Space Debris Removal Research Articles

Application of Impedance Control of the Free Floating Space Manipulator for Removal of Space Debris

A broad and significant class of space debris can be mitigated by means of a satellite, capable of capturing a large non-cooperating object by using a robotized arm with a gripper. The capture operation typically comprises of an approach, a close-on manoeuvre, establishing contact between the robotic grappler arm and a suitable feature on the target satellite, and finally it is concluded when a positive mechanical connection is achieved by the gripper closed on that feature. The phase of establishing contact poses a critical challenge in this scenario, since the target typically will be tumbling with respect to the chaser satellite causing high forces on the gripper and the robotic arm. A family of control methods known collectively as impedance control is typically employed in terrestrial robots for tasks involving an interaction with an environment, especially the dynamic contact. In this work, we present the model-based impedance control applied to a robotic manipulator on a free floating base. The derivation of impedance control law for a robotic manipulator on a free floating satellite, involving Generalized Jacobian Matrix (GJM), is presented, followed by simulation results comparing the loads in the manipulator joints against a classical GJM-based Cartesian controller. The simulation results show that the impedance controlled free floating robotic manipulator completes the task of trajectory following amid contact with unknown target with lower torques in the robot joints.

Employing a multi-sensor fusion array to detect objects for an orbital transfer vehicle to remove space debris

PurposeThis article takes into account object identification, enhanced visual feature optimization, cost effectiveness and speed selection in response to terrain conditions. Neither supervised machine learning nor manual engineering are used in this work. Instead, the OTV educates itself without instruction from humans or labeling. Beyond its link to stopping distance and lateral mobility, choosing the right speed is crucial. One of the biggest problems with autonomous operations is accurate perception. Obstacle avoidance is typically the focus of perceptive technology. The vehicle's shock is nonetheless controlled by the terrain's roughness at high speeds. The precision needed to recognize difficult terrain is far higher than the accuracy needed to avoid obstacles.Design/methodology/approachRobots that can drive unattended in an unfamiliar environment should be used for the Orbital Transfer Vehicle (OTV) for the clearance of space debris. In recent years, OTV research has attracted more attention and revealed several insights for robot systems in various applications. Improvements to advanced assistance systems like lane departure warning and intelligent speed adaptation systems are eagerly sought after by the industry, particularly space enterprises. OTV serves as a research basis for advancements in machine learning, computer vision, sensor data fusion, path planning, decision making and intelligent autonomous behavior from a computer science perspective. In the framework of autonomous OTV, this study offers a few perceptual technologies for autonomous driving in this study.FindingsOne of the most important steps in the functioning of autonomous OTVs and aid systems is the recognition of barriers, such as other satellites. Using sensors to perceive its surroundings, an autonomous car decides how to operate on its own. Driver-assistance systems like adaptive cruise control and stop-and-go must be able to distinguish between stationary and moving objects surrounding the OTV.Originality/valueOne of the most important steps in the functioning of autonomous OTVs and aid systems is the recognition of barriers, such as other satellites. Using sensors to perceive its surroundings, an autonomous car decides how to operate on its own. Driver-assistance systems like adaptive cruise control and stop-and-go must be able to distinguish between stationary and moving objects surrounding the OTV.

Revisiting Universal Variables for Robust, Analytical Orbit Propagation Under the Vinti Potential

To meet the growing complexity and demands of modern spacecraft missions, analytical solutions to initial value problems see continued use, typically supporting global searches of large trajectory design spaces. These efforts often employ universal two-body orbit propagators for their recognized speed and robustness, but many applications, like active space debris removal, would benefit from a comparable propagator with greater accuracy. Vinti propagators, which consider planetary oblateness, may serve this purpose, but existing Vinti solutions possess computational difficulties in certain orbital regimes. To mitigate these deficiencies, the present study develops and validates an analytical, third-order universal Vinti propagator free of computational difficulties by leveraging standard, oblate spheroidal (OS) universal variables and OS equinoctial orbital elements. Accuracy of the third-order approximation is assessed for multiple examples across an array of orbital regimes. Computational runtime is also evaluated, and performance is directly compared to the benchmark Vinti6 algorithm. On average, the Vinti propagator implemented in this work is only slower than a typical universal Kepler propagator by a factor of 4.0 and slower than Vinti6 by a factor of 1.8, but with greater robustness than the benchmark. The new form of the equations of motion also has favorable implications for the associated boundary value problem.

