Multi-Domain Physics-Based MDO of Multirotor UAVs: A Deterministic Framework for Discrete COTS Sizing

This paper introduces the Dynamical Vehicle Orienteering Problem (DVOP), a generalization of the Orienteering Problem (OP). The OP maximizes the reward collected from spatial targets under a limited travel budget; the DVOP extends it by accounting for both external and vehicle-actuated forces. We study the DVOP in the context of multi-rotor Unmanned Aerial Vehicle (UAV) flight planning, using a three-dimensional Point-Mass Model (PMM) constrained by maximum velocity and acceleration magnitudes and subject to gravitational acceleration, with the travel budget expressed as a maximum flight time. Because the DVOP couples reward maximization with time-optimal trajectory planning, it cannot be formulated as a simple graph problem and solved exactly without relaxing or under-actuating the vehicle dynamics. We therefore propose two solution approaches: a Branch-and-Bound (BnB) procedure that combines Non-Linear Programming (NLP) and Mixed-Integer Linear Programming (MILP) to provide high-quality solutions, and a Large Neighborhood Search (LNS) metaheuristic that supplies an initial reward bound and scales to instances intractable for the BnB. The BnB relies on a novel MILP formulation of travel costs based on minimum-time trajectory primitives through target triplets, yielding a tight reward upper bound, while the LNS uses limited thrust decomposition to compute fast, high-quality PMM trajectories. Experiments on benchmark instances show improvements of up to 37 % over state-of-the-art solutions for the Kinematic Orienteering Problem, and a real-world deployment on a multi-rotor UAV verifies the proposed PMM solution trajectories.

For non-stationary tethered multirotor UAVs in real-world conditions, simulating the forces imposed on the drone by the aerodynamic drag of the tether becomes crucial, with online use cases placing a hard bound on the maximum solve time. In previous work, a quasi-analytical catenary tether model reached a mean solve time of 0.51 ms using a general-purpose root finder, but without any worst-case guarantees or proven convergence. In this work, we reformulate the inner solver by reducing the catenary boundary-value problem to a single transcendental equation in one well-conditioned unknown. We derive a closed-form bracket and prove monotonicity and convexity as well as existence and uniqueness of the root, which together guarantee convergence of the solver. We further propose a two-regime initial guess which approximates the true root within 3.4% and reduces the mean iteration count by 68.0% to 2.36 compared to the textbook initialization. Building on the hybrid root-finding method rtsafe (Newton-Raphson with bisection fallback giving bounded iteration counts), we implement a specialized variant that exploits the problem structure to omit unnecessary checks while retaining correctness, which gives up to 1.3 times speedup. With the proposed solver the full tether model achieves a nearly constant solve time of 6.9 us on average and 7.7 us at worst, a 40 times speedup over an optimized re-implementation of the previous method, while agreeing with it to a relative deviation of 8.7e-9. Because the reformulation leaves the underlying physical model untouched, the experimental validation of the previous work carries over unchanged. We further demonstrate its suitability for embedded, resource-constrained platforms with a Lua implementation running directly in ArduPilot on a drone's flight controller, where it stays well inside the scheduling budget with a mean solve time of 0.74 ms.

Lunar micro-rovers under 50 kg are a rapidly growing vehicle class, yet open, benchmarked tools for running optimization across design trades remain scarce. Rover sizing is a highly coupled problem with a feedback loop specific to surface vehicles: a heavier rover sinks deeper into loose regolith, deeper sinkage costs more power, more power requires a larger array, and the array adds mass. We present RoverDevKit, a tradespace exploration toolkit with an open evaluator that couples a closed-form wheel-soil model with bottom-up mass, solar-power, thermal-survival, and traverse models. It is fast enough to serve as the fitness function of a multi-objective genetic algorithm (NSGA-II): one search of 3000 mission evaluations takes under a minute on a single laptop core. We use it to map the trades among distance traveled, vehicle mass, and slope capability on mare, polar, highland, and crater-rim missions. Across those missions the limiting factor changes: energy storage at high latitude, slope traction on loose highland regolith, and traverse range on mare and crater-rim terrain. The wheel-soil model matches measured single-wheel drawbar pull on two independent datasets to within the 20-30% error typically reported for this class of model, and the mass model predicts published 5-50 kg rover masses to 10.5% median absolute error. A check against five published in-class designs places them near the designs the optimizer selects. Re-running the search after applying that wheel-soil comparison error leaves these conclusions unchanged.