Spacecraft Proximity Operations Research Articles

Spacecraft Proximity Operations Under Motion and Input Constraints: A Learning-Based Robust Optimal Control Approach

Spacecraft Proximity Operations Under Motion and Input Constraints: A Learning-Based Robust Optimal Control Approach

Safe Guidance Scheme for Proximity Operations Forced Motion

Autonomous spacecraft proximity operations represent a key enabler for future mission architectures such as in-orbit servicing, active debris removal, object inspection, and in-orbit assembly. This work addresses safety concepts for the relative trajectory guidance design applicable to challenging proximity operations in the close-range domain. The relative orbital element framework is used to formulate safety checks that improve the trajectory’s robustness in case of chaser’s malfunctions or loss of control. Particularly, concepts of passive abort safety and active collision safety are applied to the trajectory design to maintain the chaser outside keep-out zones. These definitions are included within a guidance algorithm that exploits sequential convex programming to efficiently solve the fixed final time safety-constrained close-range rendezvous problem. Test cases of reconfiguration between stable relative orbits and synchronization to a rotating hold point are presented, highlighting the advantages in using these new safety concepts in terms of safety, trajectory insight, and formulation efficiency.

Consensus SE(3)-Constrained Extended Kalman Filter for Close Proximity Orbital Relative Pose Estimation

In this paper, a recently proposed SE(3)-constrained extended Kalman filter (EKF) is extended to formulate a strategy for relative orbit estimation in a space-based sensor network. The resulting consensus SE(3)-constrained EKF utilizes space-based sensor fusion and is applied to the problem of spacecraft proximity operations and formation flying. The proposed filter allows for the state (i.e., pose and velocities) estimation of the deputy satellite while accounting for measurement error statistics using the rotation matrix to represent attitude. Via a comparison with a conventional filter in the literature, it is shown that the use of the proposed consensus SE(3)-constrained EKF can improve the convergence performance of the existing filter for satellite formation flying. Moreover, the benefits of faster convergence and consensus speed by using communication networks with more connections are illustrated to show the significance of the proposed sensor fusion strategy in spacecraft proximity operations.

Meta-Reinforcement Learning for Spacecraft Proximity Operations Guidance and Control in Cislunar Space

Innovative lightweight and model-free guidance algorithms are essential to achieve full autonomy of spacecraft and address future space exploration challenges. In the near future, this type of technology will be essential for cislunar space proximity operations, such as NASA’s Artemis program and its Lunar Gateway project. In this scenario, a meta-reinforcement learning algorithm is employed to address the real-time optimal guidance problem of a spacecraft in the cislunar environment. Non-Keplerian orbits pose complex dynamics, where classic control theory may be less adaptable and more computationally expensive compared to machine learning approaches. Meta-RL stands out for its ability to learn how to learn through experience, training on various tasks to enhance efficiency, and effectiveness in tackling new ones. By modeling a stochastic optimal control problem within the circular restricted three-body problem framework as a Markov decision process, an LSTM-based network agent is trained using proximal policy optimization, considering operational constraints and stochastic effects for safety and robustness evaluation. Additionally, an MLP-based agent and an optimal control pseudo-spectral solution are assessed for comparison. The resulting tool autonomously guides spacecraft in cislunar proximity operations, approximating the optimal control solution with a versatile algorithmic framework. This ensures both robustness and computational efficiency.

Quantitative Precision Second-Order Temporal Transformation Based Pose Control for Spacecraft Proximity Operations

Quantitative Precision Second-Order Temporal Transformation Based Pose Control for Spacecraft Proximity Operations

Autonomous relative navigation using stereo-vision in a dual-agent system for proximity operations in a lunar orbit

This paper presents a novel autonomous relative navigation architecture for inspector spacecraft in proximity operations to a known structure in a lunar orbit. Autonomous on-orbit servicing and assembly of large space structures are at the forefront of research for advancing space exploration beyond low-earth orbit. Communication delays with ground stations and limited computational power located on the inspector spacecraft make current relative navigation methods unfeasible and in turn, make it difficult to maintain an accurate estimate of the relative position and orientation of the inspector spacecraft with respect to the structure. The proposed method utilizes the camera measurements from two identical inspector spacecraft, each equipped with a single camera, to estimate the relative position and orientation of the structure. This shared measurement strategy overcomes the deficiencies in monocular vision-based relative navigation techniques, such as the range ambiguities, as is proven in the simulated results of this paper. The proposed stereo-vision system in this work allows for a deterministic solution of the relative position and orientation from the measurements of each inspector spacecraft to the structure. The stereo-vision system was tested with a Multiplicative Extended Kalman Filter (MEKF) for each spacecraft to estimate the relative states of the structure while maintaining a fixed relative position to the structure. The performance of the proposed stereo-vision system was evaluated in terms of accuracy and reliability of the estimated relative position and orientation of two inspector spacecraft to the structure over 100 Monte Carlo simulations for three case studies. The results showed that the stereo-vision system significantly outperforms the monocular vision system even when fewer points on the structure are visible, as is the case for proximity operations. Additionally, the stereo-vision system is consistently more accurate for the relative velocity, attitude, and angular velocity states regardless of how many points are visible. The proposed stereo-vision relative navigation system has the potential to be applied autonomously in proximity operations of spacecraft for various space missions, such as rendezvous and docking, inspection, and on-orbit servicing.

