Rendezvous Maneuvers Research Articles

Closed-Form Solution of the l1-Optimal Bi-Impulsive Coplanar Orbital Transfer Problem

S ATELLITE orbital transfer has been studied based on two main approaches: impulsive maneuvers and continuous-thrust maneuvers. Impulsive models, in spite of being approximate, are important because they enable mission designers to obtain a preliminary fuel budget as well as maneuver scheduling. Coplanar maneuvers usually consume less propellant than more general transfers wherein the orbital planes are modified. In this context, bi-impulsive maneuvers, such as the Hohmann transfer, are useful because they require a minimum number of thruster firings for each transfer between nonintersecting orbits. Under certain conditions, Hohmann transfers are optimal in the sense of minimizing the total velocity change. However, Hohmann transfers are designed to transfer a satellite between two collinear position vectors. When the initial and final position vectors are not collinear, one should consider other strategies. Several authors have studied the problem of optimal impulsive transfers. Munick et al. [1] provided a solution for optimal transfers from elliptic orbits to coplanar nonintersecting circular orbits using two velocity impulses. Lawden [2] derived a set of algebraic equations whose solution yields the optimal bi-impulsive transfer between two coplanar elliptic orbits. The obtained set of equations must be numerically solved. Battin [3] wrote an ‘2 cost function for a bi-impulsive transfer between twopositionvectors, assuming that the initial and final position and velocity vectors are all coplanar. The minimization of this cost function relies on numerical methods, since an eight-order algebraic equation must be solved. Battin’s development leads to necessary conditions, but no closed-form expressions for the optimal solution are provided. Broucke and Prado [4] studied the optimal coplanar transfer problem with two, three, and four impulses. They also obtained sets of algebraic equations that need to be numerically solved. Won [5] derived analytical conditions for the bi-impulsive transfer between elliptic coplanar coaxial orbits that minimize either the required velocity change or the transfer time. Ma et al. [6] developed an approach using the eccentricity vector, and derived equations to obtain the optimal bi-impulsive transfer between coplanar orbits. As in the previouslymentioned cases, the equationsmust be numerically solved.Conway and Pontani [7] derived optimal four-impulse orbital rendezvous maneuvers when both the chaser and target are in the same circular orbit with an initial phase difference of rad. They obtained general expressions for the change of velocity required by each impulse, and numerically optimized the total velocity change. An implicit assumption in most of the aforementioned works is that the propellant consumption is measured by the Euclidean norm of the velocity change vectors. This is appropriate if the satellite uses a single thruster to perform themaneuver, i.e., it regulates the attitude to align the nozzle with the required vector thrust. However, as also noted by others [8], in satellites that use multiple body-fixed orthogonal thrusters the mass consumption is measured by the ‘1-norm of the thrust vector rather than Euclidean norm. Thus, if Euclidean norms were used to find the fuel-optimal transfers for satellites equipped with body-fixed orthogonal thrusters (e.g., the Mango satellite in the PRISMA mission [9]), a nonfuel-optimal maneuver would be determined. Therefore, for satellites using orthogonal thrusters the optimization approach should be modified. With this consideration in mind, this work formulates the ‘1 cost function for a general coplanar transfer between two noncollinear position vectors with prescribed terminal velocities, and analytically determines the set of points that satisfy the necessary conditions for minima. Since this set includes only 14 points, it is easy to evaluate all of theminima candidates and obtain the globally optimal bi-impulsive maneuver for the mentioned scenario, avoiding numerical optimization processes. The derived analytical solution enables real-time onboard implementation.

Complete transection of the main bile duct: minimally invasive treatment with an endoscopic-radiologic rendezvous

