2021/09/10 by Kun Cao, Muqing Cao, Cao, Kun +5 · 4 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Computer and information sciences #FOS: Mathematics #Lipid metabolism and biosynthesis #Optimization and Control (math.OC) #Robotic Path Planning Algorithms #Robotics (cs.RO)
paper · pdf · doi:10.48550/arxiv.2109.04686
openalex publication_date 2021/09/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
This paper introduces a differential dynamic programming (DDP) based framework for polynomial trajectory generation for differentially flat systems. In particular, instead of using a linear equation with increasing size to represent multiple polynomial segments as in literature, we take a new perspective from state-space representation such that the linear equation reduces to a finite horizon control system with a fixed state dimension and the required continuity conditions for consecutive polynomials are automatically satisfied. Consequently, the constrained trajectory generation problem (both with and without time optimization) can be converted to a discrete-time finite-horizon optimal control problem with inequality constraints, which can be approached by a recently developed interior-point DDP (IPDDP) algorithm. Furthermore, for unconstrained trajectory generation with preallocated time, we show that this problem is indeed a linear-quadratic tracking (LQT) problem (DDP algorithm with exact one iteration). All these algorithms enjoy linear complexity with respect to the number of segments. Both numerical comparisons with state-of-the-art methods and physical experiments are presented to verify and validate the effectiveness of our theoretical findings. The implementation code will be open-sourced,