Provably Feasible and Stable White-Box Trajectory Optimization

TL;DR

This paper introduces a white-box trajectory optimization method that ensures numerical stability and feasibility for stiff, constrained dynamic systems by customizing the solver based on system characteristics.

Contribution

It proposes a novel white-box SQP-based trajectory optimization approach that adapts to system properties, unlike traditional black-box methods.

Findings

Ensures convergence to feasible, locally optimal solutions within user-defined error bounds.

Provides a systematic way to incorporate system characteristics into the optimization process.

Demonstrates improved stability and feasibility in complex dynamic systems.

Abstract

We study the problem of Trajectory Optimization (TO) for a general class of stiff and constrained dynamic systems. We establish a set of mild assumptions, under which we show that TO converges numerically stably to a locally optimal and feasible solution up to arbitrary user-specified error tolerance. Our key observation is that all prior works use SQP as a black-box solver, where a TO problem is formulated as a Nonlinear Program (NLP) and the underlying SQP solver is not allowed to modify the NLP. Instead, we propose a white-box TO solver, where the SQP solver is informed with characteristics of the objective function and the dynamic system. It then uses these characteristics to derive approximate dynamic systems and customize the discretization schemes.