1U-Sized Deployable Space Manipulator for Future On-Orbit Servicing, Assembly, and Manufacturing

Miniaturized, multifunctional, and economical on-orbit service satellites have been increasingly used with the continuous increase of space exploration missions. In this paper, an innovative deployable manipulator is designed, named Cubot, which can be stowed in 1 U-sized ( 10 cm × 10cm × 10 cm ) space. With CubeSat as the carrier, the deployable Cubot aims to achieve a variety of on-orbit operation tasks including space debris removal and space station on-orbit maintenance, for future on-orbit servicing, assembly, and manufacturing (OSAM). A kinematics modeling method of a space manipulator with passive joints is proposed, and the motion equation of the manipulator is derived. Considered the elastic potential energy stored in the passive joint during deployment, the momentum change of Cubot is simulated and analyzed. As the main forced element, the end e ﬀ ector is analyzed using FEA. Dynamic stress response with respect to the force distribution and the clamping angle is analyzed to evaluate mechanical performances of the end-e ﬀ ector component. Deployment tests are conducted to verify the feasibility of Cubot based on a principled prototype, which aims to provide engineering and practical experience for the development of this ﬁ eld.


Introduction
With the rapid development of space technology, a growing number of launches are put on the agenda. Space stations and artificial satellites have been widely used in communications, navigation, meteorology, astronomical observation, military, etc. However, at the mercy of complex and changeable space environment, spacecrafts may be disabled due to functional module degradation, failure, and running out of fuel. These spacecrafts need to be repaired or restored in order to avoid becoming space debris. Based on this background, the on-orbit service technology came into being, which covers a wide range of fields such as on-orbit maintenance, on-orbit assembly, on-orbit detection, and space debris removal [1][2][3][4][5]. The development of on-orbit services has always been closely integrated with space robotics technology [6], and space institutes such as NASA, ESA, and JAXA have all made important contributions. From the 1980s to the present, many space-robotic pro-jects have greatly promoted the development of on-orbit service technology, including ETS-VII, Orbital Express, Deutsche Orbitale Servicing Mission, and Phoenix Project [7][8][9]. In 2020, NASA proposed the mission of on-orbit servicing, assembly, and manufacturing (OSAM), aiming to make what was once thought to be impossible in space a reality depending on robotic technology [10,11]. From extending the lifespan of satellites, to assembling massive life-seeking telescopes in space, to refueling and repairing spacecraft on journeys to distant locations, the possibilities are endless.
Besides, scholars have made many significant researches about space robotic science. Stolfi et al. [12] studied the issue of maintaining a stable first contact between the arm terminal parts and a noncooperative target satellite using improved Impedance Control (IC) algorithm. Zhang et al. [13] presented a space robotic capture system, and a dualarm space robot simulator that has the advantages of miniaturization and scalability is designed for ground tests. Jia et al. [14] studied the maneuver control and vibration suppression of a flexible free-flying space robot using variable-speed control moment gyros as actuators. Xu et al. [15] proposed a hybrid method resolving linear and angular momentum conservation equations to model and analyze the dynamic coupling of a space robotic system. Aiming to tethered space robots, Wang et al. [16] addressed a novel control scheme for achieving attitude stabilization after target capture. Zong et al. [17] proposed a control method for space manipulators rendezvousing with and capturing a target, involving concurrent operation of an optimal and a coordinated controller. He et al. and Liu et al. [18,19] proposed effective control strategy to suppress the vibrations of flexible spacecraft. Liu et al. [20] presented a soft and bistable gripper for dynamic capture. The gripper deforms on the collision with other objects, and it absorbs the kinetic energy of the objects to trigger an instability and then achieves fast grasping as well as cushioning.
However, manipulator capture devices usually account for a large proportion of the entire satellite platform, which will bring high launch costs, which restricts the application of this field. Individuals focus on the need of reducing volume of manipulators [21,22]. Whitman and Choset [23] proposed a novel method to minimize the number of joints in the mechanism while maintaining its ability to reach workspace task poses. Cubesat is a small, low-cost satellite that has emerged in recent years and has a wide range of application prospects [24,25]. Researchers are interested in debris removal missions using Cubesat. The robotic arm device based on Cubesat has also been proposed and designed. The United States Naval Academy (USNA) has proposed a next-generation Intelligent Space Assembly Robot (ISAR) system to promote autonomous assembly. ISAR is a small, low-cost, 3 U Cubesat, which consists of two key subsystems: a 60 cm 7-DOF dual-arm robot, named RSat, and a sensing system that is consisted by a 3D camera and two 2D cameras. The system is designed to prove the on-orbit assembly ability of semiautonomous robot [26,27]. Researchers from the USNA have also developed an Autonomous Mobile On-Orbit Diagnostic System (AMODS) that performs on-orbit inspections of spacecraft based on Cubesats. AMODS includes multiple Cubesat devices, one of which has an operable arm providing diagnostic and maintenance services in order to extend the life of the spacecraft [28]. The combination of robotic arm and CubeSat technology will make up for the disadvantages of high cost and large volume on the existing manipulator capture device, which has important engineering significance. Mccormick et al. [29] proposed the mission concept of REMORA CubeSat and conducted a feasibility study. The prototype of the micromanipulator was designed in this task concept.
Combining the CubeSat technology, we innovatively propose a deployable 1 U-sized space robot, named Cubot, for the on-orbit tasks of space debris removal and space station auxiliary maintenance. The main contributions of this study are summarized as follows: (i) A deployable, highly integrated manipulator with end-effector is designed, which can be stowed in 1 U-sized space (ii) A kinematic modeling method for a free-flying space robot with passive joints is developed. The deployable process of Cubot is simulated, and the change of momentum is described This paper is divided into the following 5 sections. The structure design and working process of Cubot is introduced in the Section 2. The workspaces of two different configurations for Cubot are analyzed in this section. Section 3 describes a kinematic modeling method for a free-flying space robot with passive joints. The dynamic simulation of Cubot is implemented. The stress response analysis also be simulated in this section. In Section 4, the principled prototype is processing, and ground tests are carried out to verify the deployment reliability of Cubot. Conclusions and future research works are summarized in Section 5.

