Publications

Abstract

Multi-rotor UAVs suffer from a restricted range and flight duration due to limited battery capacity. Autonomous landing on a 2D moving platform offers the possibility to replenish batteries and offload data, thus increasing the utility of the vehicle. Classical approaches rely on accurate, complex and difficult-to-derive models of the vehicle and the environment. Reinforcement learning (RL) provides an attractive alternative due to its ability to learn a suitable control policy exclusively from data during a training procedure. However, current methods require several hours to train, have limited success rates and depend on hyperparameters that need to be tuned by trial-and-error. We address all these issues in this work. First, we decompose the landing procedure into a sequence of simpler, but similar learning tasks. This is enabled by applying two instances of the same RL based controller trained for 1D motion for controlling the multi-rotor's movement in both the longitudinal and the lateral directions. Second, we introduce a powerful state space discretization technique that is based on i) kinematic modeling of the moving platform to derive information about the state space topology and ii) structuring the training as a sequential curriculum using transfer learning. Third, we leverage the kinematics model of the moving platform to also derive interpretable hyperparameters for the training process that ensure sufficient maneuverability of the multi-rotor vehicle. The training is performed using the tabular RL method Double Q-Learning. Through extensive simulations we show that the presented method significantly increases the rate of successful landings, while requiring less training time compared to other deep RL approaches. Furthermore, for two comparison scenarios it achieves comparable performance than a cascaded PI controller. Finally, we deploy and demonstrate our algorithm on real hardware. For all evaluation scenarios we provide statistics on the agent's performance. Source code is openly available at https://github.com/robot-perception-group/rl\_multi\_rotor\_landing.

Abstract

We show that quadratic constraints admit a semi-algebraic interpretation of dynamic systems. This allows us to improve the analysis of polynomial systems under nonlinear feedback laws by use of the general S-procedure. Extending results to integral quadratic constraints, with the aid of LaSalle’s invariance theorem, we obtain a general stability proof for a larger class of multipliers. Numerical results show that the resulting hierarchy of sum-of-squares problems yields much better stability estimates for an exemplary unstable system with nonlinear stabilizing feedback than local approximations.

Abstract

We propose a gradient-based method to solve quasiconvex optimization problems through decomposed optimization and prove local superlinear convergence under mild regularity assumptions at the optimal solution. A practical implementation further provides global convergence while maintaining the fast local convergence. In numerical examples from generalized cone programming, the proposed method reduced the number of iterations to 18 to 50% compared to bisection.

Abstract

Markerless human motion capture (mocap) from multiple RGB cameras is a widely studied problem. Existing methods either need calibrated cameras or calibrate them relative to a static camera, which acts as the reference frame for the mocap system. The calibration step has to be done a priori for every capture session, which is a tedious process, and re-calibration is required whenever cameras are intentionally or accidentally moved. In this letter, we propose a mocap method which uses multiple static and moving extrinsically uncalibrated RGB cameras. The key components of our method are as follows. First, since the cameras and the subject can move freely, we select the ground plane as a common reference to represent both the body and the camera motions unlike existing methods which represent bodies in the camera coordinate system. Second, we learn a probability distribution of short human motion sequences ($\sim$1 sec) relative to the ground plane and leverage it to disambiguate between the camera and human motion. Third, we use this distribution as a motion prior in a novel multi-stage optimization approach to fit the SMPL human body model and the camera poses to the human body keypoints on the images. Finally, we show that our method can work on a variety of datasets ranging from aerial cameras to smartphones. It also gives more accurate results compared to the state-of-the-art on the task of monocular human mocap with a static camera.

Abstract

For tracking and motion capture (MoCap) of animals in their natural habitat, a formation of safe and silent aerial platforms, such as airships with on-board cameras, is well suited. In our prior work we derived formation properties for optimal MoCap, which include maintaining constant angular separation between observers w.r.t. the subject, threshold distance to it and keeping it centered in the camera view. Unlike multi-rotors, airships have non-holonomic constrains and are affected by ambient wind. Their orientation and flight direction are also tightly coupled. Therefore a control scheme for multicopters that assumes independence of motion direction and orientation is not applicable. In this letter, we address this problem by first exploiting a periodic relationship between the airspeed of an airship and its distance to the subject. We use it to derive analytical and numeric solutions that satisfy the formation properties for optimal MoCap. Based on this, we develop an MPC-based formation controller. We perform theoretical analysis of our solution, boundary conditions of its applicability, extensive simulation experiments and a real world demonstration of our control method with an unmanned airship.

Abstract

Solving the decision-making problem between pursuing the objective of covering distance and exploiting thermal updrafts is the central challenge in cross-country soaring flight. The need for trading short-term rewarding actions against actions that pay off in the long term makes for a hard-to-solve problem. Policies resulting from reinforcement learning offer the potential to handle long-term correlations between actions taken and rewards received. The paper presents a reinforcement learning setup, which results in a control strategy for the autonomous soaring sample application of GPS Triangle racing. First, we frame the problem in terms of a Markov decision process. In particular, we present a straightforward model for the three-degrees-of-freedom system dynamics of a glider aircraft that does not make any simplifying assumptions regarding the wind field or the relative aircraft velocity. The competition task is decomposed into subtasks, then. Stochastic gradient ascent solves the associated hierarchical reinforcement learning problem without the designer employing any further, potentially deficient heuristics. We present an implementation of the overall policy alongside an updraft estimator on embedded hardware aboard an unpiloted glider aircraft. Flight-test results validate the successful transfer of the hierarchical control policy trained in simulation to real-world autonomous cross-country soaring.

