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This paper proposes a novel longitudinal reference trajectory tracking guidance framework for Mars atmospheric entry. Unlike traditional methods that require strict adherence to pre-defined safe trajectories, this guidance framework incorporates path constraints into the closed-loop tracking process to ensure safety. The framework comprises a safety module and a guidance law module. The safety module employs an online path constraints management algorithm that converts real-time path constraints into equivalent control constraints and applies them to the guidance module. The guidance law module uses the anti-saturation generalized super-twisting based sliding mode (ASGSTSM) guidance law, which provides sufficient rapidity and robustness to achieve trajectory tracking while accounting for uncertainties and control saturation. Simulation results demonstrate that the proposed guidance framework effectively ensures compliance of the entry vehicle with path constraints. The ASGSTSM guidance law exhibits notable speed and robustness, making it adaptable within the guidance framework. Particularly, in Monte Carlo simulations introducing significant uncertainty, incorporating the ASGSTSM guidance law within the guidance framework resulted in convergence in all trajectory tracking processes, whereas guidance laws in the control group led to numerous failures. Additionally, the paper offers practical principles for designing guidance laws within this universal framework. This facilitates future research to easily replace the guidance law module based on specific mission requirements. [ABSTRACT FROM AUTHOR]

The trim flap is an aerodynamic control surface capable of allowing Mars entry vehicles to improve landing performance during the most dangerous entry, descent, and landing (EDL) phase. In present work, a deployable trim flap system was proposed to meet the aerodynamical trim requirement of the Tianwen-1 Mars probe, which provided a mass-saving alternative to the conventional use of the center-of-gravity (CG) offset of ballast mass. In order to guide the trim flap design, theoretical and finite element (FE) models were established to predict and evaluate the deployment performance. Then, a full-scale physical prototype was manufactured for deployment experiments to verify the design effectiveness as well as validate the theoretical and FE models. Results predicted by theoretical and FE models were in good agreement with deployment experiments. Furthermore, the effects of three factors on the deployment performance were investigated, including the non-linear behavior of the damping, acceleration environment, and backshell flexibility. The manufactured prototype was installed on the Tianwen-1 Mars probe, saving more than 300 kg when compared to the conventional use of ballast mass CG offset, and assisted Tianwen-1 in achieving a successful landing, making China the first country in the world to utilize the trim flap technology for Mars EDL. [ABSTRACT FROM AUTHOR]

Flush air data system (FADS) is able to sense pressure distribution on the surface of the vehicle's forebody during Mars entry phase. Existing studies on the FADS-based aerodynamics data estimation for Mars entry have not attached adequate attention to the potential FADS fault, which should not be ignored in practice from a reliability viewpoint. In this paper, a hybrid method is proposed to simultaneously achieve aerodynamic parameters estimation of Mars entry vehicle and FADS fault detection and tolerance. The estimation procedure merges triples algorithm based coarse estimation with least-square based precise estimation. Meanwhile, a fault identifier matrix is embedded in the estimation procedure, which is worked out from chi-square detection algorithm. The estimation with FADS fault tolerance is realized by the fusion of chi-square detection, hybrid estimation, and random sample consensus algorithms. Comparison simulations demonstrate the effectiveness of the proposed technique. • A hybrid approach is proposed to estimate aerodynamic parameters during Mars entry. • FADS fault detection and tolerance are merged into estimation procedure. • Four algorithms are combined for estimation with FADS fault detection and tolerance. • Simulation results show the necessity of FADS fault detection and tolerance. [ABSTRACT FROM AUTHOR]