Prescribed performance tracking control for spacecraft proximity operations with inertia property identification

This paper investigates the integrated position and attitude tracking control with prescribed performance and inertia property identification for spacecraft proximity operations subject to unknown inertia properties, external disturbances, and input saturation. To pursue this, the radical basis function neural network is utilized to approximate the external disturbances, where the involved weight matrix, together with the unknown inertia properties, is considered as parameter uncertainty. Then, a rank condition to guarantee the parameter identification is proposed within the framework of concurrent learning. Subsequently, an integrated position and attitude tracking controller is designed based on dynamic surface method in conjunction with certain performance functions and a saturation compensator, and concurrent learning adaptive laws are developed for parameter update. It is proven that the proposed controller can achieve position and attitude tracking with prescribed performance and, meanwhile, guarantee the uniform ultimate boundedness of all the closed-loop states. Additionally, the inertia properties, including the mass, inertia matrix, and center of mass location, can be identified with high accuracy. Finally, simulation experiments are carried out to evaluate the effectiveness of the proposed control scheme.

Design Heuristics and Optimization for Simple Adaptive Controllers With Applications to Spacecraft Proximity Operations

Design Heuristics and Optimization for Simple Adaptive Controllers With Applications to Spacecraft Proximity Operations

Prescribed performance-based robust inverse optimal control for spacecraft proximity operations with safety concern

This paper explores and analyzes the robust proximity control problem for spacecraft in the presence of external disturbance, model uncertainty, and safety concern. To fulfill the safety proximity requirement, a novel two-stage time-depended performance function is constructed to guarantee the transient and steady-state proximity performance. Then, by assimilating the advantages of the prescribed performance control methodology and inverse optimal control approach, a neuroadaptive prescribed performance-based inverse optimal control scheme is proposed, which ensures all system signals comply with the preassigned performance function. The developed controller shows optimality concerning convergence performance and energy consumption, whilst satisfying the well-designed safety corridor. Finally, simulation scenarios are provided to demonstrate the effectiveness of the presented control scheme.

Relative Stereovision-Based Navigation for Noncooperative Spacecraft via Feature Extraction

Spacecraft proximity operations play an important role in guaranteeing the capture success of noncooperative targets. This article technically presents a relative stereovision-based navigation scheme that ensures accurate relative pose measurement as well as practical motion estimation for proximity operations. Specifically, features parameters of the line and circle on the noncooperative target are first obtained by the different image processing extraction algorithms. Then, the center position and normal of the circle are derived by orthogonal transformation from the circle feature parameters, and two features descriptors are defined by the redundant parameters in the stereovision to evaluate error levels of the extraction algorithms. In particular, the unavailable roll angle around the circle normal is recovered by incorporating the line and the descriptors by utilizing the least squares method, wherein the relative attitude is proved less affected by the features extraction errors, and thus, the measurement accuracy is theoretically improved. Furthermore, considering the Mahalanobis distances of the attitude and position, two outlier detectors are coupled with the 3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> rule in a multiplicative extended Kalman filter to achieve outlier rejection and motion estimation, respectively. Finally, numerical simulation and physical experiment are given to validate the effectiveness of the proposed approach.

Convex Optimization for Rendezvous and Proximity Operation via Birkhoff Pseudospectral Method

Rapid and accurate rendezvous and proximity operations for spacecraft are crucial to the success of most space missions. In this paper, a sequential convex programming method, combined with the first-order and second-order Birkhoff pseudospectral methods, is proposed for the autonomous rendezvous and proximity operations of spacecraft. The original nonlinear and nonconvex close-range rendezvous problem with thrust constraints and no-fly zone constraints is converted into its convex version by using the sequential convexification techniques; then, the Birkhoff pseudospectral method is used to transcribe the dynamic constraints into a series of linear algebraic equality constraints, in other words, a convex second-order conic programming problem with a relatively small condition number. Thus, the resulting problem can be accurately and efficiently solved by a convex solver. The simulation results indicate that the proposed methods, especially the second-order Birkhoff pseudospectral method, have obvious advantages over other methods in computational efficiency and sensitivity.