Abstract

The Laser Interferometer Space Antenna (LISA) mission is a space-borne observatory designed to detect and characterize gravitational wave sources inaccessible to ground-based detectors. The mission relies on laser interferometry to measure changes in space-time. In this context, non-avoidable noise sources within the LISA system, including tilt-to-length (TTL) coupling, reduce the detector’s resolution and complicate achieving the mission’s goals unless appropriate mitigation strategies are implemented. This paper applies time-delay interferometry infinity (TDI-) for TTL noise estimation in LISA and assesses its suitability from the perspective of system identification and calibration for the first time. The recently published TDI- concept indicates a different frequency response within the LISA measurement band compared to the standard methodology of TDI second-generation. Our main contribution is demonstrating the advantages of the TDI- algorithm for TTL noise calibration in space-borne interferometer constellations. Specifically, we show that this algorithm improves the estimation performance of TTL noise due to its frequency behavior while requiring less computation time. The reduction in computational effort afforded by the TDI- algorithm could accelerate the availability of calibrated TDI data for astrophysical analysis if required by the LISA science community. The improvement in estimation performance underscores the concept’s potential to enhance the detector’s sensitivity further.

Abstract

Future space observatories achieve detection of gravitational waves by interferometric measurements of a carrier phase, allowing to determine relative distance changes, in combination with an absolute distance measurement based on the transmission of pseudo-random noise chip sequences. In addition, usage of direct-sequence spread spectrum modulation enables data transmission. Hereafter, we report on the findings of a novel performance evaluation of planned receiver architectures, performing phase and distance readout sequentially, addressing the interplay between both measurements. An analytical model is presented identifying the power spectral density of the chip modulation at frequencies within the measurement bandwidth as the main driver for phase noise. This model, verified by numerical simulations, excludes binary phase-shift keying modulations for missions requiring pico-meter noise levels at the phase readout, while binary offset carrier modulation, where most of the power has been shifted outside the measurement bandwidth, exhibits superior phase measurement performance. Ranging analyses of the delay-locked loop reveal strong distortion of the pulse shape due to the preceding phase tracking introducing ranging bias variations. Numerical simulations show that these variations, however, which originate from data transitions, are compensated by the delay tracking loop, enabling sub-meter ranging accuracy, irrespective of the modulation type.

Abstract

This paper proposes a method for enlarging the region of attraction of Linear Model Predictive Controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the Feasibility Governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC feedback law remains feasible. Offline polyhedral projection algorithms based on multi-objective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference.

Abstract

In this practical approach to distributed propulsion, the solar-powered manned motorglider icaré 2 has been used as a testbed for wingtip propulsion. The large wingspan and slow cruising speed of icaré 2 are highly suitable to assess the influence and potential of propellers at the wingtips for yaw control. The paper describes the work of a multidisciplinary team consisting of researchers, engineers, pilots and students, starting from the initial idea to use propellers at the wingtips of icaré 2 up to the actual flight test campaign. First, the design and development of the modular wingtip pods are described to house the propeller, electric motor, battery and further sensors and control systems. Furthermore, the modifications required for integrating the wingtip pods on the aircraft itself are outlined and the electrical and mechanical interfaces are defined and described. To obtain a permit to fly for the new configuration of the aircraft, several tests on system level of the wingtip pods needed to be conducted and documented for the authorities. Finally, the flight test campaigns carried out to date are outlined and described including the planning, lessons learned and results.

Abstract

The Laser Interferometer Space Antenna (LISA) mission aims to observe gravitational waves featuring a three-spacecraft interferometer constellation with an arm length of 2.5 Mio km. In support of maximizing LISA's scientific return, the paper presents the design of coordinated spacecraft constellation maneuvers tailored for high-precision estimation of tilt-to-length (TTL) coupling noise under the influence of gravitational wave events. Tilt-to-length coupling couples the angular jitter of the three LISA spacecraft and their optomechanical assemblies to longitudinal measurement noise of the interferometers. The effect is a fundamental limitation of LISA's sensitivity and spaceborne long-arm interferometers, in general. The limitation can be avoided by estimating tilt-to-length coupling noise and correcting the scientific measurements. Former research allows limited conclusions to be drawn about the feasibility of accurate tilt-to-length coupling estimation because only the effect of system-internal noise sources has been addressed. Since tilt-to-length coupling noise in LISA is estimated and corrected based on science instrument measurements, the calibration shall be robust against the disturbing impact of gravitational wave events. The paper quantifies the deterioration of tilt-to-length parameter observabilities in the view of stellar and galactic events without maneuver execution. Then the developed maneuver design method is shown to provide accurate estimation results in the more realistic scenario. Although the approach temporarily reduces the number of independent scientific signals, the scientific operation mode of the spacecraft constellation can be maintained.

Abstract

Graph-based design languages have received increasing attention in the research community, because they offer a promising approach to address several major issues in engineering, e.g., the frequent manual data transfer between computer-aided design (CAD) and computer-aided engineering (CAE) systems. Currently, these issues prevent the realization of machine executable digital design processes of complex systems such as vehicles. Promising scenarios for urban transportation include an interconnection of mass transportation systems such as buses and subways with individual vehicles for the so-called “last mile” transport. For several reasons, these vehicles should be as small and light as possible. A considerable reduction in weight and size can be achieved, if such vehicles are tailored to the individual size, weight and proportion of the individual user. However, tailoring vehicles for the individual characteristics of each user go beyond a simple building set and require a continuous digital design process. Consequently, the topic of this paper is a digital design process of a self-balanced scooter, which can be used as an individual last-mile means of transport. This process is based on graph-based design languages, because in these languages, a digital system model is generated, which contains all relevant information about a design and can be fed into any simulation tool which is needed to evaluate the impact of a possible design variation on the resulting product performance. As this process can be automated by digital compilers, it is possible to perform systematic design variations for an almost infinite amount of parameters and topological variants. Consequently, these kinds of graph-based languages are a powerful means to generate viable design alternatives and thus permit fast evaluations. The paper demonstrates the design process, focusing on the drive system of the respective balanced two-wheel scooter and highlights the advantages (data integration and possibility for machine execution).