The trim flap is an aerodynamic control surface capable of allowing Mars entry vehicles to improve landing performance during the most dangerous entry, descent, and landing (EDL) phase. In present work, a deployable trim flap system was proposed to meet the aerodynamical trim requirement of the Tianwen-1 Mars probe, which provided a mass-saving alternative to the conventional use of the center-of-gravity (CG) offset of ballast mass. In order to guide the trim flap design, theoretical and finite element (FE) models were established to predict and evaluate the deployment performance. Then, a full-scale physical prototype was manufactured for deployment experiments to verify the design effectiveness as well as validate the theoretical and FE models. Results predicted by theoretical and FE models were in good agreement with deployment experiments. Furthermore, the effects of three factors on the deployment performance were investigated, including the non-linear behavior of the damping, acceleration environment, and backshell flexibility. The manufactured prototype was installed on the Tianwen-1 Mars probe, saving more than 300 kg when compared to the conventional use of ballast mass CG offset, and assisted Tianwen-1 in achieving a successful landing, making China the first country in the world to utilize the trim flap technology for Mars EDL.

Recently, various unmanned and manned Mars exploration programs have been proposed. To send a space vehicle safely to the ground of Mars, the vehicle needs to be protected from the aerodynamic heating. The accurate prediction of the aerodynamic heating is important for the design of safe and light-weight thermal protection system. For the accurate prediction, it is necessary to simulate the plasma generated behind the shock wave and to clarify its internal state. To investigate the state of the plasma, spectroscopic measurement is useful. We performed the spectroscopic measurements of carbon dioxide (CO2) plasma generated using microwave discharge under the pressure condition during Mars entry. To investigate the basic characteristics of microwave-discharged CO2 plasma, the spectra of the radiation were obtained in the wavelength region of 200 to 800 nm. As a result, carbon monoxide (CO) fourth positive bands, CO third positive bands, CO Ångström bands, and atomic oxygen lines were observed. Electronic excitation temperature was also estimated by the Boltzmann plot method for the atomic oxygen lines. [ABSTRACT FROM AUTHOR]

The epistemic uncertainties caused by insufficient knowledge of the atmosphere, aerodynamic coefficient, and entry state render the entry process challenging, as they not only result in the deviation of the preplanned trajectory, but also may lead to the nonsatisfaction of path constraints. Herein, a robust epistemic uncertainty optimization (REUO) method based on evidence is proposed to solve the Mars entry trajectory optimization problem under epistemic uncertainty. A two-loop nested robust optimization (RO) model is formulated, in which the outer-loop optimization searches the optimal control while the inner-loop optimization calculates the extremal trajectory performances within each focal element (FE) to evaluate the evidence level. To solve the path constraint violation problem under uncertainties, the constraint design based on limitation bounds is considered in the RO model. The polynomial chaos expansion (PCE) is employed to obtain the approximate analytic function of the trajectory performance under uncertainties. Thereafter, the optimization based on ordinary stochastic entry dynamics in the inner loop is replaced by a simple parameter optimization of the analytic functions, which can be readily and rapidly solved. The REUO method is tested in a specific Mars entry mission. The simulation results show that the proposed method can identify the most robust solutions with the optimal trajectory performance under epistemic uncertainties. • Robust trajectory optimization model under epistemic uncertainty is formulated. • A robust epistemic uncertainty optimization method based on evidence is proposed. • Employment of nonintrusive PCE technique improves the optimization efficiency. [ABSTRACT FROM AUTHOR]

Traditional studies on Mars entry, descent, and landing usually take a divide-and-conquer approach where each phase is investigated separately. This paper proposed a new approach to achieve optimal integrated guidance for mid-lift high-mass Mars entry and powered descent. First, optimal Mars atmospheric entry and optimal powered descent are respectively modeled. Second, optimal handover problem is formulated to integrate the optimal Mars entry and powered descent problems in a collaborative optimization manner. Third, hp-adaptive pseudospectral method is employed to capture optimal entry guidance and propellant-optimal powered descent guidance. Reinforcement learning methodology is adopted to obtain the optimal handover, according to a large amount of trial results obtained from solving optimal Mars entry and powered descent problems. Finally, numerical simulations verified the optimality, robustness, and accuracy of the proposed technique through comparing with successive convexification approach under the nominal conditions and uncertainties, and the comparison results demonstrated the significant benefit of the integrated optimal guidance. • Optimal integrated guidance for Mars entry and powered descent is designed. • Integrated guidance is produced in a collaborative optimization manner. • Mars entry and powered descent guidance are combined via optimal handover. • Optimal handover is achieved using reinforcement learning approach. [ABSTRACT FROM AUTHOR]

