Free-floating Space Manipulator Research Articles

An Adaptive Backstepping Control for a Free-Floating Space Manipulator Using a Linearly Parametrized Dynamic Model

An Adaptive Backstepping Control for a Free-Floating Space Manipulator Using a Linearly Parametrized Dynamic Model

Free-floating space manipulator impacting a floating object: Modeling and output SDRE controller design

This work investigates the dynamics modeling, control, and impact resolution between a floating object and a free-floating space manipulator (FFSM). The controller design is carried out by using an output- and state-dependent Riccati equation (OSDRE) approach. In a collision between an object and a mechanism, the computation of the generalized velocities and the impact force or impulse, which are interrelated, is a challenging problem. Taking into account the free-floating conditions of the space environment, the conservation of linear and angular momentum equations, combined with the conservation of kinetic energy under the elastic impact assumption, are used to find the unknown variables of the impact problem. The control problem addressed for the FFSM is to regulate its end-effector in a point-to-point motion scenario, this while the space manipulator suffers an unintended impact with a floating object, such as a damaged satellite or space debris. By proposing a safety pause starting with the occurrence of impact and for a short duration thereafter, the proposed OSDRE design succeeds in achieving the end-effector regulation control. Although the FFSM can reach the target point, it is shown that maintaining the end-effector regulation at the target is not feasible due to the momentum imparted to the FFSM as a result of the collision. To this end, we employ a simple thruster control on the space manipulator base to complete the regulation task. The theoretical development and controller design are demonstrated through a simulation case study of a spacecraft equipped with a three-link manipulator colliding with an object.

Double-layer prescribed performance control of free-floating space manipulators after capturing unknown targets

This paper studies the parameter identification and prescribed performance control of the free-floating space manipulator after capturing unknown targets. A novel finite-time concurrent learning (FT-CL) parameter identification algorithm utilizing suitable historical data is proposed. This algorithm guarantees the finite-time convergence of the parameter estimation error without using the persistent excitation condition. Then, we apply the dual modeling approach and view the end-effector states as generalized coordinates of novel virtual dual dynamics. This technique bypasses solving the inverse kinematics and calculating the Jacobi matrix, laying the foundation for Jacobi-free pose control of the end-effector. Besides, stabilizers of prescribed performance reference acceleration are carefully designed in a double-layer form for regulating end-effector pose and base attitude. Finally, the Jacobi-free controllers satisfying the double-layer performance constraints are developed. The efficacy of the proposed parameter identification scheme and control strategy is validated through numerical simulations.

Active 6 DoF Force/Torque Control Based on Dynamic Jacobian for Free-Floating Space Manipulator

Abstract In-orbit capture of a non-cooperative satellite will be a major challenge in the proposed servicing and active debris removal missions. The contact forces between the manipulator end-effector and the elements of the target object will occur in the grasping phase. In this paper, an active 6 Degrees of Freedom (DoF) force/torque control method for manipulator mounted on a free-floating servicing satellite is proposed. The main aim of the presented method is to balance the relation between end-effector position and force along each direction in the Cartesian space. The control law is based on the Dynamic Jacobian, which takes into account the influence of the manipulator motion on the state of the servicing satellite. The proposed approach is validated in numerical simulations with a simplified model of contact. Comparison with the classical Cartesian control shows that the active 6 DoF force/torque control method allows to obtain better positioning accuracy of the end-effector and lower control torques in manipulator joints in the presence of external forces.