Abstract

In this letter, we introduce a deep reinforcement learning (DRL) based multi-robot formation controller for the task of autonomous aerial human motion capture (MoCap). We focus on vision-based MoCap, where the objective is to estimate the trajectory of body pose, and shape of a single moving person using multiple micro aerial vehicles. State-of-the-art solutions to this problem are based on classical control methods, which depend on hand-crafted system, and observation models. Such models are difficult to derive, and generalize across different systems. Moreover, the non-linearities, and non-convexities of these models lead to sub-optimal controls. In our work, we formulate this problem as a sequential decision making task to achieve the vision-based motion capture objectives, and solve it using a deep neural network-based RL method. We leverage proximal policy optimization (PPO) to train a stochastic decentralized control policy for formation control. The neural network is trained in a parallelized setup in synthetic environments. We performed extensive simulation experiments to validate our approach. Finally, real-robot experiments demonstrate that our policies generalize to real world conditions.

Abstract

The reduction of rotor-induced vibrations has been a major concern in the history of helicopter engineering. This has led to the development of numerous countermeasures, which cause the vibration levels to decrease considerably. Recent findings have shown that the reduced level of rotor vibrations highlights the importance of turbulence for the ride qualities. The rejection of atmospheric disturbances is a key task of the flight control system (FCS). However, the FCS design is currently focused on stability and handling qualities rather than ride qualities. This work addresses this shortcoming by the introduction of a systematic control design procedure. The improvement of ride qualities is achieved by linking an existing discomfort criterion to parameters of the sensitivity function. This allows the systematic modification of these parameters according to their contribution to discomfort. The approach is embedded into a design framework for systematic compliance with stability and handling quality specifications. The procedure is applied to the control design of a light helicopter resulting in considerably improved ride qualities, while compliance with stability and handling quality specifications is maintained. This represents an important step towards a more comprehensive ride quality engineering for rotorcraft that goes beyond the reduction of rotor-induced vibrations.

Abstract

This work presents a new approach to integrated localization and characterization of multiple thermal updrafts. A particle-filter-based method is proposed, which allows estimating position, strength, and spread of several thermals at once. To assess the achievable accuracy of an estimate, the Cramér–Rao lower bound for the specific filtering problem is evaluated. An analysis highlights how the most common flight patterns harm observability. Monte Carlo simulation results for a fixed-wing aircraft encountering several thermals showcase the unique ability of the proposed updraft estimator to localize multiple thermals rapidly. The mapping of a transient thermal cell is assessed with respect to an observability measure derived from the estimated Fisher information. Feasibility of the approach is demonstrated by evaluating real flight data of a glider aircraft circling thermal updrafts.

Abstract

© 2020 American Institute of Aeronautics and Astronautics Inc.. All rights reserved. Beyond aerodynamic stall, the analysis of aircraft flight requires models accurately representing nonlinearities and instabilities. Previous bifurcation analysis studies therefore had a priori knowledge of the aircraft dynamics including dynamic damping. Yet, unlike airliners, extensive wind-tunnel tests and high-fidelity models are rarely available for small unmanned aircraft. Instead, continuous fluid dynamic simulations may provide basic insights into the aerodynamics, however limited to static conditions. In this paper, bifurcation analysis is presented as a tool to discuss the effects of unidentified pitch-damping dynamics during deep-stall transition that allows development of a nonlinear pitch-damping model for a small unmanned aircraft. By preliminary study of the static case, the model is extended based on deep-stall flight data to predict dynamics and stability. As a result, the deep-stall modes of the extended model are investigated in full envelope.

Abstract

© 2019 Elsevier Ltd Polynomial switching systems such as multivariate splines provide accurate fitting while retaining an algebraic representation and offering arbitrary degrees of smoothness; yet, application of sum-of-squares techniques for local stability analysis is computationally demanding for a large number of subdomains. This communiqué presents an algorithm for region of attraction estimation that is confined to those subdomains actually covered by the estimate, thereby significantly reducing computation time. Correctness of the results is subsequently proven and the run time is approximated in terms of the number of total and covered subdomains. Application to longitudinal aircraft motion concludes the study.

Abstract

Certification of inflight loss-of-control recovery is complicated by the highly nonlinear flight dynamics beyond stall. In lieu of extensive Monte Carlo simulations for flight control certification, sum-of-squares programming techniques provide an algebraic approach to the problem of nonlinear control synthesis and analysis. However, reliance on polynomial models has hitherto limited applicability to aeronautical control problems. Taking advantage of recently proposed piecewise polynomial models, this paper revisits sum-of-squares techniques for recovery of an aircraft from deep-stall conditions using a realistic yet tractable aerodynamic model. The local stability analysis of classical controllers is presented as well as synthesis of polynomial feedback laws with the objective of enlarging their nonlinear region of attraction. A newly developed synthesis algorithm for infinite-horizon backward reachability facilitates the design of recovery control laws, ensuring stable recovery by design. The paper's results motivate future research in aeronautical sum-of-squares applications.

