Fuel-optimal asteroid hopping with physics-informed Bayesian optimization

What the work claims

The paper claims that a physics-informed Bayesian optimization (BO) warm-start can replace the usual straight-line reference for sequential convex programming (SCP) when planning fuel-optimal powered hops on the irregular asteroid 433 Eros.¹ The straight chord between representative surface sites on Eros passes through the body interior, so a straight-line initial guess starts SCP from a deeply infeasible region. The proposed warm-start searches over a single Bézier control point using an inverse-dynamics cost that penalizes collision, thrust infeasibility, and control effort, requires no offline training data, and completes in roughly 10 seconds.

The authors report that, applied to all 20 ordered transfers among five representative sites and tested under 10 random seeds, the framework converges for every mission, reduces mean SCP iterations from 8.8 to 5.9 in a seed-0 ablation, and cuts mean mission delta-V by about 34 percent relative to an idealized flat-body two-impulse ballistic estimate.¹ A representative five-site tour is projected to consume 6.06 kg of propellant, about 20.2 percent of the 30 kg budget implied by the modeled wet mass of 250 kg and dry mass of 220 kg.

How it works

The optimizer works in three stages: a stochastic BO warm-start, a successive-convexification trajectory solver, and a discrete Pareto sweep over flight time. All dynamics are modeled in an asteroid-fixed rotating frame using the 1708-face polyhedral shape and gravity model of Eros derived from NEAR Shoemaker data.¹

The warm-start parameterizes a quadratic Bézier arc by its single interior control point P1. The endpoints are fixed at the departure and arrival surface sites, so tuning P1 moves the mid-arc by up to about 7.5 km in any direction, comparable to the 11.2 km short axis of Eros. Each candidate arc is scored by inverse dynamics: the required control acceleration is computed from the polyhedral gravity field, Coriolis and centrifugal terms, and the commanded path, and a cost penalizes control effort, surface penetration, and commanded accelerations that exceed the 10 N thruster limit normalized by wet mass.¹ MATLAB's bayesopt minimizes this cost with a Gaussian process surrogate and expected-improvement acquisition over 50 evaluations.

The SCP stage linearizes the nonconvex problem about the warm-start reference. A log-mass change of variables makes propellant depletion linear and exact for the minimum-thrust-zero case, while the thrust ceiling is linearized about a reference mass trajectory. Gravity is linearized via a precomputed spline interpolant of the polyhedral gravity Jacobian at interval midpoints. State propagation uses trapezoidal integration augmented with virtual-control slack. Collision avoidance is enforced by nearest-facet half-spaces on the full 1708-face polyhedron, with a 50 m safety margin, rather than by a coarse few-sphere approximation.¹

Because including flight time as a decision variable would introduce bilinear terms, the authors solve SCP on a fixed grid of nine flight times from 1.5 to 4.5 hours and select the fuel-priority point by weighted utopia-point distance. The fuel axis is weighted by the inverse propellant mass fraction so that propellant shortage directly drives the selection.¹

The strongest case

The strongest case is that the method solves a genuinely hard problem cheaply. Powered hopping on a rotating, irregular small body is nonconvex because of coupled polyhedral gravity, thrust-mass depletion, and terrain avoidance. Prior approaches either used a straight-line reference that fails on Eros, or learned references that need offline training on a solved-trajectory dataset. The physics-informed BO warm-start needs neither: it exploits the polyhedral gravity model directly, costs about 10 seconds, and gives SCP a feasible-enough starting point that the median solver converges in 4 iterations.¹

The results also suggest that the optimization is robust enough for preliminary mission design. Closed-loop Monte Carlo tracking with a simple proportional-derivative guidance law, 10 m initial position dispersion, and 2 percent actuation noise yields a 99.7th-percentile terminal miss distance of 4.2 m across 100,000 runs, with terminal velocity error below 75 mm/s.¹ A target-perturbation study displaces each landing target by 15 m and re-optimizes 2000 times; no case jumps basins, and the average maximum fuel deviation is 8.6 g. These are simulation metrics, not flight data, but they indicate the open-loop trajectories are dynamically consistent.

