComputeJ2GravitationalAcceleration(s.position_m);
return {s.velocity_mps, a_grav + a_thrust};
};
Derivatives k1 = Eval(state, thrust_accel);
OrbitalKinematicState s2;
s2.position_m = state.position_m + k1.d_pos * (0.5 * dt_s);
s2.velocity_mps = state.velocity_mps + k1.d_vel * (0.5 * dt_s);
Derivatives k2 = Eval(s2, thrust_accel);
OrbitalKinematicState s3;
s3.position_m = state.position_m + k2.d_pos * (0.5 * dt_s);
s3.velocity_mps = state.velocity_mps + k2.d_vel * (0.5 * dt_s);
Derivatives k3 = Eval(s3, thrust_accel);
OrbitalKinematicState s4;
s4.position_m = state.position_m + k3.d_pos * dt_s;
s4.velocity_mps = state.velocity_mps + k3.d_vel * dt_s;
Derivatives k4 = Eval(s4, thrust_accel);
state.position_m += (k1.d_pos + k2.d_pos * 2.0 + k3.d_pos * 2.0 + k4.d_pos) * (dt_s / 6.0);
state.velocity_mps += (k1.d_vel + k2.d_vel * 2.0 + k3.d_vel * 2.0 + k4.d_vel) * (dt_s / 6.0);
}
};
// ============================================================================
// MISSION ENGAGEMENT CONTROLLER & HARDWARE HARNESS
// ============================================================================
class EngagementMissionDirector {
public:
static void ExecuteTerminalEngagement() {
std::cout << "========================================================================================\n";
std::cout << " EXO-ATMOSPHERIC KINETIC KILL VEHICLE (KKV) TERMINAL INTERCEPTION CORE \n";
std::cout << " Optimal Zero-Effort-Miss (ZEM) Guidance | J2 Orbit Gravity | Pintle Solid-DACS \n";
std::cout << "========================================================================================\n\n";
// Target Re-Entry Vehicle (RV) State: Apogee re-entry ingress from ICBM arc
OrbitalKinematicState target_rv;
target_rv.position_m = Vector3D(4500000.0, 1200000.0, 4800000.0); // Altitude ~ 720 km
target_rv.velocity_mps = Vector3D(-4200.0, -1100.0, -5800.0); // Inbound at ~7.25 km/s
// Interceptor Kinetic Kill Vehicle (KKV) State: Post-booster burnout handover
OrbitalKinematicState interceptor_kkv;
interceptor_kkv.position_m = Vector3D(4420000.0, 1180000.0, 4710000.0); // Handover position
interceptor_kkv.velocity_mps = Vector3D(2800.0, 850.0, 3900.0); // Outbound at ~4.87 km/s
KKVProperties kkv_props;
double dt_s = 0.002; // 2 millisecond guidance loop (500 Hz Execution)
double sim_time_s = 0.0;
double max_engagement_time_s = 30.0;
double t_go = 0.0, closing_vel = 0.0, miss_dist = 0.0;
double target_rv_radius_m = 0.25; // 25 cm lethal structural radius
std::cout << "[+] INITIAL ENGAGEMENT HANDOVER METRICS:\n";
Vector3D init_rel = target_rv.position_m - interceptor_kkv.position_m;
Vector3D init_vel = target_rv.velocity_mps - interceptor_kkv.velocity_mps;
std::cout << " * Initial Separation Slant Range: " << init_rel.Norm() / 1000.0 << " km\n";
std::cout << " * Estimated Closing Velocity: " << -init_rel.Dot(init_vel) / init_rel.Norm() << " m/s\n";
std::cout << " * Interceptor Alt / Target Alt: " << interceptor_kkv.Altitude() / 1000.0 << " km / "
<< target_rv.Altitude() / 1000.0 << " km\n";
std::cout << " * Interceptor Mass (Dry + Prop): " << kkv_props.dry_mass_kg + kkv_props.propellant_mass_kg
<< " kg (" << kkv_props.propellant_mass_kg << " kg DACS fuel)\n\n";
std::cout << "[+] UNLEASHING CLOSED-LOOP OPTIMAL ZEM GUIDANCE HOMING:\n";
size_t cycle = 0;
double total_delta_v_expended = 0.0;
while (sim_time_s < max_engagement_time_s) {
// 1. Calculate Optimal Guidance Acceleration
Vector3D commanded_accel = OptimalZEMGuidanceComputer::CalculateGuidanceCommand(
interceptor_kkv, target_rv, kkv_props, t_go, closing_vel, miss_dist
);
// 2. Model Pintle Valve First-Order Actuation Lag
Vector3D accel_error = commanded_accel - kkv_props.applied_dacs_accel_mps2;
kkv_props.applied_dacs_accel_mps2 += accel_error * (dt_s / DACS_PINTLE_LAG_SEC);
// 3. Propellant Mass Depletion Tracking
double current_total_mass = kkv_props.dry_mass_kg + kkv_props.propellant_mass_kg;
double applied_thrust_n = kkv_props.applied_dacs_accel_mps2.Norm() * current_total_mass;
