DIRECT: a differential dynamic programming based framework for trajectory generation

• Main Authors: Cao, Kun, Cao, Muqing, Yuan, Shenghai, Xie, Lihua
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2022
• Subjects: Engineering::Electrical and electronic engineering; Constrained Motion Planning; Optimization and Optimal Control
• Online Access: https://hdl.handle.net/10356/162410
• Institution: Nanyang Technological University

This letter 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. [Online] Available: https://github.com/ntu-caokun/DIRECT