A New Recursive Framework for Trajectory Generation of UAVs

Letizia, Nunzio A.; Salamat, Babak; Tonello, Andrea M.

doi:10.1109/aero47225.2020.9172656

Cited by 2 publications

(5 citation statements)

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“…They are often smooth functions (e.g. polynomials [17]) and smoothness in control inputs is a desired property [19]. Furthermore, they can be easily implemented in microcontrollers.…”

Section: Analytic Expression Of the Optimal Control Inputsmentioning

confidence: 99%

“…To approximate the numerical solutions obtained in Section III, we firstly use polynomials as basis functions and we exploit the Recursive Smooth Trajectory (RST) generation method recently introduced in [19], [20]. Lastly, we introduce a novel interpolation method, based on the RST algorithm, which utilizes as basis the rational functions.…”

Section: Analytic Expression Of the Optimal Control Inputsmentioning

confidence: 99%

“…The RST algorithm was proposed in [19], [20] as an iterative interpolation method. The idea is to recursively build an unique polynomial function f k (t) knowing the associated…”

Section: A Recursive Smooth Trajectorymentioning

confidence: 99%

“…k, where N + 1 and k are the number of waypoints and the number of derivative constraints, respectively. Indeed, it has been shown in [19], [20] that, defined the polynomial function as…”

Section: A Recursive Smooth Trajectorymentioning

confidence: 99%

“…Splines are easy to be constructed and provide bounded trajectories although the continuity of the derivatives (smoothness) at the waypoints is only guaranteed up to a certain order. A recent methodology that avoids solving an inverse problem has been proposed in [19], [20]. Therein, the authors developed a recursive methodology to build a unique smooth polynomial trajectory satisfying the kinematic constraints.…”

Section: Introductionmentioning

confidence: 99%

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Control Based Motion Planning Exploiting Calculus of Variations and Rational Functions: A Formal Approach

2021

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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 closedform 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 L 2 -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.

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“…They are often smooth functions (e.g. polynomials [17]) and smoothness in control inputs is a desired property [19]. Furthermore, they can be easily implemented in microcontrollers.…”

Section: Analytic Expression Of the Optimal Control Inputsmentioning

confidence: 99%

Section: Analytic Expression Of the Optimal Control Inputsmentioning

confidence: 99%

“…The RST algorithm was proposed in [19], [20] as an iterative interpolation method. The idea is to recursively build an unique polynomial function f k (t) knowing the associated…”

Section: A Recursive Smooth Trajectorymentioning

confidence: 99%

“…k, where N + 1 and k are the number of waypoints and the number of derivative constraints, respectively. Indeed, it has been shown in [19], [20] that, defined the polynomial function as…”

Section: A Recursive Smooth Trajectorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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