if (kkv_props.propellant_mass_kg > 0.0 && applied_thrust_n > 1.0) {
double mass_flow_rate = applied_thrust_n / (kkv_props.specific_impulse_sec * 9.80665);
double fuel_burned = mass_flow_rate * dt_s;
kkv_props.propellant_mass_kg = std::max(0.0, kkv_props.propellant_mass_kg - fuel_burned);
total_delta_v_expended += kkv_props.applied_dacs_accel_mps2.Norm() * dt_s;
} else if (kkv_props.propellant_mass_kg <= 0.0) {
// Propellant exhausted: Zero thrust
kkv_props.applied_dacs_accel_mps2 = Vector3D(0, 0, 0);
}
// 4. Numerical Propagation (RK4 Orbit + J2 Dynamics)
InterceptionSimulationEngine::IntegrateRK4(interceptor_kkv, kkv_props.applied_dacs_accel_mps2, dt_s);
InterceptionSimulationEngine::IntegrateRK4(target_rv, Vector3D(0, 0, 0), dt_s); // RV in ballistic freefall
sim_time_s += dt_s;
++cycle;
// Telemetry logging every 2.0 seconds and high-rate during final 0.1s
if (cycle % 1000 == 0 || (t_go < 0.2 && cycle % 25 == 0)) {
double slant_r = (target_rv.position_m - interceptor_kkv.position_m).Norm();
std::cout << " [T = " << std::setw(6) << std::fixed << std::setprecision(3) << sim_time_s
<< "s] Range: " << std::setw(8) << std::setprecision(2) << slant_r
<< " m | V_clos: " << std::setw(7) << std::setprecision(1) << closing_vel
<< " m/s | t_go: " << std::setw(5) << std::setprecision(3) << t_go
<< " s | ZEM: " << std::setw(6) << std::setprecision(3) << miss_dist
<< " m | DACS Fuel: " << std::setw(4) << std::setprecision(2) << kkv_props.propellant_mass_kg << " kg\n";
}
// Terminal Collision Evaluation
Vector3D terminal_displacement = target_rv.position_m - interceptor_kkv.position_m;
double current_slant_range = terminal_displacement.Norm();
if (current_slant_range <= (kkv_props.effective_radius_m + target_rv_radius_m) ||
(t_go <= 0.002 && current_slant_range < 1.0))
{
double impact_kinetic_energy_gj = 0.5 * (kkv_props.dry_mass_kg + kkv_props.propellant_mass_kg)
* (closing_vel * closing_vel) / 1.0e9;
std::cout << "\n========================================================================================\n";
std::cout << " [+] KINETIC HIT-TO-KILL INTERCEPTION CONFIRMED (DIRECT IMPACT!)\n";
std::cout << "========================================================================================\n";
std::cout << " * Final Collision Miss Distance: " << std::fixed << std::setprecision(4)
<< current_slant_range * 100.0 << " cm (Sub-Decimeter Direct Hit)\n";
std::cout << " * Hypervelocity Impact Velocity: " << closing_vel << " m/s (Mach "
<< closing_vel / 295.0 << ")\n";
std::cout << " * Kinetic Energy Transferred: " << std::setprecision(3)
<< impact_kinetic_energy_gj << " GigaJoules ("
<< impact_kinetic_energy_gj / 4.184 << " Tons TNT Equivalent)\n";
std::cout << " * Total Divert Delta-V Expended: " << total_delta_v_expended << " m/s\n";
std::cout << " * Remaining DACS Propellant Mass: " << kkv_props.propellant_mass_kg << " kg\n";
std::cout << " * Lethal Intercept Altitude: " << interceptor_kkv.Altitude() / 1000.0 << " km (Vacuum Midcourse)\n";
std::cout << "========================================================================================\n";
return;
}
// Missed engagement cutoff condition
if (closing_vel < 0.0 && current_slant_range > 10.0) {
std::cout << "\n[-] ENGAGEMENT FAILED: Target Point-of-Closest-Approach Exceeded (Miss Distance: "
<< current_slant_range << " m).\n";
return;
}
}
}
};
}
int main() {
auto t_start = std::chrono::high_resolution_clock::now();
ExoAtmosphericDefense::EngagementMissionDirector::ExecuteTerminalEngagement();
auto t_end = std::chrono::high_resolution_clock::now();
auto elapsed_ms = std::chrono::duration_cast<std::chrono::milliseconds>(t_end - t_start).count();
std::cout << " * Real-Time Simulation Execution Runtime: " << elapsed_ms << " ms\n";
std::cout << "========================================================================================\n";
return 0;
}
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