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Title: DIRECT: a differential dynamic programming based framework for trajectory generation
Authors: Cao, Kun
Cao, Muqing
Yuan, Shenghai
Xie, Lihua
Keywords: Engineering::Electrical and electronic engineering
Issue Date: 2022
Source: Cao, K., Cao, M., Yuan, S. & Xie, L. (2022). DIRECT: a differential dynamic programming based framework for trajectory generation. IEEE Robotics and Automation Letters, 7(2), 2439-2446.
Journal: IEEE Robotics and Automation Letters
Abstract: 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:
ISSN: 2377-3766
DOI: 10.1109/LRA.2022.3142744
Rights: © 2022 IEEE. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:EEE Journal Articles

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