Open-Source Visualization of Reusable Rockets Motion: Approaching Simulink - FlightGear Co-simulation

This paper shows how to approach effective visualization of the motion of reusable rocketsby combining Simulink / Matlab modeling with the capabilities of FlightGear, a state-of-the-artopen-source tool typically used for aircraft simulation in the gaming community. We describethe entire open-source toolchain and the steps needed for the coupling of the involved software,with detailed code provided as Appendices. Finally, We propose a concrete example, associatedwith the application to the motion of reusable rockets

Costate Convergence with Legendre-Lobatto Collocation for Trajectory Optimization

This paper introduces a new method of discretization that collocates both endpoints of the domain and enables the complete convergence of the costate variables associated with the Hamilton boundary-value problem. This is achieved through the inclusion of an \emph{exceptional sample} to the roots of the Legendre-Lobatto polynomial, thus promoting the associated differentiation matrix to be full-rank. We study the location of the new sample such that the differentiation matrix is the most robust to perturbations and we prove that this location is also the choice that mitigates the Runge phenomenon associated with polynomial interpolation. Two benchmark problems are successfully implemented in support of our theoretical findings. The new method is observed to converge exponentially with the number of discretization points used

Attentional biases toward threat: the concomitant presence of difficulty of disengagement and attentional avoidance in low trait anxious individuals.

Attentional biases toward threats (ABTs) have been described in high anxious individuals and in clinical samples whereas they have been rarely reported in non-clinical samples (Bar-Haim et al., 2007; Cisler and Koster, 2010). Three kinds of ABTs have been identified (facilitation, difficulty of disengagement, and avoidance) but their mechanisms and time courses are still unclear. This study aimed to understand ABTs mechanisms and timing in low trait anxiety (LTA) and high trait anxiety (HTA) anxious individuals. In particular, in an exogenous cueing task we used threatening or neutral stimuli as peripheral cues with three presentation times (100, 200, or 500 ms). The main results showed that HTA individuals have an attentional facilitation bias at 100 ms (likely automatic in nature) whereas LTA individuals show attentional avoidance and difficulty to disengage from threatening stimuli at 200 ms (likely related to a strategic processing). Such findings demonstrate that threat biases attention with specific mechanisms and time courses, and that anxiety levels modulate attention allocation

Onboard Guidance for Reusable Rockets: Aerodynamic Descent and Powered Landing

This paper describes a novel general on-board guidance strategy which can be applied toboth the aerodynamically-controlled descent and the powered landing phase of reusable rockets.The proposed guidance method is based on sequential convex optimization applied to a Cartesianrepresentation of the equations of motion. The contributions are an exploitation of convexand non-convex contributions, which are processed separately to maximize the computationalefficiency of the approach, the inclusion of highly nonlinear terms represented by aerodynamicaccelerations, a complete reformulation of the problem based on the use of Euler angle rates ascontrol means, an improved transcription based on the use of a generalized hp pseudospectralmethod, and a dedicated formulation of the aerodynamic guidance problem for reusable rockets.The problem is solved for a 40 kN-class reusable rocket. Results show that the proposedtechnique is a very effective methodology able to satisfy all the constraints acting on the system,and can be potentially employed online to solve the entire descent phase of reusable rockets inreal-time

Cathodal Transcranial Direct Current Stimulation over Posterior Parietal Cortex enhances distinct aspects of Visual Working Memory

In this study, we investigated the effects of tDCS over the posterior parietal cortex (PPC) during a visual working memory (WM) task, which probes different sources of response error underlying the precision of WM recall. In two separate experiments, we demonstrated that tDCS enhanced WM precision when applied bilaterally over the PPC, independent of electrode configuration. In a third experiment, we demonstrated with unilateral electrode configuration over the right PPC, that only cathodal tDCS enhanced WM precision and only when baseline performance was low. Looking at the effects on underlying sources of error, we found that cathodal stimulation enhanced the probability of correct target response across all participants by reducing feature-misbinding. Only for low-baseline performers, cathodal stimulation also reduced variability of recall. We conclude that cathodal- but not anodal tDCS can improve WM precision by preventing feature-misbinding and hereby enhancing attentional selection. For low-baseline performers, cathodal tDCS also protects the memory trace. Furthermore, stimulation over bilateral PPC is more potent than unilateral cathodal tDCS in enhancing general WM precision

Physical Modeling and Simulation of Reusable Rockets for GNC Verification and Validation

Reusable rockets must rely on well-designed Guidance, Navigation and Control (GNC) algorithms. Because they are tested and verified in closed-loop, high-fidelity simulators, emphasizing the strategy to achieve such advanced models is of paramount importance. A wide spectrum of complex dynamic behaviors and their cross-couplings must be captured to achieve sufficiently representative simulations, hence a better assessment of the GNC performance and robustness. This paper focuses on of the main aspects related to the physical (acausal) modeling of reusable rockets, and the integration of these models into a suitable simulation framework oriented towards GNC Validation and Verification (V&V). Firstly, the modeling challenges and the need for physical multibody models are explained. Then, the Vertical Landing Vehicles Library (VLVLib), a Modelica-based library for the physical modeling and simulation of reusable rocket dynamics, is introduced. The VLVLib is built on specific principles that enable quick adaptations to vehicle changes and the introduction of new features during the design process, thereby enhancing project efficiency and reducing costs. Throughout the paper, we explain how these features allow for the rapid development of complex vehicle simulation models by adjusting the selected dynamic effects or changing their fidelity levels. Since the GNC algorithms are normally tested in Simulink®, we show how simulation models with a desired fidelity level can be developed, embedded and simulated within the Simulink® environment. Secondly, this work details the modeling aspects of four relevant vehicle dynamics: propellant sloshing, Thrust Vector Control (TVC), landing legs deployment and touchdown. The CALLISTO reusable rocket is taken as study case: representative simulation results are shown and analyzed to highlight the impact of the higher-fidelity models in comparison with a rigid-body model assumption

An Instantaneous Impact Point Guidance for Rocket with Aerodynamics Control

This paper aims to propose a new guidance algorithm for a rocket with aerodynamics control for launch operations, based on the concept of the instantaneous impact point (IIP). In this study, the rocket with aerodynamics control is considered with the purpose of reducing dispersion of the impact point after separation of the rocket for safety reasons. Since a very limited aerodynamic maneuverability is typically allowed for the rocket due to the structural limit, a guidance algorithm producing a huge acceleration demand is not desirable. Based on this aspect, the proposed guidance algorithm is derived directly from the underlying principle of the guidance process: forming the collision geometry towards a target point. To be more specific, the collision-ballistic-trajectory where the instantaneous impact point becomes the target point, and the corresponding heading error are first determined using a rapid ballistic trajectory prediction technique. Here, the trajectory prediction method is based on the partial closed-form solutions of the ballistic trajectory equations considering aerodynamic drag and gravity. And then, the proposed guidance algorithm works to nullify the heading error in a finite time, governed by the optimal error dynamics. The key feature of the proposed guidance algorithm lies in its simple implementation and exact collision geometry nature. Hence, the proposed method allows achieving the collision course with minimal guidance command, and it is a desirable property for the guidance algorithm of the rocket with the aerodynamics control. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed guidance algorithm