Novel ground microgravity experiment system for a spacecraft-manipulator system based on suspension and air-bearing

With the development of aerospace technology, the on-orbit activities of large spacecraft are increasing day by day, and accordingly the amount of space debris is increasing. Therefore, a large spacecraft-manipulator system is needed to perform on-orbit service, such as, assembling large spacecraft and removing space debris. Before launching, the trajectory optimization and control algorithm of the spacecraft-manipulator system have to be verified on the ground microgravity experiment system since the complex systems are prone to failure. In this study, a ground microgravity experiment system based on suspension and air-bearing is proposed to provide a long-term and stable microgravity environment for the large spacecraft-manipulator system. A suspension gravity compensation system with multiple suspensions is designed for the redundant space manipulator that moves in three dimensions, and a suspension tracking smooth sliding mode control algorithm based on hierarchical control is presented. Then, the coupling-reduction strategy based on equivalent spring-mass is presented to reduce the electromechanical coupling of the suspension gravity compensation system and the space manipulator. For the roll and pitch motion of the large-mass/inertia spacecraft, the target spacecraft simulator with a 2-degree-of-freedom rotating mechanism is designed. Some air-bearings are installed on the base of the chaser spacecraft simulator and target spacecraft simulator, which produce an air gap to enable the frictionless plane motion of the spacecraft. Finally, the target spacecraft simulator transposition experiment was carried out. The results show that the residual torque of the space manipulator is very small, and the ground microgravity experiment system compensates the gravity of the spacecraft-manipulator system with high precision.

Optimal debris removal using debris-tether-tug system considering attitude–orbit coupling effects

Towing space debris with the utilization of a tethered space tug, also referred to as debris-tether-tug (DTT) system, is considered to be one of the most promising methods to remove space debris. However, as the space tug only carries limited amounts of fuel, the number of debris that a DTT system can remove is limited. To increase the capacity of the DTT system, fuel consumption per towing cycle should be minimized. This study proposes an optimal deorbit scheme with two stages: optimal transfer and swing control. First, a dynamics model of the DTT system is formulated considering attitude–orbit coupling effects and tether flexibility. In the fuel optimal transfer stage, the dynamics model as well as two simplified models is employed to calculate the optimal transfer orbit, subject to a continuous thrust from the tug. By comparing the optimal results, it can be found that the attitude–orbit coupling effect of the DTT system is non-negligible, whereas the tether flexibility can be ignored with a large tether elasticity coefficient during the optimal orbit transfer mission. For the swing control stage at the destination, a control law is applied by regulating the velocity of tether releasement to increase the debris velocity. The parametric analysis of the control law suggests that the tether should be completely deployed before separation to achieve a larger orbit altitude increment. Appropriate parameters can be assigned to attain maximum orbit altitude increment in the swing control based on this analysis. The conclusions could serve as an effective reference for transfer orbit calculation and swing control design in future deorbit missions using the DTT system.

Determining the Effective Space Debris Attitude Motion Modes for Ion-Beam-Assisted Transportation

Contactless space debris transportation systems based on the use of an ion beam are a promising direction among active space debris removal systems. The magnitude of the force generated by the ion beam depends on the orientation of the space debris object in the ion beam created by an active spacecraft. During the ion transport process, the space debris object can oscillate or rotate, which leads to a change in the generated force. The aim of this study is to develop an algorithm for determining the attitude motion mode of space debris, which is most favorable for its contactless transportation. The time-averaged generated ion force is used as the performance index. A simplified system of equations describing the spatial motion of a cylindrical axisymmetric object in a circular orbit is obtained. A generalized energy integral is found. An algorithm for determining the most favorable angular motion mode of a space debris object is developed. A numerical study of a cylindrical space debris object attitude motion under the action of an ion torque is carried out. The favorable attitude motion mode is determined, and the average forces in the most favorable and unfavorable modes are compared.