Cubot System Design
The current space on-orbit operation tasks are tending to be lightweight, miniaturized, multimodule, and multifunctional [30,31]. The CubeSat was born under this background. In Section 2.1, we innovatively propose a modular structure design method for a space manipulator, with the purpose of facilitating the configuration and application of the manipulator in CubeSat. Two working modes of Cubot for on-orbit service are introduced in Section 2.2. The mechanism analysis is carried out for the two different configurations (deployment process and after deployment) of Cubot in Section 2.3.

Structural Design.
The deployable Cubot can be regarded as a module of CubeSat. As shown in Figures 1(a) and 1(d), Cubot is composed of three parts, including active joints, passive joints, and end effectors. There are three active joints: the rotating base of Cubot is a worm gear driven by motor A, which can realize 360°rotation. Active joints A and B are driven by motors B and C, respectively. Active joint A drives a pitching motion of robot links, while active joint B drives a pitching motion of the end effector. There are three passive joints, including passive joints A, B, and C, which conduct deployable actions through torsion springs. In the stowed state, torsion springs store elastic potential energy through the pretightening force [32]. The interior of each passive joint is designed with a regulating plug, which is convenient to adjust the value of pretightening force. The torsion spring converts elastic potential energy into kinetic energy to realize the rotation of the passive joint. When passive joints are released, torsion springs drive their rotating until passive joints complete selflocking. The locking mechanism is composed by spring, torsional spring, and two parts with coupled profiled surfaces. The spring push two parts fit each other to self-lock when the torsional spring rotates into the designed angle. The inner details of passive joint are shown in Figure 2  Space: Science & Technology movement, unless a manually unlocking, so the deployment process of the passive joint is irreversible. Cubot can get a deployment length of 303.5 mm (exclusive end effector), and the deployment ratio is 1 : 3.
To obtain a larger clamping range, the end effector needs to occupy a larger volume ratio in the manipulator, which is not conducive to the storage in the CubeSat. Therefore, we adopted a design method similar to that of passive joints. The clamping part of the end effector is composed of long rod and short rod. The short rod and end base are connected by finger joint B, and a torsion spring is installed in the joint location to connect long rod and short rod. The preset angle of the torsion spring is 180°. Long rods are designed in a reasonable size range, which makes the long rod can be completely stowed in the 1 U space, as shown in Figure 1(b). The long rod and the short rod can rotate before Cubot deploying. After receiving the signal of deployment action, the torsion spring releases the elastic potential energy to achieve a 180°rotation. The spring at the joint pushes the long rod and short rod couple to realize a locking of end effector. Figure 1(c) shows the state of the deployed end effector. Four chutes are designed in the cross connector, which composes four mobile pairs with short rods and realizes the small range movements of the short rods in chutes. The cross connector, the finger joint B, the long rod, and the short rod constitute a crank-slider mechanism. The cross connector moves along the central axis by motor D, resulting the change of clamping angle, which achieve the capture of the target object. The passive joint and end effector have a similar locking mechanism. The details for structure design are shown in Figure 2. Different torsional springs and shape designs for profiled surfaces can achieve a different rotation angle.
The main innovation of this paper is to propose an integrated, modularized design method for space deployable manipulators. The design parameters including rod length, passive joint number, and the size of end-effector can be adjusted flexibly and customized according to specific onorbit missions. As a principle of the design parameters, the link length and link offset can be confirmed according to required storage size. Therefore, Cubot can be designed flexibly serving for suitable Cubesat space.

