Convex optimization of stochastic path-constrained trajectories near asteroids

The environment around asteroids is of significant uncertainties, which could cause great challenges of exploration missions to asteroids. This paper presents a novel approach to stochastic optimal problem in path-constrained trajectory optimization near asteroids based on convex approach. The path constraints that prevent the spacecraft from colliding with asteroid in different scenarios are composed of keep-out zone constraint and glide-slope constraint, which are formulated in chance-constraint forms due to the uncertain state. To convexify these constraints, the first-order Taylor expansion is applied for linearization and the nonconvexity is tackled with the introduction of additional intermediate variable and virtual buffer. Thereafter, a convex optimization based method is proposed to solve stochastic optimal problem. The effectiveness of the proposed method is validated through simulations of soft landing and hopping transfer scenarios near irregular-shaped asteroid 1996HW1. The results indicate that the proposed method can generate path-constrained trajectories under uncertainties using convex optimization.