Trajectory Optimization for Free-Flying Robots in Microgravity Using Convex Obstacle Representation

Planning collision-free and dynamically feasible trajectories is crucial to enable autonomous robotic operations. For freeflying robots in microgravity environments, such as the International Space Station, this problem is particularly challenging due to the complexity and variability of the environment We propose a two-step solution to this problem. In the first step, a collision-free geometric path is computed without dynamic constraints. In the second step, this path is optimized into a time-parameterized trajectory that is dynamically feasible, using a convexified representation of the environment. Unlike most prior works that rely on non-convex free space decomposition into unions of convex sets, our method convexifies obstacles through planar approximations of relevant obstacles. The proposed method also considers a convexified representation of the robot, that is not approximated as sphere, allowing for accurate consideration of the volume occupied by the robot in space, without obstacle inflation or extreme robot simplifications. This approach reduces computational cost both during obstacle computation in new maps and during the optimization stage. We validate our method in environments of increasing complexity, demonstrating its efficiency and its ability to represent multiple environments through planar approximation.