Marco Sagliano

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

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...

Hybrid Jacobian Computation for Fast Optimal Trajectories Generation

Nowadays the new, increased capabilities of CPUs have constantly encouraged researchers and engineers towards the investigation of numerical optimization as an analysis and synthesis tool in order to generate optimal trajectories and the controls to track them. In particular, one of the most promising techniques is represented by direct collocation methods. Among these, Pseudospectral Methods are gaining popularity for their straightforward implementation and some useful properties, like the possibility to remove the Runge phenomenon present in traditional interpolation techniques and the “spectral” convergence observable in the case of smooth problems. Experience shows that the quality of the results and the computation time are strongly affected by the jacobian matrix describing the transcription of the optimal control problem as an NLP. In this paper, the structure of the Jacobian matrix is analyzed, taking advantage of the sparse nature of such matrices. Additionally, its systematic “hybridization” will be discussed and implemented in order to speed up the simulations. Two different problems will be then described and solved with this approach and the results will be shown. Finally, a quantitative analysis of the performances deriving from the use of the hybrid jacobian compared to a traditional numerical technique will be shown as well.

Performance analysis of linear and nonlinear techniques for automatic scaling of discretized control problems

Abstract This paper introduces three (one linear and two nonlinear) automatic scaling techniques for NLPs with states and constraints spread over several orders of magnitude, without requiring complex off-the-shelf external tools. All of these methods have been compared to standard techniques and applied to three problems using SNOPT and IPOPT. The results confirm that the proposed techniques significantly improve the NLP conditioning, yielding more reliable and in some cases, faster NLP solutions.

SHEFEX-3 Optimal Feedback Entry Guidance

SHEFEX is a DLR-led series of missions for scienti c experiments and reentry technology development. SHEFEX-2 was successfully launched from Norway (Andoya Rocket Range) in June 2012. To go on with the e ort to increase the technological level for real space missions, a new challenge in the next years with the development of SHEFEX-3 arises. SHEFEX-3, foreseen to be launched in 2016, will be more complex than SHEFEX-2 in virtue of the presence of a real guided re-entry phase, while for SHEFEX-2 an autonomous Guidance and Control phase was only partially foreseen. As a consequence, the mission will be ambitious, especially in the development of the GNC subsystem. DLR GNC Systems Department will be responsible for the development of Guidance and Navigation modules, while Control will be developed by Airbus Defense and Space, in cooperation with DLR. In this work the development of the nominal entry guidance, based on the use of PseudoSpectral Methods, is discussed. This feedforward control is then coupled with a Gain-Scheduled LQR tracking controller to reduce the error on the terminal points of the mission. Results show that the proposed approach meets the requirements on the physical constraints and the terminal states, satisfying at the same time the strong limitations coming from the need to have a highly-constrained angle of attack pro le.

Pseudospectral Convex Optimization for Powered Descent and Landing

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...

SPARTAN: A Novel Pseudospectral Algorithm for Entry, Descent, and Landing Analysis

In the last decades the theoretical development of more and more refined direct methods, together with a new generation of CPUs, led to a significant improvement of numerical approaches for solving optimal-control problems. One of the most promising class of methods is based on Pseudospectral Optimal Control. These methods not only provide an efficient algorithm to solve optimal-control problems, but also define a theoretical framework for linking the discrete numerical solution to the analytical one in virtue of the covector-mapping theorem. However, several aspects in their implementation can be refined. In this framework SPARTAN, the first European tool based on flipped Radau pseudospectral methods, has been developed. The tool, and the method behind it include two novel aspects. First, the discretized problem is automatically scaled with a novel technique, called Projected-Rows Jacobian Normalization. This avoids ill-conditioned problems, which could lead to non-reliable solutions. Second, the structure of the Jacobian matrix is exploited, and the dual-number theory is used for its computation. This yields faster and more accurate solutions, since the associated Jacobian matrix computed in this way is exact. Two concrete examples show the validity of the proposed approach, and the quality of the results obtained with SPARTAN.

Exact Hybrid Jacobian Computation for OptimalTrajectory Generation via Dual Number Theory

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.

Simulations and Flight Tests of a New Nonlinear Controller for the EAGLE Lander

This paper describes the complete control strategy developed for EAGLE, a Vertical Takeoff, Vertical-Landing vehicle conceived and realized by the German Aerospace Center for the testing and the validation of GNC technologies. A nonlinear controller, divided in thrust-vector control and position control, based on Sliding Mode Theory, has been developed. Simulations and real flight tests, realized in a DLR ad-hoc facility, are described. Results show that the proposed control strategy is able to successfully control EAGLE in a highly constrained scenario, as well as in the presence of multiple uncertainties and disturbances.

Stochastic Optimal Trajectory Generation via Multivariate Polynomial Chaos

This thesis presents a framework that has been developed in order to compute stochastic optimal trajectories. This is achieved by transforming the initial set of stochastic ordinary differential eq ...

Optimal Drag-Energy Entry Guidance via Pseudospectral Convex Optimization

In this paper a new drag-energy scheme, based on the use of pseudospectral methods and convex optimization, is proposed. One of the most successful technologies to deal with atmospheric entry is the class of drag-tracking schemes, a direct heritage of the Space Shuttle program. The method that we propose exploits the drag-dynamics, and allows for an e�cient automatic design of an optimal entry pro�le satisfying all the longitudinal constraints acting on the vehicle. A new representation of the entry-guidance problem, able to loss-less convexify the formulation, is provided. Numerical simulations con�rm the validity of the proposed scheme as tool for further improving the autonomy of modern entry guidance systems, with a mean �nal range-to-go error in the order of three hundred meters, and the capability to re-compute a complete constrained trajectory to meet the mission requirements.