Fixed-time control for free-floating space manipulators with prescribed constraints and input saturation

Abstract This paper investigates the issue of tracking control for a free-floating space manipulator with prescribed performance constraints, considering the inertia uncertainties, internal disturbances and input saturation. An inherently continuous adaptive controller is proposed by incorporating non-singular fixed-time sliding mode control, prescribed performance control (PPC), and auxiliary compensation. First, a modified non-singular fast fixed-time terminal sliding surface is constructed, which has a shorten convergence time than the conventional fixed-time sliding surface. Unlike the existing complicated PPCs, a simple structure controller is developed to satisfy prescribed performance constraints through a unique tangent-type PPC technique. The input saturation is then compensated adaptively by an auxiliary mechanism. The Lyapunov theory thoroughly validates the stability and fixed-time convergence of the closed-loop tracking system. With the suggested control scheme, the system states can converge quickly to a small neighbourhood around the origin within a preassigned time, while the position tracking error can be confined within a prescribed performance bounds even in the presence of input saturation. Compared to the existing tracking methods, the suggested control approach has the advantages of faster transient convergence, higher steady-state tracking precision, and stronger robustness. Simulation comparisons demonstrate the effectiveness and superiority of the proposed controller.

Time-Optimal Path Tracking for Dual-Arm Free-Floating Space Manipulator System Using Convex Programming

In this paper, the time-optimal path tracking problem of the dual-arm free-floating space manipulator (FFSM) system is solved by using convex programming. Firstly, we construct a continuous nonlinear optimization problem that considers system dynamics and constraints along the path, including torque, velocity and acceleration. Subsequently, the original optimization problem is transformed into a convex optimal control problem by using scalar path coordinate and nonlinear variables. To characterize the problem in a more manageable form, we apply the direct transcription method and discretize the problem into a sparse convex optimization program. Numerical results demonstrate that the proposed approach efficiently determines the trajectory of the FFSM along the preset path. Meanwhile, the base's velocity can be limited to a small region, which is an essential requirement for ensuring the stability of the satellite. Furthermore, an experiment is conducted using GLUON robots. The tracking error between the actual and preset pose of the target verifies the feasibility of the proposed method.

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.

Image based target capture of free floating space manipulator under unknown dynamics

Target capture is the basis of many space missions. With free-floating space manipulators(FFSM) are more and more widely used in various space tasks, using FFSM to catch space targets has become a research hotspot. In this research, we propose an end-to-end capture strategy under unknown dynamics based on deep reinforcement learning, which directly controls the manipulator with the raw camera image as the input. The algorithm take imitation learning for pre-training. The policy after pre-training process will explore high-reward regions in the state space with higher probability. This will improve the efficiency of DRL exploring in the high-dimensional state space composed of images. We built a simulation environment in CoppeliaSim to train and test our algorithm. The results show that our algorithm has achieved good results in end-to-end target capture task without dynamic modeling and is more efficient than pure model free reinforcement learning.

End-to-end active non-cooperative target tracking of free-floating space manipulators

Active non-cooperative target tracking is an important ability for free-floating space manipulator (FFSM) systems. Aiming at the difficulty of pose and posture estimation of non-cooperative targets and the complexity of FFSM planning and control, the paper proposed an end-to-end target tracking algorithm using deep reinforcement learning (DRL) algorithm. The algorithm uses raw camera images as input and directly outputs the manipulator joint velocities. To deal with the partially observable Markov decision processes (POMDP) problem caused by single image input, we combine the soft actor–critic algorithm with recurrent neural networks. Therefore, the velocity information of the target is introduced to transform the task into a fully observable Markov decision-making process (MDP). Our approach is completely data-driven. It avoids the position and posture estimation of non-cooperative target and the complex modeling motion planning process of FFSM. We trained and tested the algorithm by building a simulation environment in CoppeliaSim. The results showed that our approach achieved good results in active non-cooperative target tracking of FFSM systems and demonstrated the great potential of DRL algorithms in solving space tasks.

Passivity based nonlinear model predictive control (PNMPC) of multi-robot systems for space applications.

