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Control Based Motion Planning Exploiting Calculus of Variations and Rational Functions: A Formal Approach
- Source :
- IEEE Access, Vol 9, Pp 121716-121727 (2021)
- Publication Year :
- 2021
- Publisher :
- IEEE, 2021.
-
Abstract
- This paper presents a control-based trajectory generation approach for unmanned aerial vehicles (UAVs) under dynamic constraints. It exploits the concept of optimal control to find closed-form differential equations that satisfy any arbitrary dynamic limitation mapped into kinematic constraints. Pontryagin’s Minimum Principle applies to derive a set of differential equations in which the dynamic environment is considered in the constrained Hamiltonian function. In particular, we aim to minimize the L2-norm of the control input avoiding dynamic obstacles, given initial and final boundary conditions. Lastly, this paper proposes a novel interpolation algorithm based on rational functions, referred to as rational recursive smooth trajectory (RRST) method. The method generates an analytic expression that approximates the control inputs, for which no closed-form solutions are in general attainable.
- Subjects :
- Mathematical optimization
General Computer Science
Dynamical systems theory
Computer science
Differential equation
steepest descent
General Engineering
calculus of variations
dynamic interpolation
Rational function
Optimal control
TK1-9971
Computer Science::Robotics
optimal control
function interpolation
Trajectory
General Materials Science
Calculus of variations
Motion planning
Electrical engineering. Electronics. Nuclear engineering
Interpolation
Aerospace
Subjects
Details
- Language :
- English
- ISSN :
- 21693536
- Volume :
- 9
- Database :
- OpenAIRE
- Journal :
- IEEE Access
- Accession number :
- edsair.doi.dedup.....59aef63016e33be79f7ad13c076c0b32