Constrained Trajectory Optimization
The goal is to find controls with the least effort that satisfy a specification.
The conjunction at the top of the specification is imposed exactly as constraints. Since each extremum node is nonsmooth in the optimization variables, a gradient-based solver replaces every extremum node in the graph with a smooth function of its children, then solves the resulting optimization problem with a margin. The smoothing therefore determines both the feasible set of the optimization problem and the solver’s search direction.
Acknowledgment
The authors acknowledge using Claude LLMs for code development, visualizations, and manuscript review.
Frequently Asked Questions
What is the trajectory optimization objective? The objective is to find controls with the least effort that satisfy a specification.
How is the conjunction at the top of the specification handled? It is imposed exactly as constraints.
Why does the solver smooth extremum nodes? Each extremum node is nonsmooth in the optimization variables, so the gradient-based solver replaces it with a smooth function of its children.
What does the smoothing affect? It determines the feasible set and the solver’s search direction.