In the past 2 decades, there has been increasing interest in autonomous multi-robot systems for space use. They can assemble space structures and provide services for other space assets. The utmost significance lies in the performance, stability, and robustness of these space operations. By considering system dynamics and constraints, the Model Predictive Control (MPC) framework optimizes performance. Unlike other methods, standard MPC can offer greater robustness due to its receding horizon nature. However, current literature on MPC application to space robotics primarily focuses on linear models, which is not suitable for highly non-linear multi-robot systems. Although Nonlinear MPC (NMPC) shows promise for free-floating space manipulators, current NMPC applications are limited to unconstrained non-linear systems and do not guarantee closed-loop stability. This paper introduces a novel approach to NMPC using the concept of passivity to multi-robot systems for space applications. By utilizing a passivity-based state constraint and a terminal storage function, the proposed PNMPC scheme ensures closed-loop stability and a superior performance. Therefore, this approach offers an alternative method to the control Lyapunov function for control of non-linear multi-robot space systems and applications, as stability and passivity exhibit a close relationship. Finally, this paper demonstrates that the benefits of passivity-based concepts and NMPC can be combined into a single NMPC scheme that maintains the advantages of each, including closed-loop stability through passivity and good performance through one-line optimization in NMPC.

Singularity-robust full-pose workspace control of space manipulators with non-zero momentum

We address the end-effector full-pose tracking control problem in free-floating space manipulators, experiencing constant non-zero linear and angular momentum. The aim is to develop an output-tracking (workspace) control law free of singularities due to parameterizing the end-effector motion and being robust against singularities of the input–output decoupling matrix (generalized Jacobian matrix). Space manipulators are modeled as open-chain multi-body systems with single- and multi-degree-of-freedom joints, whose kinematics and dynamics are formulated on the Special Euclidean group SE(3). Such systems exhibit conserved (not necessarily zero) total momentum when operating in the free-floating regime, which we use to systematically reduce their dynamical equations by eliminating the base spacecraft’s motion. To avoid parameterizing the end-effector motion, we consider its full pose as the system output and develop a novel feedback linearization technique on the matrix Lie group SE(3) in the reduced phase space of the space manipulator. We then propose an intrinsic feedforward, feedback proportional–integral–derivative workspace controller involving a coordinate-free pose error function on SE(3) and velocity error on its Lie algebra. Using a Lyapunov candidate, this controller is proven to stabilize the end-effector pose to a feasible desired trajectory. The input–output decoupling matrix in the proposed control law can lose rank at some regions of the configuration space; hence, we implement a singularity-robust inverse, derived from the damped least squares method, to avoid impractical joint torques in these regions. The developed controller is implemented on a 7-degree-of-freedom manipulator onboard a spacecraft and its efficacy and robustness are demonstrated through a series of simulations.

Pseudospectral Convex Programming for Free-Floating Space Manipulator Path Planning

To efficiently plan the point-to-point path for a 7-degrees-of-freedom (7-DOF) free-floating space manipulator system, a path planning method based on Legendre pseudospectral convex programming (LPCP) is proposed. First, the non-convex dynamics are approximated by utilizing the first-order Taylor expansion in the vicinity of the initial guess path, which results in a convex system. Next, the linearized dynamics are discretized at Legendre–Gauss–Lobatto collocation points to transcribe the differential equations to a set of equality constraints. To obtain a reliable initial guess trajectory, the auxiliary path planning problem of the 7-DOF space manipulator with a fixed base is initially resolved. Additionally, the penalty function method is introduced to enhance the convergence performance of the LPCP. Finally, simulation results show that the proposed algorithm in this paper can generate the point-to-point path and has higher computational efficiency than the general sequential convex programming method while ensuring optimality.

Disturbance observer-based fractional-order sliding mode control for free-floating space manipulator with disturbance

This paper proposes a fractional-order sliding mode control scheme based on disturbance observer for tracking control of free-floating space manipulators (FFSM), regarding system uncertainties and disturbances. To mitigate the effect of disturbance, a fast fractional-order disturbance observer (FFODOB) is proposed, which can estimate the disturbances in finite time. It relaxes the assumption of first-order differentiable of the disturbances, which is common in many existing disturbance observers, to continuous but not necessarily differentiable, making it more suitable for practical applications. Besides, a new fractional-order nonsingular terminal sliding mode (FONTSM) controller is designed, in which, a fractional-order integral term is introduced into the conventional nonsingular terminal sliding mode surface. The presented FONTSM improves the transient response and tracking precision of FFSM. Stability of the closed-loop system and finite-time convergence are proved theoretically. Simulations are performed for different situations, and the results demonstrate the effectiveness and superiorities of the proposed methods over the existing methods.

