Parameterized Differential Dynamic Programming

Oshin, Alex; Houghton, Matthew D.; Acheson, Michael J.; Gregory, Irene M.; Theodorou, Evangelos A.

doi:10.48550/arxiv.2204.03727

Cited by 1 publication

(3 citation statements)

References 17 publications

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“…The PDDP algorithm is a variant of the DDP algorithm that optimizes both control sequences and unknown parameters [42]. By abstracting the terminal time as an unknown parameter, PDDP is able to address the spatial-temporal trajectory optimization issue without presetting a terminal time of the UAV.…”

Section: Parameterized Differential Dynamic Programming (Pddp)mentioning

confidence: 99%

“…To ensure the convergence of the PDDP algorithm, the feedforward terms k k of δu * k and −V −1 θθ,1 V θ,1 of δθ * need to be scaled by the damping coefficient α l , where α l can be determined by the linear search method [42], and…”

Section: Parameterized Differential Dynamic Programming (Pddp)mentioning

confidence: 99%

“…The work published in Science Robotics by Foehn et al developed time-optimized quadrotor flight trajectory planning with multiple waypoints, and the proposed algorithm optimizes both the time allocation of the trajectory and the trajectory itself [38], but the work was still performed on a PC rather than on an airborne computer. Oshin et al [42] proposed a parameterized differential dynamic programming (PDDP) method for simultaneous optimization of parameters and control inputs, which was able to fast and stable converge to the minimum cost via rigorous mathematical demonstrations. Setting the flight time as an unknown parameter can solve the free terminal time problem using PDDP.…”

Section: Introductionmentioning

confidence: 99%

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Constrained Parameterized Differential Dynamic Programming for Waypoint-Trajectory Optimization

Zheng,

Xia,

Lin

et al. 2024

Aerospace

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Unmanned aerial vehicles (UAVs) are required to pass through multiple important waypoints as quickly as possible in courier delivery, enemy reconnaissance and other tasks to eventually reach the target position. There are two important problems to be solved in such tasks: constraining the trajectory to pass through intermediate waypoints and optimizing the flight time between these waypoints. A constrained parameterized differential dynamic programming (C-PDDP) algorithm is proposed for meeting multiple waypoint constraints and free-time constraints between waypoints to deal with these two issues. By considering the intermediate waypoint constraints as a kind of path state constraint, the penalty function method is adopted to constrain the trajectory to pass through the waypoints. For the free-time constraints, the flight times between waypoints are converted into time-invariant parameters and updated at the trajectory instants corresponding to the waypoints. The effectiveness of the proposed C-PDDP algorithm under waypoint constraints and free-time constraints is verified through numerical simulations of the UAV multi-point reconnaissance problem with five different waypoints. After comparing the proposed algorithm with fixed-time constrained DDP (C-DDP), it is found that C-PDDP can optimize the flight time of the trajectory with three segments to 7.35 s, 9.50 s and 6.71 s, respectively. In addition, the maximum error of the optimized trajectory waypoints of the C-PDDP algorithm is 1.06 m, which is much smaller than that (7 m) of the C-DDP algorithm used for comparison. A total of 500 Monte Carlo tests were simulated to demonstrate how the proposed algorithm remains robust to random initial guesses.

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Section: Parameterized Differential Dynamic Programming (Pddp)mentioning

confidence: 99%

Section: Parameterized Differential Dynamic Programming (Pddp)mentioning

confidence: 99%