钻臂轨迹优化的分数阶目标驱动复合方法

Fractional Order Objective-Driven Composite Method for Optimizing Drilling Arm Trajectory

摘要: 在高精度机器人任务中，传统的轨迹优化方法主要依赖于整数阶微积分模型，在精确捕捉与优化轨迹固有的非线性动态特性及长时记忆效应方面存在固有的局限性。为突破此性能上限，本文提出了一种融合分数阶微积分理论的新型轨迹优化框架。该框架构建了一个复合目标函数，该函数创新性地为平滑性融入了分数阶范数与分数阶导数，并采用fmincon优化器进行求解。为全面验证其有效性，所提出的方法——复合分数阶目标轨迹优化(CFOTO)与已发表文献中的三种经典及前沿轨迹规划方法进行了严格的基准测试。结果表明，本文的方法不仅取得了顶尖的综合性能得分，还在轨迹平滑度和算法收敛速度方面展现了全面的优越性。

Abstract: In high-precision robot tasks, traditional trajectory optimization methods mainly rely on integer order calculus models, which have inherent limitations in accurately capturing and optimizing the inherent nonlinear dynamic characteristics and long-term memory effects of trajectories. To break through this performance limit, this paper proposes a novel trajectory optimization framework that integrates fractional calculus theory. This framework constructs a composite objective function that innovatively incorporates fractional norm and fractional derivative for smoothness, and is solved using the fmincon optimizer. To comprehensively verify its effectiveness, the proposed method, Composite Fractional Objective for Trajectory Optimization (CFOTO), was rigorously benchmarked against three classic and cutting-edge trajectory planning methods in published literature. The results indicate that our method not only achieved top-notch comprehensive performance scores, but also demonstrated comprehensive superiority in trajectory smoothness and algorithm convergence speed.