This paper presents a new guidance method for a quadrotor uncrewed aerial vehicle to perform standoff inspection from specific viewpoints arranged along a circular periphery surrounding a structure. The proposed approach leverages a bifurcation-theory-based framework to realize multiple inspection modes: reaching a specific viewpoint, switching between viewpoints along the inspection circle, and continuous circumnavigation, as the bifurcation parameter is varied. A stability analysis establishes that the quadrotor achieves the desired inspection mode. Analytical expressions relate the control parameters to the desired settling time for the inspection modes. A qualitative comparison with existing circumnavigation methods highlights the flexibility and computational feasibility of the proposed strategy. The efficacy of the guidance approach is demonstrated through numerical simulations using a six-degree-of-freedom quadrotor model.
In this study, two machine learning (ML) techniques—genetic programming (GP) and deep reinforcement learning (DRL)—are leveraged to derive a reentry guidance law and are evaluated using a high-fidelity six-degree-of-freedom simulator developed for validating the Reusability Flight Experiment (ReFEx) vehicle guidance, navigation, and control (GNC) subsystem. Both methods are benchmarked against each other and against the baseline ReFEx optimization-based guidance strategy to assess their applicability to a real mission and to understand their respective strengths and weaknesses. The ReFEx mission focuses on the reentry phase, wherein GP and DRL models are applied to generate real-time corrections to precomputed reference guidance commands, thereby compensating for external disturbances and model inaccuracies. GP is selected for its ability to produce human-readable, continuous, and differentiable models that yield smooth guidance commands, whereas DRL employs a fully connected neural network (NN), delivering superior performance at the expense of a black-box model and nonsmooth guidance signals. The results demonstrate that DRL and GP achieve performance comparable to the mission baseline guidance, hence validating their applicability in mission-grade applications. Moreover, both ML approaches achieve faster online execution times than the baseline guidance method.
A novel orbit determination method for unknown-maneuvering spacecraft is proposed, enabling the simultaneous estimation of orbital states and maneuver parameters using angle-only observations. A hyperbolic-tangent function is introduced to smoothly parameterize both impulsive and constant-thrust maneuvers, providing accurate maneuver-profile representation and enforcing continuous differentiability of the orbital state across maneuvers. On this basis, the smoothed extended state transition tensors are derived to construct the parameter-to-observation mapping and formulate a second-order correction equation that captures key nonlinear effects. Furthermore, the influence of the smoothing factor on the mapping precision is analyzed, leading to an adaptive smoothing-factor selection strategy that minimizes mapping errors and enhances the accuracy of computed corrections. Finally, a three-layer iterative correction framework is developed, where the inner layer iteratively solves the second-order correction equation to compute accurate corrections; the middle layer adaptively selects the smoothing factor to preserve mapping fidelity under maneuver-epoch uncertainty and find the optimal corrections; the outer layer updates the estimated parameters based on the selected results. Numerical simulations covering impulsive and constant-thrust maneuvers in both Low‐Earth Orbit and Medium‐Earth Orbit scenarios validate the approach, demonstrating rapid convergence, high estimation accuracy, insensitivity to large initial errors and scenario adaptability and showing more reliable convergence performance over existing maneuver-reconstruction techniques.
The principle of optimality ensures that the tail segment of an optimal trajectory provides an optimal solution to the original trajectory optimization problem, provided that the problem is formulated in standard Mayer, Lagrange, or Bolza form and that the initial states of the reoptimized tail align with the optimal reference solution. In desensitized optimal control (DOC) problems, the final values of both physical and sensitivity states often appear on the right-hand side of the differential equations. Transforming such problems into standard form necessitates introducing additional states with trivial dynamics and free initial values to represent the final values of the physical and sensitivity states. Numerical tests reveal that tail reoptimization in DOC problems can enhance performance if the initial values of these artificial states are left unconstrained. However, by virtue of the principle of optimality, this reoptimized tail cannot yield performance improvements for the overall path-planning problem starting from the initial time of the optimal reference solution. This counterintuitive result leads to the distinction between the planning phase and the execution phase. Moreover, for broad classes of DOC and stochastic optimal control problems, it implies that optimal trajectories can become suboptimal once execution begins, necessitating continuous reoptimization of the tail segment during execution to maintain optimality.
The computation of finite-thrust extremal arcs in the elliptic restricted three-body trajectory optimization problem is considered. Libration-point orbits are approximated to near-machine precision using a fast Fourier transform of the sampled values of the state vector at Chebyshev-Gauss-Lobatto points. Checkable optimality conditions are derived by applying Pontryagin's principle to minimum-time and time-constrained minimum-propellant problems. These necessary conditions include criteria for optimal departure and arrival points. For propellant consumption, a recently developed computational model is employed. This model is agnostic to the specific impulse of the propellant and varies as the inverse quadratic of a cosine term. Candidate optimal solutions are generated by combining the universal Birkhoff theory for trajectory optimization with the fast, guess-free spectral algorithm. The extremality of the Birkhoff-computed solution is validated against the Hamiltonian minimization condition and the transversality conditions. It is shown that the Birkhoff-theoretic spectral algorithm can generate verifiable extremals without any assistance or initialization from dynamical systems theory.