Cubot On-Orbit Operation Process.
Cubot is stowed in a 1 U space bound by cables. When performing on-orbit tasks, the cable is cut, and all joints conduct deployment action. In order to ensure Cubot get the largest working space, the preset angles of the torsion springs are, respectively, set as follows: passive joint A is 90°, and passive joints B and C are 180°, which ensures the corresponding linkage vertical with the plane of the base. The driving angles of active joints during deployment are controllable, so the deployment posture can be adjusted according to surroundings. The Cubot can perform multiple on-orbit tasks that rely on the CubeSat system. Two working modes, A and B, are listed as follows.
Mode A. Space station on-orbit maintenance. Extravehicular working of is dangerous for astronauts. "Replace people by machine" is the most efficient solving method.  When a failure occurs on the periphery of the space station or parts need to be replaced, Cubot can replace astronauts in space operations to reduce the risk of on-orbit missions. The work process of space station on-orbit maintenance is shown in Figure 3(a). This working model required the CubeSat equipped with a great ability of human-computer interaction, which will be researched in our future works.
Mode B. Active removal of space debris. Relying on the CubeSat system, Cubot can complete the debris capturing in the range of low to high orbit. CubeSat locates and tracks the target debris and then releases Cubot to conduct the capture mission. CubeSat deorbits and drags it into graveyard orbits when the target is captured [33,34]. Considering the size of Cubot, the farthest distance of opposite fingers is 80 mm while the biggest gap of adjacent fingers is 56 mm, so the size range of debris is about 50 mm-75 mm. Cubot cannot capture the debris that is high spinning because the despinning device is not designed. For the debris that is no spinning or low spinning, Cubot is operable, and this kind of debris can keep relative status by the friction with gripper. In this way, Cubot can perform capture missions for many times, which reduce the launch cost greatly. The work process of mode B is shown in Figure 3(b).

Workspaces in Two
Configurations. Workspaces of Cubot in two different configurations, during deployment and after deployment, are analyzed in this section. Passive joints will be locked by internal locking mechanisms after the torsion springs release elastic potential energy. In this situation, the two links connected to the passive joint will be fitted and become one link, as shown in Figure 4, which forms two different configurations during and after deployment of Cubot. During the deployment process, the passive joint can be regarded as an active joint with angular limitation, and the limiting angle is determined by the preset angle of the torsion spring. In addition, the long rod size of the end effector has a huge impact on the deployment space, so we regard the long rod as a link. Coupled with the worm and gear at the bottom, the Cubot in the deployment process can be regarded as a 7-DOF manipulator, as shown in Figure 4(a).
According to the designed size parameters and the configuration characteristics of Cubot, the D-H parameters in the deployment process are determined, as shown in Table 1. After completing the deployment process, two links connected to the passive joint are merged into one, all the passive joints disappear, and only active joints remain. In   Table 2.
We analyze the workspaces of Cubot in two different configurations, respectively. The Monte Carlo method is used to solve the workspace of Cubot. Joint 1 can rotate 360°in two different configurations, and the work space is symmetrical along any plane including link 1. Therefore, we ignore the link 1 and draw the x − y planar workspace of Cubot in order to a clearer expression, as shown in Figure 5. Figures 5(a) and 5(b) show the work spaces during and after the deployment process. The workspace of Figure 5(b) is less than a half of Figure 5  In the most situations, the position adjustment for Cubot is controlled by Cubesat. Therefore, there is redundant to design too many DOFs for Cubot. On the contrary, passive joints with self-locking function can enhance the stiffness of the manipulator, which is more important for capturing a motional target.

Kinematic Modeling and Dynamic Simulation
Cubot carried out operations based on a satellite platform. The position and attitude of the satellite platform are actively controllable, which can move freely or remain stationary, so Cubot is classified in a free-flying space robot. The motion equation of a space manipulator with passive joints is proposed. We simulated the movement state of Cubot with active and passive joints using ADAMS. In addition, considering the structural particularity of the Cubot end effector, we conducted a structural dynamics simulation on the end assembly with respect to stress and strain, in order to determine the grasping range and grasping ability of Cubot.

