{"ID":2862966,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.26575","arxiv_id":"2509.26575","title":"The Trajectory Bundle Method: Unifying Sequential-Convex Programming and Sampling-Based Trajectory Optimization","abstract":"We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a sequence of convex optimization problems, where the cost and constraint functions are approximated locally through Taylor series expansions. This presents a challenge for functions where differentiation is expensive or unavailable. In this work, we present a derivative-free approach to form these convex approximations by computing samples of the dynamics, cost, and constraint functions and letting the solver interpolate between them. Our framework includes sample-based trajectory optimization techniques like model-predictive path integral (MPPI) control as a special case and generalizes them to enable features like multiple shooting and general equality and inequality constraints that are traditionally associated with derivative-based sequential convex programming methods. The resulting framework is simple, flexible, and capable of solving a wide variety of practical motion planning and control problems.","short_abstract":"We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a sequence of convex optimization problems, where the cost and constraint functions a...","url_abs":"https://arxiv.org/abs/2509.26575","url_pdf":"https://arxiv.org/pdf/2509.26575v1","authors":"[\"Kevin Tracy\",\"John Z. Zhang\",\"Jon Arrizabalaga\",\"Stefan Schaal\",\"Yuval Tassa\",\"Tom Erez\",\"Zachary Manchester\"]","published":"2025-09-30T17:34:36Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.RO\"]","methods":"[]","has_code":false}