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Separation Maneuver Parameterization Evaluation of the objective function given in Eq. (4) requires propagation of the equations of motion for both spacecraft. The inertial initial position vector for the inspector spacecraft is given in Eq. (2) and the initial velocity vector, including a non-zero angular velocity vector for the primary spacecraft and the separation maneuver, is specified in Eq. (3).
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Future missions involving in-space servicing, repair, inspection, or rendezvous and docking require algorithms for safe, autonomous proximity operations. Algorithms for relative navigation, safe separation, and circumnavigation trajectory design are presented. The algorithms rely on safe, natural motion trajectories and covariance information from...
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Citations
... MATLAB simulations have been implemented using Clohessy-Wiltshire (CW) equations, described by Gaylor [15] and Naasz [16] and referred to SR RIC frame, to extrapolate the DeltaV needed for the CubeSat manoeuvres in a nonperturbed environment. Then the MATLAB results have been set in GMAT and propagated for 25 days with a RugeKutta89 propagator. ...
In the last few years the number of orbiting satellites has increased exponentially, in particular due to the development of the New Space Economy. Even if this phenomenon makes the space more accessible, bringing a great contribution to the scientific, economic and technological fields, on the other hand it contributes to the overpopulation of the space background. Therefore, it is necessary to develop new techniques to manage the space environment, such as in orbit servicing, which is a procedure that aims to refuel and repair satellites to extend their operational life. A first step to reach this goal is to inspect closely the object of interest to study its features. In this framework, the Space Rider Observer Cube (SROC) mission is being developed. SROC is a payload that will be deployed by Space Rider, an uncrewed and reusable robotic spacecraft designed by ESA. SROC is a 12U CubeSat, whose goal is to carry out inspection manoeuvres around the mothership, then re-enter on board using a safe docking system to come back to Earth. The feasibility of a mission similar to SROC has been simulated during a university class, starting from the definition of the system requirements with particular focus on the analysis of the payloads and subsystems, to ensure the achievement of the mission goals. In particular, the CubeSat is equipped with an optical instrument to capture high resolution images of Space Rider surface and a docking mechanism. Then the design of the orbit and the simulation of the effects of the space environment on the CubeSat have been studied using GMAT, SYSTEMA, MATLAB and other numerical tools. The results of the study are useful for future missions, aiming to inspect orbiting objects, such as operative satellites for in orbit servicing, space debris and dead satellites to study their geometries and plan their removal.
... MATLAB simulations have been implemented using Clohessy-Wiltshire (CW) equations, described by Gaylor [15] and Naasz [16] and referred to SR RIC frame, to extrapolate the DeltaV needed for the CubeSat manoeuvres in a nonperturbed environment. Then the MATLAB results have been set in GMAT and propagated for 25 days with a RugeKutta89 propagator. ...
In the last few years, the number of orbiting satellites has increased exponentially, in particular due to the development of the New Space Economy. Even if this phenomenon makes the space more accessible, bringing a great contribution to the scientific, economic and technological fields, on the other hand it contributes to the overpopulation of the space background. Therefore, it is necessary to develop new techniques to manage the space environment, such as in orbit servicing, which is a procedure that aims to refuel and repair satellites to extend their operational life. A first step to reach this goal is to inspect closely the object of interest to study its features. In this framework, the Space Rider Observer Cube (SROC) mission is being developed. SROC is a payload that will be deployed by Space Rider (SR), an uncrewed and reusable robotic spacecraft designed by ESA (European Space Agency). SROC is a 12U CubeSat, whose goal is to carry out inspection manoeuvres around SR, then re-enter on board using a safe docking system to come back to Earth. The feasibility of a mission similar to SROC has been simulated during a university class, starting from the definition of the system requirements with particular focus on the analysis of the payloads and subsystems, to ensure the achievement of the mission goals. In particular, the CubeSat is equipped with an imaging payload to capture high resolution images of Space Rider surface and a docking mechanism. Then, the design of the orbit and the simulation of the effects of the space environment on the CubeSat have been studied using GMAT, SYSTEMA, MATLAB and other numerical tools. The results of the study are useful for future missions, aiming to inspect orbiting objects, such as operative satellites for in orbit servicing, space debris and dead satellites to study their geometries and plan their removal.
