The Trajectory Bundle Method: Unifying Sequential-Convex Programming and Sampling-Based Trajectory Optimization

2025-09-30

AI Summary

Trajectory optimization for non-convex, differentially expensive or non-differentiable systems remains challenging, particularly under general equality and inequality constraints. Method: This paper proposes a gradient-free sequential convex programming (SCP) framework that constructs local convex approximations via interpolation of sampled points from dynamics, cost, and constraint functions—compatible with multiple-shooting and arbitrary constraints. Contribution/Results: It is the first to integrate sampling-based stochastic optimal control methods (e.g., Model Predictive Path Integral control) into the SCP paradigm, enabling derivative-free convexification. The framework unifies gradient-based deterministic and sampling-based stochastic approaches, drastically reducing reliance on gradient information while fully preserving compatibility with conventional SCP implementations. Empirical evaluation demonstrates high efficiency and robustness in motion planning and real-time control tasks.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Solving trajectory optimization without derivative information
• Unifying sampling-based and sequential-convex optimization methods
• Handling general constraints in derivative-free motion planning

Innovation

• Derivative-free sequential convex programming for trajectory optimization
• Using function samples instead of derivatives for approximations
• Unifying sampling-based and sequential convex optimization methods