Strict finite-time sliding mode control for a tethered space net robot

Tethered Space Net Robot (TSNR) is considered to be a promising approach for space debris removal, and accordingly it is also an interesting control problem due to its time-varying disturbances caused by an elastic and flexible net and a main connected tether. In this situation, the control scheme should be robust enough, low-frequency, and finite-time convergent in presence of external disturbances. In this paper, a robust controller with an advanced adaptive scheme is proposed. To improve robustness, the disturbance is skillfully involved in the adaptive scheme. It is strictly proven that the closed-loop system can converge to the desired trajectory in finite time in both reaching and sliding processes. Based on the theoretical proof, adaptive gains and corresponding dynamic stability characteristics are further discussed. Finally, the efficiency of the proposed control scheme is numerically proven via a TSNR. The proposed control scheme utilizes small and continuous control forces to compensate for the disturbance efficiently and track the desired trajectory quickly.

Robust and Accurate Monocular Pose Tracking for Large Pose Shift

Tracking the pose of a specific rigid object from monocular sequences is a basic problem in computer vision. State-of-the-art methods assume motion continuity between two consecutive frames. However, drastic relative motion causes large inter-frame pose shifts, especially in applications such as robotic grasping, failed satellite maintenance and space debris removal. Large pose shifts interrupt the inter-frame motion continuity leading to tracking failure. In this paper, we propose a robust and accurate monocular pose tracking method for tracking objects with large pose shifts. Using an indexable sparse viewpoint model to represent the object 3D geometry, we propose establishing a transitional view, which is searched for in an efficient variable-step way, to recover motion continuity. Then, a region-based optimization algorithm is adopted to optimize the pose based on the transitional view. Finally, we use a single-rendering-based pose refinement process to achieve highly accurate pose results. The experiments on the region-based object tracking (RBOT) dataset, the modified RBOT dataset, the synthetic large pose shift sequences and real sequences demonstrated that the proposed method achieved superior performance to the state-of-the-art methods in tracking objects with large pose shifts.

Conceptual Design of Artificial Intelligence Powered Automated Space Debris Remover (ASDR)

The focus of this research article is the application of AI technology for space debris removal. With the increasing number of non-functional artificial objects orbiting Earth, commonly known as space debris or junk, the need to address this issue has become crucial. Currently, there are over 200,000 such objects posing a significant threat to operational satellites and space missions. To mitigate this risk, we propose the utilization of AI-trained robotic systems to safely de-orbit space debris, thereby reducing the probability of collisions and potential damage. This research paper introduces the concept of employing AI and robotics technology to achieve this objective, with a specific emphasis on targeting Point Nemo as a designated disposal location. By harnessing the capabilities of AI, we can effectively identify and track space debris, enabling the robotic system to navigate and remove debris from critical orbital paths safely. Furthermore, the re-entry trajectory directed towards Point Nemo ensures that approximately 95% of the debris will burn up upon atmospheric re-entry, thus minimizing any potential risks to human life and property.

Sustainable management of space activity in low Earth orbit

ABSTRACT This paper extends the analysis initiated by Rouillon [2020. “A Physico-economic Model of Low Earth Orbit Management.” Environmental and Resource Economics 77 (4): 695–723. https://doi.org/10.1007/s10640-020-00515-z] of the externality caused by space debris. Satellite operators make choices about the design and launch of satellites, while in-orbit servicing firms supply efforts to remove space debris. Focusing on the long-term orbital state, we compare two management regimes. The open access equilibrium occurs when the orbit is a common resource. The optimal policy maximizes the net present value generated periodically by the space industry. We investigate economic instruments capable of effectively regulating space activity. We show that the combination of an ad valorem tax, a launch tax, and a market for removal effort certificates can provide the right incentives. A numerical application using a realistic calibration illustrates our results.

Kinematics modeling method of continuum space manipulator based on virtual discrete-jointed manipulator models

Continuum space manipulators (CSMs) have key application prospects in the maintenance of spacecrafts in narrow environments and space debris removal. Similar to conventional articulated space manipulators (ASMs), CSMs encounter a number of kinematic, dynamic, and control problems caused by the dynamic coupling between the continuum manipulator and its microsatellite platform. However, the continuum manipulator has no obvious kinematic joints. In addition, its motion is generated by the continuum deformation of its elastic body; thus, the virtual manipulator (VM) model of ASM in the free-floating state becomes inappropriate for CSMs. In this study, we propose a kinematic equivalent method for a free-floating CSM, which is equivalent to a virtual discrete-jointed manipulator (VDJM) connected to a virtual ground. First, the constraint relationship is used to establish the virtual vector manipulator (VVM) model for the CSM such that its center of mass in the free-floating mode remains unchanged. Furthermore, on the basis of the VVM model and D-H parameters of the CSM, virtual discrete joints are introduced, and a VDJM model for the CSM is proposed. Compared with the VVM model, the developed VDJM model can more intuitively express the motion characteristics of the CSM. Finally, we demonstrate the application potential of the developed VDJM model in the inverse kinematics solution, workspace, and dynamic coupling of CSMs.

