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Physics-Informed Bayesian Optimization Warm-Starts for Sequential Convex Programming in Asteroid Surface Hopping

This paper demonstrates that a physics-informed Bayesian Optimization warm-start significantly enhances the reliability and fuel efficiency of Sequential Convex Programming for asteroid surface hopping by overcoming the convergence failures of standard straight-line initializations and achieving meter-level accuracy with reduced propellant consumption.

Original authors: Baran Ekşi, Tufan Kumbasar

Published 2026-08-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Baran Ekşi, Tufan Kumbasar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Exploring the surfaces of small, irregular asteroids has long been a challenge for space engineers. Unlike planets, which are roughly spherical and have predictable gravity, these rocky worlds are often lumpy, elongated, and spin in complex ways. Their gravity is weak and uneven, meaning a spacecraft cannot simply roll or drive across them like a rover on Mars. Instead, the most promising way to move between different scientific sites is to hop. This involves firing a thruster to lift off, coasting through the air, and landing at a new location. However, planning these hops is incredibly difficult. The spacecraft must carry enough fuel to make the jump, but not so much that it becomes too heavy to lift. It must also navigate a path that avoids crashing into the rocky surface, all while the asteroid's strange gravity pulls it off course. If the path is calculated poorly, the spacecraft could crash into the ground or run out of fuel before reaching its destination.

To solve this, researchers have turned to a mathematical approach called sequential convex programming. This method breaks a complex, difficult problem into a series of simpler, solvable steps. Imagine trying to find the best route through a mountainous landscape; instead of seeing the whole jagged terrain at once, you approximate it as a series of flat, smooth slopes that you can solve one by one. The catch is that this method needs a good starting guess. If you start with a guess that goes straight through the mountain, the computer gets confused and fails to find a solution. For the asteroid Eros, which is shaped like a giant, uneven potato, a straight line between two points on its surface would pass directly through the rock itself. This makes the standard starting point useless, often causing the computer to give up or find a very inefficient path.

In a recent study, researchers at Istanbul Technical University developed a new way to generate these starting guesses for hopping on the asteroid 433 Eros. They created a system that uses a technique called physics-informed Bayesian optimization. Instead of relying on a pre-trained computer model that requires massive amounts of data, this system uses the actual laws of physics to test potential paths. It treats the path as a flexible curve, similar to a bow, and adjusts a single point in the middle of that curve to see if it clears the surface. The computer tests thousands of these slight adjustments very quickly, looking for a path that stays above the ground and requires a reasonable amount of thrust. This process acts as a "warm-start," giving the main calculation a head start with a path that is already safe and realistic.

The researchers tested this method by planning a complete tour of five different sites on Eros, covering all possible trips between them. They found that their new warm-start method was far superior to the old way of guessing. When using the traditional straight-line guess, the computer failed to find a solution for one of the twenty trips and took significantly longer to solve the others. With the new physics-based guess, the computer solved every single trip without failure. The resulting paths were not only successful but also highly efficient. The spacecraft could visit all five sites in a single tour using only about one-fifth of its total fuel supply. Compared to a rough estimate of what a simple, unpowered jump would require, the optimized powered hops saved roughly one-third of the fuel.

The study also revealed that the asteroid's irregular shape forces the spacecraft to take winding routes rather than direct lines. In many cases, the optimal path hugs the surface closely, skimming just fifty meters above the rocks to take advantage of the local gravity. This low-altitude corridor is something that simpler models, which treat the asteroid as a collection of spheres, would miss entirely. The researchers validated their findings by simulating the spacecraft's flight thousands of times, adding random errors to mimic real-world conditions like wind or sensor noise. In every simulation, the spacecraft landed within a few meters of the target, proving that the calculated paths are robust enough for a real mission.

One surprising discovery was that the computer's starting guess, which involves a random element, actually helped the researchers find better solutions. Because the asteroid's shape creates many different "valleys" of possible paths, a single fixed starting point might get stuck in a poor local solution. By running the calculation with slightly different random starting points, the team was able to explore these different valleys and find the absolute best route for each trip. This turned a potential weakness of the method into a strength, allowing the system to map out the best possible paths without needing to know the answer in advance.

The work demonstrates that hopping across an asteroid is not only possible but also fuel-efficient if the right mathematical tools are used. The researchers showed that by respecting the actual shape of the asteroid and using a smart, physics-based way to start the calculation, a spacecraft can navigate the treacherous, lumpy terrain of Eros with confidence. While the study focused on Eros, the methods developed could be applied to other small bodies in the solar system, opening the door for future missions that can visit multiple scientific sites on a single, irregular world. The results suggest that with the right guidance, a small spacecraft can dance across the surface of a distant asteroid, stopping at specific points of interest with meter-level precision, all while carrying a modest amount of fuel.

Technical Summary: Physics-Informed Bayesian Optimization Warm-Starts for Sequential Convex Programming in Asteroid Surface Hopping

Problem Statement
The paper addresses the challenge of designing fuel-optimal, collision-free surface-hopping trajectories for small-body exploration, specifically targeting asteroid 433 Eros. Unlike planetary landing, hopping on an irregular, rotating body involves a nonconvex optimal control problem (OCP) driven by three coupled factors: an irregular polyhedral gravity field, thrust-mass coupling, and continuous collision-avoidance constraints.