In this paper, we present an adaptive mesh refinement method that is used in conjunction with local direct collocation methods for solving Mars entry trajectory optimization problems with a maximum parachute deployment altitude. The study focuses on the capability of the mesh refinement method to solve Mars entry trajectory optimization problems and the potential benefits of enabling angle-of-attack control. The numerical results show that Mars entry trajectory optimization problems can be solved accurately and efficiently using the proposed method. The accuracy is found to be comparable to that of indirect methods, and the computational time is on the order of several seconds, depending on the complexity of the problem. Furthermore, it is found that parachute deployment altitude gains of 2.2–3.1 km over pure bank control are possible if angle-of-attack control is enabled for a Mars Science Laboratory-type vehicle. Efforts are also made to investigate the influences of bank angle limits on entry trajectories, and it is found that the structure of the optimal bank angle profiles are generally similar for different bank angle limits, but a larger bank angle range allows an higher maximum parachute deployment altitude. • Mars entry trajectory optimization problems are solved accurately and efficiently. • The influence of bank limits on the terminal altitude can be as large as 1.4 km. •The terminal altitude can be increased by 2.2-3.1 km if AOA control is enabled. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a novel adaptive sliding‐mode control (ASMC) method for Mars entry guidance and the finite‐time convergence in the presence of large uncertainties can be guaranteed. With the help of gain adaptive law, the nonoverestimating value of control gains can be achieved, and then, the chattering can be attenuated by the proposed ASMC method. Meanwhile, the extended state observer is introduced to estimate and compensate for uncertainties and the nonoverestimating problem is resolved further. In addition, the proposed method does not require any knowledge on the upper bound of uncertainty, which yields to be used in practical systems. Finally, the numerical simulation results are given to demonstrate the effectiveness of the proposed guidance law. [ABSTRACT FROM AUTHOR]

Abstract The capability of autonomous fault detection and reconstruction is essential for future manned Mars exploration missions. Considering actuator failures and atmosphere uncertainties, we present a new active fault-tolerant control algorithm for Mars entry by use of neural network and structure adaptive model inversion. First, the online BP neural network is adopted to conduct the fault detection and isolation. Second, based on the structure adaptive model inversion, an adaptive neural network PID controller is developed for Mars entry fault-tolerant control. The normal PID controller will be automatically switched into neural network PID controller when an actuator fault is detected. Therefore, the error between the reference model and the output of the attitude control system would be adjusted to ensure the dynamic property of the entry vehicle. Finally, the effectiveness of the algorithm developed in this paper is confirmed by computer simulation. [ABSTRACT FROM AUTHOR]

Parameter uncertainties which may lead to divergence of traditional Kalman filters during Mars entry are investigated in this paper. To achieve high precision navigation, a Derivative-free Nonlinear version of an Extended Recursive Three-Step Filter (DNERTSF) is introduced, which suits nonlinear systems with arbitrary parameter uncertainties. A DNERTSF can estimate the state and the parameters simultaneously, and Jacobian and Hessian calculations are not necessary for this filter. Considering the uncertainties in atmosphere density, ballistic coefficient and lift-to-drag ratio, a numerical simulation of Mars entry navigation is carried out. Compared with the standard Unscented Kalman Filter (UKF), DNERTSF can effectively reduce the adverse effects of parameter uncertainties and achieve a high navigation accuracy performance, keeping position and velocity estimation errors at a very low level. In all, the DNERTSF in this paper shows good advantages for Mars entry navigation, providing a possible application for a future Mars pinpoint landing. [ABSTRACT FROM AUTHOR]