Abstract

This work addresses the problem of three-dimensional target motion analysis from bearing measurements. The established description of uncertain directional data involves azimuth and elevation angles with additive Gaussian noise. Investigation of this widely accepted representation in terms of the corresponding Fisher information matrices reveals that the underlying probability densities are only valid for small absolute elevation angles and precise measurements. Employing spherical statistics, an alternative representation is proposed that is sensible for the whole state space and arbitrarily imprecise bearing sensors. Based on this, a globally valid posterior Cramér-Rao lower bound is derived.

Abstract

© 2018 Several techniques have been proposed for piece-wise regression as extension to standard polynomial data fitting, either selecting the joints a priori or adding computational load for optimal joints. The pwpfit1 toolbox provides piece-wise polynomial fitting without pre-selection of joints using linear-least square (LSQ) optimization only. Additional constraints are realised as constraint matrices for the LSQ problem. We give an application example for the multi-variable aerodynamic coefficients of the general transport model in pre-stall and post-stall.

Abstract

This work presents a new description of the three-dimensional bearings-only tracking problem. A review of established approaches reveals that the common use of elevation and azimuth angles in the state or the measurement model can cause unrealistic error distributions and is not well-suited to Kalman filtering under certain relevant circumstances. It is furthermore shown that such methods immanently corrupt rotational invariance and thus let estimation performance rely on a fortunate choice of the inertial reference system. Based on these considerations, an alternative representation is derived that aims at eliminating the prior identified shortcomings. A corresponding tracking filter is designed and demonstrated to give equivalent or superior performance compared to usual approaches.

Abstract

In this paper, a particle filter is proposed to estimate attitude and velocity onboard a small unmanned aerial system using GPS, gyro, and accelerometer measurements. For the proposed filter setup, attitude observability heavily depends on the vehicle trajectory. Therefore, a measure of nonobservability is introduced to track the uncertainty in the attitude estimate. For the nonlinear estimation problem at hand, the use of a particle filter instead of a classical extended Kalman filter has shown to be advantageous in terms of robustness. However, particle filters are computationally very demanding, and thus, are usually not applicable for navigation onboard small unmanned aerial systems. To overcome this problem, an onboard computer system has been developed, which comprises a field programmable gate array as coprocessor. To get a quantitative measure on the performance of the proposed algorithm, the field-programmable-gate-array-based onboard computer system running a pipelined particle filter for attitude and velocity estimation has been flight tested on a civil-aviation aircraft equipped with a high-precision attitude and heading reference system. Further tests have been carried out with a fixed-wing small unmanned aerial system, in which the pipelined particle filter has been used as attitude reference in a simple waypoint-navigation scenario.

Abstract

In-orbit rendezvous is a key enabling technology for many space missions that already enjoys significant heritage. However, complex hardware is generally required in order to measure the relative range. Achieving rendezvous employing only bearing/angle measurements would simplify the relative navigation hardware currently required, increasing robustness and reliability by reducing complexity, launch mass, and cost. The problem of bearings-only navigation has been intensively studied by the naval and military communities. Several authors have discussed the robustness and stability advantages of pseudomeasurement filters in two dimensions, where the nonlinear measurement equation is recast in a linear form with respect to the states. Motivated by these potentials, this work explores its extension into three-dimensional space, when the complexity of the measurement equations makes it impossible to directly apply existing formulations. In this paper, the three-dimensional measurement equation is recast using pseudomeasurements with a multiplicative noise term, and an optimal filter suited for this pseudomeasurement structure is developed. Finally, the resulting bearings-only pseudomeasurement filter is implemented for the case of in-orbit relative navigation. Monte Carlo simulations show this filter exhibits far superior performance and robustness when initialization errors are significant, compared to a traditional extended Kalman filter implementation.

Abstract

Future drag-free missions for space-based experiments in gravitational physics require a Gravitational Reference Sensor with extremely demanding sensing and disturbance reduction requirements. A co...

Abstract

Achieving precision pointing performance plays a decisive role in future space missions. Pointing performance is specified by a set of requirements consisting of absolute, window- and stability-time errors. The European Cooperation for Space Standardization categorizes this set in the following pointing performance error indices: absolute performance error (APE), mean performance error (MPE), relative performance error (RPE), performance drift error (PDE) and performance reproducibility error (PRE). The analysis of pointing error indices in time-simulations is straightforward as error data time-series can be described by standard statistics. However, for design purposes there exists no method that can directly and systematically handle control loop performance in terms of window- and stability-time pointing error indices. In this article we extend the standard multi-objective H2/H∞ control problem to explicitly take into account requirements on pointing error index performance. The main topic, however, is the derivation of a control design approach that subjects the closed-loop control system to only one matrix criterion, the H∞-norm. Therefore an optimization is set up to map pointing error index requirements into closed-loop specifications. The advantage of this approach is that the derived closed-loop specifications serve as indicators for the direct identification of design drivers, limits of performance and eventually systematic design trade-offs. Unlike in multi-objective H2/H∞ control design approaches, this can be done even before controller synthesis, and thus independently of the specified control problem feasibility. Moreover, the derived approach enables control design in the H∞ closed-loop shaping framework. Thus, various design objectives including pointing performance and robustness can be treated with one matrix criterion.

