Abstract-This paper presents an algorithm for designing spacecraft reconfiguration maneuvers, which is a difficult 6 DOF trajectory design problem with nonlinear attitude dynamics and non-convex constraints. In addition, some of the constraints couple the positions and attitudes of the spacecraft, which makes the problems high-dimensional. The essential feature of the design methodology is the separation into a simplified path planning problem obtaining a feasible solution, then improving it significantly by a smoothing operation. The first step is solved using a Rapidly-exploring Random Tree. The smoother then optimizes the trajectories by iteratively solving a linear program using a linearization of the cost function, dynamics, and constraints about the initial feasible solution. Examples are presented to demonstrate the validity of the approach for complex problems with four spacecraft.

The paper presents a two-stage approach for designing optimal reconfiguration maneuvers for multiple spacecraft in close proximity. These maneuvers involve well-coordinated and highly-coupled motions of the entire fleet of spacecraft while satisfying an arbitrary number of constraints. This problem is complicated by the nonlinearity of the attitude dynamics, the non-convexity of some of the constraints, and the coupling that exists in some of the constraints between the positions and attitudes of all spacecraft. While there has been significant research to solve for the translation and/or rotation trajectories for the multiple spacecraft reconfiguration problem, the approach presented in this paper is more general and on a larger scale than the problems considered previously. The essential feature of the solution approach is the separation into two stages, the first using a simplified planning approach to obtain a feasible solution, which is then significantly improved using a smoothing stage. The first stage is solved using a bi-directional Rapidly-exploring Random Tree (RRT) planner. Then the second step optimizes the trajectories by solving an optimal control problem using the Gauss pseudospectral method (GPM). Several examples are presented to demonstrate the effectiveness of the approach for designing spacecraft reconfiguration maneuvers.

Abstract-This paper presents an improvement of the standard randomized path planning algorithm, and uses this new approach to design reconfiguration maneuvers for large formations of spacecraft. A spacecraft reconfiguration maneuver is a difficult 6 DOF trajectory design problem with nonlinear attitude dynamics and non-convex constraints. In addition, some of the constraints couple the positions and attitudes of the spacecraft, which makes the problems high-dimensional. A key step in the overall design is to find a feasible trajectory using a randomized path planner, which typically requires a large fraction of the total computation time. This paper presents an improvement to the path planner that greatly reduces the solution time and enables the solution of very large problems. The primary modification is to change the function that connects two points, which is a key component of the randomized planner. The standard approach is to use a simple and fast function, which is changed here to one that is slower, but much more effective in linking two points. The new connection function finds a link between the points by minimizing a distance function to the target point with a feasible optimizer that accounts for the constraints. The examples presented demonstrate the significant speed improvement of the new planner and that the algorithm can solve problems with up to 16 spacecraft with numerous constraints.