Active object tracking of free floating space manipulators based on deep reinforcement learning

Free-floating space manipulators(FFSM) are more and more widely used in various space tasks, and active object tracking(AOT) is the basis of many missions in space. AOT of FFSM systems has two main difficulties: modeling and control of FFSM systems and tracking motion planning of space manipulators. To deal with these problems, the paper proposed an active object tracking proposal of FFSM systems using deep reinforcement learning(DRL) algorithm, Proximal Policy Optimization(PPO). Our approach is completely data-driven, which avoids the complex modeling process of FFSM and does not require motion planning for space manipulators, which is more concise than traditional algorithms. We trained and tested the algorithm by building a simulation environment in CoppeliaSim, and compared with the resolved motion rate control(RMRC). The results showed that our approach achieved good results in active object tracking of FFSM systems and demonstrated the great potential of DRL algorithms in solving space tasks.

Adaptive reactionless control of free-floating space manipulators for detumbling a target with dynamic uncertainties

Detumbling targets in the post-capturing phase is significant for an on-orbit capturing mission. However, the momenta of targets usually cause disturbances to the attitude of a free-floating base during the detumbling process. This paper proposes an adaptive controller for free-floating space manipulators detumbling targets with dynamic uncertainties in the post-capturing phase. The key feature of the controller, termed as adaptive reactionless detumbling controller (ARDC), is that it can produce null disturbance to base attitude. First, a reaction null-space controller is established based on momentum conservation, by which the null disturbance can be achieved at the displacement level. Second, considering the target’s dynamic uncertainties, an adaptive dynamic compensation is included. Furthermore, the reaction null-space vector in the controller is determined by an optimization model with the aim of detumbling target. A reference guiding vector is defined in the optimization model to ensure a steady detumbling process. Finally, the stability of the proposed controller is verified using the Lyapunov theory. The effectiveness of our proposed controller is validated through simulations, wherein the effect of the initial velocity and dynamic uncertainties of the target and the parameters of the controller are also studied.

Impedance Control Using Selected Compliant Prismatic Joint in a Free-Floating Space Manipulator

The success of space missions like capture-and-deorbit or capture-and-service relies on the ability of the capturing satellite to establish a stable mechanical connection by its gripping tool with the object being intercepted. Most of the potential objects of capture missions are not equipped with dedicated docking ports; hence, the satellite robot intercepting them will have to provide the mechanical compliance necessary for the safe establishment of contact between the two structures. Articulated robotic arms with controlled mechanical impedance are one set of promising solutions for this challenge. In this study, the authors discuss how the mechanical impedance realized only along a single axis can be useful for facilitating the contact between the manipulator arm’s end effector of a free-floating robot and an uncooperative object in microgravity. By distinguishing a dominant direction in the final approach and contact establishment maneuver, the need for impedance control of six degrees of freedom may be relaxed, and a single prismatic joint with controlled impedance can be used at the end effector. Such architecture is simulated and compared with the full model-based six-degree-of-freedom Cartesian impedance control of a free-floating manipulator. Authors then discuss the limitations and possibilities of such architecture in a potential practical setting.

Application of bidirectional rapidly exploring random trees (BiRRT) algorithm for collision-free trajectory planning of free-floating space manipulator