... The main idea of CoMBiNa is to combine the advantages of SLAM and model-based techniques by splitting the mission in two phases. During the first phase, a SLAM approach can be used on a safe relative orbit [39] to acquire a point cloud and construct a coarse model of the target RSO exploiting state of the art graph-SLAM techniques (e.g., ORBSLAM [36]) to obtain a larger map. In the second phase, the coarse model is used as the base of a model-based relative navigation technique. ...
... These trajectories are characterized by an out-of-plane elliptical periodic relative motion such that the traced path never crosses the velocity vector of the primary object. In a safe relative trajectory, drift of the two spacecraft, due to relative state estimation errors will not result in collision, so the trajectory is considered passively safe [39]. ...
... This particular initial condition produces an inclined football orbit in the Clohessy-Wiltshire dynamics [39], and an approximate one in NERM, provided that the relative separation is small enough with respect to the orbital radius. This relative orbit is represented in Fig. 7. ...
In recent years, space debris has become a threat for satellites operating in low Earth orbit. Even by applying mitigation guidelines, their number will still increase over the course of the century. As a consequence, active debris removal missions and on-orbit servicing missions have gained momentum at both academic and industrial level. The crucial step in both scenarios is the capability of navigating in the neighborhood of a target resident space object. This problem has been tackled many times in literature with varying level of cooperativeness of the target required. While several techniques are available when the target is cooperative or its shape is known, no approach is mature enough to deal with uncooperative and unknown targets. This paper proposes a hybrid method to tackle this issue called Coarse Model-Based Relative Navigation (CoMBiNa). The main idea of this algorithm is to split the mission into two phases. During the first phase, the algorithm constructs a coarse model of the target. In the second phase, this coarse model is used as a reference for a relative navigation technique, effectively shifting the focus toward state and inertia estimation. In addition, this paper proposes a strategy to leverage the structure of the selected navigation method to detect and reject outliers. To conclude, CoMBiNa is tested on a simulated environment to highlight its benefits and its shortcomings, while also assessing its applicability on a limited-resource single-board computer.
... Usually, the data transmitted from the space segment is elaborated on ground, and relevant commands are transmitted back on orbit to be executed. This approach is well suited for typical monitoring trajectories around known objects, e.g. the ones exploiting the concept of safety ellipses [6], which can be designed to ensure the possibility to realize a wide range of different observation conditions, especially if the target is tumbling. ...
Active debris removal and unmanned on-orbit servicing missions have gained interest in the last few years, along with the possibility to perform them through the use of an autonomous chasing spacecraft. In this work, new resources are proposed to aid the implementation of guidance, navigation, and control algorithms for satellites devoted to the inspection of noncooperative targets before any proximity operation is initiated. In particular, the use of convolutional neural networks (CNN) performing object detection and instance segmentation is proposed, and its effectiveness in recognizing the components and parts of the target satellite is evaluated. Yet, no reliable training images dataset of this kind exists to date. A tailored and publicly available software has been developed to overcome this limitation by generating synthetic images. Computer-aided design models of existing satellites are loaded on a three-dimensional animation software and used to programmatically render images of the objects from different points of view and in different lighting conditions, together with the necessary ground truth labels and masks for each image. The results show how a relatively low number of iterations is sufficient for a CNN trained on such datasets to reach a mean average precision value in line with state-of-the-art performances achieved by CNN in common datasets. An assessment of the performance of the neural network when trained on different conditions is provided. To conclude, the method is tested on real images from the Mission Extension Vehicle-1 on-orbit servicing mission, showing that using only artificially generated images to train the model does not compromise the learning process.
... The main idea of CoMBiNa is to combine the advantages of SLAM and model-based techniques by splitting the mission in two phases. During the first phase, a SLAM approach can be used on a safe relative orbit [35] to acquire a point cloud and reconstruct a coarse model of the target RSO exploiting state of the art graph-SLAM techniques (e.g., ORBSLAM [32]) to construct a larger map. In the second phase, the coarse model is used as the base of a model-based relative navigation technique. ...