Abstract

<p><strong>Abstract.</strong> UAVs are becoming standard platforms for applications aiming at photogrammetric data capture. Since these systems can be completely built-up at very reasonable prices, their use can be very cost effective. This is especially true while aiming at large scale aerial mapping of areas at limited extent. Within the paper the capability of UAV-based data collection will be evaluated. These investigations will be based on flights performed at a photogrammetric test site which was already flown during extensive tests of digital photogrammetric camera systems. Thus, a comparison to conventional aerial survey with state-of-the-art digital airborne camera systems is feasible. Due to this reason the efficiency and quality of generating standard mapping products like DSM and ortho images from UAV flights in photogrammetric block configuration will be discussed.</p>

Abstract

Propulsion system characteristics determine to a large extent the dynamic behavior of a spacecraft. For many future science missions technologically novel micro-propulsion systems are required. In order to support its characterization, in-orbit experiments and subsequent data processing on ground can be an appropriate add-on to ground-based laboratory measurements. In this paper two identification methods for three major thruster parameters, thrust gain, thrust direction, and lever arm, are presented and compared. They are based on measurements of a precise inertial instrument that consists of two test masses, whose degrees of freedom are ``mixed'' with respect to its control principle, i.e. they are either drag-free controlled (free-flying) or suspension controlled (accelerometer mode). Using drag-free coordinates is a novel approach. It is related and compared to the more conventional approach using ``accelerometer-like'' measurements.

Abstract

The LISA Pathfinder Drift Mode is an experimental mode proposed for the LISA Pathfinder drag free space mission. The Drift Mode's specificity is to switch off a possibly noisy actuator periodically in order to minimize the actuation noise. The experiment delivers a measurement that includes data segments virtually free of any actuation force noise. The corresponding acceleration data is then used to estimate the experiment disturbance spectrum, using a calibrating and gap-filling algorithm.

Abstract

Drag-free control is an important technology required for scientific experiments in space that need free-fall conditions. This chapter describes a control design of a drag-free system that uses test masses with cubic shape (rather than spherical or cylindrical). Three interconnected control problems are considered: drag-free control of the test masses, suspension control of the test masses, and attitude control of the spacecraft. The case of two test masses is treated here rather generally, such that an application to more than two test masses or a reduction to a single test mass is straightforward. Both the derivation of the control structure and the performance optimization procedure of the feedback loops are described. It is shown that the proposed control design yields a very simple architecture of the onboard software for drag-free control and furthermore that it leads to an extreme operational flexibility for the experimentalist with respect to redefinition of control modes and performance optimization, on ground and in-flight.

Abstract

In this chapter $\mu$-analysis is applied to HIRM+RIDE using Trends and Bands type linear fractional transformation (LFT) based uncertainty models. An LFT representation for the stability margin criterion using Padée approximations is developed. Different general analyses are performed, such as tests for parametric interdependencies, decreased size of intervals for AoA and $\mu$ assessments treating Mach number and altitude as uncertain parameters. An optimisation based skew $\mu$ calculation is developed which avoids the risk of missing steep $\mu$ peaks, which has proven to be essential for problems with pure real value parameters. Both singleloop and multi-loop stability margin criteria are assessed for lateral and longitudinal dynamics.

Abstract

To solve the multipoint boundary-value problem (MPBVP) associated with a constrained optimal control problem, one needs a good guess not only for the state but also for the costate variables. A direct multiple shooting method is described, which yields approximations of the optimal state and control histories. The Kuhn--Tucker conditions for the optimal parametric control are rewritten using adjoint variables. From this representation, estimates for the adjoint variables at the multiple shooting nodes are derived. The estimates are proved to be consistent, in the sense that they converge toward the MPBVP solution if the parametrization is refined. An optimal aircraft maneuver demonstrates the transition from the direct to the indirect method.

Abstract

Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.

Abstract

This dataset contains detailed information, source code, and benchmark tests for CaΣoS: A nonlinear sum-of-squares optimization suite.Please refer to the "supplementary.pdf" for more information.

Abstract

This dataset contains source code and numerical examples for quasiconvex sum-of-squares problems via decomposed optimization. Usage NotesThe files in the examples folder correspond to the numerical examples provided in Section 6 of the accompanying publication.Before running the examples,Download required software from the links below; or unpack archives in the library folder.Add file gradsosopt.m as well as required software to MATLAB path.

Abstract

A nonlinear model predictive control (NMPC) approach for rate damping control of a low Earth orbit satellite in the initial acquisition phase is proposed. The only available actuators are magnetic coils which impose control torques on the satellite in interaction with the Earth's magnetic field. In the initial acquisition phase large rotations and high angular rates, and therefore strong nonlinearities must be dealt with. The proposed NMPC method, which is shown to guarantee closed-loop stability, efficiently reduces the kinetic energy of the satellite while satisfying the constraints on the magnetic actuators. Furthermore, due to the prediction of future trajectories, the negative effect of the well-known controllability restriction in magnetic spacecraft control is minimized. It is shown via a simulation example that the obtained closed-loop performance is improved when compared to a classical P-controller.

Abstract

The article presents an integrated approach for the design and control of entry trajectories. The output of the analytical design process is a drag profile together with the nominal sink rate and bank control. All quantities are functions of specific energy. The trajectory design is strongly related to a path control law, which consists of a linear feedback of the drag and sink rate errors. The control design is based on the solution of a globally valid linear model. In simulations, the guidance and control algorithm produces smooth and precise flight paths.

Abstract

Optimal guidance of a dynamic process requires a fast algorithm for the computation of optimal trajectories. The method described in this paper modifies the conventional ``direct approach'' with control parametrisation. Piecewise linearisation of the dynamic system accelerates the solution of initial value problems and facilitates the computation of gradients. A control transformation involving a simple feedback term allows to provide starting values automatically and increases the robustness of the method. The real-time capability is demonstrated at an aircraft which is to intercept a moving target in minimum time.