AbstractOn-orbit servicing and active debris removal missions will rely on the use of unmanned satellite equipped with a manipulator. Capture of the target object will be the most challenging phase of these missions. During the capture manoeuvre, the manipulator must avoid collisions with elements of the target object (e.g., solar panels). The dynamic equations of the satellite-manipulator system must be used during the trajectory planning because the motion of the manipulator influences the position and orientation of the satellite. In this paper, we propose application of the bidirectional rapidly exploring random trees (BiRRT) algorithm for planning a collision-free trajectory of a manipulator mounted on a free-floating satellite. A new approach based on pseudo-velocities method (PVM) is used for construction of nodes of the trajectory tree. Initial nodes of the second tree are selected from the set of potential final configurations of the system. The proposed method is validated in numerical simulations performed for a planar case (3-DoF manipulator). The obtained results are compared with the results obtained with two other trajectory planning methods based on the RRT algorithm. It is shown that in a simple test scenario, the proposed BiRRT PVM algorithm results in a lower manipulator tip position error. In a more difficult test scenario, only the proposed method was able to find a solution. Practical applicability of the BiRRT PVM method is demonstrated in experiments performed on a planar air-bearing microgravity simulator where the trajectory is realised by a manipulator mounted on a mock-up of the free-floating servicing satellite.

Output- and state-dependent Riccati equation: An output feedback controller design

An output- and state-dependent Riccati equation (OSDRE) is investigated for a set of coupled k-th order ordinary differential equations (ODEs) in the framework of nonlinear optimal control, in terms of stability, optimality, and application. A state-feedback control is a dominant part of the SDRE in the literature in comparison with an output feedback design. The output feedback design removes outer layers of kinematics or coordinate transformations in some systems and directly controls the output dynamics. This enables efficient control over many systems in which there is an indirect relation between outputs and states such as robots, mobile manipulators, autonomous vehicles, unmanned aerial vehicles, etc. To present the OSDRE, the co-state vector of the optimal control must include both state and output vector; and then the optimality conditions result in a control law and a Riccati equation, which are derived based on the output vector. The application of the OSDRE is devoted to the control of free-floating space manipulators (FFSM). The end-effector position of the FFSM is a function of mobile base coordinates (position and orientation) that are not actuated due to the free-floating condition. Then the output feedback SDRE directly controls the end-effector and guides the mobile base to provide enough reaction force/moment to push the gripper towards the desired end-point. So, the workspace analysis is crucial since the motion of the end-effector depends on the distance and configuration between the initial and final conditions. Simulation results for a mathematical third-order coupled ODE and a three-link FFSM confirm success in the control of the output dynamics. It was shown that the output of the mathematical model successfully tracked the desired output regardless of the individual state regulation. The FFSM has also tracked the desired output position with an accuracy of 0.02% of the travel distance.

Direct Trajectory Optimization of Free-Floating Space Manipulator for Reducing Spacecraft Variation

This letter investigates the direct trajectory optimization of the free-floating space manipulator (FFSM). The main purpose is to plan the joint space trajectories to reduce the spacecraft motion due to the joint rotation during the FFSM performing tasks. To improve the calculation efficiency, the adaptive Radau pseudospectral method (A-RPM) is applied to discretize the system dynamics and transform the formulated optimal problem into a nonlinear programming problem (NLP). By adaptively subdividing the current segment and assigning collocation points according to the solution error, high-degree interpolation polynomials are avoided. To verify the effectiveness of the proposed method, a ground micro-gravity platform of the FFSM system is designed by using the air-bearing technique, on which experiments are carried out. The results show that the variation of the base spacecraft is dramatically reduced if the joints rotate along the optimized trajectories.

Constrained Motion Planning of 7-DOF Space Manipulator via Deep Reinforcement Learning Combined with Artificial Potential Field

During the on-orbit operation task of the space manipulator, some specific scenarios require strict constraints on both the position and orientation of the end-effector, such as refueling and auxiliary docking. To this end, a novel motion planning approach for a space manipulator is proposed in this paper. Firstly, a kinematic model of the 7-DOF free-floating space manipulator is established by introducing the generalized Jacobian matrix. On this basis, a planning approach is proposed to realize the motion planning of the 7-DOF free-floating space manipulator. Considering that the on-orbit environment is dynamical, the robustness of the motion planning approach is required, thus the deep reinforcement learning algorithm is introduced to design the motion planning approach. Meanwhile, the deep reinforcement learning algorithm is combined with artificial potential field to improve the convergence. Besides, the self-collision avoidance constraint is considered during planning to ensure the operational security. Finally, comparative simulations are conducted to demonstrate the performance of the proposed planning method.