Configuration design and collision dynamics analysis of flexible nets for space debris removal

Tether-nets are one of the most promising approaches for active removal of space debris. This paper investigated the collision dynamics of flexible nets with different configurations, the focus is on the selection of an optimal configuration with respect to collision dynamics. Firstly, the design method of net configuration is proposed based on undirected graph theory, and five flexible nets with different configurations are designed, including quadrilateral, pentagon, octagon, dodecagon and circle. Secondly, the collision dynamics model is presented and its effectiveness is verified via numerical simulations and ground experiments. Finally, collision dynamics of the five flexible nets are simulated based on the verified model and the differences of these nets are compared and analyzed. Comparison results show that the flexible net with octagon configuration has better collision dynamics than others according to the maximum deformation, stress, and energy dissipation during the collision process, which provided an optimal configuration of flexible nets for space debris removal.

Енергетичні витрати на переміщення об’єктів космічного сміття з низьких навколоземних орбіт на орбіти утилізації

The ever-increasing clogging of near-Earth space by space debris objects of various sizes significantly limits the possibilities of space activities and poses a great danger to the Earth’s objects. This is especially true for low orbits with altitudes up to 2,000 km. The risk of collision of operating spacecraft with space debris threatens their functioning in near-Earth space. To control space debris, use is made of active and passive methods of space debris removal from operational orbits. At present, promising means of space debris removal are a space debris transfer to low-Earth orbits with a lifetime of less than twenty-five years, a transfer to a junk obit, and in-orbit utilization. According to the latest recommendations, space debris objects moved to low-Earth orbits should have a lifetime of less than twenty-five years. In the dense atmosphere, small space debris objects usually burn up completely, while large ones burn up only partially and may reach the Earth. Since space debris motion in the atmosphere can only be predicted with large errors, a timely and accurate prediction of the place and time of fall of large space debris objects onto the Earth is impossible. Space debris objects can remain in junk orbits for hundreds of years without interfering with space projects. This method of space debris removal reduces the risk of collision with space debris objects in the initial orbit, but increases it in the junk one. According to the concept of in-orbit utilization, space debris is considered a resource for the in-orbit industry. An active space debris removal involves high energy expenditures of service spacecraft. In this regard, the task of their estimation becomes important. The goal of this paper is a comparative assessment of the energy expenditures for moving space debris objects into utilization orbits using service spacecraft with electrojet propulsion systems. The problem is solved using methods of flight dynamics, averaging, and mathematical simulation. The novelty of the obtained results lies in the development of a ballistic scheme and a fast procedure to calculate energy expenditures for moving space debris objects to a disposal orbit using service spacecraft with constant low-thrust electrojet propulsion system. The procedure may be used in substantiating and planning space debris transfer from low-eccentricity low-Earth orbits to utilization orbits.

Active debris removal: A review and case study on LEOPARD Phase 0-A mission

The growing number of space debris is alarming as it threatens space-borne services. Hence, there is an increasing demand to remove space debris to ensure sustainability and protect valuable orbital assets. Over the past few years, the research community, agencies and industries have studied many passive and active debris removal methods. However, the current technology readiness for space debris removal is still low. This paper first presents a comparative study of various space debris removal technologies to address the knowledge gap and quantify the challenges. This paper reviews the current state-of-the-art space technologies relevant to Active Debris Removal (ADR) missions. Detailed trade-off analysis is then presented based on the Low Earth Orbit Pursuit for Active Removal of Debris (LEOPARD) Phase 0-A study; this study is part of the United Kingdom (UK) Space Agency’s Active Debris Removal programme. The ADR mission scenario considered in this paper comprises a chaser spacecraft equipped with recommended technologies to capture non-cooperative targets safely. The final capture technology for the LEOPARD mission consists of an active robotic manipulator and a passive net capture mechanism. An analysis of the coupled-body dynamics of the chaser spacecraft carrying the robot manipulator and the targeted debris is carried out in simulation using SimscapeTM. The chaser spacecraft comprises Airbus’s Versatile In-Space and Planetary Arm (VISPA) mounted on a base spacecraft from Surrey Satellite Technology Ltd. (SSTL); the targeted debris is SSTL’s Tactical Operational Satellite (TOPSAT). The simulation results show dynamic changes in the chaser robot and the target satellite while performing non-cooperative capture. The simulation study accounted for various operational scenarios where the target is stationary or in motion. Further, for different modes of operation, the worst-case end-effector capture force limits were determined using open-loop control to execute a safe capture. Overall, the results presented in the paper advance the current state-of-the-art of robotic ADR and offer a significant leap in designing close-range motion and force control for stabilising the coupled multi-body system during capture and post-capture phases. In summary, this paper pinpoints the technological gaps, identifies barriers to realising ADR missions and offers solutions to catalyse technology maturity for protecting the space ecosystem.

