Entry Trajectory Research Articles

Entry trajectory generation with complex constraints based on three-dimensional acceleration profile

A new entry trajectory generation based on three-dimensional acceleration profile is proposed for hypersonic glide vehicles, meeting range requirement while taking waypoint and no-fly zone constraints into consideration. Firstly, the path constraints, such as maximum dynamic pressure, total overload and peak heating flux at the stagnation-point, are transformed into longitudinal and lateral flight corridors. And the initial lateral and longitudinal sub-profiles are obtained in sequence based on a layered strategy. Secondly, in order to accurately guide the vehicle to reach a target, a method based on Newton's iterative and bisection search is proposed, and the three-dimensional acceleration profile satisfying the mission requirement is quickly obtained. Further, this approach is extended to accommodate the trajectory generation with regarding the waypoint and no-fly zone constraints. Finally, a three-dimensional tracking law is designed to follow the reference trajectory, verifying the feasibility and accuracy of the proposed method.

Comparison of the One-Time Accuracy of Simulated Freehand and Navigation Simulated Pedicle Screw Insertion

To compare one-time accuracy rate between simulated freehand (SFH) and navigation simulated (NS) pedicle screw insertion, assuming no second chance to correct screws. A simulated, comparative, cross-sectional study was conducted on 69 patients undergoing lumbar spine surgery. An intraoperative registration system captured the planned point of entry and trajectory of pedicle screws for both SFH under direct visualization and NS under navigation-aided visualization. Pedicle screw insertion was simulated for each captured image (370 screws) using Surgimap. Rajasekaran's method helped evaluate the point of entry accuracy and trajectory. Accuracy rate was better for the NS method (97.8%) than for the SFH method (63.8%). Of 370 screws in the SFH group, 134 penetrated the cortex, with 31 resulting in >4 mm penetration. Of 370 screws in the NS group, 8 penetrated the cortex, <4 mm penetration. Of 134 misplaced screws in the SFH group, 64 were due to error in the point of entry, 63 were due to error in the trajectory angle, and 7 were due to both errors. Of 8 errors in the NS group, 7 were due to the point of entry. Intraoperative navigation had significantly better one-time accuracy of pedicle screw insertion than freehand insertion and should be used to avoid injury to the pedicle and surrounding tissue from screw reinsertion.

Rapid trajectory optimization for hypersonic entry using convex optimization and pseudospectral method

Purpose This paper aims to develop a novel trajectory optimization algorithm which is capable of producing high accuracy optimal solution with superior computational efficiency for the hypersonic entry problem. Design/methodology/approach A two-stage trajectory optimization framework is constructed by combining a convex-optimization-based algorithm and the pseudospectral-nonlinear programming (NLP) method. With a warm-start strategy, the initial-guess-sensitive issue of the general NLP method is significantly alleviated, and an accurate optimal solution can be obtained rapidly. Specifically, a successive convexification algorithm is developed, and it serves as an initial trajectory generator in the first stage. This algorithm is initial-guess-insensitive and efficient. However, approximation error would be brought by the convexification procedure as the hypersonic entry problem is highly nonlinear. Then, the classic pseudospectral-NLP solver is adopted in the second stage to obtain an accurate solution. Provided with high-quality initial guesses, the NLP solver would converge efficiently. Findings Numerical experiments show that the overall computation time of the two-stage algorithm is much less than that of the single pseudospectral-NLP algorithm; meanwhile, the solution accuracy is satisfactory. Practical implications Due to its high computational efficiency and solution accuracy, the algorithm developed in this paper provides an option for rapid trajectory designing, and it has the potential to evolve into an online algorithm. Originality/value The paper provides a novel strategy for rapid hypersonic entry trajectory optimization applications.

Rapid trajectory optimization for hypersonic entry using a pseudospectral-convex algorithm

Aiming at improving the autonomy of hypersonic entry vehicles, a rapid trajectory optimization algorithm, which has the potential to be implemented online and onboard, is proposed in this paper. The nonlinear and nonconvex hypersonic entry trajectory optimization problem is transformed into a series of convex subproblems through a proper combination of the pseudospectral method and an improved successive convexification method; thus, the high discretization accuracy of the pseudospectral method and the fast and deterministic convergence properties of the convex-optimization-based algorithm can be simultaneously exploited. The resulting subproblems can be solved efficiently by matured interior-point methods, and the solution converges rapidly by adopting a novel dynamic trust-region updating approach. The optimality of the solution is verified by the optimal control theory. The effectiveness of the algorithm is demonstrated by numerical experiments.

