Jianping Yuan

Invariant Manifold and Bounds of Relative Motion Between Heliocentric Displaced Orbits

This paper discusses a methodology for modeling the relative motion between heliocentric displaced orbits by using the Cartesian state variables in combination with a set of displaced orbital elements. Similar to classical Keplerian orbital elements, the newly defined set of displaced orbital elements has a clear physical meaning and provides an alternative approach to obtain a closed-form solution to the relative motion problem between displaced orbits, without linearizing or solving nonlinear equations. The invariant manifold of relative motion between two arbitrary displaced orbits is determined by coordinate transformations, thus obtaining a straightforward interpretation of the bounds, namely, maximum and minimum relative distances of three directional components. The extreme values of these bounds are then calculated from an analytical viewpoint, both for quasi-periodic orbits in the incommensurable case and periodic orbits in the 1:1 commensurable case. Moreover, in some degenerate cases, the extre...

Lunar soft landing rapid trajectory optimization using direct collocation method and nonlinear programming

Direct collocation method has been widely used for trajectory optimization. In this paper, the application of direct optimization method (direct collocation method & nonlinear programming (NLP)) to lunar probe soft-landing trajectory optimization is introduced. Firstly, the model of trajectory optimization control problem to lunar probe soft landing trajectory is established and the equations of motion are simplified respectively based on some reasonable hypotheses. Performance is selected to minimize the fuel consumption. The control variables are thrust attack angle and thrust of engine. Terminal state variable constraints are velocity and altitude constraints. Then, the optimal control problem is transformed into nonlinear programming problem using direct collocation method. The state variables and control variables are selected as optimal parameters at all nodes and collocation nodes. Parameter optimization problem is solved using the SNOPT software package. The simulation results demonstrate that the direct collocation method is not sensitive to lunar soft landing initial conditions; they also show that the optimal solutions of trajectory optimization problem are fairly good in real-time. Therefore, the direct collocation method is a viable approach to lunar probe soft landing trajectory optimization problem.

Robust adaptive fault tolerant control for a class of linearly parameterized uncertain nonlinear systems: An integrated method

In the fault tolerant control systems, there often exist coupled uncertainties between the fault estimate subsystems and the state control subsystems. The coupled uncertainties are often ignored in the conventional separated design approaches, and the control performance degradation or even in-stability may be induced. To address this problem, an integrated fault tolerant control method is developed in this paper. The key point of this paper is to design the fault estimator and the fault tolerant controller from the perspective of the composite system comprised of the two subsystems. A combined weight update law, associating with both the state control dynamic equation and the observation error subsystem, is obtained. A new sufficient condition for the closed-loop stability is derived in terms of linear matrix inequalities. Based on a combined Lyapunov function, the composite closed-loop system is proven to be globally stable. Meanwhile, with the parameterized nonlinear functions and the unknown actuator/sensor faults, the coupled uncertainties are analyzed. Several illustrative examples are employed and the simulation results demonstrate the effectiveness of the proposed method.

Adaptive model-free constrained control of postcapture flexible spacecraft: a Euler–Lagrange approach:

This paper investigates an adaptive model-free constrained prescribed performance control approach for flexible spacecraft with an unknown captured object subject to unknown inertial properties, elastic vibration, actuator saturation, and external disturbance. First, the attitude kinematics and dynamics of the postcapture flexible spacecraft are transformed into a Euler–Lagrange form, based on which a model-free constrained attitude prescribed performance controller comprising a nominal control term and an adaptive compensation control term is developed. Then, by employing norm equalities of the Euler–Lagrange systems, a model-free adaptive scheme is designed to improve the robustness with respect to uncertainty, actuator saturation, and external disturbance just only using the state information. Compared with the existing works, the primary advantage is that the resultant controller and adaptive scheme are computationally very simple without any requirement of unknown inertial information. But the transient and steady-state performance is a priori guaranteed without resorting to repeated regulations of the controller parameters. Finally, the application to attitude stabilization and tracking of postcapture flexible spacecraft along with active vibration suppression is employed to validate the effectiveness of the proposed approach.