Finite-time extended state observer based prescribed performance fault tolerance control for spacecraft proximity operations

Relative motion control with six degrees of freedom (6-DOF) for spacecraft proximity operations in prescribed performance control (PPC) framework has become a hot issue in recent years, but actuator failure is seldom involved in controller design. In this paper, we introduce a complete thruster model to describe the actuator characteristics for thruster-only spacecraft, considering efficiency loss, thrust fluctuation and saturation. Besides, the barrier Lyapunov function (BLF) method and homeomorphic mapping method are often used in the PPC framework to constrain transformed errors. However, the two methods have singularity and infinite control effort problem once the constraints are not satisfied because of the actuator failure or other disturbance. In this paper, a novel bounded BLF (BBLF) is proposed to solve this problem. The proposed BBLF can still maintain bounded control effort and guarantee the system stability even if the transformed errors exceed the boundary. Further, the model uncertainty, actuator output uncertainty and external disturbance are summarized as lumped disturbances. A finite-time extended state observer (FTESO) is constructed to estimate the lumped disturbances. Finally, based on the estimated information from FTESO, an adaptive backstepping controller is proposed to track the desired trajectory. Numerical simulation results show the excellent dynamic response and steady-state accuracy of the proposed control strategy.

Constrained Guidance for Spacecraft Proximity Operations Under Electrostatic Perturbations

Electrostatic perturbations can have significant effects during terminal proximity operations in high Earth orbits, with torque levels exceeding during severe charging events. These torques can impart rotational rates to uncontrolled bodies, such as debris or servicing clients, during rendezvous and proximity operations. A suboptimal, but deterministic and computationally efficient, sampling-based method is presented here to minimize the impact of these torques during rendezvous, combining prior innovations in rapidly computing the electrostatic torque between bodies and in determining the electrostatic potential on objects remotely. This method is applied to a simulated servicing scenario, and found to reduce the accumulated rotational rates of the target by over 50%, yielding significant improvements in control effort, and potential improvements in safety. This iterative method is compared to an optimized strategy to minimize final rotational rate of a target, using a pseudospectral collocation-based approach. The globally optimized approach requires a priori knowledge of both spacecraft potentials throughout the approach, which limits its applicability in practice, but was found to be robust to moderate misestimates in potentials.

Indirect-Neural-Approximation-Based Fault-Tolerant Integrated Attitude and Position Control of Spacecraft Proximity Operations.

In this paper, a neural adaptive fault-tolerant control scheme is proposed for the integrated attitude and position control of spacecraft proximity operations in the presence of unknown parameters, disturbances, and actuator faults. The proposed controller is made up of a relative attitude control law and a relative position control law. Both the relative attitude control law and relative position control law are designed by adopting the neural networks (NNs) to approximate the upper bound of the lumped unknowns. Benefiting from the indirect neural approximation, the proposed controller does not need any model information for feedback. In addition, only two adaptive parameters are required for the indirect neural approximation, and the online calculation burden of the proposed controller is therefore significantly reduced. Lyapunov analysis shows that the overall closed-loop system is ultimately uniformly bounded. The proposed controller can ensure the relative attitude, angular velocity, position, and velocity stabilize into the small neighborhoods around the origin. Lastly, the effectiveness and superior performance of the proposed control scheme are confirmed by a simulated example.

Pose Tracking Control for Spacecraft Proximity Operations Using the Udwadia–Kalaba Framework

This paper develops an analytical dynamics-based approach for simultaneous position and orientation tracking control of a chaser spacecraft with respect to an uncontrolled target. The control requirements are formulated as holonomic or nonholonomic constraints, which are expressed as linear and angular acceleration constraints. The complete six-degree-of-freedom formulation of the Udwadia–Kalaba-based pose tracking controller generating exact real-time control forces and torques is presented. For design purposes, the method assumes a precise knowledge of the system parameters and states, along with perfect control action by the actuators. The exponential convergence of the constraint dynamics is proven using the Lyapunov stability theory. Simulation results demonstrate exponentially stable position and orientation tracking for close-proximity operations in perturbed low Earth orbits. Finally, the controller is experimentally validated using the Spacecraft Proximity Operations Testbed at Carleton University.