Abstract

Numerical solutions of multi-phase optimal control problems are considered, where a phase is defined as a subinterval in which the right-hand sides of the differential equations are continuous. At the phase boundaries, the state, control, and design vectors may have jumps; in addition, the dimension of these vectors as well as the dimension of the right-hand sides may change. Two direct methods for solving such problems are presented : a multiple-shooting approach and a collocation method. Both methods avoid the adjoint differential equations. By these transcriptions, the optimal control problem is converted into a nonlinear programming problem (NLP), which is solved using standard sequential quadratic programming (SQP) algorithms. The methods are applied to determine optimal ascent and reentry trajectories of a two-stage-to-orbit vehicle. Both methods are embedded into an advanced user interface which allows a user to edit most of the necessary input in a simple way. This utility is described briefly.

Abstract

We show that Newton methods for generalized equations are input-to-state stable with respect to perturbations such as due to inexact computations. We then use this result to obtain convergence and robustness of a multistep Newton-type method for multivariate generalized equations. We demonstrate the usefulness of the results with other applications to nonlinear optimization. In particular, we provide a new proof for (robust) local convergence of the augmented Lagrangian method.

Abstract

This paper presents a flight simulator study that examines whether a display inside the cockpit can aid helicopter pilots with little to no experience in completing basic maneuvers. The study participants have no prior experience as helicopter pilots. The flight simulation uses a dynamic model of a coaxial ultralight helicopter horizontal motion that includes a stability augmentation system. A virtual reality headset is used to give the participants a realistic sense of perspective. The benchmark task includes decelerating into hover and hovering above a target for a given time. Three cueing configurations are compared. One includes visual cues on the ground that mark the hover target position. The two others add either a heads down display or a heads up display inside the cockpit, which visualize the relative target position and a prediction of the helicopter motion. With the proposed displays available inside the cockpit, participants tend to reach the target faster and more consistently. Hover performance is not improved by an additional display as the pilots mostly rely on visual cues on the ground during hover. In summary, both log data and pilot feedback suggest that the proposed displays are primarily beneficial in flight phases where the helicopter moves.

Abstract

Machine Learning algorithms are used in this paper to synthesize models for an ultralight coaxial helicopter pilot controlling the roll- and pitch motion during stationary hover. Different topologies of neural networks modeling the pilot are evolved with a neuroevolutionary algorithm, and trained via a data-driven approach using datasets that are collected from both real hover sequences and piloted flight simulations. The models are validated using flight test data and evaluated in a closed loop simulation alongside helicopter and turbulence models. Results demonstrate the models capability to stabilize the helicopter during hover and thus, to imitate human pilot behavior.

Abstract

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local linearizations leading to tractable, convex sum-of-squares problems. Local convergence is proven under the assumption of strong regularity and the new approach is applied to estimate the region of attraction of a polynomial aircraft model.

Abstract

Bistable structures show promise for morphing applications as they have the capability of obtaining two stable shapes which do not require energy to be maintained. The vibration of a bistable structure has been modelled previously as a Duffing-Holmes oscillator. To control the motion of a bistable structure from one equilibrium point to the other, a hybrid unstable-then-stable position feedback controller has been successfully employed. The hybrid controller destabilizes the structure around the initial equilibrium position then stabilizes it around the second equilibrium point. Previously, the decision to switch from destabilization mode to stabilization mode is made based upon the position of the structure. In the present research, new methods for determining when to activate and deactivate the stabilizing and destabilizing control schemes are presented. The proposed methods employ optimization techniques, model predictive control, and energy methods to determine when to activate or deactivate each scheme. Results of numerical simulations for the proposed switching methods are presented in this work.

Abstract

Fixed wing and multirotor UAVs are common in the field of robotics. Solutions for simulation and control of these vehicles are ubiquitous. This is not the case for airships, a simulation of which needs to address unique properties, i) dynamic deformation in response to aerodynamic and control forces, ii) high susceptibility to wind and turbulence at low airspeed, iii) high variability in airship designs regarding placement, direction and vectoring of thrusters and control surfaces. We present a flexible framework for modeling, simulation and control of airships. It is based on Robot operating system (ROS), simulation environment (Gazebo) and commercial off the shelf (COTS) electronics, all of which are open source. Based on simulated wind and deformation, we predict substantial effects on controllability which are verified in real-world flight experiments. All our code is shared as open source, for the benefit of the community and to facilitate lighter-than-air vehicle (LTAV) research. (Source code: https://github.com/robot-perception-group/airship\_simulation.)

Abstract

UAVs have found an important application in archaeological mapping. Majority of the existing methods employ an offline method to process the data collected from an archaeological site. They are time-consuming and computationally expensive. In this paper, we present a multi-UAV approach for faster mapping of archaeological sites. Employing a team of UAVs not only reduces the mapping time by distribution of coverage area, but also improves the map accuracy by exchange of information. Through extensive experiments in a realistic simulation (AirSim), we demonstrate the advantages of using a collaborative mapping approach. We then create the first 3D map of the Sadra Fort, a 15th Century Fort located in Gujarat, India using our proposed method. Additionally, we present two novel archaeological datasets recorded in both simulation and real-world to facilitate research on collaborative archaeological mapping. For the benefit of the community, we make the AirSim simulation environment, as well as the datasets publicly available (Project web page: http://patelmanthan.in/castle-ruins-airsim/).