Complete transection of the common bile duct (CBD) is a dramatic and often extremely difficult-to-repair event after surgery. Abdominal biliary fluid collection or jaundice is the initial symptom, and ERCP is the determinant for diagnosis. To evaluate the safety and efficacy of a combined endoscopic-radiologic technique for the reconstruction of the CBD. Single-center retrospective study. Tertiary-care center for biliary surgery. This study involved 22 patients with complete transection of the CBD after cholecystectomy. A guidewire is passed in the subhepatic space through the endoscopic approach. A snare loop is advanced from the percutaneous entry site to catch the free end of the wire and then pulled outside the body: a percutaneous biliary-duodenal (PTBD) drainage is put in place. After a new contralateral PTBD, 4 plastic stents are inserted. The stents are removed endoscopically after 8 to 12 months. Success of the rendezvous maneuver, patient recovery, and patient mortality. After a mean follow-up period of 4 years, 16 patients are asymptomatic. Two patients are still under treatment, and 4 patients underwent surgery, as was the surgeon's choice. Single-center, retrospective study with a small population. Interruption of the biliary tree does not represent an indication for an often-difficult surgical treatment, because the CBD is often thin in the presence of biliary peritonitis. However, the condition can be treated with a rendezvous technique. Surgery can be performed in elective conditions or completely avoided when conservative therapy is selected.

Rendezvous Maneuver with Stent Deployment for a Completely Obstructing Malignant Esophageal Tumor

Purpose: Esophageal cancer may present at an advanced stage with nearly complete obstruction of the esophageal lumen. In those severe cases, the patient's ability to swallow salivary secretions may be limited, and it becomes necessary to intervene to restore function, prior to initiating curative therapy. A rendezvous technique to place an esophageal stent has been reported for patients with benign strictures. This report describes a completely obstructing squamous cell carcinoma (SCCA) of the esophagus in which patency was restored with an Evolution® Controlled Release Esophageal Stent (Cook Medical, NC, USA) placement via a rendezvous maneuver. Methods: A 59-year old African-American man with a history of SCCA of the epiglottis (T2N2c) treated with chemoradiotherapy 7 years ago, initially presented with dysphagia for 6 months. EGD revealed an area of narrowing at 27 cm from the gums with mucosal irregularities that were negative for malignancy. At that time, a PEG tube was placed to assist with feeding. After the patient developed an inability to swallow saliva, a repeat EGD showed a completely obstructing mass at 25 cm from entry, which demonstrated SCCA. A PET/CT scan did not show any evidence of distant metastasis. It was decided that esophageal stent placement would help the patient handle secretion and prevent further morbidities. Results: The proximal end of the completely obstructing mass was visualized by EGD at 25 cm from the entry. An ERCP guide wire through a standard biliary catheter could not be cannulated via the mass under fluoroscopy while utilizing occlusion balloon esophagraphy. A pediatric endoscope after removal of the existing PEG tube was passed via the PEG tube site through the stomach. A hydrophilic biliary guide wire was then transversed in a retrograde fashion through the mass with fluoroscopic monitoring. The guide wire was proximately advanced until it was visualized in the esophagus from above. The guide wire was then drawn out of the mouth. Both ends of the wire were pulled in order to create tension that would prevent a misalignment of the stent. Without pre-dilation of the esophageal lumen, the Evolution® Controlled Release Esophageal Stent with dual flanges (12.5 cm with inner caliber of 20 mm and outer diameter of 25 mm) was successfully placed over the guide wire under fluoroscopic guidance. Stent expansion was confirmed after placement. Conclusion: Combined antegrade and retrograde rendezvous maneuver for Evolution® Controlled Release Esophageal Stent placement appears to be a safe and effective technique for restoring the esophageal lumen in a patient with a completely obstructing esophageal cancer even before curative therapies.

Predictive Guidance-Based Navigation for Mobile Robots: A Novel Strategy for Target Interception on Realistic Terrains

This paper presents a novel online trajectory planning method for the autonomous robotic interception of mobile targets in the presence of dynamic obstacles. The objective is time-optimal position and velocity matching (also referred to as rendezvous) while traversing realistic terrains with uneven topologies. The primary novelty of the proposed interception method lies in its ability to minimize rendezvous time with the target, as well as energy consumption, by directly considering the dynamics of the obstacles and the target while accurately determining a feasible way to travel through the realistic terrain. This objective is achieved by computing rendezvous maneuvers using an advanced predictive guidance law. The method is designed to effectively cope with maneuvering targets/obstacles by predicting their future velocities and accelerations. Obstacle avoidance and terrain navigation are seamlessly integrated. Extensive simulation and experimental analyses, some of which are reported in this paper, have clearly demonstrated the time efficiency of the proposed rendezvous method.