Uncertainties present in the Mars atmospheric entry process may cause state deviations from the nominal designed values, which will lead to unexpected performance degradation if the trajectory is designed merely based on the deterministic dynamic model. In this paper, a linear covariance based entry trajectory optimization method is proposed considering the uncertainties presenting in the initial states and parameters. By extending the elements of the state covariance matrix as augmented states, the statistical behavior of the trajectory is captured to reformulate the performance metrics and path constraints. The optimization problem is solved by the GPOPS-II toolbox in MATLAB environment. Monte Carlo simulations are also conducted to demonstrate the capability of the proposed method. Primary trading performances between the nominal deployment altitude and its dispersion can be observed by modulating the weights on the dispersion penalty, and a compromised result referring to maximizing the 3σ lower bound of the terminal altitude is achieved. The resulting path constraints also show better satisfaction in a disturbed environment compared with the nominal situation. [ABSTRACT FROM AUTHOR]

Supposing future orbiting and landing collaborative exploration mission as the potential project background, this paper addresses the issue of Mars entry integrated navigation using radio beacon, flush air data sensing system (FADS), and inertial measurement unit (IMU). The range and Doppler information sensed from an orbiting radio beacon, the dynamic pressure and heating data sensed from flush air data sensing system, and acceleration and attitude angular rate outputs from an inertial measurement unit are integrated in an unscented Kalman filter to perform state estimation and suppress the system and measurement noise. Computer simulations show that the proposed integrated navigation scheme can enhance the navigation accuracy, which enables precise entry guidance for the given Mars orbiting and landing collaborative exploration mission. [ABSTRACT FROM AUTHOR]

High-precision entry navigation capability is essential for future Mars pinpoint landing missions. An augmented robust three-stage extended Kalman filter (ARThSEKF) for integrated navigation algorithm of Mars atmospheric entry with models containing parameter uncertainties and measurement errors is presented in this paper. The derivation is conducted, and the character of stability has also been analysed, in which it has been proved to be uniformly asymptotically stable. In the further simulation of Mars entry-phase navigation, ARThSEKF showed a good performance to compare with the standard extended Kalman filter. As the atmosphere density uncertainties and unknown measurement errors have been estimated precisely, the state estimation errors were controlled to a low level, of which the position and velocity were less than 100 m and 5 m/s, respectively. Therefore, ARThSEKF is suitable for dealing with non-linear systems in the presence of parameter uncertainties and unknown measurement errors, which can fulfil the requirement of future pinpoint Mars landing mission. [ABSTRACT FROM PUBLISHER]

Reachable set (RS) is a useful tool in assessing the flight capability of the entry vehicle with the given initial entry state and the required control and path constraints. The evolution of the RS under the effects of uncertainties of some important entry parameters is also beneficial to the mission design and analysis. The objective of this paper is to investigate the RS evolution under parameter uncertainties. It would be computationally intensive to compute all the elements of the RS, and therefore only the RS boundary (RSB) extreme points, which well characterize the RS, are considered. The method of tracking drag profile is employed to generate each point of the RSB. By parameterizing the random uncertainties and introducing random parameters in uncertainties, the uncertainty analysis problem of the RSB is converted to a stochastic trajectory approximation problem, which can be solved by the polynomial chaos expansion-based method. The evolutions of the RSB under uncertainties of initial flight path angle, lift-to-drag ratio and atmospheric density are illustrated by a specific Mars entry mission. With uncertainty analysis of the RSB, the robustness of deployment site selection and the satisfaction of path constraints under uncertainties can be quantified in the entry mission design, thus enhancing the safety, reliability and accuracy of entry missions. [ABSTRACT FROM AUTHOR]

The real-time trajectory replanning method which is used for the guidance of Mars entry is investigated in this paper. Comparing with the traditional Mars entry guidance methods, such as the reference-trajectory tracking guidance and predictor–corrector guidance, the real-time trajectory replanning method can increase the reliability of the mission remarkably. When faults occur during the Mars entry phase, a replacement trajectory will be planned quickly. Due to the limited onboard computing capacity, replanning the trajectory onboard is a challenging task. Corresponding to this problem, the neural network is trained to approximate the dynamics of the atmospheric entry. The uncertain factor of the atmospheric density is also included in the neural network. Then, by using the characters of the neural network, the analytical expressions of the Jacobian which are needed in trajectory optimization are derived. Finally, an estimation-replanning guidance procedure is introduced. The numerical simulation shows that the proposed guidance strategy can decrease the error of final states effectively, and the neural network approximation improves the computational speed of the nonlinear programming solver remarkably, which makes the method more suitable for use onboard. [ABSTRACT FROM AUTHOR]

