1. Introduction
In September 2021, for the first time in the history of space development, all-civilian and all-private spacecraft orbited the Earth. Private spaceflight is still in the development phase, but it will become more common in the future. With more people staying in space, we need to think about how to move efficiently and safely in a space station. The expansion of human-occupied space facilities, such as the International Space Station, is expected to increase this tendency. In addition, the general contractor Obayashi Corporation in Japan has announced the “Space Elevator Construction Concept” to construct a space elevator by 2050 [
1]. Because it is assumed that the interiors of such occupied space facilities will have microgravity conditions, a special means of mobility is needed for humans to perform efficiently.
The use of space tethers in such a space environment has been proposed [
2]. Since space tethers were first proposed by Tsiolkovsky, space tethers have been widely used in space missions such as attitude stabilization, momentum exchange, and space elevators. Many space tether concepts have been proposed, and missions have been carried out [
3]. Tethers have the advantages of being lightweight and compact. A compact tether system has been proposed for microgravity environments [
4]. For instance, a tethered robot system was developed for use under microgravity conditions [
5]. Furthermore, an extension method based on the Lorentz effect was proposed, and its control method was developed [
6]. Furthermore, a number of tethered deorbiting missions were proposed [
7,
8]. A system using net-shaped tethers has been developed [
9]. In addition, there is also a system proposal using a tether for the safety of astronauts [
10]. As shown in these studies, the tether is useful as an actuator in space. However, the flexibility and elasticity of space tethers creates problems. Therefore, there are many development items as research themes. Moreover, many proposals for using tethers have been proposed in other fields. There has been research on the use of tethers for automatic landing [
11], anti-vibration, and energy supply for helicopters [
12]. In addition, there are Remotely Operated Vehicles in the deep sea [
13].
We developed the Tether Space Mobility Device (TSMD) for facilitating human mobility within an occupied space facility in a microgravity environment [
14]. This system was proposed by us as a tool for humans to move by using the tether as an actuator.
Figure 1 shows the concept of the TSMD. The tether is shot out from the TSMD, and the end of the tether is attached to the target point. Then, the tether is wound into the TSMD by an actuator, pulling the operator toward his or her desired destination. However, because this system only uses the tension in the tether for movement, as shown in
Figure 2a, when the center of gravity of the target user moves away from the line of action of the tension, a moment due to the tension is applied, as shown in
Figure 2b, and the problem of rotational motion occurs. Therefore, it is necessary to adopt a control method to suppress this rotational motion. For cable control, cooperative control is applied to the gantry robot under tension [
15]. There is research on the design of the control system with the observer to suppress the vibration of the crane [
16] and the design of the control system to move the load of the crane [
17]. Regarding tension control, research on applying fuzzy PID to an automatic winding machine to control tension [
18] and a method of controlling the tension of a machine for feeding paper has been proposed [
19]. There is a study that controls the tension by feedback control for the tethered space-tug system [
20]. In the above research, control under the condition that tension acts the system is examined. However, in the proposed system, when the tether is wound up, and the human is moved, there is a time when the tether undergoes deflection due to the inertial force of the human, and the tension becomes zero. Then, the tension is generated again by winding the tether. In other words, it is the system in which there is a time when there is no tension used for control, and control is not possible.
In this study, we focused on the kinetic energy related to rotation and developed an attitude control method that converges the angular velocity during the winding of the tether to 0 deg/s. Then this control method has been shown to be effective by the numerical simulation model [
21].
In this paper, we designed and built the proposed control system. This system was installed in the experimental device for validating the numerical simulation model. Therefore, we targeted the TSMD motion during the winding of the tether and verified the attitude control method by focusing on the kinetic energy related to rotation using actual machine experiments. Furthermore, the usefulness of the proposed method is shown in the results obtained using a numerical simulation model.