Multiple spacecraft rendezvous maneuvers by differential drag and low thrust engines

A novel two-phase hybrid controller is proposed to optimize propellant consumption during multiple spacecraft rendezvous maneuvers in Low Earth Orbit. This controller exploits generated differentials in aerodynamic drag on each involved chaser spacecraft to effect a propellant-free trajectory near to the target spacecraft during the first phase of the maneuver, and then uses a fuel optimal control strategy via continuous low-thrust engines to effect a precision dock during the second phase. In particular, by varying the imparted aerodynamic drag force on each of the chaser spacecraft, relative differential accelerations are generated between each chaser and the target spacecraft along two of the three translational degrees of freedom. In order to generate this required differential, each chaser spacecraft is assumed to include a system of rotating flat panels. Additionally, each chaser spacecraft is assumed to have continuous low-thrust capability along the three translational degrees of freedom and full-axis attitude control. Sample simulations are presented to support the validity and robustness of the proposed hybrid controller to variations in the atmospheric density along with different spacecraft masses and ballistic coefficients. Furthermore, the proposed hybrid controller is validated against a complete nonlinear orbital model to include relative navigation errors typical of carrier-phase differential GPS (CDGPS). Limitations of the proposed controller appear relative to the target spacecraft’s orbit eccentricity and a general characterization of the atmospheric density. Bounds on these variables are included to provide a framework within which the proposed hybrid controller can effect an extremely low propellant rendezvous of multiple chaser spacecraft to a desired target spacecraft.

Optimal Orbital Rendezvous Maneuvering for Angles-Only Navigation

A NGLES-ONLY navigation has great potential for orbital rendezvous, satellite formation flight, and other relative motion applications, but is often discarded because of its inherent and misunderstood limitation in determining range. A common consensus in the published literature, regardless of the application, is that maneuvers are generally required to obtain target observability when using only anglemeasurements [1–6]. For the bearings-only tracking problem, Nardone and Aidala [7] and Hepner and Geering [8] also showed that certain types of maneuvers, particularly those maneuvers that cause position changes that lie along the instantaneous bearing lines associated with a constant velocity trajectory, do not necessarily guarantee observability. If certain maneuvers produce observability and others do not, then the next natural step that has received considerable attention is to determinewhichmaneuvers and trajectories are optimal in maximizing observability [9–16]. Despite these significant advances in deriving optimal maneuvers for the bearings-only tracking problem, these results are typically established on the premise of a constant moving target, an assumption valid for many naval applications that motivated the earlier research efforts but not applicable to orbital rendezvous. Although the influence of maneuvering for angles-only navigation has been considered for orbital rendezvous [17–19], there does not exist in the published literature derivations of performing optimal maneuvers to maximize observability. This Note develops the mathematical framework to analytically derive optimal maneuvers for angles-only navigation using a previously derived observability criteria [20–22]. The concept of having levels or degrees of observability is formally defined as a function of the measurement error and then used to form the theoretical foundation to derive optimal maneuvers that maximize the observability of the relative state. A simple yet common orbital rendezvous example is provided to illustrate the possibility of designing optimal orbital rendezvous maneuvers for angles-only navigation. Although the topic is introduced in the context of orbital rendezvous, the fundamental concepts can be applied to any linear dynamic system (and extended to nonlinear systems) for which the relative position and velocity are estimated using only angular measurements.

Analysis and implementation of in-plane stationkeeping of continuously perturbed Walker constellations

The stationkeeping of symmetric Walker constellations is analyzed by considering the perturbations arising from a high order and degree Earth gravity field and the solar radiation pressure. These perturbations act differently on each group of spacecraft flying in a given orbital plane, causing a differential drift effect that would disrupt the initial symmetry of the constellation. The analysis is based on the consideration of a fictitious set of rotating reference frames that move with the spacecraft in the mean sense, but drift at a rate equal to the average drift rate experienced by all the vehicles over an extended period. The frames are also allowed to experience the J 2 -precession such that each vehicle is allowed to drift in 3D relative to its frame. A two-impulse rendezvous maneuver is then constructed to bring each vehicle to the center of its frame as soon as a given tolerance deadband is about to be violated. This paper illustrates the computations associated with the stationkeeping of a generic Walker constellation by maneuvering each leading spacecraft within an orbit plane and calculating the associated velocity changes required for controlling the in-plane motions in an exacting sense, at least for the first series of maneuvers. The analysis can be easily extended to lower flying constellations, which experience additional perturbations due to drag.

