The working principle behind SALTRO

SALTRO, as in the name, uses the Augmented Lagrangian TRajectory Optimizer (Howell et al., 2020) for specifically the satellite attitude (pointing) problem.

ALTRO iteratively refines a trajectory by solving fast local optimal control problems while progressively enforcing constraints via an augmented Lagrangian, combining the speed of iLQR/DDP with robust constraint satisfaction.

Pseudocode

Derivation

This is a detailed version of the ALTRO derivation, specifically the AL-iLQR step, based on ALTRO: A Fast Solver for Constrained Trajectory Optimization (Howell et al., 2020) and AL-iLQR Tutorial (Jackson, 2020).

• Iterative Linear Quadratic Regulator (iLQR)
• Augmented Lagrangian
• Augmented Lagrangian Iterative Linear Quadratic Regulator (AL-iLQR)
• Line Search
• Cholesky Decomposition
• Projected Newton Method