Comparative Analysis: Multi-Flyby B-Plane vs. Advanced Autopilot Algorithms (kOS & kRPC)

1. Context and Problem Definition

The automation of complex spaceflight operations in Kerbal Space Program (KSP) is heavily dictated by the underlying computational architecture.

• Native kOS Architecture: The KerboScript virtual machine operates under strict Instruction Per Update (IPU) limits and lacks native linear algebra or convex solvers.
• Hybrid kRPC/Python Architecture: Bypasses the IPU limit by streaming telemetry to an external Python server over TCP/IP, unlocking native matrix math (NumPy), optimization (SciPy), and convex solvers (CVXPY).

This note evaluates advanced guidance algorithms (B-Plane Targeting, Q-law, eMPC, G-FOLD, and NPCG) across both architectural paradigms.

2. Core Candidate: B-Plane Targeting for Multi-Flyby Optimization

B-Plane Parameterization reduces the three-dimensional targeting problem of a gravity assist into a two-dimensional intersection on the asymptotic plane of the target body.

• Mathematics: Optimizing a sequence of flybys involves solving a Multiple-Shooting Boundary Value Problem (BVP) where the roots of the mismatch between the outgoing $V_{\infty }^{+}$ and incoming $V_{\infty }^{-}$ must be driven to zero using a Newton-Raphson solver.
• kOS Native Viability: High. KSP utilizes patched-conic mechanics, meaning analytical gradients for Keplerian propagation can be derived locally. It is heavily geometric, avoiding massive matrix inversions.
• kRPC Viability: Trivial. Python’s scipy.optimize.root solves the Jacobian matrix instantly.

---

3. Comparative Algorithms

A. Q-law (Low-Thrust Heuristic Optimization)

• Concept: A Lyapunov feedback control law utilizing Gauss’s Variational Equations to maximize the rate of change of a proximity quotient $Q$.
• kOS Viability: High. Computationally lightweight as it relies on an analytical feedback law rather than iterative solvers.
• kRPC Viability: High. Allows for high-fidelity continuous trajectory propagation using scipy.integrate.
• Zettel Link: Lyapunov Control in Orbital Mechanics

B. eMPC (Explicit Model Predictive Control)

• Concept: Traditional Model Predictive Control solves a finite-horizon open-loop optimal control problem. eMPC solves this optimization offline via multi-parametric quadratic programming, dividing state space into polyhedra mapped to affine control laws.
• kOS Viability: Low. State-space partitions scale exponentially, requiring massive memory overhead for the VM.
• kRPC Viability: Extremely High. Python natively manages the memory footprint and evaluates the active polyhedral region with zero latency. Ideal for rover navigation.

C. G-FOLD (Guidance for Fuel-Optimal Large Diversions)

• Concept: Powered-descent guidance utilizing Lossless Convexification to transform the minimum-fuel planetary landing problem into a Second-Order Cone Program (SOCP).
• kOS Viability: Impossible. Implementing a robust primal-dual interior-point SOCP solver in KerboScript is mathematically prohibitive.
• kRPC Viability: The Ultimate Standard. Passing the state vector to Python allows ecos via cvxpy to solve the convex program in real-time, matching SpaceX flight software architecture.

D. NPCG (Nonlinear Programming Collocation Guidance)

• Concept: Direct transcription pseudospectral methods discretize trajectory optimization into a large-scale Nonlinear Programming (NLP) problem.
• kOS Viability: Impossible natively.
• kRPC Viability: High, though requires robust solvers like IPOPT. Highly applicable for complex ascent trajectories.

---

4. Synthesis and Research Vector Recommendation

The optimal research vector bifurcates based on the chosen development architecture:

1. If constrained to Native kOS: Multi-Flyby B-Plane Targeting is the pinnacle. It relies on analytical orbital state propagation (Kepler’s Equation) rather than numerical integration, maximizing IPU efficiency while achieving a “Grand Tour” automation capability.
2. If utilizing the kRPC/Python Architecture: Convexified MPC (G-FOLD) is the absolute winner. It explicitly leverages the very reasons for upgrading to Python (convex solvers and matrix algebra) to execute mathematically guaranteed, optimal propulsive landings.

Conclusion: Native kOS is built for geometric and orbital mechanics mastery. kRPC unlocks modern optimal control theory and real-time convex optimization.