Optimised collision avoidance for an ultra-close rendezvous with a failed satellite based on the Gauss pseudospectral method

Mathematical Problems in Engineering

2019

On-orbit servicing for GEO targets has attracted great attention due to particular significance. In this study, the GEO nearby flying is considered, which denotes that the servicing spacecraft approaches GEO targets within tens of meters. Based on the analysis of differential spherical Earth gravity, J2 perturbation, third-body perturbation, and solar radiation pressure (SRP) between two spacecraft, a relative dynamics of GEO nearby flying is built, in which the differential SRP has great influence on relative motion. Therein, considering the differential SRP, an analytical solution to relative dynamics is obtained, which is an extension to CW equation’s solution. Based on the derived relative dynamics, a novel control method utilizing feedback compensation and artificial potential is developed for spacecraft orbital transfer and hovering at the desired position. During orbital transfer, a bounded space is constrained with maximum and minimum relative distance between two spacecraft. An improved repulsive potential based on Gauss function is designed to drive the servicer off the bound and guarantee the potential value converge to zero at the desired position. Meanwhile, a novel attractive potential about relative distance that drives the servicer to the desired position and to hover with high accuracy against perturbations is designed. Besides, a velocity potential with variable gain is designed to ensure that the servicer achieve the desired position without overshoot. The stability of the system is proved with Lyapunov theory, and the feasibility of the proposed control law is verified through numerical simulations with obvious advantages.

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Automated Orbital Transfer and Hovering Control Using Artificial Potential

Wang

Mathematical Problems in Engineering

2019

“…Given the complex state or control constraints, it is difficult to solve analytic solutions to optimal control. In reference [17], the Gauss pseudospectral method was employed to solve the optimal rendezvous trajectory with certain constraints. In references [18][19][20], Pontryagin's minimum principle was combined with numerical methods to formulate and solve the optimal rendezvous trajectory by considering collision avoidance.…”

Section: Introductionmentioning

confidence: 99%

“…If the center of ellipsoid is located at target's mass center, d = 0 is satisfied. The parametric equation of the original ellipsoid is given as follows [17]:…”

mentioning

confidence: 99%

Model Predictive Control to Autonomously Approach a Failed Spacecraft

Wang

International Journal of Aerospace Engineering

2018

In this study, a model predictive control (MPC) method is developed for a servicer spacecraft autonomously approaching a tumbling failed spacecraft at an ultraclose range. Flight safety and collision avoidance are basic requirements during the approach. Two types of a failed spacecraft with complex configurations are considered, and a double-ellipsoid composite envelope strategy is designed to model their keep-out zones. Given the keep-out zone of the servicer, two expanded ellipsoids are subsequently introduced to determine the collision and sufficient conditions for collision avoidance are derived by using the form of concave constraint. The tumbling motion of the target is considered, and a CW-based translational dynamics and derived attitude dynamics of the target are formulated to predict the motion of the docking point and keep-out zone. The MPC is formulated to drive the servicer tracking the docking point with collision avoidance and handle constraints including control input saturation and relative velocity bound. Convexification of the collision avoidance constraint and sequential convex programming are adopted for the implementation of MPC. Scenarios on the servicer with different initial positions approaching the target with different angular velocities are simulated, and the simulation results indicate that the proposed MPC method is effective.

“…5 Employing the standard Gauss pseudospectral optimization solver (GPOPS), 16 a fuel-optimal rendezvous trajectory of ultra-close proximity for a failed GEO satellite is solved subject to path constraints and uncertainties. 17 Given the constrained angular velocity and control torque of rotational motion, the GPM is also adopted to analyze the time-optimal slew properties for agile attitude maneuvering. 18…”

Section: Introductionmentioning

confidence: 99%

Translational and rotational motion planning for spacecraft close proximity using sampling-based methods

Ding

Proceedings of the Institution of Mechanical Engineers, Part G:

et al. 2018

For autonomous spacecraft close proximity under environments containing multiple obstacles and complicated constraints, incrementally rapid planning approaches stemming from sampling-based methods are investigated in this paper. Exploring planners are separately developed for the impulsive maneuvered translation and the piecewise constant controlled rotation, which, however, is constrained by the pointing limits coupling with relative positions during the proximity. Using a cost-informed parent-connecting strategy originating from dynamic programming as well as a sweeping growth fashion balanced between tree-based and graph-based methods, an asymptotically optimal unidirectional exploration method is proposed to search energy-efficient translational trajectory without collision. As for the rotation planning, the pointing constraints are taken as virtual obstacles in the state-space augmented with time horizon planned by the translation and, accordingly, a bidirectional exploration method is developed to generate constraint-satisfied slew paths with fast convergence rate. Numerical experiments indicate that the proposed sampling-based methods can rapidly return asymptotic optimal translation trajectory and rotation path satisfying collision avoidance and sensor field-of-view constraints.