Adaptive robust fault-tolerant control scheme for spacecraft proximity operations under external disturbances and input saturation

Adaptive robust fault-tolerant control scheme for spacecraft proximity operations under external disturbances and input saturation

Learning-Based 6-DOF Control for Autonomous Proximity Operations Under Motion Constraints

This article proposes areinforcement learning (RL)-based six-degree-of-freedom (6-DOF) control scheme for the final-phase proximity operations of spacecraft. The main novelty of the proposed method are from two aspects: 1) The closed-loop performance can be improved in real-time through the RL technique, achieving an online approximate optimal control subject to the full 6-DOF nonlinear dynamics of spacecraft; 2) nontrivial motion constraints of proximity operations are considered and strictly obeyed during the whole control process. As a stepping stone, the dual-quaternion formalism is employed to characterize the 6-DOF dynamics model and motion constraints. Then, an RL-based control scheme is developed under the dual-quaternion algebraic framework to approximate the optimal control solution subject to a cost function and a Hamilton–Jacobi–Bellman equation. In addition, a specially designed barrier function is embedded in the reward function to avoid motion constraint violations. The Lyapunov-based stability analysis guarantees the ultimate boundedness of state errors and the weight of NN estimation errors. Besides, we also show that a PD-like controller under dual-quaternion formulation can be employed as the initial control policy to trigger the online learning process. The boundedness of it is proved by a special Lyapunov strictification method. Simulation results of prototypical spacecraft missions with proximity operations are provided to illustrate the effectiveness of the proposed method.

Online collision avoidance trajectory planning for spacecraft proximity operations with uncertain obstacle

The spacecraft relative motion trajectory planning is one of the enabling techniques for autonomous proximity operations, especially in the increasingly complicated mission environments. Most traditional trajectory planning methods focus on improving the performance criteria in the deterministic conditions, whereas various uncertain elements in practice would significantly degrade the trajectory performance. Considering the uncertainties underlying the collision avoidance constraints, this paper suggests a model predictive control based online trajectory planning framework in which the obstacle information in higher-precision would be consistently updated by the onboard sensor. To improve the computational efficiency of the online planning framework, the rotating hyperplane (RH) technique is utilized to transform the nonlinear ellipsoidal keep-out zone constraints into convex formulations. And the concept of rotation window is introduced to eliminate the unexpected mismatch between the spacecraft motion and hyperplane rotation in the conventional RH method, which in sequence improves the RH method’s capability for multiple obstacle avoidance problem. Moreover, a three-dimensional (3-D) extension strategy is proposed to simplify the computation procedure when applying the RH method for a 3-D collision avoidance problem. Numerical simulations are carried out to validate the performance of the proposed online trajectory planning framework in addressing the uncertain collision avoidance constraints.

Adaptive saturated tracking control for spacecraft proximity operations via integral terminal sliding mode technique

AbstractThis study presents a tracking control strategy for spacecraft proximity operations subjected to kinematic couplings, input saturation, modeling uncertainties, and external disturbances. First, a coupled six degrees of freedom dynamics is modeled to depict the relative motion between the pursuer and target spacecrafts. To address the input saturation problem, a dead‐zone operator‐based model is introduced. Subsequently, a finite‐time controller is proposed by exploiting the non‐singular integral terminal sliding mode method. By employing the adaptive technique, the proposed control strategy enjoys the feature that it can avoid requiring the prior knowledge of the lumped uncertainty's bounds. Using the Lyapunov theory, the designed controller is proved to guarantee that the translational and rotational tracking errors can converge to the origin within finite time. Finally, numerical simulations are performed to illustrate that the developed control scheme possesses a strong robustness, a fast convergence rate, input saturation elimination as well as chattering suppression.

Adaptive Pose Control for Spacecraft Proximity Operations With Prescribed Performance Under Spatial Motion Constraints

In this article, a novel pose (i.e., concurrent position-attitude) tracking control framework is proposed for spacecraft proximity operations with a freely tumbling target, employing the prescribed performance control (PPC) methodology. Especially, the whole operations involved are divided into two synchronously occurring maneuvers: relative position tracking and boresight pointing adjustment. For the former, a new relative translational dynamics is established to facilitate its problem formulation and solving, while, for the latter, the desired attitude is extracted to align the boresight of the pursuer's onboard vision sensor toward the target. Given this, a noncertainty-equivalence adaptive pose controller is designed based on the PPC design approach integrating a class of appointed-time performance functions. It is shown that the designed controller is able to achieve prescribed performance guarantees for the pose tracking errors and, meanwhile, guarantee asymptotic convergence of both the velocity and angular velocity errors, regardless of mass and inertia uncertainties. The salient feature of the proposed method is that, by judiciously imposing the performance specifications on the pose tracking errors, it can: 1) enable the pursuer to accomplish the proximity operations in a designer-appointed time and 2) ensure compliance with spatial motion constraints and avoid singularity of the attitude extraction algorithm. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.