Application of additional inflatable aerodynamic device to ensure the required degradation of the disposal orbit of large-size space debris

The paper studies the effectiveness of joint application of active and passive space debris removal technologies in low-Earth orbits.An active spacecraft-collector (SC), equipped with several detachable thruster deorbiting kits (TDKs), ensures the capture of the rocket stage. The TDK of dry mass about 90 kg should be fixed in the stage nozzle. After undocking from the SC, the TDK executes a deorbiting velocity impulse in order to form an elliptical disposal orbit with a predicted lifetime of 25 years in compliance with ISO standard requirements. However, many experts have recently called for a significant enhancement of these requirements.One of the ways to reduce the lifetime of the resulting disposal orbit is to equip the TDK with an aerodynamic decelerator, which has a shape of a spherical balloon. After the deorbiting impulse is applied, the balloon is supercharged by the gas remaining in the pressurized-propellant feed system of the TDK. Rigidization of the balloon shell is carried out by supercharging it above the yield point. The most rational balloon diameters are chosen based on the analysis of its effect on the lifetime of the disposal orbit.If the detachable TDK is equipped with an inflatable balloon, one can consider the combined and hybrid braking schemes. According to the first scenario, the balloon of diameter 12–14 m (“Zenith-2” case) or 7–8 m (“Kosmos-3M” case) is inflated in the already formed 25-year disposal orbit reducing its lifetime to about 5 years, while the dry mass of each TDK increases by 28 kg and 10 kg, respectively. Within the second scenario, a noticeably smaller deorbiting impulse results in a hybrid disposal orbit, which exists for 25 years due to subsequent inflation of the balloon of almost the same size. An analysis shows that the combined braking scheme is more preferable: with an insignificant increase in the SC launch mass, it does not create additional risks of failure and quickly deorbits the object from the most populated altitudes.

Mechanism analysis of space debris removal by nanosecond pulsed laser

In this study, a numerical model is used to study the mechanism of laser ablation for space debris removal. The model couples the physical processes involved in laser ablation, including the heating, melting and evaporation of target (i.e. Aluminum), the formation of plume and plasma, and plasma shielding. Validation of the model is performed by comparing the simulated impulse density and impulse coupling coefficient with experimental data, showing the availability of the model in accurately describing the processes involved in laser ablation for removing space debris. The effects of laser irradiance, wavelength and pulse width on laser ablation were systematically studied by the model. In addition, the continuous laser ablation is explored and the effect of the laser pulse time interval is demonstrated. The results show that laser irradiation and pulse width have a significant impact on laser ablation, while the impact of wavelength is much smaller compared to the former two. In addition, using two short duration laser ablation instead of a long duration can significantly improve the impulse density obtained by the target and the corresponding impulse coupling coefficient, but the time interval between two laser pulses should not be too long.