Mars atmospheric entry trajectory optimization with maximum parachute deployment altitude using adaptive mesh refinement

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.

Optimal trajectories and normal load analysis of hypersonic glide vehicles via convex optimization

Hypersonic trajectory optimization has been intensively investigated through different approaches; however, the normal-load-optimal entry problems were barely studied and reported in the literature. Finding the optimal trajectories with maximum or minimum peak normal load is essential to evaluate the maneuverability and structural strength of the vehicle. In this paper, both the maximum and minimum peak-normal-load entry trajectories are explored using convex optimization. Based on the previous work, the maximum-peak-normal-load entry problem is firstly addressed by a Big-M method and a line-search approach. Through successive relaxations, the nonconvex discrete-event optimal control problem associated with maximum-peak-normal-load entry is transformed into a sequence of mixed-integer convex optimization problems. Then, a line-search technique is introduced to improve the convergence of the proposed method. Additionally, a sequential convex programming method is designed to solve the minimum-peak-normal-load entry problem to comprehensively analyze the normal load during the entry flight. There are efficient solvers that can solve each relaxed convex subproblem with a global optimum if the feasible set of the subproblem is nonempty. The convergence and accuracy of the proposed methodologies are demonstrated by numerical simulations, and the feasibility of the converged solutions is discussed based on an entry-corridor approach.

Coupled Aerostructural Modeling of Deployable Aerodecelerators for Mars Entry

An analysis of deployable aerodecelerators has been performed using a developed six-degree-of-freedom entry trajectory simulator coupled with a structural model of the deployable structural members, or ribs, to investigate the effect of aerodecelerator flexibility on the trajectory and configuration design. The modified Newtonian method is used in the entry trajectory simulator, and the deployable ribs are modeled as Euler–Bernoulli beams. It is shown that, although flexibility is beneficial in reducing the mass and volume of the deployed ribs, an increase in peak heat flux will result. However, if mass savings from flexible ribs can be reallocated toward increasing the diameter of the entry vehicle, significant benefits can be gained.

A model for thermal radiation from the Tunguska airburst

This paper develops a model for simulating the radiative flux reaching the ground originating from a meteor shock-layer and wake. The area of radiant burn measured for the Tunguska event provides a test case for the developed model. This model applies recently developed computational fluid dynamic simulations, which include the impact of ablation and radiation on the shock-layer flowfield, and ray-tracing radiation transport with atmospheric absorption. The impact of the meteor view angle is shown to significantly impact the radiative flux. Looking at the meteor along the flight path (head-on) results in lower radiative heating because it reduces the wake field of view, where the large radiating wake is shown to provide a significant contribution to the radiative flux (when viewed from the side). The impact of ablation on the ground radiative flux is negligible because the ablation products are limited to the optically-thick core of the wake. The resulting simulated radiative flux values are correlated as a function of velocity, altitude, view angle, and meteoroid radius. This correlation is then applied to potential Tunguska entry trajectories to provide a simulated ground heating footprint. Comparing this simulated footprint with the measured radiant burn area provides a metric for assessing unknown Tunguska entry parameters. Using this approach, the initial radius resulting in good agreement with the measured radiant burn footprint was found for a range of maximum debris cloud radii, entry angles, and velocities. The resulting optimal initial radii were between 30 and 45 m for the entire range of cases considered. This provides a valuable constraint on initial radius for complementary Tunguska studies, such as blast-wave simulations that aim to reproduce the tree-fall pattern.

Extra-articular, Intraepiphyseal Drilling for Osteochondritis Dissecans of the Knee: Characterization of a Safe and Reproducible Surgical Approach.

