Minimum Mixed Time–Energy Trajectory Planning of a Nonlinear Vehicle Subject to 2D Disturbances

The problem of a planar vehicle moving on a surface, such as aerial drones or small naval vessels, can be treated as a series of trajectory planning problems between way-points. While nominally the movement between each two fourth-dimensional points (positions and velocities) can be treated as a 1D...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 192; no. 2; pp. 725 - 757
Main Authors Taitler, Ayal, Ioslovich, Ilya, Karpas, Erez, Gutman, Per-Olof
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2022
Springer Nature B.V
Subjects
Acceleration
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Control theory
Drone aircraft
Drone vehicles
Energy
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Maximum principle
Naval vessels
Operations Research/Decision Theory
Optimal control
Optimization
Planning
Theory of Computation
Trajectory planning
Velocity
Variational analysis
49K99
Trajectory planning
49J53
Optimal control
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Summary:The problem of a planar vehicle moving on a surface, such as aerial drones or small naval vessels, can be treated as a series of trajectory planning problems between way-points. While nominally the movement between each two fourth-dimensional points (positions and velocities) can be treated as a 1D projection of the movement on the vector connecting the two points, in the presence of arbitrary disturbance the full problem on a plane must be considered. The mixed minimum time–energy optimal solution is now dependent on the value and direction of the disturbance, which naturally affects the structure and completion of the movement task. In this work, we address the minimum time–energy problem of a movement on a 2D plane with quadratic drag, under norm state (velocity) and norm control (acceleration) constraints. The structure and properties of the optimal solution are found and analyzed. The Pontryagin’s maximum principle (PMP) with control and state constraints is utilized. Simulations supporting the results are provided and compared with those of the open-source academic optimal control solver Falcon.m .
Bibliography:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01990-0