Analytical Solution for Power-Limited Optimal Rendezvous near an Elliptic Orbit

This paper presents an analytical solution to the problem of the optimal rendezvous using power-limited propulsion for a spacecraft in an elliptic orbit in a gravitational field. The derivation of the result assumes small relative distances, but does not make any assumption on the eccentricity of the orbit and does not require numerical integration. The results are generalized to include the possibility of different weights on the control effort for each axis (radial, along-track, and out-of-plane). When the weights on the control efforts are unequal, several integrals are used whose solutions may be represented by infinite series in a small parameter dependent on the eccentricity. A methodology is introduced where the series can be extended trivially to as many terms as desired. Furthermore, for a given numerical tolerance, an upper bound on the number of terms required to represent the series is also obtained. When the weights are equal for all the three axes, the series representations are no longer necessary. The results can be used easily to design optimal feedback controls for rendezvous maneuvers, or for generating initial guesses for two-point boundary-value problems for numerical solutions to the nonlinear rendezvous problem.

Debridement and drainage of walled-off pancreatic necrosis by a novel laparoendoscopic rendezvous maneuver: experience with 6 cases

Walled-off pancreatic necrosis (WOPN) is a known complication of acute and chronic pancreatitis. Indications for treatment of WOPN are infection, a rapid increase in size, pain, or biliary or duodenal obstruction. Endoscopic transgastric treatment of pseudocysts with liquid content is successful in approximately 90% of patients; however, the treatment of WOPN is less satisfactory. A demonstration of a novel minimally invasive approach to adequately remove and drain pancreatic necrosis. Between June 2004 and June 2006, a nonrandomized observational study was conducted with 6 consecutive patients. WOPN was treated by a minimally invasive laparoendoscopic rendezvous technique. All patients were examined at the university hospital in Freiburg, Germany. Six patients were treated for WOPN of an average diameter of 13 cm (range 9-20 cm). In 5 cases, the WOPN was a consequence of acute pancreatitis; there was 1 case of chronic pancreatitis. The average interval between diagnosis and initial treatment was 14 weeks (range 6-20 weeks). Conventional surgery was avoided in 5 patients (83%) over a median follow-up of 14 months (range 1.5-27 months). Six endoscopic sessions (range 4-11) were performed during the entire treatment period. One patient needed emergency surgery on day 4 after the intervention for a perforation because of gastric-wall separation from the necrotic cavity. There was 1 lethal gastric variceal bleeding, which occurred when a gastrostomy tube was removed 46 days after the initial treatment. The small number of patients. In selected cases, minimally invasive laparoendoscopic treatment of WOPN is possible without the need of laparotomy or laparoscopy.

Optimal Starting Conditions for the Rendezvous Maneuver, Part 2: Mathematical Programming Approach

In a companion paper (Part 1, J. Optim. Theory Appl. 137(3), [2008]), we determined the optimal starting conditions for the rendezvous maneuver using an optimal control approach. In this paper, we study the same problem with a mathematical programming approach.

Optimal Starting Conditions for the Rendezvous Maneuver, Part 1: Optimal Control Approach

We consider the three-dimensional rendezvous between two spacecraft: a target spacecraft on a circular orbit around the Earth and a chaser spacecraft initially on some elliptical orbit yet to be determined. The chaser spacecraft has variable mass, limited thrust, and its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We seek the time history of the controls in such a way that the propellant mass required to execute the rendezvous maneuver is minimized. Two cases are considered: (i) time-to-rendezvous free and (ii) time-to-rendezvous given, respectively equivalent to (i) free angular travel and (ii) fixed angular travel for the target spacecraft.