Background:Osteochondritis dissecans (OCD) is an idiopathic focal condition affecting the subchondral bone of joints, and it is increasingly prevalent among the active young adult population. For lesions that have failed nonoperative management, transarticular drilling and extra-articular drilling are surgical options. Although the extra-articular approach preserves the articular cartilage, it is technically challenging and could benefit from a study of surgical approach.Purpose:To use 3-dimensional modeling of magnetic resonance imaging (MRI) scans from skeletally immature individuals to characterize safe tunnel entry points, trajectories, and distances from the physeal and articular cartilage along the course of the distal femoral epiphysis to the OCD target in their most common location of the medial femoral condyle (MFC).Study Design:Descriptive laboratory study.Methods:A total of 17 MRI scans from skeletally immature patients were used to create 3-dimensional models of the knee joint. Virtual representations of an OCD lesion were placed in the lateral aspect of the MFC; cylinders simulating tunnel length, diameter, and trajectory were superimposed onto the models; and measurements were taken.Results:Two safe tunnels were identified, 1 anterior and 1 posterior to the medial collateral ligament (MCL). The anterior tunnel had a diameter of 10.3 ± 1.4 mm, skin entry point of 16.9 ± 12.1 mm anterior and 7.1 ± 5.9 mm superior to the medial epicondyle, bony entry point of 12.1 ± 3.5 mm anterior and 2.4 ± 3.5 mm inferior to the medial epicondyle, and tunnel length of 31.8 ± 3.7 mm. The posterior tunnel had a diameter of 7.8 ± 1.8 mm, skin entry point of 9.4 ± 5.1 mm posterior and 26.0 ± 14.0 mm superior to the medial epicondyle, bony entry point of 8.6 ± 2.6 mm posterior and 5.1 ± 4.2 mm superior to the medial epicondyle, and tunnel length of 33.5 ± 4.5 mm.Conclusion:This anatomic characterization study identifies and defines 2 safe and reproducible tunnel approaches, 1 anterior and 1 posterior to the MCL, for drilling or creating tunnels to OCD lesions of the MFC in an extra-articular fashion.Clinical Relevance:The study findings provide valuable anatomic references for surgeons performing extra-articular drilling or tunneling of OCD lesions.

Mars entry trajectory robust optimization based on evidence under epistemic uncertainty

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.

Endoscopic Route for Excision of Intraventricular Neurocysticercosis: Light at the End of the Tunnel

Poor sanitation, poor hygiene, and archaic cooking practices have led to neurocysticercosis (NCC) being endemic in India. Apart from a cortical location that leads to seizures, intraventricular NCC can present with hydrocephalus and sudden deterioration in sensorium. Consequently, endoscopic excision plays an important role in its treatment because a dilated ventricle offers a minimally invasive and less traumatic route to the pathology. All endoscopically excised intraventricular NCC cases operated were retrospectively analyzed from 2014 to 2017, discussing surgical nuances and postoperative outcome. Twelve such cases were found (mean age, 21.9 ± 8.36 years; 9 men and 3 women). The mean follow-up period was 21.17 ± 13.96 months (range, 2-40 months). The most common site was the aqueduct and fourth ventricle. An endoscopic approach is a feasible and safe tool for treating this disease. Technical nuances such as entry point and trajectory of endoscope need to be kept in mind while operating.

Image-Guided Navigation in Anterior Cervical Spine Surgery using a Cranial Frame

Background Data: Cervicothoracic, high thoracic, and craniocervical instrumented anterior spinal procedures pose a considerable challenge to the surgeon, mainly because intraoperative imaging by fluoroscopy is inadequate. To a certain extent the surgeon can make use of 3D-fluoroscopy for intraoperative control of the implants. To ease this process, the surgeon can make use of the so-called cranial frame which is attached to the Mayfield clamp, in combination with navigated 3D-fluoroscopy. The use of the cranial frame for navigated anterior craniocervical approaches as in the case of transnasal procedures at the clivus and foramen magnum is quite widespread. In the literature, the use of this technique for spine approaches is limited to a few case reports.Purpose: To present the feasibility of 3D-fluoroscopy navigation in anterior cervical spine procedures with the use of cranial frame.Study Design: Retrospective clinical case cohort.Patients and Methods: We present our experience in the technique of navigation in 5 patients of anterior cervical spine procedures. Anterior instrumented fusion in the cervicothoracic spine was performed in 4 patients and in the last patient anterior C1/2 fixation was performed. We used a system composed of Arcadis Orbic 3D C-arm by Siemens Medical Solutions, Erlangen, Germany, for acquisition of 3D images and the Stealth Station system by Medtronic Inc., Louisville, USA, for navigation. We used a so-called cranial frame for navigation that is fixed to the Mayfield head holder; a preoperative 3D scan was performed in some patients. The intraoperative 3D scan was performed after removal of the retractors, and additional 3D scan was beneficial in some patients during the surgical procedure.Results: Navigation was helpful in identification of the entry points and trajectories of the screws especially in the cervicothoracic region with no need for fluoroscopy. Additional advantage of the use of this system is the possibility of performing intraoperative 3D scan after instrumentation to verify hardware placement.Conclusion: The illustrated cases demonstrate the advantages of 3D-fluoroscopy navigation with use of the cranial frame in the upper transitional zones. Disadvantages of this method are the complex intraoperative draping and logistics and the possible inaccuracy because of long distances and spinal mobility. Carbon Mayfield may facilitate positioning but is not mandatory. (2018ESJ173)