Kinematic Modeling.
In this section, we will derive the kinematics equations of the single-arm free-flying space robot with several passive joints [32]. A mathematical description of the space robot with passive joints is shown in Figure 6. Assuming that the link number of space robot is n, the active links is n a while the link is n p , so n = n a + n p . The centroid position vector of link i can be expressed as The end-vector can be expressed as Assuming that before link i (including i), the robot consists of i a active links and i p passive links, and the centroid velocity vector of link i can be expressed as where P a j is the position vector of the j-th active joint J a j , while P p j is the position vector of the j-th active joint J p j . Because the angular velocity of the passive joint _ θ p j is not controlled by the input signal during the deployment process, it is only determined by the parameters of the torsion spring, which can be regarded as a time-varying parameter. The relationship between and t can be expressed as where k j and α j , respectively, represent the torsion coefficient and preset torsion angle of the j-th passive joint, and I j represents the moment of inertia of the link connected to the passive joint. Consider the active joints as controllable joints and the passive joints as uncontrollable joints. Accordingly, Eq. (3) can be rewritten as Combine Eqs. (4) and (5) However, the torque expression is different depending on the different type of torsion spring, so Eq. (6) is not The angular velocity vector ω i of the joint i can be expressed as The angular velocity vector of the end effector can be expressed as From Eqs. (5) and (9), we can get where J e ∈ ℝ 6×6 , J A ∈ ℝ 6×6 , and J P ∈ ℝ 6×6 can be expressed as Equation (10) is the kinematics equation of a free-flying robot with passive joints, which is a time-varying system during deployment.

Dynamic
Simulation. The mathematical model in Section 3.1 shows a high motion complexity during the deployment of Cubot. Therefore, the dynamic analysis of Cubot plays a crucial role. First derive the total energy of the system and total kinetic energy is represented by T.
The deployment process of Cubot is simulated by ADAMS, and the time sequence is shown in Figure 7. Active joints are highlighted in yellow for the convenience of observation. The active joints are controlled to move to the location where they can reach the farthest distance. From the derivation in Section 3.1, the speed and acceleration of passive joints are functions of time. In order to simulate this process, time-varying torques are used in all passive joints in a manner similar to real torsion springs. Passive joint A applies a preset angle of 90°, and passive joints B and C apply a preset angle of 180°, respectively. Torsion springs in the end effector apply a preset angle of 200°, which ensures the locking between long rods and short rods.
The torque M of the passive joints is shown in Figure 8(a). The torque of the torsion spring presents a fast-attenuating simple harmonic change with time changing, which also affects the motion of other joints. Figure 8(b) shows the angular velocity ω changes of the active joints and the end effector. It indicated that each joint has varying degrees of fluctuation within 0-2 s affected by the action of the torsion spring. And the end effector is most affected.
The momentum Pt shows the energy exchange that occurs when the mechanism moves, which can judge the damage severity of parts if occurs impact. Figure 9 shows the momentum change of Cubot during the deployment process. Huge kinetic energy is generated in 0-1 s, because the elastic potential energy inside Cubot has just been released. Under the current driving signal, Pt generated by the active joint B is the largest, and the probability of collision damage is the largest. Therefore, physical interference between the robotic arm and other objects should be avoided as much as possible during the deployment of Cubot, including CubeSat's structural parts and surrounding space debris.

Stress Response Analysis of End
Effector. Based on the special space structure design, the size of the two rods (long rods and short rods) of the end effector affects capture ability to targets. End effector is the main stress part on the on-orbit task, so the analysis of mechanical properties for end effector is important. In this section, we will conduct stress response analysis of end effector, and the finite element model is shown in Figure 10.
The main stressed components of the end effector include long rods, short rods, the cross connector, and the end base. There are three main factors that affect the stress value and stress distribution of the parts when executing clamping action: the magnitude of clamping force, the force position, and the clamping angle. Obviously, when the force position and the clamping angle are determined, the magnitude of clamping force and the stress value presents a linear relationship, and the stress distribution position will not be affected. So, we focus on the influence of the force position distribution and the clamping angle when analyzing the stress response of the end effector.
Assuming that the target grasped by the end effector is completely symmetric about axis-z, the clamping forces F are applied on the contact surface between A and B. Obviously, the position distribution of F on the four long rods is symmetric about axis-z, and the stress magnitudes are equal. The mechanism analysis in Section 2 shows that the movement of cross connector drives the change of the clamping angle θ c , and the range of θ c is -22.3°~12.5°. Loads are distributed on the long rod, and the range depends on the length of long rod. The load and boundary conditions we confirmed is where X f is loading position. Note that θ c refers to the angle between the long rod and the axis-z, so the corresponding opening angle of the end effector is -44.6°~25°. The stress response at different force distribution positions and clamping angles is analyzed using ANSYS, and the maximum stress response surfaces are obtained, as shown in Figure 11. From the analysis results of the response graph and simulation data, the following conclusions can be drawn. (i) The maximum stress of each part shows an overall downward trend as the force distribution is far from the end of long rod (ii) The long rod can be regarded as a cantilever beam, whose maximum stress shows a linear relationship with force position distribution, but is not affected by clamping angle. In contrast, the other components show nonlinearity in force distribution and clamping angle (iii) Compared with the cross connector and the end base, long rods and short rods are more prone to failure. As the force distribution position and clamping angle changes, the maximum stress position of the end effector alternates between long rods and short rods (iv) The stress response surface of the cross connector performs a strong-nonlinearity. The reason is that the maximum stress position of the cross connector is uncertain, which alternates between the hinged support connected to the short rod and inside of the chute When Cubot grasps targets with different sizes, the failure location and the maximum allowable clamping force can be determined by the maximum stress response surface, which has important engineering significance.