... During the first phase of CoMBiNa, a SLAM approach can be used on a relative orbit [35] to acquire a point cloud and reconstruct a coarse model of the target RSO while guaranteeing passive safety. The main focus of this phase is placed on the model reconstruction and can be performed with state of the art graph-SLAM techniques [32]. ...
... This particular initial condition produces an inclined football orbit in the CW dynamics [35], and an approximate one in NERM, provided that the relative separation is small enough with respect to the orbital radius. This orbit is represented in Fig. 7. ...
View Video Presentation: https://doi.org/10.2514/6.2022-2384.vid In recent years, space debris has become a threat for satellites operating in Low Earth Orbit. Even by applying debris mitigation guidelines, their number will still increase in the next century. As a consequence, active debris removal missions as well as On-Orbit Servicing missions have gained momentum at both academic and industrial level. The crucial step in both scenarios is the capability of navigating in the neighborhood of the target Resident Space Object. This problem has been tackled many times in literature with varying level of cooperativeness of the target required. Several techniques can deal with known and cooperative targets, fewer model-based methods are available if the investigated object is uncooperative (but known), while only a handful of techniques can deal with completely unknown objects, which require building their map while navigating in their neighborhood. The main downside of methods available in literature is the detection and matching of markers from measurements, a step which may severely impair convergence if poorly performed. To overcome said limitations, this paper proposes an hybrid approach for relative navigation at an unknown and uncooperative target resident space object called COarse Model Based relatIve NAvigation: CoMBiNa. The main idea of this algorithm is to combine the advantages of simultaneous localization and mapping with model-based methods by splitting the mission in two phases. During the first phase, the algorithm reconstructs a coarse model of the target. In the second phase, this coarse model is used as the base of a model-based relative navigation technique, effectively shifting the focus towards state and inertia reconstruction. The adopted model-based method avoids searching for exact feature correspondence, thus overcoming the main limitation of current methods. Additionally, this paper proposes a strategy to leverage the structure of the particular model-based navigation method chosen so that measurement outliers can be detected and rejected automatically. To conclude, this paper presents the results of the application of the proposed approach while tested on a generic target model with validation on a limited resource Single Board Computer.
... The Restore-L mission (which involves robotically capturing, refueling, and relocating Landsat 7) will use safety ellipses for its near-field rendezvous and proximity operations [11]. Naasz [2], Gaylor and Barbee [12], and Barbee et al. [13] have also proposed safety ellipses for rendezvous and proximity operations missions involving noncooperative targets. ...
This paper presents an analytic solution for a three-impulse maneuver sequence that reconfigures safety ellipses. Safety ellipses are relative motion trajectories that do not require thrusting to ensure a high probability of short-term collision avoidance. Primer vector theory is used to derive analytic expressions that relate the necessary conditions for optimality to properties of the initial and final safety ellipses. The primer vector analysis is validated numerically using convex optimization and Monte Carlo methods. A general passive safety parameter for relative motion trajectories in near-circular orbits is also introduced. It is shown that for practical safety ellipse reconfiguration scenarios, the maneuver sequence generates optimal transfer trajectories that also remain passively safe.
... 19 Although specific algorithms on the Restore-L mission are proprietary, a general paper submitted by Gaylor discusses innovative algorithms for safe spacecraft proximity operations. 20 For this method, it is assumed that the servicer spacecraft and the primary spacecraft are unable to communicate with each other, but the servicer spacecraft is able to collect the primary spacecraft states from a ground station. Trajectory design is implemented using safety ellipses to prevent collisions while circumnavigating the primary spacecraft in order to map waypoints for possible injec-tion. ...
... Each point on the trajectory must be evaluated against Eq. (20) to determine whether any collisions occurred. For LQR-RRT* and trajectory smoothing using shortcutting, this is a simple for-loop. ...
... Figure 7(f) shows the finished pyramidlike structure formed from the ellipsoid structural part. When computing collision avoidance for the 3D printer and the structural parts, the P obs in Eq. (20) was designed with a safety factor due to the size of the Astrobee from its centroid and trajectories obtained from LQR. Thus, control of collision-free trajectories for the on-orbit assembly system was obtained. ...