Abstract

Autonomous soaring constitutes an appealing academic sample problem for investigating machine learning methods within the scope of aerospace guidance, navigation, and control. The stochastic nature of small-scale meteorological phenomena renders the task of localizing and exploiting thermal updrafts suited for applying a reinforcement learning approach. Within this work, we present a training setup for learning an integrated control strategy for autonomous localization and exploitation of thermal updrafts. In particular, we propose a deep artificial neural network featuring a Long Short-Term Memory to represent the policy. Instead of just implementing a static control law, the recurrent structure facilitates observability and enables mapping the hard-to-model dynamics of thermal updrafts. The end-to-end type control policy integrates an estimator for updraft localization, including a latent state-transition model. We show in simulation, that the trained agent autonomously localizes and exploits stochastic, non-stationary thermal updrafts. The unaltered reinforcement learning setup can be deployed to further improve the control policy through real-world interactions.

Abstract

This paper presents a new control co-design optimization (CCDO) framework to integrate controller-agnostic, nonlinear viability constraints informed by the solutions to optimal control problems into the multidisciplinary design process. To implement the optimization, procedures to evaluate the sensitivity of the controllability constraint to variations in the design are defined. Two supersonic aircraft examples associated with low-speed flight regime constraints illustrate the new methodology and the steps involved in the process.

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This paper presents a methodology based on optimal control to characterize the ability of a supersonic aircraft to reject atmospheric disturbances during its final approach to land. A longitudinal flight dynamics model is considered for which a set of rejectable disturbances is defined based on the values of three proposed barrier functionals. The problem of finding an admissible control input is then converted into a discrete nonlinear optimal control problem (NOCP) by defining an objective function based on an augmented discretized nonlinear dynamics that takes into account the disturbance models. It uses the Kreisselheimer-Steinhauser aggregation function to enable the application of gradient-based optimization methods. As an illustration, such an approach is applied to three different configurations of a supersonic business jet in the landing flight phase and under gust and turbulence disturbances.

Abstract

Especially in urban environments where space is closely confined, VTOL vehicles used for Urban Air Mobility will need to be controlled with respect to ground in the horizontal plane in order to comply with path restrictions set by fixed obstacles. This work presents a control scheme in the horizontal plane that allows a pilot to command ground-based velocities with respect to the vehicle heading and inherently coordinates the turn whenever a change of heading is commanded. The turn coordination algorithm is adapted based on the flight state of the vehicle in order to compensate for the varying influence of wind. It is shown that the adaption improves the control performance during turning flight.

Abstract

This paper introduces the Feasibility Governor (FG): an add-on unit that enlarges the region of attraction of Model Predictive Control by manipulating the reference to ensure that the underlying optimal control problem remains feasible. The FG is developed for linear systems subject to polyhedral state and input constraints. Offline computations using polyhedral projection algorithms are used to construct the feasibility set. Online implementation relies on the solution of a convex quadratic program that guarantees recursive feasibility. The closed-loop system is shown to satisfy constraints, achieve asymptotic stability, and exhibit zero-offset tracking.

Abstract

© 2021, American Institute of Aeronautics and Astronautics Inc, AIAA. All Rights Reserved. Current flight control validation is heavily based on linear analysis and high fidelity, nonlinear simulations. Continuing developments of nonlinear analysis tools for flight control has greatly enhanced the validation process. Many analysis tools are reliant on assuming the analytical flight dynamics but this paper proposes an approach using only simulation data. First, this paper presents improvements to a method for estimating the region of attraction (ROA) of nonlinear systems governed by ordinary differential equations (ODEs) based only on trajectory measurements. Faster and more accurate convergence to the true ROA results. These improvements make the proposed algorithm feasible in higher-dimensional and more complex systems. Next, these tools are used to analyze the four-state longitudinal dynamics of NASA's Generic Transport Model (GTM) aircraft. A piecewise polynomial model of the GTM is used to simulate trajectories and the developed analysis tools are used to estimate the ROA around a trim condition based only on this trajectory data. Finally, the algorithm presented is extended to estimate the ROA of finitely many equilibrium point systems and of general equilibrium set (arbitrary equilibrium points and limit cycles) systems.

Abstract

Rate-limited actuators introduce nonlinearities into a control system, which results in a loss of phase and a reduction of amplitude of the control signal. These effects have been identified as being a main contributor to pilot induced oscillation incidents and therefore methods were developed in the field of aircraft control systems in order to compensate the detrimental effects. This work evaluates the application of such a method when used for rate-limited electric motors in a large-scale (man-carrying) multicopter vehicle. An approach using a feedback-type method is presented and its performance evaluated using a simulation model. It can be shown that the approach improves the vehicle behavior and stability in situations where extreme changes of the motor turning speeds are required.

Abstract

© 2020 IEEE. Aircraft upsets are a major cause of fatalities in civil aviation. Unfortunately, recovery from upset scenarios is challenging due to the combination of nonlinearities, actuator limits, and upset modes. In this paper, we consider the use of Model-Predictive Control (MPC) in combination with a recently proposed piecewise polynomial prediction model, for six degree-of-freedom upset recovery. MPC naturally handles nonlinearities and constraints and has a provably large closed-loop region of attraction making it an appealing methodology for upset recovery problems. We present a recovery formulation then illustrate its utility through high fidelity simulation case studies, using the Generic Transport Model, of recovery from oscillatory spin and steep spiral upset conditions.

Abstract

© The Author(s) 2019. Flow visualisations are essential to better understand the unsteady aerodynamics of flapping wing flight. The issues inherent to animal experiments, such as poor controllability and unnatural flapping when tethered, can be avoided by using robotic flyers that promise for a more systematic and repeatable methodology. Here, we present a new flapping-wing micro air vehicle (FWMAV)-specific control approach that, by employing an external motion tracking system, achieved autonomous wind tunnel flight with a maximum root-mean-square position error of 28 mm at low speeds (0.8–1.2 m/s) and 75 mm at high speeds (2–2.4 m/s). This allowed the first free-flight flow visualisation experiments to be conducted with an FWMAV. Time-resolved stereoscopic particle image velocimetry was used to reconstruct the three-dimensional flow patterns of the FWMAV wake. A good qualitative match was found in comparison to a tethered configuration at similar conditions, suggesting that the obtained free-flight measurements are reliable and meaningful.