Standard Sequential Convex Programming (SCP) is effective for such problems but relies heavily on the quality of the initial reference trajectory. A straight-line initialization is geometrically infeasible for Eros; the straight chord between surface sites penetrates the asteroid's interior on every transfer considered. This forces the SCP solver to start from a deeply infeasible region, often leading to convergence failures or entrapment in poor local optima. Existing learned references require offline training and datasets, which limits their applicability. The paper identifies a gap for an initialization method that respects the body's actual geometry, requires no training data, and is computationally inexpensive to generate online.

Methodology
The authors propose a three-component framework to solve the nonconvex OCP:

Physics-Informed Bayesian Optimization (BO) Warm-Start:
Instead of a straight line, the method generates a near-feasible reference trajectory using a quadratic Bézier curve defined by fixed endpoints and a single free control point ( $P_1$ ). A Gaussian Process (GP) surrogate model optimizes $P_1$ to minimize a cost function derived from inverse dynamics. This cost function penalizes surface penetration (collision), thrust infeasibility, and control effort. Crucially, this approach is "physics-informed" because the cost is computed directly from the hop dynamics rather than a learned model, eliminating the need for offline training data. The optimization completes in approximately 10 seconds.
Sequential Convex Programming (SCP):
The BO-generated reference initializes an SCP solver that iteratively linearizes the dynamics and constraints. Key convexification techniques include:
- Log-mass transformation: Replacing mass with its logarithm ( $z = \ln m$ ) to linearize thrust-mass coupling.
- Collision Avoidance: Enforcing clearance via nearest-facet half-spaces on a 1708-face polyhedral model of Eros. This preserves low-altitude corridors that simpler sphere-based approximations would exclude.
- Trust Regions: Adaptive trust regions ensure the linearization remains valid during iteration.
Automated Pareto Time-of-Flight Selection:
To avoid introducing bilinear terms that would break convexity, the final time ( $t_f$ ) is not a decision variable but is swept over a discrete grid. For each $t_f$ , an SCP solution is found. The resulting set of time-fuel pairs forms a discrete Pareto front. A utopia-point criterion, weighted by the inverse propellant mass fraction, automatically selects the fuel-priority solution without manual tuning.

Key Contributions

Novel Initialization: A physics-informed BO warm-start that tunes a single Bézier control point to generate a near-feasible reference, requiring no offline training.
High-Fidelity Collision Avoidance: Implementation of collision constraints using nearest-facet half-spaces on a high-resolution polyhedral model, enabling trajectories to hug the true surface geometry.
Automated Trade-off Selection: A discrete time-of-flight sweep coupled with a utopia-point selection metric to automate the time-fuel trade-off while maintaining convexity.
Large-Scale Validation: A comprehensive validation across a catalog of 20 ordered transfers between five representative sites on Eros, tested under 10 random seeds (200 total runs).

Results
The framework was applied to all 20 inter-site transfers on 433 Eros:

Convergence and Efficiency: The physics-informed warm-start reduced the mean SCP iteration count from 8.8 (straight-line initialization) to 5.9 and eliminated the single convergence failure observed with the straight-line baseline.
Fuel Efficiency: The optimized trajectories achieved a mean $\Delta V$ reduction of roughly 34% compared to an idealized two-impulse ballistic estimate. For a representative five-site tour, the total propellant consumption was approximately 6.06 kg, representing only 20.2% of the vehicle's propellant budget.
Robustness: In closed-loop Monte Carlo simulations (100,000 runs with PD guidance), all trajectories tracked to meter-level terminal accuracy (99.7th percentile miss distance of 4.2 m).
Stochasticity as an Asset: The stochastic nature of the BO warm-start acted as a multi-start global search. While 16 of 20 missions were deterministic across seeds, the remaining 4 revealed distinct local basins (e.g., "over-the-top" vs. "equatorial" corridors). The framework successfully identified the globally superior basin in most cases, demonstrating that the randomness aids in escaping poor local optima.
Sensitivity: Solutions varied smoothly with target perturbations (15 m displacement), with no jumps between local basins, confirming the stability of the selected corridors.

Significance and Claims
The paper claims that the proposed framework makes powered hopping on irregular small bodies like Eros propellant-affordable and computationally tractable. It demonstrates that:

Initialization is critical: A straight-line guess is insufficient for non-spherical bodies; a physics-informed, geometry-aware initialization is necessary for reliable convergence.
Stochastic warm-starts are beneficial: Rather than a liability, the randomness of the BO search serves as a cheap, effective multi-start strategy to explore the nonconvex solution space.
Feasibility of Complex Tours: A multi-site tour can be executed with a fraction of the available propellant, and the resulting trajectories are robust enough to be tracked by simple guidance laws in the presence of noise and model uncertainty.

The study concludes that while attitude dynamics, plume-surface interactions, and sub-resolution terrain uncertainty remain outside the current scope, the framework provides a solid foundation for future autonomous surface mobility on asteroids and potentially the Moon.

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