1. Introduction
Space operation and control refer to the on-orbit activity for specific targets with or without people’s participation to achieve proximity detection, auxiliary orbit maneuvers, fault maintenance, fuel filling, system upgrades, assembly, construction, rescue and space debris removal [
1]. From the Lunakod/Luna project of the Soviet Union and the SAINT (Satellite Inspector) project of the US to Phoenix and SMART-OLEV, the development of space operation and control has always been promoted by the Space Age. A series of experiments have been carried out to develop and verify relevant technologies by the space powers of the world. Space operation and control have become an important indicator of a country’s space force. A review of the development of space operation and control projects around the world is summarized in [
2]. Space robot motion and control are the core of space operation and control.
Whether it is on-orbit service (OOS), on-orbit assembly or space debris removal, the approach to non-cooperative targets is important. These non-cooperative targets usually have complex attitude movements, including spins, precession and tumbling, which greatly affect the approach process. In order to avoid adverse damage to service satellites and targets during operation and improve safety and reliability, it is necessary to study how to eliminate or reduce the rotation of the target. Generally speaking, as long as the relative state of the service satellite and target meets certain requirements, effective acquisition can be achieved. From the perspective of detumbling, detumbling can be divided into relative detumbling and absolute detumbling. Relative detumbling means that it does not change the target’s motion state but uses the service satellite’s own adjustment capabilities to change its own motion state to meet relative state constraints. For example, approaching from the target spin axis direction [
3] is a typical relative detumbling strategy.
This article focused on absolute detumbling, that is, through the direct or indirect interaction between the service satellite and target, the target state is changed to satisfy the capture condition. In principle, the main operation to make the target detumble is to apply additional torque to the target. According to the different torque sources, absolute detumbling can be divided into contact detumbling and non-contact detumbling. A series of technical verification tests was conducted by the space powers, proposing numerous detumbling methods. These methods are shown in
Table 1.
Considering technical maturity and energy consumption, among these methods, the robotic contact method is the most feasible to implement and verify. Additionally, this method combines capture and detumbling together which is very suitable for OOS. As one of the key technologies in space robot control, path planning generates a motion sequence to guide the robot from the initial state to the goal state safely. Path planning is widely used in the field of robotics and has accumulated a wide range of research results [
29,
30]. Roughly, path planning can be divided into two categories: complete planning and sampling-based planning.
Complete path planning is usually planned directly in the state space, with the Depth First Search (DFS), Breadth First Search (BFS) and Dijstra algorithms representing the original algorithms, and the Astar algorithm representing the most commonly used algorithm. The advantage of this method is that it can completely obtain the solution, but the cost is that the algorithm will become very complicated. This cost is not obvious in path planning in low-dimensional spaces but becomes very prominent in high-dimensional spaces. Since the actual work space-to-state space mapping is non-linear, it is very troublesome to represent obstacles and constraints in the state space. The usual approach is to discretize the space and detect the discrete parts. However, as mentioned earlier, this type of discretization is fine in low-dimensional spaces, but it will bring unimaginable complex calculations in high-dimensional spaces, which directly promotes the generation of sampling-based path planning algorithms.
Sampling-based path planning generally does not plan directly in the state space but randomly arranges a certain density of the sample space to approximate the state space. Sampling-based path planning is also divided into two types: One is graph-based, which scatters sampling points in the original state space and extracts the path by connecting those points with consideration of constraints, such as the probabilistic road map (PRM) algorithm and its improvement. The other is tree-based, which randomly arranges a point in the state space and iteratively grows the tree with the purpose of connecting the starting and ending points, such as the rapid exploration random tree (RRT) algorithm and its improvement. Whether graph-based or tree-based, these algorithms do not need to consider the distribution of obstacles in space but only need to perform collision detection on random sampling points. The planning speed is quite fast and can be used in any dimensional space, and, in particular, path planning has been widely used in high-dimensional spaces.
Due to the complexity of characterizing obstacles and constraints in the state space, complete planning is usually limited to handling low-dimensional problems with simple-shaped obstacles. Sampling-based planning does not need to express obstacles and constraints explicitly but instead combines search-based sampling and performs safety verification through a collision detection algorithm. By separating the planning problem from the actual physical and geometric problems, sampling-based planning greatly accelerates the speed of planning, especially in high-dimensional problems with complex-shaped obstacles.
Space detumbling is a multi-disciplinary complex system engineering problem involving basic disciplines such as mathematics, physics and materials and combining technical disciplines such as control, computer and simulation. Measurement noise, actuator noise, high-order dynamics and orbital perturbations all contribute to the complexity and uncertainty of space detumbling. Considering the uncertainty in space robot motion and control, robot platforms need to have near real-time planning ability in order to handle various uncertainties quickly and safely. Now, the solution for handling uncertainty is mainly divided into three categories. One is to optimize the design of a new spatial structure, as in [
31,
32]; another is to change the way of thinking and decompose the problem reasonably and abstractly, as explored by Kumar et al., where they decomposed any 3D motion into a 3D translation and three rotations about specific axes related to the object, which allows planning for 3D dexterous in-hand manipulation with a moderate increase in complexity in just a few seconds [
33]; the third is to use probabilistic analysis methods. Sampling-based path planning achieves an optimal solution under probability analysis through a reduction in constraints and backward detection and evaluation, which can not only ensure the calculation efficiency but also deal with various constraints well.
