Fuel-Optimal Ascent Trajectory Problem for Launch Vehicle via Theory of Functional Connections

In this study, we develop a method based on the Theory of Functional Connections (TFC) to solve the fuel-optimal problem in the ascending phase of the launch vehicle. The problem is first transformed into a nonlinear two-point boundary value problem (TPBVP) using the indirect method. Then, using the function interpolation technique called the TFC, the problem’s constraints are analytically embedded into a functional, and the TPBVP is transformed into an unconstrained optimization problem that includes orthogonal polynomials with unknown coefficients. This process effectively reduces the search space of the solution because the original constrained problem transformed into an unconstrained problem, and thus, the unknown coefficients of the unconstrained expression can be solved using simple numerical methods. Finally, the proposed algorithm is validated by comparing to a general nonlinear optimal control software GPOPS-II and the traditional indirect numerical method. The results demonstrated that the proposed algorithm is robust to poor initial values, and solutions can be solved in less than 300 ms within the MATLAB implementation. Consequently, the proposed method has the potential to generate optimal trajectories on-board in real time.

Security Efficiency Maximization for Multi-UAV–Aided Network With Mobile Edge Computing

In this study, we consider a security efficiency maximization problem in a multiple unmanned aerial vehicle (UAV)-aided system with mobile edge computing (MEC). Two kinds of UAVs, including multiple computing UAVs (CUAVs) and multiple jamming UAVs (JUAVs), are considered in this system. CUAVs would receive partial computation bits and send the computation results to ground users. JUAVs do not undertake computing tasks and only send interference signals to counter potential ground eavesdroppers. We jointly optimize the ground user scheduling, UAV power, and UAV trajectory to maximize the security efficiency. The original problem is non-convex and difficult to solve. We first use the Dinkelbach method combined with continuous convex approximation technology, and then propose three corresponding subproblems, including user scheduling subproblem, UAV power subproblem, and UAV trajectory problem. Further, we apply the branch and bound method to solve the user scheduling subproblem, and optimize the two remaining subproblems by introducing auxiliary variables and Taylor expansion. The simulation results show that the proposed scheme can obtain better secure off-loading efficiency with respect to the existing schemes.

Multilane Spatiotemporal Trajectory Optimization Method (MSTTOM) for Connected Vehicles

It is agreed that connected vehicle technologies have broad implications to traffic management systems. In order to alleviate urban congestion and improve road capacity, this paper proposes a multilane spatiotemporal trajectory optimization method (MSTTOM) to reach full potential of connected vehicles by considering vehicular safety, traffic capacity, fuel efficiency, and driver comfort. In this MSTTOM, the dynamic characteristics of connected vehicles, the vehicular state vector, the optimized objective function, and the constraints are formulated. The method for solving the trajectory problem is optimized based on Pontryagin’s maximum principle and reinforcement learning (RL). A typical scenario of intersection with a one-way 4-lane section is measured, and the data within 24 hours are collected for tests. The results demonstrate that the proposed method can optimize the traffic flow by enhancing vehicle fuel efficiency by 32% and reducing pollutants emissions by 17% compared with the advanced glidepath prototype application (GPPA) scheme.

Efficient and Safe Motion Planning for Quadrotors Based on Unconstrained Quadratic Programming

SUMMARY An autonomous motion planning framework is proposed, consisting of path planning and trajectory generation. Primarily, a spacious preferred probabilistic roadmap algorithm is utilized to search a safe and short path, considering kinematics and threats from obstacles. Subsequently, a minimum-snap and position-clearance polynomial trajectory problem is transformed into an unconstrained quadratic programming and solved in a two-step optimization. Finally, comparisons with other methods based on statistical simulations are implemented. The results show that the proposed method achieves computational efficiency and a safe trajectory.

Neuromorphic estimation of the parameters of the object’s motion according to the positioning data of GLONASS

The article is devoted to the problem of expanding the capabilities of onboard GLONASS. In GLONASS, the implementation of various methods is possible to determine the parameters of the object’s trajectory. Pseudo-range method is supplemented with well-known error compensation methodologies. In particular, a two-frequency error determination method introduced to compensate errors of radio signal passed through the ionosphere. This makes it possible to solve the problem of precise estimation of object’s location coordinates very effectively. It is actual to consider the location coordinates as the initial information in the construction of onboard navigation algorithms for estimating other parameters of the trajectory, among which the most important is the velocity vector of the object relative to the Earth surface. The article presents a mathematical model of the inverse trajectory problem, the purpose of which is to evaluate object’s location coordinates derivatives, described the used technology, research is carried out and procedures are proposed to improve the solvability of the problem under conditions of finite accuracy of measurements and representation of numbers in a computing environment. To solve the problem, a neural-like algorithm of the Kalman type is proposed. The results of computational experiments are also presented.

Optimization of the launcher ascent trajectory leading to the global optimum without any initialization: the breakthrough of the Hamilton–Jacobi–Bellman approach

The resolution of the launcher ascent trajectory problem by the so-called Hamilton–Jacobi–Bellman (HJB) approach, relying on the Dynamic Programming Principle, has been investigated. The method gives a global optimum and does not need any initialization procedure. Despite these advantages, this approach is seldom used because of the dicculties of computing the solution of the HJB equation for high dimension problems. The present study shows that an eccient resolution is found. An illustration of the method is proposed on a heavy class launcher, for a typical GEO (Geostationary Earth Orbit) mission. This study has been performed in the frame of the Centre National d’Etudes Spatiales (CNES) Launchers Research & Technology Program.