Complete observability of dynamic system is a major concern of navigation in Mars precision landing exploration missions. It is demonstrated that, however, the current measurements used for navigation during Mars entry cannot guarantee the complete observability of the dynamic system. This paper proposes an integrated navigation scheme for Mars entry phase using the dynamic pressure and accelerations from inertial measurement unit (IMU). The dynamic pressure derived from the Mars Entry Atmospheric Data System (MEADS), and the triaxle accelerations from IMU are integrated in a filter as navigation measurements to increase the dynamic system observability and perform state estimation on-board. Afterward, the perturbation of the dynamic caused by parameter uncertainties is built. In order to address the impact of perturbation on state estimation, an adaptive estimator based on modified mixture-of-expert framework is given. Numerical simulation results demonstrate that the proposed integrated navigation scheme can ensure the complete observability of the dynamic system, and the state estimation are converged with entry time after the dynamic pressure has built up. [ABSTRACT FROM AUTHOR]

The conventional Mars entry tracks a fixed reference drag profile (FRDP). To improve the landing precision, a novel guidance approach that utilizes an adaptive reference drag profile (ARDP) is presented. The entry flight is divided into two phases. For each phase, a family of drag profiles corresponding to various trajectory lengths is planned. Two update windows are investigated for the reference drag profile. At each window, the ARDP is selected online from the profile database according to the actual range-to-go. The tracking law for the selected drag profile is designed based on the feedback linearization. Guidance approaches using the ARDP and the FRDP are then tested and compared. Simulation results demonstrate that the proposed ARDP approach achieves much higher guidance precision than the conventional FRDP approach. [ABSTRACT FROM AUTHOR]

The navigation capability of the proposed Mars network based entry navigation system is directly related to the beacon number and the relative configuration between the beacons and the entry vehicle. In this paper, a new beacon configuration optimization method is developed based on the Fisher information theory and this method is suitable for any number of visible beacons. The proposed method can be used for the navigation schemes based on range measurements provided by radio transceivers or other sensors for Mars entry. The observability of specific state is defined as its Fisher information based on the observation model. The overall navigation capability is improved by maximizing the minimum average Fisher information, even though the navigation system is not fully observed. In addition, when there is only one beacon capable of entry navigation and the observation information is relatively limited, the optimization method can be modulated to maximize the Fisher information of the specific state which may be preferred for the guidance and control system to improve its estimation accuracy. Finally, navigation scenarios consisted of 1–3 beacons are tested to validate the effectiveness of the developed optimization method. The extended Kalman filter (EKF) is employed to derive the state estimation error covariance. The results also show that the zero-Fisher information situation should be avoided, especially when the dynamic system is highly nonlinear and the states change dramatically. [ABSTRACT FROM AUTHOR]

