This chapter relates the notions of mutations with the concept of graphical derivatives of set-valued maps and more generally links the above results of morphological analysis with some basic facts of set-valued analysis that we shall recall.

Set-valued analysis

Over the last years, two new technologies to solve optimal-control problems were successfully developed: that is, pseudospectral optimal control and convex optimization, with the former for solving...

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Pseudospectral Convex Optimization for Powered Descent and Landing

In this paper, an adaptive, disturbance-based sliding-mode controller for hypersonic-entry vehicles is proposed. The scheme is based on high-order sliding-mode theory, and is coupled to an extended...

/pdf/adaptive-disturbance-based-high-order-sliding-mode-control-402tx13s3n.pdf

Adaptive Disturbance-Based High-Order Sliding-Mode Control for Hypersonic-Entry Vehicles

Nonlinear PID Controller Design for a 6-DOF UAV Quadrotor System

One of the most powerful analysis tools to deal with entry-guidance problems is the possibility to formulate them as optimal control problems. Environmental constraints, actuator limits, and strict requirements on the final conditions can be efficiently transcribed, resulting in a discrete, finite-dimension nonlinear programming (NLP) problem. However, NLP problems require a computational power, which often exceeds the vehicle’s onboard capabilities. Moreover, it is important to ensure that the solution can be adapted to the actual flight conditions, which can differ from the nominal scenario. This paper proposes an approach based on an efficient use of multivariate pseudospectral interpolation scheme to generate real-time capable entry guidance solutions. The proposed onboard trajectory generation algorithm is able to deal with wide dispersions at the entry interface, and can improve the lateral performance in cases where the classic bank-reversal logic is not sufficient. The interpolation is applied to subspaces of a database of pre-computed trajectories, which can be efficiently stored onboard. The method is here proposed for initial-conditions variations, but can be applied to every mission parameter, which allows to find a corresponding optimal solution. Results have been generated for SHEFEX-3, an entry demonstrator vehicle, which was planned by the German Aerospace Center. Monte-Carlo simulations show how this approach is applicable, and yields significant improvements both in longitudinal and lateral guidance performance, with an improvement of the dispersion area of about 96%.

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Onboard Trajectory Generation for Entry Vehicles via Adaptive Multivariate Pseudospectral Interpolation

Safe landing area determination for a Moon lander by reachability analysis

Usage of numerical optimization for generation and analysis of optimal trajectories has rapidly increased over the years. The approach presented here allows for the generation of numerical guidance schemes, which are not possible with analytical methods. SPARTAN (Shefex-3 Pseudospectral Algorithm for Re-entry Trajectory Analysis) is a tool based on the use of the global Pseudospectral methods for the transcription of optimal control problems. This method has several advantages. It removes the Runge phenomenon and it has an exponential convergence to the corresponding Optimal Control Problem (OCP) that can be numerically validated when it is applied to smooth problems. The initial infinite dimensional OCP is transcribed into a Non-Linear Programming (NLP) problem by a proper collocation of the differential equations and the constraints for the related problem. The resulting NLP can then be solved by off-the-shelf solvers. Two realistic example problems are given to demonstrate the performance of SPARTAN, and optimal trajectories were generated for both problems.

SPARTAN: An Improved Global Pseudospectral Algorithm for High-Fidelity Entry-Descent-Landing Guidance Analysis

In this paper, we compare two control techniques for a DJI F450 quadcopter which is controlled and stabilized by a non-rooted onboard Android smartphone, without the aid of an external IMU. Specifically, we compare an advanced modelfree PID and LQI controller. Since Android is not a realtime system, the control commands and sensor measurements are subject to significant latencies, and hence the PID controller is modified to account for non-trivial measurement asynchronicities. We also show that some features can be added to the widely used baseline PID to obtain better performance in the presence of latencies and noise. Finally, we introduce a LQI controller which is capable of satisfactorily tracking a reference command in the presence of errors, noise, and model uncertainties, and compare the results to the PID controller.

A comparison between advanced model-free PID and model-based LQI attitude control of a quadcopter using asynchronous android flight data

In this paper the effects of the use of the dual-based hybrid Jacobian computation in combination with the Pseudospectral Methods are thoroughly inspected. The dual-step differentiation method is implemented in SPARTAN (SHEFEX-3 Pseudospectral Algorithm for Re-entry Trajectory ANalysis), a tool based on the use of the global Flipped Radau Pseudospectral method for the transcription of optimal control problems. The dual number theory is exploited to provide an exact computation of the Jacobian matrix associated with the NonLinear Programming (NLP) problem to be solved. The dual-step differentiation method is compared to standard differentiation schemes (the central difference and the complex-step approximations) and applied in the solution of two examples of optimal control problem using two different off-the-shelf NLP solvers (SNOPT and IPOPT). Differentiation based on dual number theory is proved to be a valid alternative to the traditional, well-known, differentiation schemes as its use improves, for the problems analysed, the accuracy of the results, especially in combination with SNOPT.

/pdf/exact-hybrid-jacobian-computation-for-optimaltrajectory-4vzk31grpc.pdf

Exact Hybrid Jacobian Computation for OptimalTrajectory Generation via Dual Number Theory

Developments in space technology have paved the way for more challenging missions which require advanced guidance and control algorithms for safely and autonomously landing on celestial bodies. Instant determination of hazards, automatic guidance during landing maneuvers and likelihood maximization of safe landing are of paramount importance

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Yunus Emre Arslantas

Papers

Safe landing area determination for a Moon lander by reachability analysis

SPARTAN: An Improved Global Pseudospectral Algorithm for High-Fidelity Entry-Descent-Landing Guidance Analysis

A comparison between advanced model-free PID and model-based LQI attitude control of a quadcopter using asynchronous android flight data

Exact Hybrid Jacobian Computation for OptimalTrajectory Generation via Dual Number Theory

Approximation of attainable landing area of a moon lander by reachability analysis