A Composite Objective-Driven Framework for High Performance Robotic Trajectory Optimization

In high-precision robotic tasks, achieving optimal trajectory smoothness and dynamic performance is a critical challenge. Traditional integer-order optimization methods often fail to accurately capture intrinsic nonlinear dynamics and long-term memory effects, creating a performance bottleneck. To overcome these limitations, this paper proposes a novel framework: Composite Fractional Objective for Trajectory Optimization (CFOTO). By integrating fractional calculus theory, we construct a composite objective function that incorporates both a fractional norm and a fractional-order smoothness term, which is solved using the fmincon solver. Extensive comparative simulations benchmark CFOTO against three classical and state-of-the-art planning methods. The results demonstrate that CFOTO achieves superior overall performance, exhibiting distinct advantages in trajectory smoothness and algorithmic convergence speed. This research provides a high-performance solution for robotic trajectory planning and offers practical evidence for applying fractional calculus in intelligent control.