Translaminar facet joint screw insertion with a rapid prototyping guide template: a cadaver study

It is technically demanding and requires rich experience to insert the translaminar facet screw(TFS) via the paramedian mini-incision approach. It seems that it is easy to place the TFS using computer-assisted design and rapid prototyping(RP) techniques. However, the accuracy and safety of these techniques is still unknown. The aim of this study is to assess the accuracy and safety of translaminar facet screw placement in multilevel unilateral transforaminal lumbar interbody fusion using a rapid prototyping drill guide template system. A patient-matched rapid prototyping translaminar facet screw guide was examined in fourteen cadaveric lumbar spine specimens. A three-dimensional (3D) preoperative screw trajectory was constructed using spinal computed tomography scans, from which individualized guides were developed for the placement of translaminar facet screws. Following bone tunnel establishment, the 3D positioning of the entry point and trajectory of the screws was compared to the preoperative plan as found in the Mimics software.Among 60 trajectories eligible for assessment, no cases of clinically significant laminar perforation were found. The mean deviation between the planned and the actual starting points on spinous process was 1.22 mm. The mean tail and submergence angle deviation was found to be 0.68°and 1.46°, respectively. Among all the deviations, none were found to have any statistical significance. These results indicate that translaminar facet screw placement using the guide system is both accurate and safe.

Entry Guidance With No-Fly Zone Avoidance Using Linear Pseudospectral Model Predictive Control

This paper presents an efficient entry guidance law for no-fly zone avoidance, which is based on the recently developed linear pseudospectral model predictive control. First, a simple mapping relation of the position of the no-fly zone between the inertial frame (IF) and the auxiliary geographical frame (AGI) is derived in a geometric manner. Second, a model predictive method is used to judge whether the constraint of the no-fly zone is activated in AGI. Then, additional bank reversal is performed to shape the entry trajectory at the right time so as to avoid the no-fly zone. This method is very easy to be implemented onboard and does not increase the additional computational burden. The nominal and Monte Carlo simulations are conducted to show that the proposed method consistently offers very great, stable, and robust performances.

Entry Trajectory Options for High Ballistic Coefficient Vehicles at Mars

Future large-scale Mars surface exploration missions require landed masses beyond the capability of current entry, descent, and landing technology. Hypersonic trajectory options for large ballistic coefficient vehicles are explored to assess the potential for improved landed mass capability in the absence of landed accuracy requirements. Hypersonic trajectories appropriate for use with supersonic parachute and supersonic retropropulsion descent systems are studied. Optimal control techniques are used to determine hypersonic bank-angle control profiles that achieve favorable conditions at terminal descent initiation. Terminal descent initiation altitude-maximizing bank strategies for parachute descent systems are explored across vehicle and mission design parameters of interest. A tradeoff between altitude and flight-path angle at terminal descent initiation is identified. Hypersonic trajectories that minimize required propellant for propulsive descent are identified and studied parametrically. A hypersonic ballistic coefficient and lift-to-drag ratio are shown to have the largest effects on required propellant mass fraction; changes to the vehicle state at entry interface have a smaller effect. The space of reachable supersonic retropropulsion ignition states is presented over a range of vehicle and trajectory parameters. Overall, results indicate execution of an appropriate hypersonic bank profile can significantly increase the parachute deploy altitude for parachute descent systems or reduce the amount of propellant required when compared to full lift-up entry for supersonic retropropulsion descent systems operating at Mars.

Smoothness of the School-to-Work Transition: General versus Vocational Upper-Secondary Education

This article analyses the effect of vocational education on school-to-work transitions for the 2006 cohort of Dutch graduates of upper-secondary education (ISCED Level 3). Using sequence analysis, it uncovers ideal-typical school-to-work transition trajectories representing the first 7 years in the labour market. It then analyses the effect of vocational education on trajectories and wages. Specific attention is paid to the moderating influence of vocational sector and type of programme: classroom-taught or workplace-based. The results indicate that, compared to entrants with general education, vocationally educated entrants are less likely to have problematic labour market entry trajectories. Vocational field has a moderating effect on the prevalence of particular trajectories. Those with a vocational education enjoy higher wages on labour market entry but are soon overtaken by their counterparts with a general education.

