  Future spacecraft and surface robotic missions require increasingly capable
autonomy stacks for exploring challenging and unstructured domains and
trajectory optimization will be a cornerstone of such autonomy stacks. However,
the nonlinear optimization solvers required remain too slow for use on
relatively resource constrained flight-grade computers. In this work, we turn
towards amortized optimization, a learning-based technique for accelerating
optimization run times, and present TOAST: Trajectory Optimization with Merit
Function Warm Starts. Offline, using data collected from a simulation, we train
a neural network to learn a mapping to the full primal and dual solutions given
the problem parameters. Crucially, we build upon recent results from
decision-focused learning and present a set of decision-focused loss functions
using the notion of merit functions for optimization problems. We show that
training networks with such constraint-informed losses can better encode the
structure of the trajectory optimization problem and jointly learn to
reconstruct the primal-dual solution while also yielding improved constraint
satisfaction. Through numerical experiments on a Lunar rover problem, we
demonstrate that TOAST outperforms benchmark approaches in terms of both
computation times and network prediction constraint satisfaction.