Commonly used sampling-based path planning algorithms include PRM [
34], RRT [
35] and EST [
36]. These algorithms can quickly find a feasible path, especially in high-dimensional spaces. However, when the sampling points are too few or the distribution is unreasonable, sampling-based path planning only obtains a feasible path, not the optimal path. In order to solve this problem, scholars have proposed asymptotically optimal versions, PRM* [
37] and RRT* [
38], where, as the number of samples increases, the solution path obtained will inevitably converge to a global optimum, as with BIT* [
39] and RRT# [
40]. It is particularly worth noting that the fast marching tree (FMT*) algorithm proposed by Janson et al. [
41] is a conceptually novel sampling-based path planning algorithm, and numerical simulation experiments have shown that the FMT* algorithm can converge to the optimal solution faster than PRM* and RRT* in the face of a high-dimensional state space and complex collision detection.
Although sampling-based path planning has not been applied in space missions, its effects and advantages for solving problems with high dynamics and uncertain environments have been verified in ground practical systems. In the Urban Challenge held by the Defense Advanced Research Projects Agency (DARPA), almost all of the winners adopted sampling-based path planning [
42,
43,
44,
45]. Since the path planning framework is universal, it seems that those research results can be applied to space path planning in theory. However, spacecraft motion is very different from ground robots, especially in space mapping and the C-space [
46,
47,
48,
49], meaning these planners cannot be directly applied to space missions without modification. Some scholars have studied the feasibility of sampling-based path planning in space missions [
50,
51,
52,
53], especially the studies by Starek et al. [
54,
55,
56,
57], in which the real-time implementability, safety and propellant efficiency of path planning by using FMT* or Bi-FMT* were thoroughly discussed in detail.
In the early stage, an improved sampling-based approach for spacecraft proximity operation path planning under Clohessy–Wiltshire–Hill dynamics based on a modified version of the FMT* algorithm with a safety strategy was proposed and analyzed in [
58]. In this work, the dynamics and robot arm deployment path planning problem of a certain space detumbling robot were analyzed.
Section 2 introduces the design and structure of the space detumbling robot. The kinematics and dynamics of the robot are also analyzed in this section. Then, the detumbling robot arm deployment path planning by using the Bi-FMT* algorithm is described based on the prevention model in detail from the aspects of problem description, constraint analysis and algorithm implementation in
Section 3. Additionally, the proposed approach is illustrated by using two numerical experiments in
Section 4. Finally, the conclusion and future work directions are provided in
Section 5.
5. Conclusions and Future Work
With the development of space exploration technology and space commercial activities, the number of spacecrafts in space is sharply increasing, and space resources and the environment are facing enormous challenges. On-orbit service (OOS, which consists of on-orbit refueling, on-orbit repairing, on-orbit upgrading and space debris removal) is an effective means to achieve successful space exploration missions and keep the space environment safe. Whether on-orbit assembly or space debris removal, the proximity to non-cooperative targets is important. However, these non-cooperative targets usually have complex attitude movements, which greatly affect the proximity operation process. In order to avoid damage to service satellites and targets during operation and improve safety and reliability, it is necessary to study how to eliminate or reduce the rotation of targets. A series of technical verification tests have been conducted by the space powers, proposing numerous detumbling methods, including friction, static, net, auxiliary device and electromagnetic. Considering technical maturity and energy consumption, among these methods, frictional detumbling is the most feasible. This paper focused on a space detumbling robot and studied the related technologies including space detumbling robot dynamics and robot arm path planning. A certain space detumbling robot with a ‘platform + manipulator + end effector’ configuration was proposed. By considering the end effector as a translational joint, the kinematic and dynamic model of the space detumbling robot was presented. Then, ADAMS and MATLAB were used to simulate and verify the model. After that, the robot arm deployment problem was analyzed in detail, and path planning based on the Bi-FMT* algorithm was also proposed and verified by simulation.
Space detumbling is a multi-disciplinary complex system engineering problem involving basic disciplines such as mathematics, physics and materials and combining technical disciplines such as control, computer and simulation. In contrast, the research work conducted in this article is only a small part of the solution, there is still a big gap to fill before practical engineering applications and theoretical research needs to be improved. On the basis of this article, future work directions include the following:
(1) The platform, manipulator and target are all regarded as rigid bodies; in practice, both the manipulator and solar panels have a certain degree of flexibility, and modeling under the condition of multiple flexible bodies is an important research direction.
(2) Semi-physical design and simulation verification of detumbling platforms and mechanisms.