2. Control Method for Winding up the Tether
This section provides an overview of the winding tether control method we developed. Details are given in [
21]. The proposed control method focused on the change in kinetic energy related to the rotation of the rigid system and applied a control method [
22] that converges the angular velocity of the rigid system generated during tether recovery to 0 deg/s. This form of control automatically achieves optimum winding of the tether based on the motion of the TSMD.
First, the conditions under which the tension of the tether attenuates the rotational motion of the rigid system are derived.
Figure 3 shows the TSMD model with the tether stretched. Here, no relative motion is assumed between the TSMD and the unit for simulating the influence of the weight of a human body (hereinafter referred to as the rigid body). The symbols in the figure are defined as follows:
- :
Tension of the tether
- :
Angle formed by the axis and the tether
- :
Moment of inertia of the TSMD
- - :
Body coordinate system with the center of gravity of the rigid body as the origin
- :
Distance from the tip of the inlet to
- :
Angle of the tip of the inlet in the object coordinate system
- :
Rotation angle of the rigid body
The equation of motion for the rotational motion of the rigid system in
Figure 3 is given by:
The kinetic energy
related to the rotational motion of the rigid system is given by the following equation:
It can be seen that when
,
from Equation (2). The following equation is obtained by differentiating Equation (2) with respect to time and substituting Equation (2) for Equation (1):
Here, from
and
, the following relations hold:
When
is switched as follows,
and the passage of time makes
and
. Moreover, because
is the TSMD and the human unit are fixed at 90 deg by a joint in this paper, it has the following value:
Next, consider the winding tether control rule that satisfies Equation (4). Let
be the length of the tether that has not been collected inside the rigid body and let
be the target value for the length of the tether. For simplification, the transfer function from
to
is given by Equation (7).
Therefore, the acceleration
of the tether length is given by the following equations:
and
Moreover,
is determined as follows with reference to Equation (4):
where
is the distance from the origin of the global coordinate system to the tip of the suction port, and
and
are control inputs when
and
, respectively. In this paper, let
,
, and
. By defining
as in Equation (10), when tension increases the kinetic energy of the rigid system, the tether flexes to counteract the tension, and when the tension reduces the kinetic energy of the rigid system, the tether is stretched so that tension is applied. By repeating this, the angular velocity of the rigid system can converge to
over time.
4. Discussion
In this section, we discuss the effectiveness of attitude control based on the experimental results. A numerical simulation model proposed in the literature [
21] is used for comparison because the experimental setup is affected by friction and gravity acting on the tether. First, the effect of control is verified by the experimental results and simulation results. Furthermore, the effectiveness of the proposed method is shown by comparing the results under attitude control.
First, the control effect is examined based on the experimental results.
Figure 11 shows the time history of the angular velocity obtained from the experimental results. It can be seen that from 0 to 1.3 s, the angular velocity without control increased rapidly and then decreased rapidly. Because the angular velocity is never negative between 1.3 and 6.0 s but remains a constant positive value, the TSMD continues to rotate counterclockwise. This indicates that the rotational motion is excited by the tension in the tether in the initial state, and the rotational motion is not controlled. In contrast, with control, the TSMD moves in a similar manner from 0 to 1.3 s, but after that, the angular velocity settles at a constant value at around 1.5 s. Then, due to the tension in the tether generated by the attitude control, the angular velocity begins to decrease again and converges to about 0 deg/s after 3.2 s. The rapid change in angular velocity after 5.7 s with attitude control was caused by the device approaching the edge of the flight table and is thus not related to control performance.
Next, the effect of control is examined based on the numerical simulation results.