This paper presents a class of problems arising from applications in which vehicles move on spherical surfaces. It addresses the problem of prediction, avoidance, and achievement of positional conjunctions of such vehicles on spherical manifolds. To this end, the notion of collision triangles on spheres is developed, and analytical conditions governing the speed ratios and directions of motion of point objects that lead to conjunction are derived. These fundamental results are then extended to circular patch-shaped objects, which are realistic representations of vehicles moving on the surface of the sphere, thereby generalizing the notion of Euclidean collision cones to spherical manifolds. It is shown that these collision cones can be used to generate geodesic paths via guidance commands for speed and/or heading angle maneuvers. They can also be used to facilitate coverage path planning/information transfer between vehicles when the patches approximate sensing/communication footprints. The results are extended to multiple revolutions of the vehicles on the sphere, establishing a close link with Diophantine equations. These results address guidance problems in applications involving multiple satellites moving on spherical manifolds, as well as multiple aerial vehicles performing cooperative maintenance and inspection tasks on spherical domes and tanks.
The increasing use of unmanned aerial vehicles for long-duration missions has heightened safety concerns, motivating the introduction of backup plan safety (BPS) for autonomous vehicles. BPS refers to the capability of executing an alternative mission in the event of primary mission abortion. In path planning, BPS integrates alternative destinations, serving as backup safety landing sites, into the decision-making process, maximizing the feasibility of reaching potential destinations. Consequently, the trajectory is adjusted to redirect toward alternative destinations, minimizing the time required to reach a safe landing site if the primary site becomes inaccessible. To address BPS, we formulate the Feasibility Maximization Problem (FMP) based on multi-objective model predictive control (MPC), balancing the costs of multiple missions. The FMP enhances the evaluation of objectives, corresponding to each mission’s cost, by incorporating control input horizons for all alternative missions alongside the horizon for the primary mission. The proposed Generalized-Backup-Plan-constrained MPC (GBP MPC) generates control inputs by solving the FMP and minimizing a weighted cost that reflects tradeoffs between the primary and alternative missions. To guarantee stability, GBP MPC departs from the step-by-step decrease in weighted cost required in Backup Plan constrained MPC and instead generalizes the decrease to a parameterized multistep period.
Motivated by second-order optimization and estimation applications, the Kepler initial value problem is revisited with the goals of fast runtime, robust convergence, and accurate computation of the state transition matrix and tensor. Goodyear’s universal time equation and Pitkin’s sensitivity formulation are extended with computational improvements, including a new recursive formula for arbitrary-order partial derivatives of Kepler’s time equation with respect to the universal variable. A new initial guess algorithm, applicable to other formulations, is combined with a ninth-order correction step to globally converge the root solve in 1 or 2 iterations. A new mapping of partial derivatives between independent variables leads to both time-fixed and universal variable-fixed sensitivities. The latter is new and particularly useful for regularized applications. The former provides a quadratic, synchronous relative motion model that is functionally equivalent to Pitkin’s. Problem regions in the parameter space are identified to mitigate numerical difficulties. The resulting root solver and state and sensitivity propagators are extensively validated over the complete domain through numerical self-consistency checks and benchmarking against existing solvers. The new propagators demonstrate strong robustness and consistency in terms of both speed and accuracy, especially in the problematic regions of the parameter space. The accompanying code is open source.
Traditional methods for parameterizing and storing periodic orbit families use discretized representations of the family. In this work, continuous parameterizations of periodic orbit families in the Earth/Moon system are developed using techniques from machine learning. Autoencoder neural networks are used to parameterize periodic orbit families in terms of a single, continuous parameter and a discrete angle. The recovered one-dimensional latent space is monotonic and allows for the unique identification of an orbit throughout a family. This work also demonstrates the ability of a single autoencoder neural network to generate orbits across multiple families in the Circular Restricted Three-Body Problem (CR3BP) connected using a bifurcation diagram. The approach allows for a versatile and efficient method to generate orbits in the CR3BP and can be applied to mission design and trajectory optimization.
A novel predictive controller is introduced for rendezvous with non-cooperative tumbling targets in active debris removal applications, based on the model predictive control for tracking (MPCT) framework, which improves the robustness and computational efficiency of conventional MPC by optimizing the system toward artificial equilibrium points rather than fixed references. This paper aims to provide a computationally efficient and theoretically sound control strategy that enables reliable proximity operations around tumbling objects, despite their complex rotational motion. The target’s nonperiodic rotational dynamics and state and control constraints are considered. The approach is based on applying an intermediate coordinate transformation that eliminates the time dependency due to rotations in the constraints. The proposed algorithm leverages feasible trajectories, obtained through the conservation of momentum and energy of rotating bodies, to obtain strong convergence guarantees on arbitrary horizons. A control law is then found as the solution to a quadratic programming problem that provides feasibility and stability guarantees by means of a terminal virtual controller. The main result is an MPCT-based controller for linear time-varying systems induced by rotational dynamics, with provable feasibility and stability guarantees. A near-rendezvous simulation with the Envisat spacecraft confirms the practical relevance and performance of the proposed controller.