Ground Experiment Verification
In this section, preliminary prototype was manufactured and tested. Motors, springs, and worm gears were defined according to actual working conditions of Cubot. Figure 12(a) shows the stowed state of Cubot. It can be seen that Cubot with the end effector can be completely stowed in a 1 U space, which realizes the design idea of miniature and modular. The deployed state of Cubot is shown in Figure 12(b). Figure 13 shows the time sequence of Cubot. Cubot initially is bound in a 1 U space using nylon ropes. In actual working conditions, the thermal resistance wire is usually used to fuse nylon ropes. The feasibility of this method has  Space: Science & Technology also been verified in many space deployment mechanisms [35]. We use a scissor to replace the function of thermal resistance wires, in order to simplify the fusing process and carry out multiple sets of deployment tests. As shown in Figures 13(a)-13(c), the end effector bounces instantly under the action of torsion springs at the moment nylon ropes are cut, when the duration is less than 1 s. After that, active joints driven by 12 V motors and passive joints move at the same time. Figures 13(d)-13(f) show the process of movement and self-locking for passive joints. Figures 13(g)-13(i) show the movement process of active joints after passive joints achieve self-locking. The whole process from (a)-(i) takes 3-5 s. In this paper, a total of 10 sets of deployment tests are performed. All passive joints and the end-effector can be deployed smoothly, which verifies the deployment feasibility and reliability of Cubot.  In addition, the verification experiment has been executed for the end effector of Cubot. As shown in Figure 14, we test Cubot capturing different irregular objects in different pos-tures, and the end effector can achieve all the tests effectively. In a real implementation, some of design of increasing friction can be used in the long rod in order to a better capturing.

Conclusions and Future Works
A 1 U-sized deployable space robot Cubot is designed innovatively in this paper. Related research and analysis conclusions are as follows: (i) With full consideration of economy, compactness, and working space, the robotic arm and end effector are configured to meet the modular design requirements of CubeSat. Cubot can be stowed in a 1 U space, and the maximum deployment distance is about 303 mm. In addition, the long rod length of the gripper can reach 90 mm, and the opening angle of the gripper is -44.6°~25°. A high expansion ratio is achieved, and a target with a larger size range can be clamped (ii) We derived a general kinematics model for the freeflying space robot with passive joints, which is a time-varying system. The movement state of the deployment process is closely related to the physical properties of the passive joint and the applied preset angle (iii) The momentum changes of the joints during the deployment process are analyzed. The result shows that the system has a greater impulse at the beginning of the deployment process, and the active joint   Space: Science & Technology B has the largest impulse. These analyze data supports for the attitude adjustment of CubeSat (iv) The stress response of the end effector with respect to the force distribution and the clamping angle was obtained by FEA. The results show that the maximum value of the end effector will alternate between long rods and short rods (v) Cubot was processed, and the relevant tests were conducted, which verified the feasibility of this model Our current works mainly focus on the configuration design, principled verification, and dynamic analysis. These works are the basis of Cubot from theory to application. In the future, we will make Cubot and the solar sail as the two modules of the CubeSat to study the coupling dynamics. In the field of control, we will focus on the control problems of space debris capture coupled with Cubot and CubeSat, including desorption and deorbit. Our goal is to verify the feasibility of Cubot for on-orbit services through on-orbit tests and make new contributions in the field of space onorbit services.

Data Availability
The data used to support the findings of this study are available from the author upon request.