Feature extraction algorithm for space targets based on fractal theory

In order to offer a potential for extending the life of satellites and reducing the launch and operating costs, satellite servicing including conducting repairs, upgrading and refueling spacecraft on-orbit become much more frequently. Future space operations can be more economically and reliably executed using machine vision systems, which can meet real time and tracking reliability requirements for image tracking of space surveillance system. Machine vision was applied to the research of relative pose for spacecrafts, the feature extraction algorithm was the basis of relative pose. In this paper fractal geometry based edge extraction algorithm which can be used in determining and tracking the relative pose of an observed satellite during proximity operations in machine vision system was presented. The method gets the gray-level image distributed by fractal dimension used the Differential Box-Counting (DBC) approach of the fractal theory to restrain the noise. After this, we detect the consecutive edge using Mathematical Morphology. The validity of the proposed method is examined by processing and analyzing images of space targets. The edge extraction method not only extracts the outline of the target, but also keeps the inner details. Meanwhile, edge extraction is only processed in moving area to reduce computation greatly. Simulation results compared edge detection using the method which presented by us with other detection methods. The results indicate that the presented algorithm is a valid method to solve the problems of relative pose for spacecrafts.

Robust adaptive fault tolerant attitude control for post-capture non-cooperative targets with actuator nonlinearities

This paper develops an attitude takeover control structure for post-capture non-cooperative targets with actuator nonlinearities and faults. In this paper, the contingent actuator gain faults, deviation faults and the undesirable non-symmetric dead-zone nonlinearities of the actuator are all under consideration. An effective robust adaptive fault tolerant attitude control method is synthesized such that the actuator nonlinearities and faults can be well handled. As a result, the accurate attitude stabilization and tracking are maintained. Moreover, an extended fault tolerant attitude control scheme that can work well in the presence of inaccurate measurement information is proposed. Based on a quadratic Lyapunov function, the proof of the convergence is completed. Simulation results demonstrate the effectiveness and advantages of the proposed method.

Adaptive second-order sliding mode control: A unified method

This paper develops a unified adaptive second order sliding mode (ASOSM) control method. By using the proposed control structure, the upper bounds of uncertainties are not required, the over-estimation of the control gains are avoided, and the chattering of the conventional sliding mode controllers can be attenuated. It should be noted that the adaptive gains are obtained based on the switching function and its derivative; as a result, the gains keep updating before and after the practical sliding mode is established. Meanwhile, the finite time convergence is proved based on a quadratic Lyapunov approach. Finally, to illustrate the performance of the presented method, an ASOSM controller is designed for a pendulum system and several simulations are performed.

Non-linear disturbance observer-based adaptive composite anti-disturbance control for non-linear systems with dynamic non-harmonic multisource disturbances:

In this paper, an adaptive composite anti-disturbance control structure is constructed for a class of non-linear systems with dynamic non-harmonic multisource disturbances. The key point of this paper is that a kind of non-harmonic disturbance, which has non-linear internal dynamics and complex features, is involved. A non-linear exogenous system is employed to describe the dynamic non-harmonic disturbances and several useful assumptions are introduced. By introducing a non-linear damping term, a novel adaptive non-linear disturbance observer is constructed. Based on the disturbance/uncertainty estimation and attenuation (DUEA) schemes, a composite anti-disturbance control structure is synthesized. Meanwhile, a new sufficient condition is derived and the stability of the closed-loop system is proved. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.

GPS Based Reduced-Dynamic Orbit Determination for Low Earth Orbiters with Ambiguity Fixing

With the ever-increasing number of satellites in Low Earth Orbit (LEO) for scientific missions, the precise determination of the position and velocity of the satellite is a necessity. GPS (Global Positioning System) based reduced-dynamic orbit determination (RPOD) method is commonly used in the post processing with high precision. This paper presents a sequential RPOD strategy for LEO satellite in the framework of Extended Kalman Filter (EKF). Precise Point Positioning (PPP) technique is used to process the GPS observations, with carrier phase ambiguity resolution using Integer Phase Clocks (IPCs) products. A set of GRACE (Gravity Recovery And Climate Experiment) mission data is used to test and validate the RPOD performance. Results indicate that orbit determination accuracy could be improved by 15% in terms of 3D RMS error in comparison with traditional RPOD method with float ambiguity solutions.

Partial stabilization of underactuated post-capture combination with inaccurate measurement information and unknown disturbances

This paper aims to address the attitude stabilization issue of post-capture combination with underactuated actuators, measurement inaccuracy and unknown external disturbances during on-orbit servicing. A precise and practical form of underactuated attitude dynamics is proposed for the asymmetric combination with two control torques. With the adopted partial stabilization strategy, a sliding mode controller is first proposed to achieve partial stabilization of the combination against the effect of unknown external disturbances. Through the additional consideration of the measurement inaccuracy in the inertia tensor and the mass centroid, an underactuated adaptive sliding mode controller with compensation laws is proposed in presence of uncertainties and disturbances. Numerical simulations validate the effectiveness of proposed partial attitude stabilization controllers.