Figure 12 shows the time history of the angular velocity in the numerical simulation, and
Figure 13 shows the shape of the system at each time step. From
Figure 12, it can be seen that from 0 to 1.3 s, the angular velocity under both conditions increases rapidly and then decreases rapidly to a negative value. In contrast to the experimental results, the reason the values became negative under both conditions can be considered to be the lack of frictional force. After that, the angular velocity without control converges to a constant value after 1.3 s and then remains at almost the same value. This indicates that the TSMD continues to rotate in the same direction as the initial rotation. In contrast, with control, the angular velocity becomes negative and then increases and converges to about 0 deg/s after 2.9 s. This is because the tension in the tether was induced multiple times by the energy control, which controlled the rotational motion. The generation of this tension can also be confirmed from by shape of the system in
Figure 13. The tether without control is not greatly deformed from the start of winding to about 1.5 s, and the tether is moving while being greatly deformed after 1.5 s so that it is not stretched again. In other words, it can be considered that the TSMD is moved by only the inertial force. Conversely, the tether under the condition of attitude control deforms in a manner similar to that when there is no energy control from 0 to 1.5 s. However, the tether under attitude control does not deform significantly from 1.5 to 3.0 s, and the deflection of the tether is eliminated. This is because the winding speed of the tether is automatically adjusted by the attitude control. After that, the deflection of the tether caused by the rotational motion of the TSMD is eliminated by attitude control. It can also be seen that the TSMD is moving when its rotation is suppressed. The difference between the experimental and numerical results may be due to the influence of the frictional force between the TSMD and the flight table. However, it is considered that this difference does not affect attitude control since this difference also exists under uncontrolled conditions.
Therefore, the effect of attitude control on the rotational motion of the TSMD is to automatically change the winding speed in both the experimental and numerical results.
Next, to verify the attitude control from the viewpoint of the control mechanism, the timing of the control input was examined.
Figure 14 and
Figure 15 show the time histories of the control input and angular velocity in the experimental and numerical results, respectively. In
Figure 14 and
Figure 15, the following common tendencies can be seen. At 1.0 s, when control starts, control input
causes the tether to stretch, and the tension acts in a direction that reduces the kinetic energy. After that, the control input switches from
to
when the angular velocity shows a negative value and the control input
prevents an increase in kinetic energy. Then, the angular velocity is stable at negative values. Switching the control input from
to
generates tension in the tether. The tension, which acts in a direction that reduces kinetic energy, increases the angular velocity, which converges to approximately 0 deg/s. Regarding the number of times the control input is switched, it can be seen that in the experimental results, the control input is switched one more time than in the numerical simulation results because the control input is switched to u_ from 1.8 to 1.9 s in the experimental results. Because the control input is switched depending on the sign of the conditional expression
in Equation (10), the reason is obtained from the time history of
Figure 16 shows the time history of
When the control input becomes
, it can be seen that
becomes negative from 1.8 to 1.9 s. At other times, the control input is switched depending on the sign of
. It can be seen that the control input is switched appropriately. Because the sign of
is determined by the angular velocity
and the angles
and
, the reason the sign changes twice between 1.6 and 2.1 s is that the angle
changes due to the sudden change in angular velocity
and
from 1.4 to 2.1 s.
Therefore, the control target of converging the angular velocity of the TSMD to about 0 deg/s over time is achieved. In addition, attitude control is realized by a similar mechanism both experimentally and numerically. Based on these results, the effectiveness of attitude control is established.
5. Conclusions
In this study, as fundamental research on a TSMD system designed to be used under microgravity conditions, an attitude control method was adapted. The proposed method aims to automatically achieve optimum winding of the tether based on the motion of the TSMD. This control method was verified only by the numerical simulation model. Then, an experimental device based on the proposed control system was designed. A control system was implemented by a gyro sensor and a distance sensor. Therefore the effectiveness of the proposed attitude control method was experimentally verified, and it was shown that the rotational motion of the TSMD was reduced. Using this method, the angular velocity, which is the control target, could be set to 0 deg/s. This indicates that stable automatic winding of the tether was realized by using rotational energy. In future work, the proposed control will be implemented using a Kalman filter instead of a distance sensor. Because the distance sensor cannot be used unless the wall is flat, it is not preferable to use it in a structure with a complicated shape. Moreover, the calculation of distance using the accelerometer has an error caused by two integrations. So, a Kalman filter will be used to solve these problems. In addition, disturbance experiments related to human movement as the device is used will be conducted.