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The transient dynamic behaviour of supersonic disk-gap-band parachutes in a Mars entry environment involving fluid structure interactions is studied. Based on the multi-material Arbitrary Lagrange–Euler method, the coupling dynamic model between a viscous compressible fluid and a flexible large deformation structure of the parachute is solved. The inflation performance of a parachute with a fixed forebody under different flow conditions is analysed. The decelerating parameters of the parachute, including drag area, opening loads, and coefficients, are obtained from the supersonic wind tunnel test data from NASA. Meanwhile, the evolution of the three-dimensional shape of the disk-gap-band parachute during supersonic inflation is presented, and the structural dynamic behaviour of the parachute is predicted. Then, the influence of the presence of the capsule on the flow field of the parachute is investigated, and the wake of unsteady fluid and the distribution of shock wave around the supersonic parachute are presented. Finally, the structural dynamic response of the canopy fabric under high-pressure conditions is comparatively analysed. The results show that the disk-gap-band parachute is well inflated without serious collapse. As the Mach numbers increase from 2.0 to 2.5, the drag coefficients gradually decrease, along with a small decrease in inflation time, which corresponds with test results, and proves the validity of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In order to compute the sequential state estimation of Mars entry dynamic system from noisy observations, a deterministic square-root Kalman filter is developed with the implementation of polynomial chaos expansion. The filter allows for the nonlinearity of dynamic system and observation model without the need for assumption about the Gaussian distribution of state. In the algorithm, a minimum variance based data assimilation scheme is developed. The resulting Kalman type updates of state's mean and deviations are performed separately and the square-root formulation of coefficients of polynomial chaos can be computed directly from the polynomial chaos expansion of forecasted states and observations. Two autonomous navigation scenarios based on the Mars Network are considered to quantify the benefits of polynomial chaos based square-root Kalman filter over the other usual nonlinear filters. Additionally, the contrastive analysis of propagations with non-Gaussian states is conducted. Simulation results show that a more accurate estimation and faster convergence can be achieved from the proposed nonlinear filter. Finally, the accuracy and time efficiency of the polynomial chaos based square-root Kalman filter are further analyzed and the optimal order of polynomial chaos is recommended. [ABSTRACT FROM AUTHOR]

A robust integrated navigation algorithm based on a special robust desensitized extended Kalman filtering with analytical gain (ADEKF) during the Mars atmospheric entry is proposed. The robust ADEKF is realized by minimizing a new function penalized by a trace weighted norm of the state error sensitivities and giving a closed-form gain matrix. The uncertainties of the Mars atmospheric density and the lift-to-drag ratio are modeled. Sensitivity matrices are defined to character the parameter uncertainties, and corresponding perturbation matrices are introduced to describe the navigation errors with respect to the parameter uncertainties. The numerical simulation results show that the robust integrated navigation algorithm based on the robust ADEKF effectively reduces the negative effects of the two parameter uncertainties and has good consistency during the Mars entry. [ABSTRACT FROM AUTHOR]

Advanced navigation systems for pinpoint landing are required in the Mars entry, descent, and landing (EDL) phases. Some new high-precision EDL navigation technologies based on beacons have been presented; however, the measurement bias errors of the beacons-- range, position, and velocity errors--have not been considered in the past, which may lead to severe degradation in filtering process. The lack of navigation accuracy may result in a large growth of spurious navigations. In this paper, the Schmidt-Kalman filter is formulated for mitigating the effects of the systematic bias errors. This filter incorporates statistics of measurement errors into the system formulation; instead of only estimating them, it considers the cross correlation between the states and the measurement bias errors, leading to a realistic covariance estimate. Additionally, the UD decomposition is implemented in the Schmidt-Kalman filter to avoid the matrix inversion operation and ensure the numerical stability of the filtering. Monte Carlo simulation results are presented to demonstrate good performance of the Schmidt-Kalman filter with UD decomposition for navigation during the Mars entry. The Schmidt-Kalman filter not only refrains from the divergence of the filtering but also significantly improves the state accuracy. [ABSTRACT FROM AUTHOR]

Accurate navigation systems are required for future pinpoint Mars landing missions. A radio ranging augmented inertial measurement unit (IMU) navigation system concept is considered for the guided atmospheric entry phase. The systematic errors associated to the radio ranging and inertial measurements, and the atmospheric mission uncertainties are considered to be unknown. This paper presents the extension of an unbiased minimum-variance (EUMV) filter of a radio beacon/IMU navigation system. In the presence of unknown dynamics inputs, the filter joins the system state and the unknown systematic error estimation of a stochastic nonlinear time-varying discrete system. 3-DOF simulation results show that the performances of the proposed navigation filter algorithm, 100 m estimated altitude error and 8 m/s estimated velocity error, fulfills the need of future pinpoint Mars landing missions. [ABSTRACT FROM AUTHOR]