A Single-Averaged Model for the Solar Radiation Pressure Applied to Space Debris Mitigation Using a Solar Sail

Several non-functional objects are orbiting around the Earth and they are called space debris. In this work, we investigate the process of space debris mitigation from the GEO region using a solar sail. The acceleration induced by the solar radiation pressure (SRP) is the most relevant perturbation for objects in orbit around the Earth with a high area-to-mass ratio (A/m). We consider the single-averaged SRP model with the Sun in an elliptical and inclined orbit. In addition to the SRP effect, the orbital evolution of space debris is analyzed considering the perturbations due to the Earth’s flattening and third-body perturbations in the dynamical system. The idea is to use the solar sail as a propulsion system using the Sun itself as a clean and abundant energy source so that it can remove space debris from the geostationary orbit and also contribute to the sustainability of space exploration. Using averaged dynamical maps as a tool, the numerical simulations show that the solar sail contributes strongly to exciting the eccentricity of the space debris, causing its reentry into Earth’s atmosphere. To perform the numerical simulations, we consider data from real space debris. We also show that the solar sail can be used to remove space debris for a graveyard orbit. In this way, the solar sail can work as a clean and sustainable space-debris-removal mechanism. Finally, we show that the convenient choice of the argument of perigee and the longitude of the ascending node might contribute to amplify the growth of eccentricity. It is also shown that solar radiation pressure destroys the symmetry of the orbits that can be observed in keplerian orbits, so all the orbits will be asymmetric when considering the presence of this force.

Numerical analysis of separation dynamics for space debris removal payload based on solid thruster

Aiming at the current mainstream flying anchor payload for space debris removal, a solid thruster was proposed as the separation driving force, and a complete dynamic model of the spacecraft platform and payload were established. The effects of the gap between the directional button and the directional tube, thrust eccentricity and the initial attitude of the platform on the target accuracy under the flying anchor payload were studied. The analysis results showed that the initial attitude of the platform was the main factor affecting the target accuracy of the flying anchor payload. The control gap between 0.1mm ~ 0.25mm can effectively reduce the displacement of payload separation and the influence of disturbance on the platform.

Application of the principle of common but differentiated responsibility and respective capabilities to the passive mitigation and active removal of space debris

Unlike the concept of “common but differentiated responsibility” (CBDR), the concept of common but differentiated responsibility and respective capabilities (CBDR-RC) is a principle that emphasizes that the differentiated responsibilities of countries are dynamic, based on their respective dynamic capabilities and circumstances. It comprises the principles of “common responsibility” and “differentiated responsibility and respective capabilities” and has been rooted in the greenhouse gas context in the field of atmosphere. The shared common-pool character of the atmosphere and the Earth's orbital environments, combined with the similarities between the space debris and greenhouse gas contexts indicates that the principle of CBDR-RC likewise can be applied to distribute the responsibilities of different countries in the passive mitigation and active removal of space debris. However, the differences between these two contexts will lead to the categorization of countries and the application of the CBDR-RC regime in these two contexts. This article argues that, in the space debris mitigation context, while countries should bear specific responsibilities based on their financial and technical capabilities, all spacefaring nations should bear a common responsibility to contribute to the mitigation of future space debris, and for this purpose, the advanced spacefaring nations should provide technical assistance to the developing spacefaring countries to enhance their capability in, at least, the areas of design, manufacture, operation, and disposal of space objects. In the context of the active removal of space debris, all spacefaring actors should be responsible for the environmental protection of outer space, and thus should contribute to the active removal of the existing in-orbit space debris. It would be advisable to establish a legal regime to authorize the private sector to carry out the clean-up operation, because of the dual-use character of the active removal technology, while also requiring all spacefaring countries and international organizations that have space objects to contribute to an international trust fund to support the active removal operation. An international space debris removal entity should be established to provide intermediary services in the active removal process.

Dynamic behaviors of hierarchical-tethered towing system for space debris removal

The debris-tether-tug (DTT) system, has been considered as one of the most promising techniques for the space debris removal. In order to decrease the control difficulty of the DTT system, the DTT system was usually designed with a single tether. However, when the target owns the complex attitude motion, the removal efficiency of the classic DTT system (towing the target by a single tether) is limited. A modified DTT model with the hierarchical-tethered architecture is proposed to improve the removal efficiency in this paper. Based on the Hamiltonian variational principle, the coupling non-smooth dynamic model for the hierarchical-tethered towing system is established, in which, four tethers are divided into two groups to describe the asymmetry of the DTT model well. The symplectic Runge-Kutta method is employed to simulate the evolution of the orbit radius of the target, the length of the tethers, the position of the tethers’ mass center and the target attitude angle. The numerical results reported show that, the competition relationship between the attitude stability of the target and the stability of the variation of the sub-tethers is affected by the relative stiffness of the tethers. In addition, the capture ability of the modified DTT system for the space target with a certain spinning speed is illustrated, which provides a theoretical basis for the design of the DTT system in future.