无需梯度即可统一求解轨迹优化问题，支持复杂约束与多段规划。
The Trajectory Bundle Method: Unifying Sequential-Convex Programming and Sampling-Based Trajectory Optimization
- 用采样点插值替代梯度，实现无导数的凸近似。
- 兼容多段射击与等式/不等式约束，扩展了采样方法能力。
- 适用于运动规划与控制，尤其适合难求导的系统。
我们提出一种统一框架，通过序列凸规划在无梯度条件下求解轨迹优化问题。传统方法依赖泰勒展开进行局部凸近似，但对难以求导或导数代价高的函数不适用。本文提出基于动态、代价和约束函数采样的方法，让求解器在采样点间插值以构建凸近似。该框架包含模型预测路径积分（MPPI）控制作为特例，并将其推广至支持多段射击及一般等式与不等式约束，这些特性原本属于有梯度的序列凸规划方法。所提方法简单灵活，能解决多种实际运动规划与控制问题。
原文摘要 · Abstract (English)
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.
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