Hybrid procedures as a combined endovascular and open approach for pararenal and thoracoabdominal aortic pathologies

to report our experience with hybrid vascular procedures in patients with pararenal and thoracoabdominal aortic pathologies. 68 patients were treated for thoracoabdominal aortic pathologies between October 1999 and February 2004; 19 patients (16 men; mean age 68, range 40-79) with high risk for open thoracoabdominal repair were considered to be candidates for combined endovascular and open repair. Aortic pathologies included five thoracoabdominal Crawford I aneurysms, one postdissection expanding aneurysm, three symptomatic plaque ruptures (Crawford IV), five combined thoracic descending and infrarenal aneurysms with a healthy visceral segment, three juxtarenal or para-anastomotic aneurysms, and two patients with simultaneous open aortic arch replacement and a rendezvous maneuver for thoracic endografting. Commercially available endografts were implanted with standardized endovascular techniques after revascularization of visceral and renal arteries. Technical success was 95%. One patient developed a proximal type I endoleak after chronic expanding type B dissection and currently is waiting conversion. Nine patients underwent elective, five emergency and five urgent (within 24 h) repair. 17 operations were performed simultaneously, and 2 as a staged procedure. Postoperative complications include two retroperitoneal hemorrhages, and one patient required long-term ventilation with preexisting subglottic tracheal stenosis. Thirty-day mortality was 17% (one multiple organ failure, one secondary rupture after open aortic arch repair, one myocardial infarction). Paraplegia or acute renal failure were not observed. Total survival rate was to 83% with a mean follow-up of 30 months. Midterm results of combined endovascular and open procedures in the thoracoabdominal aorta are encouraging in selected high risk patients. Staged interventions may reduce morbidity.

Optimal robust linearized impulsive rendezvous

The optimization of time-fixed linearized impulsive rendezvous with control uncertainty is investigated. One performance index related to the variances of the terminal state error is defined as the performance index of robustness which is calculated by linear covariance method. The two-objective optimization problem of minimizing the total characteristic velocity and the performance index of robustness is formulated based on the Clohessy–Wiltshire (C-W) system and solved by the nondominated sorting genetic algorithm. The Pareto-optimal solution sets of one homing rendezvous mission are provided and the Pareto optimality is verified by comparing with the fuel-optimal and the robustness-optimal solutions. It is shown that the proposed approach can quickly investigate the relation between the fuel cost and the trajectory robustness, besides evaluate different rendezvous maneuver schemes.

Optimal Trajectories for Spacecraft Rendezvous

The efficient execution of a rendezvous maneuver is an essential component of various types of space missions. This work describes the formulation and numerical investigation of the thrust function required to minimize the time or fuel required for the terminal phase of the rendezvous of two spacecraft. The particular rendezvous studied concerns a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and separation velocity in all three dimensions. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max-thrust acceleration via the sequential gradient-restoration algorithm. Then, the time-optimal rendezvous for given fuel and the fuel-optimal rendezvous for given time are investigated. There are three controls, one determining the thrust magnitude and two determining the thrust direction in space.

逐次モンテカルロ法に基づく宇宙機異常診断法

We propose a new framework for spacecraft fault diagnosis based on combined parameter and mode online estimation using a sequential Monte Carlo method. Our method can detect and diagnose faults as parameter changes and hence can be considered as a probabilistic approach for the parameter-estimation-based fault diagnosis method which is one of the methodologies on quantitative model-based diagnosis. We derive an algorithm for spacecraft fault diagnosis by describing the parameter-estimation-based fault diagnosis method as a probabilistic inference problem and applying a modified sequential Monte Carlo method, obtained by incorporating fault-modes, risk-sensitivities on modes and kernel-smoothing techniques into the original method, to the problem. The proposed fault-diagnosis algorithm was applied to an artificial data simulating malfunctions of thrusters in rendezvous maneuver of spacecraft, and the feasibility of the method was confirmed.

Rendezvous phasing special-point maneuvers mixed discrete-continuous optimization using simulated annealing

The design of a rendezvous phasing special-point maneuvers can be formulated as a mixed one-zero, integer and continuous design variables problem. A hybrid approach combining simulated annealing (SA) with Newton's method is proposed for solving this problem. An integer-coded SA is used to handle the discrete design variables, while Newton's method is applied to handle the continuous design variables. Three improvements are employed to make the proposed approach more efficient and robust. A two-day low-earth rendezvous-phasing problem is used as an example. The effects of the improvements are investigated. The results show that the SA based hybrid approach is very effective and efficient and the SA has better convergence ability compared with an integer-coded genetic algorithm.

Gibt es eine nichtchirurgische Therapie der Gallenwegskarzinome?