Where a skeptic should push

The single largest limitation is maturity. Everything reported is simulation: trajectory optimization in a modeled gravity field, closed-loop tracking in Monte Carlo, and re-optimization under perturbed targets. The paper never claims hardware-in-the-loop testing, flight software implementation, or validation against real asteroid dynamics. The spacecraft parameters in Table I, including the 250 kg wet mass, 220 kg dry mass, 10 N maximum thrust, and 220 s specific impulse, are modeling assumptions, not an existing vehicle.

The collision-avoidance claim also needs softening. Although all 200 selected open-loop trajectories are reported as collision-free, the nearest-facet audit found one node of mission M06 on two seeds dipping to 26 m, below the 50 m safety margin, because the facet assignment lagged one iteration.¹ The authors show that recomputing facet assignments from the converged geometry restores the margin, but that confirmatory pass is not applied to the catalog figures. This is a small anomaly, but it is a reminder that the 50 m clearance is a solver artifact, not a hard geometric proof.

Important physics are excluded. The model treats the hopper as a point mass with attitude ignored; plume-surface interaction, terrain uncertainty below the shape-model resolution, and solar radiation pressure are outside the scope.¹ The authors explicitly note these as future work. For a real mission, plume impingement during hover near the surface could alter both the effective thrust and the surface properties of the landing site, and shape-model errors could invalidate the low-altitude corridors the optimizer exploits.

What it means for small-body mobility energy budgets

The non-obvious implication is that the energy cost of surface mobility is not simply proportional to distance. On a nonconvex body, the optimizer exploits low-altitude gravity corridors so that some long transfers cost less delta-V than short ones across rough terrain: the paper reports delta-V reductions of 55 to 61 percent on the longest transfers, while some short saddle-to-ridge hops barely beat the impulsive estimate.¹ A mission designer cannot budget propellant from a rule-of-thumb delta-V per kilometer; the budget must come from shape-aware trajectory optimization that treats the asteroid's irregular gravity as a resource rather than a perturbation.

The genuine threat is reserve erosion. A planner could be tempted to treat the simulated 20.2 percent five-site tour cost as a flight number and size the propellant tank accordingly. But the simulation omits attitude dynamics, plume effects, and terrain uncertainty, and the 26 m clearance dip on M06 shows that the solver can produce margin violations before post-processing.¹ If a real hopper carries only the simulated propellant plus a standard margin, an unmodeled corridor change or landing dispersion could strand the vehicle or force an abort.

The opportunity is onboard adaptive planning for propellant-limited rovers. The BO warm-start is stochastic and cheap enough to serve as a multi-start search: running 10 seeds at roughly 10 seconds each maps distinct local basins, and selecting the cheapest converged solution eliminates basin penalties such as the 0.78 kg difference seen on mission M02.¹ For a hopper refueled by in-situ resource utilization, the same solver could re-plan between sites as new shape-model or terrain data arrive, trading computation time for propellant mass rather than carrying a worst-case reserve.

The bottom line

What is established is a promising trajectory-optimization method, demonstrated in simulation for a 1708-face Eros model and a 250 kg-class hopping vehicle. The physics-informed BO warm-start reliably clears the asteroid surface, reduces SCP iterations, and finds low-altitude corridors that cut fuel use relative to a flat-body ballistic estimate. Confidence in the algorithm is moderate to high within its modeling assumptions. Confidence in its flight relevance is lower: the work is simulation-only, excludes attitude and plume physics, and reports a collision-margin violation that required a post-hoc fix. The claim would be strengthened by hardware-in-the-loop testing or flight-software timing on a representative processor; it would be undercut if shape-model errors or plume-surface interaction force the trajectories away from the optimized low-altitude corridors.