Abstract

Aircraft upset recovery requires aggressive control actions to handle highly nonlinear aircraft dynamics and critical state and input constraints. Model predictive control is a promising approach for returning the aircraft to the nominal flight envelope, even in the presence of altered dynamics or actuator limits; however, proving stability of such strategies requires careful algebraic or semi-algebraic analysis of both the system and the proposed control scheme, which can be challenging for realistic control systems. This paper develops economic model predictive strategies for recovery of a fixed-wing aircraft from deep-stall. We provide rigorous stability proofs using sum-of-squares programming and compare several economic, nonlinear, and linear model predictive controllers.

Abstract

© 2018 IEEE. In this paper, we consider a small unmanned aircraft and data collected during regular and deep-stall flight. We present an identification method for the thrust force generated by the propulsion system based on the in-flight measurements where we make use of the well-known linear and quadratic approximations of the lift and drag coefficients, respectively, for low angles of attack. This overcomes the lack of propeller thrust measurements and the obtained models are successfully evaluated against CFD simulation. The identified thrust model proves applicable beyond low angles of attack, thus enabling force estimation in the full flight envelope.

Abstract

© 2018, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. Aeronautical research has investigated the Generic Transport Model (GTM) in windtunnel studies and provides today an elaborated aerodynamic model for designing methods dedicated to convergence analysis or control problems of aerial vehicles. In this paper, we propose a novel approach for fitting aerodynamic coefficients, namely piece-wise polynomial identification, which is based on measurements in both pre- and post-stall region. The developed method suggests a systematic approach to determine full envelope better than the purely polynomial models published yet. As a result, an analysis of GTM's longitudinal trim conditions has been successfully applied on the piece-wise identified model and achieves better results than polynomial models. Based on the trim conditions, safe set computation for linear-quadratic controllers is argued to be a powerful tool for verification of nonlinear control systems. Using common and multiple Lyapunov-functions theory, we are able to present a method for the safe set computation with piece-wise defined systems dynamics.

Abstract

© 2017 IEEE. Polynomial models for the aerodynamic coefficients are not able to incorporate the full-envelope aerodynamics and offer only vaguely fitting at high angles of attack. In this paper, we propose a novel approach, namely piece-wise polynomial identification; this method provides a systematic approach for full-envelope aerodynamic fitting, considering measurements both of the pre-stall and post-stall region. As a result, a six-degrees-of-freedom, full-envelope analysis of trim conditions has successfully been applied for a large unmanned aerial vehicle.

Abstract

In-flight loss-of-control (LOC-I) still poses a severe threat to today's commercial aviation. Hence, we review the literature for non-linear analysis and control methods of LOC-I and upset recovery. Using state-of-the-art methods such as continuation theory and reachability estimation, we sketch an analysis of an aircraft's flight envelope in terms of its trim conditions and propose control approaches both within and outside the envelope.

Abstract

This paper addresses the design and verification of an attitude control system for an agile satellite using experimental data. Typical agile satellites are equipped with control momentum gyros, which allow for the generation of high internal reaction torques and hence attitude maneuvers with high angular rates. The architecture of the attitude control system with design implications is presented and discussed. In order to mitigate the risks associated with design and verification of the highly demanding agile attitude control, experimental results involving a hardware in-the-loop demonstrator are presented. The overall design process and closed loop performance evaluation allows an increasing technology readiness level for target missions.

Abstract

Three degree of freedom (3-DOF) ACS satellite testbed systems are essential hardware-in-loop testing facilities for the construction of a wide range of intelligent AOCS algorithms. Intrepid is a 3-DOF spherical air-bearing satellite testbed custom designed at the Surrey Space Centre, UK, and installed on-site at Airbus DS in Friedrichshafen, Germany for the AOCS & GNC Group. The testbed consists of a table-top for the mounting of satellite hardware, 4 control moment gyroscopes (CMGs) mounted in a pyramid configuration and a sensor suite including an IMU. Under normal operation the CMGs can be used to command the table to required angles thus testing the AOCS alogrithms using only the IMU as an attitude sensor. Satellites require long-term stable and short-term high resolution attitude measurements, which are fused on-board to estimate the attitude. The IMU provides high resolution attitude information, but has the drawback of not knowing the initial attitude and also drifting over time. This paper concerns the development of an absolute attitude determination system (AADS) that utilises an infra-red camera, a series of LEDs positioned across the table-top, and intelligent software to independently determine the absolute attitude of the table-top. The system thus provides long-term stable attitude measurements and overcomes the shortcomings of the IMU. The newly installed AADS software contains vision processing and triangulation algorithms that provide real-time absolute attitude information to the host computer. The vanilla system can achieve attitude determination accuracy within 1 degree in yaw and 2 degrees in pitch and roll. The software can calibrate itself compensating for intrinsic and extrinsic offsets including incorrectly placed LEDs and a misaligned camera system. A sub-pixel feature detection technique is utilised to enhance the accuracy of the system. It is shown that by modifying the position of the LEDs or modifying the placement of the camera, more optimal attitude accuracies along different axes can be obtained.This paper will detail the main operation of the system from both a hardware and software perspective and provide experimental results during operation.