Nonsurgical treatment aims at controlling disease and improving survival and quality of life in patients with nonresectable, recurrent metastatic cholangiocarcinomas. After R0 resection, percutaneous or intraluminal radiotherapy with adjuvant radiochemotherapy may improve survival. Available data, however, are still unsatisfactory, and the efficacy of adjuvant radiochemotherapy after R0 resection remains to be confirmed. Exclusive chemotherapy fails to improve survival postoperatively while, in adequate patients, neoadjuvant chemotherapy can improve R0 resection results. Palliative chemotherapy yielded improved survival and quality of life in only one small prospective randomized trial and cannot be generally recommended at present. Previous biliary stenting for relieving jaundice is mandatory. Beyond established regimens employing 5-fluorouracil/leukovorin and gemcitabine plus platin-based agents, ongoing trials are focussing on topoisomerase-and thyrosine kinase inhibitors. Palliative stenting of malignant bile duct stenoses may eliminate or at least relieve jaundice and pruritus. Single stenting is sufficient for distal bile duct stenoses. In patients with liver metastasis and life expectancy of <6 months, temporary plastic prostheses with 4-6-month patency are sufficient. When the prognosis is for >6 months, self-expanding permanent metal stents, with their significantly longer patency, are superior. In hilar tumors, obstruction of plastic prostheses occurs earlier than in distal bile duct stenoses. Thus, patients with Bismuth II-IV tumors benefit from self-expanding metal stents. These may be inserted by an endoscopic, retrograde approach, percutaneously, or by a combined rendez-vous maneuver. The superiority of bilateral vs unilateral stenting has yet to be proven in Bismuth II-IV tumors. Photodynamic therapy followed by stenting appears to improve survival rates by delaying stent occlusion rather than by regression of the tumoric disease itself.

Spacecraft Diagnosis Method Using Dynamic Bayesian Networks

Development of sophisticated anomaly detection and diagnosis methods for spacecraft is one of the important problems in space system operation. In this study, we propose a diagnosis method for spacecraft using probabilistic reasoning and statistical learning with Dynamic Bayesian Networks (DBNs). In this method, the DBNs are initially created from prior knowledge, then modified or partly re-constructed by statistical learning from operation data, as a result adaptable and in-depth diagnosis is performed by probabilistic reasoning using the DBNs. This method fuses and uses both knowledge and data in a natural way and has the both ability which two polar approaches; knowledge-based and data-driven have. The proposed method was applied to the telemetry data that simulates malfunction of thrusters in rendezvous maneuver of spacecraft, and the effectiveness of the method was confirmed.

回帰学習による逐次予測を用いた宇宙機の適応的リミットチェック

This paper proposes a novel “knowledge-free” anomaly detection method for spacecraft based on regression techniques. This method learns a linear or nonlinear probabilistic regression model in the learning phase by applying a regression technique to a massive telemetry data of spacecraft, and then monitors the real-time telemetry data using the constructed model. This approach can be seen as adaptive limit-checking because it sequentially predicts proper envelop of a target time-series based on the past data of itself and other relevant series. We have confirmed the effectiveness of the proposed anomaly detection method by applying it to the telemetry data obtained from a simulator of an orbital transfer vehicle designed to make a rendezvous maneuver and from actual space operation of Engineering Test Satellite VII (ETS-VII).

Peer-to-Peer Refueling for Circular Satellite Constellations

The scheduling problem arising from refueling multiple satellites in a circular constellation is studied. It is assumed that no fuel is delivered to the constellation from an external source. Instead, all satellites in the constellation are assumed to be capable of refueling each other [peer-to-peer (P2P) refueling]. The total time to complete the rendezvous maneuvers including the refueling itself is specified. During the refueling period, each satellite may conduct a fuel exchange with at most one other satellite. Whenever two satellites perform a fuel transfer, only one is active; that is, only one of the two satellites initiates an orbital transfer to rendezvous with the inactive satellite. After the transfer of fuel is completed, the active satellite returns to its original orbital slot. The goal is to equalize the fuel among the satellites in the constellation after one refueling period while minimizing the total fuel consumed during the orbital transfers. It is shown that this problem can be formulated as a maximum-weight-matching problem on the reduced constellation graph, which can be solved using standard numerical methods. Numerical results indicate the benefits of a P2P strategy over a single-spacecraft refueling strategy for constellations with a large number of satellites.