  Sequential Convex Programming (SCP) has recently seen a surge of interest as
a tool for trajectory optimization. However, most available methods lack
rigorous performance guarantees and they are often tailored to specific optimal
control setups. In this paper, we present GuSTO (Guaranteed Sequential
Trajectory Optimization), an algorithmic framework to solve trajectory
optimization problems for control-affine systems with drift. GuSTO generalizes
earlier SCP-based methods for trajectory optimization (by addressing, for
example, goal-set constraints and problems with either fixed or free final
time) and enjoys theoretical convergence guarantees in terms of convergence to,
at least, a stationary point. The theoretical analysis is further leveraged to
devise an accelerated implementation of GuSTO, which originally infuses ideas
from indirect optimal control into an SCP context. Numerical experiments on a
variety of trajectory optimization setups show that GuSTO generally outperforms
current state-of-the-art approaches in terms of success rates, solution
quality, and computation times.