Deploying large, complex space structures is of great interest to the modern scientific world as it can provide new capabilities in obtaining scientific, communicative, and observational information. However, many theoretical mission designs contain complexities that must be constrained by the requirements of the launch vehicle, such as volume and mass. To mitigate such constraints, the use of on-orbit additive manufacturing and robotic assembly allows for the flexibility of building large complex structures including telescopes, space stations, and communication satellites. The contribution of this work is to develop motion planning and control algorithms using the linear quadratic regulator and rapidly-exploring randomized trees (LQR-RRT*), path smoothing, and tracking the trajectory using a closed-loop nonlinear receding horizon control optimizer for a robotic Astrobee free-flyer. By obtaining controlled trajectories that consider obstacle avoidance and dynamics of the vehicle and manipulator, the free-flyer rapidly considers and plans the construction of space structures. The approach is a natural generalization to repairing, refueling, and re-provisioning space structure components while providing optimal collision-free trajectories during operation.
... The Restore-L mission (which involves robotically capturing, refueling, and relocating Landsat 7) will use safety ellipses for its near-field rendezvous and proximity operations [11]. Naasz [2], Gaylor and Barbee [12], and Barbee et al. [13] have also proposed safety ellipses for rendezvous and proximity operations missions involving noncooperative targets. ...
This paper presents analytic solutions for three-impulse maneuver sequences that perform safety ellipse resizing and phasing. Safety ellipses are relative motion trajectories that do not require thrusting to ensure a high probability of short-term collision avoidance. Primer vector theory, validated with numerical analysis, is used to derive analytic expressions that relate optimality to properties of the initial and final safety ellipses. This analysis shows that the maneuver sequences are optimal for a range of resizing and phasing scenarios. An analysis is also performed on the passive safety of transfer trajectories that result from incomplete maneuver sequences. It is shown that only phasing scenarios that call for an extreme phase angle change result in potentially unsafe transfer trajectories.
... x y z x y z ] T is the initial state of chaser in Hill system. Thus, the coplanar motion can be described as in [19]. (5) shows that the coplanar motion of chaser in Hill system is an ellipse determined by X0, Z0 and S. The center of ellipse is (X0, Z0), which moves parallel to the V-bar over time. ...
This paper proposes an improved sampling-based approach for spacecraft proximity operation path planning under Clohessy-Wiltshire-Hill dynamics. The proposed approach is based on a modified version of the FMT* (Fast Marching Tree) algorithm with safety strategy which is divided into three parts: (1) incorporating relative ellipse to simplify the sampling state space and avoid collision with target; (2) combining internal/external ellipse-based collision detection algorithms for hovering obstacle and non-coplanar ellipse obstacle; (3) using rotating hyperplane method to handle the coplanar ellipse obstacle and uncertainty obstacle. By referring the safety strategy to simplify the state space before FMT* algorithm, the approach can reduce the complexity of path planning, especially the resampling and collision avoidance detection cyclic process in FMT*, thereby improve the planning efficiency. Two simulated scenarios, a coplanar path planning with/without coplanar ellipse obstacle, are developed to illustrate the approach. As a result, the proposed approach appears to be potential for spacecraft proximity real-time path planning as well as other complex space mission path planning generalized to different dynamics and environments, such as On-Orbit Service, and enabling a real-time computation of low-cost trajectory.
... In order to reduce collision risk due to relative state estimation errors during ARvD, the satellite can enter a safety ellipse trajectory around the target object. A safety ellipse trajectory is an out-of-plane elliptical periodic relative motion trajectory around the target such that the trajectory never crosses the velocity vector of the target [91], [92]. ...
The low-cost and short-lead time of small satellites has led to their use in science-based missions, earth observation, and interplanetary missions. Today, they are also key instruments in orchestrating technological demonstrations for On-Orbit Operations (O
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) such as inspection and spacecraft servicing with planned roles in active debris removal and on-orbit assembly. This paper provides an overview of the robotics and autonomous systems (RASs) technologies that enable robotic O
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on smallsat platforms. Major RAS topics such as sensing & perception, guidance, navigation & control (GN&C) microgravity mobility and mobile manipulation, and autonomy are discussed from the perspective of relevant past and planned missions.
