8 citations · 21 across the 7 of their papers we have counts for
8 papers
Transversality Conditions for Boundary Constraints Defined by Differential Equations
Isaac M Ross
What are the transversality conditions for an optimal control problem when the boundary conditions are defined by differential equations? This seemingly bizarre question is motivat…
Nechvile-Transformed Spacecraft Dynamics and Propellant Computation in the 3-Body Problem
Michael J. Dixon, Isaac M. Ross
The uncontrolled equations of motion in the Nechvile frame for the restricted three-body problem have been well-known since at least the 1960s. It would seem that adding an externa…
Universal Birkhoff Method for Computing Extremals in the Elliptic Restricted Three-Body Problem
Michael J. Dixon, Isaac M. Ross
The computation of finite-thrust extremal arcs in the elliptic restricted three-body trajectory optimization problem is considered. Libration-point orbits are approximated to near-…
On The Mathematics of the Natural Physics of Optimization
I. M. Ross
A number of optimization algorithms have been inspired by the physics of Newtonian motion. Here, we ask the question: do algorithms themselves obey some ``natural laws of motion,''…
Hessians in Birkhoff-Theoretic Trajectory Optimization
I. M. Ross
This paper derives various Hessians associated with Birkhoff-theoretic methods for trajectory optimization. According to a theorem proved in this paper, approximately 80% of the ei…
Unscented Trajectory Optimization
I. M. Ross, R. J. Proulx, M. Karpenko
In a nutshell, unscented trajectory optimization is the generation of optimal trajectories through the use of an unscented transform. Although unscented trajectory optimization was…
Implementations of the Universal Birkhoff Theory for Fast Trajectory Optimization
R. J. Proulx, I. M. Ross
This is part II of a two-part paper. Part I presented a universal Birkhoff theory for fast and accurate trajectory optimization. The theory rested on two main hypotheses. In this p…
A Universal Birkhoff Theory for Fast Trajectory Optimization
I. M. Ross
Over the last two decades, pseudospectral methods based on Lagrange interpolants have flourished in solving trajectory optimization problems and their flight implementations. In a…