Spacecraft Rendezvous Guidance via Factorization-Free Sequential Convex Programming using a First-Order Method

Abstract

We implement a fully factorization-free algorithm for nonconvex, free-final-time trajectory optimization. This algorithm is based on sequential convex programming and utilizes an inverse-free, exact discretization procedure to ensure dynamic feasibility of the converged trajectory and PIPG, a fast, first-order conic optimization algorithm as the subproblem solver. Although PIPG requires the tuning of a hyperparameter to achieve fastest convergence, we show that PIPG can be tuned to a nominal trajectory optimization problem and it is robust to variations in initial condition. We demonstrate this with a monte carlo simulation of the free-final-time rendezvous problem, using Clohessy-Wiltshire dynamics, an impulsive thrust model, and various state and control constraints including a spherical keepout zone.

Figures (9)

• Figure 1: Rendezvous trajectory with spherical keepout
• Figure 2: Thruster $\Delta v$
• Figure 3: Vehicle speed
• Figure 4: Runtime distribution for 128 solves of the nominal problem
• Figure 5: Monte carlo rendezvous trajectories with spherical keepout