QLaw.jl

Julia implementation of the Q-Law Lyapunov-based feedback control law for low-thrust orbit transfers. Repo: HAMMERHEAD-Space/QLaw.jl

Architecture

Spacecraft Types

QLawSpacecraft            # Constant thrust (dry, wet, thrust, isp)
SEPQLawSpacecraft         # Solar electric (+ r_ref for 1/r^2 scaling)

Control Types

# Effectivity (coasting logic)
AbsoluteEffectivity       # Coast when absolute effectivity < threshold
RelativeEffectivity       # Coast when relative effectivity < threshold

# Convergence criteria
SummedErrorConvergence    # Sum of weighted element errors
MaxElementConvergence     # Maximum individual element error
VargaConvergence          # Varga's convergence metric

Problem/Solution Types

QLawParameters            # Algorithm configuration (smoothing, tolerances)
QLawWeights               # Element weights for proximity quotient Q
QLawProblem               # Problem definition (SciML pattern)
QLawSolution              # Transfer result (converged, time, mass, trajectory)

Source Layout

src/
  QLaw.jl                # Module entry
  types.jl               # All type definitions
  api.jl                 # qlaw_problem(), solve(), remake()
  qlaw_core.jl           # Q function, optimal thrust angles (α*, β*), effectivity
  dynamics.jl            # ODE RHS: Gauss VE in modified equinoctial elements

Key Patterns

SciML Interface

# Define transfer
prob = qlaw_problem(oe0, oeT, tspan, μ, spacecraft;
    weights=QLawWeights(...),
    qlaw_params=QLawParameters(...))

# Solve
sol = solve(prob)

# Remake
prob2 = remake(prob; spacecraft=new_spacecraft)

Modified Equinoctial Elements

Q-Law operates in modified equinoctial elements [p, f, g, h, k, L]:

oe0 = ModEq(kep_initial, μ)   # Convert from Keplerian via AstroCoords
oeT = ModEq(kep_target, μ)

Q-Law Core Math

• Proximity quotient Q: Weighted sum of squared element errors, penalized near singularities
• Optimal thrust angles: α* (in-plane) and β* (out-of-plane) computed via ForwardDiff of dQ/doe
• Effectivity: Measures how efficiently current thrust reduces Q; used for coasting decisions
• Smooth activations: tanh for AD-compatible coasting thresholds

Weight Optimization

# Global optimization via BlackBoxOptim
# Local optimization via SAMIN (Optim.jl)
# Both through Optimization.jl unified interface

Perturbation Support

Integrates with AstroForceModels.jl for:

• J2+ gravity harmonics
• Third-body perturbations (Moon, Sun)
• Eclipse/shadow modeling

Integration with Ecosystem

• AstroCoords: Coordinate conversions (Keplerian <-> ModEq)
• AstroPropagators: ODE integration infrastructure
• AstroForceModels: Perturbation force models
• ComponentArrays: Named state vectors

Adding New Features

New Convergence Criterion

1. Define struct NewConvergence type
2. Implement convergence check dispatch
3. Test on known reference transfers

New Effectivity Model

1. Define effectivity type struct
2. Implement smooth (AD-compatible) effectivity computation
3. Verify ForwardDiff compatibility

Dependencies

• AstroCoords 0.3, AstroForceModels 0.3, AstroPropagators 0.2
• ComponentArrays 0.15, ForwardDiff 1, StaticArrays 1
• Optim 2 (local optimization for weight tuning)
• OrdinaryDiffEqAdamsBashforthMoulton 1.5, OrdinaryDiffEqCore 1
• SciMLBase 2