Probabilistic assessment of Tunguska-scale asteroid impacts

The Tunguska meteor airburst has been extensively studied and modeled in attempts to deduce its size, properties, and impact characteristics. However, most of the existing modeling and simulation studies have investigated a small subset of cases based on assumptions of representative densities, velocities, or other properties. In this study, we use a probabilistic asteroid impact risk model to assess the entry, burst, and ground damage from 50 million Tunguska-scale asteroid impacts, covering a full range of potential impactor properties. The impact cases are sampled from probabilistic distributions representing our current knowledge of asteroid properties, entry trajectories, and size frequencies. The results provide a broader characterization of the range and relative likelihood of asteroid properties that could yield Tunguska-scale impacts. Results show that Tunguska-like events can be produced by a broad range of impact scenarios, and prevailing size and energy estimates of 50–80 m or 10–20 Mt remain within the relatively likely property ranges. However, our results suggest that objects with slightly larger initial energies of 20–30 Mt and diameters 70–80 m are more likely to cause Tunguska-scale damage areas than objects on the smaller end of the potential size range. Even when relative size frequencies are accounted for, the greater damage potential of larger objects outweighs their rarity, while the low damage potential of small objects counteracts their frequency.

Efficient Evaluation of Mars Entry Terminal State Based on Gaussian Process Regression

Trajectory optimization technology used for Mars entry is one of the key technologies for planetary exploration. Evaluation of the performance of the entry trajectory under conditions of complex atmospheric dynamics, various vehicular design parameters, and multiple constraints in the process of entry, are important issues pertaining to the design of trajectories. In this study, an efficient evaluation approach of the terminal state for Mars entry is proposed based on Gaussian process regression to evaluate the maximum terminal altitude for different entry velocities, terminal Mach numbers, and vehicular parameters. Additionally, the influences of entry flight-path angle, lift-drag ratio, and ballistic coefficient, on the maximum terminal altitude are analyzed. A genetic algorithm is used in the optimization solver to avoid local minima and to guarantee the data quality of the training samples used for Gaussian process regression. The mean function, kernel function, and hyperparameters are selected as the optimization parameters for Gaussian process regression to describe the correlation between samples, and the maximum terminal altitude prediction model is then established. Numerical simulations demonstrate that the proposed method can achieve the evaluation of more than 3000 group scenarios within tens of seconds with a mean relative error that is less than 4%.

Entry trajectory planning with terminal full states constraints and multiple geographic constraints

This paper proposes an online entry trajectory planning algorithm satisfying terminal full states constraints, path constraints and multiple geographic constraints for lifting-body entry vehicles. The vehicle is considered as a 3DOF point mass. The entry trajectory is divided into the initial descent phase, gliding phase and terminal guidance phase. In the gliding phase, a piecewise polynomial in the altitude-versus-velocity plane is used to plan the longitudinal trajectory and a new heading angle corridor based bank angle reversal logic is designed to satisfy all geographic constraints simultaneously. In the terminal guidance phase, an optimal guidance law with terminal angle constraints is adopted to generate the trajectory. Finally, the terminal full states constraints including terminal velocity direction constraints are implemented by iterating over the altitude in the gliding phase. Then the highly constrained entry trajectory planning problem is converted into a one-parameter search problem. The key of this planning algorithm is the use of terminal guidance phase, through which the terminal velocity direction is constrained strictly rather than kept around the line-of-sight angle and the range error caused by great arc assumption is also avoided. Simulation results with the CAV-H model show that this algorithm can generate entry trajectories satisfying complex constraints rapidly and is suitable for various missions.

Time-optimal memetic whale optimization algorithm for hypersonic vehicle reentry trajectory optimization with no-fly zones

A novel time-optimal memetic whale optimization algorithm (WOA) integrating the Gauss pseudo-spectral methods (GPM), is proposed in this paper for the hypersonic vehicle entry trajectory optimization problem with no-fly zones. The WOA is featured with the strong global search ability and non-sensitive to the initial values, but also shows poor searching convergence speed around the global optimum. Conversely, GPM may be sensitive to the initial solution and easily trapped in a local optimum, but it also possesses more rapid convergence speed around the optimum and higher searching accuracy. Thus, a memetic optimization algorithm which contains a two-stage approach mechanism is proposed for searching the global optimum. The first searching stage, which is driven by an improved WOA (IWOA), works as an initializer of the entire searching due to its strong global search ability and non-sensitive to the initial values. The local optimum reservation and adaptive amplitude factor updating strategy are established to improve the convergent speed and the global search ability of the WOA. Once the changing of fitness value satisfies the predefined criterion, the next searching stage driven by GPM will take the place of the IWOA to expedite the search process around optimum and to obtain a precise global optimal solution. By this hybrid way, the proposed optimization algorithm may find an optimum more quickly and accurately. Simulation results show the proposed algorithm possesses faster convergence speed, higher accuracy, and stronger robustness for the hypersonic vehicle entry trajectory optimization.