Alternating Minimization Based Trajectory Generation for Quadrotor Aggressive Flight

Wang, Zhepei; Zhou, Xin; Xu, Chao; Chu, Jian; Gao, Fei

doi:10.1109/lra.2020.3003871

Cited by 35 publications

(22 citation statements)

References 20 publications

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“…Based on the work in [ 31 ], in which a super computational efficient optimal spatial–temporal trajectory planner was proposed, we developed our method to ensure the smoothness throughout the approaching and landing maneuver. This method can improve the computational efficiency, which enables this planner to generate a trajectory within a few microseconds.…”

Section: System Architecturementioning

confidence: 99%

Proactive Guidance for Accurate UAV Landing on a Dynamic Platform: A Visual–Inertial Approach

Chang

Cheung

et al. 2022

Sensors

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This work aimed to develop an autonomous system for unmanned aerial vehicles (UAVs) to land on moving platforms such as an automobile or a marine vessel, providing a promising solution for a long-endurance flight operation, a large mission coverage range, and a convenient recharging ground station. Unlike most state-of-the-art UAV landing frameworks that rely on UAV onboard computers and sensors, the proposed system fully depends on the computation unit situated on the ground vehicle/marine vessel to serve as a landing guidance system. Such a novel configuration can therefore lighten the burden of the UAV, and the computation power of the ground vehicle/marine vessel can be enhanced. In particular, we exploit a sensor fusion-based algorithm for the guidance system to perform UAV localization, whilst a control method based upon trajectory optimization is integrated. Indoor and outdoor experiments are conducted, and the results show that precise autonomous landing on a 43 cm × 43 cm platform can be performed.

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Section: System Architecturementioning

confidence: 99%

Proactive Guidance for Accurate UAV Landing on a Dynamic Platform: A Visual–Inertial Approach

Chang

Cheung

et al. 2022

Sensors

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show abstract

“…Although it performs reasonably well for low-order Bézier curves in practice, this simple but conservative approach is suboptimal for high-order Bézier curves since the convex hull of Bézier control points significantly overestimates the smallest convex region containing by the actual curve, especially for higher-order polynomials. On the other hand, exact and fast continuous constraint verification with polynomial curves is possible based on the separation of polynomial extremes [24], the sign change of polynomials [25], and their root existence test based on Sturm's theorem [26], but these methods result in highly complex nonlinear optimization constraints. Our approach for approximating high-order Bézier curves by loworder Bézier segments allows one to use the convexity of low-order Bézier curves in high-order polynomial trajectory optimization in a less conservative way.…”

Section: A Motivation and Related Literaturementioning

confidence: 99%

Adaptive Bézier Degree Reduction and Splitting for Computationally Efficient Motion Planning

Arslan¹,

Tiemessen²

2022

Preprint

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As a parametric polynomial curve family, Bézier curves are widely used in safe and smooth motion design of intelligent robotic systems from flying drones to autonomous vehicles to robotic manipulators. In such motion planning settings, the critical features of high-order Bézier curves such as curve length, distance-to-collision, maximum curvature/velocity/acceleration are either numerically computed at a high computational cost or inexactly approximated by discrete samples. To address these issues, in this paper we present a novel computationally efficient approach for adaptive approximation of high-order Bézier curves by multiple low-order Bézier segments at any desired level of accuracy that is specified in terms of a Bézier metric. Accordingly, we introduce a new Bézier degree reduction method, called parameterwise matching reduction, that approximates Bézier curves more accurately compared to the standard least squares and Taylor reduction methods. We also propose a new Bézier metric, called the maximum control-point distance, that can be computed analytically, has a strong equivalence relation with other existing Bézier metrics, and defines a geometric relative bound between Bézier curves. We provide extensive numerical evidence to demonstrate the effectiveness of our proposed Bézier approximation approach. As a rule of thumb, based on the degree-one matching reduction error, we conclude that an n th -order Bézier curve can be accurately approximated by 3(n − 1) quadratic and 6(n − 1) linear Bézier segments, which is fundamental for Bézier discretization.

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“…They are usually chosen by heuristics and this provides room for optimization of time allocations. Wang et al [13] propose an alternating method but it lacks the ability to handle complex spatial constraints. Recent work [14] uses mixed-integer QP to solve for trajectories and guarantees safety by always having a feasible, safe back-up trajectory.…”

Section: A Trajectory Optimization For Uavsmentioning

confidence: 99%

“…Then by [30,Th. 3.1] the sequence generated by (13) approximates the trajectory of the differential inclusion.…”

Section: A Clarke Subdifferentialmentioning

confidence: 99%

Fast UAV Trajectory Optimization Using Bilevel Optimization With Analytical Gradients

Sun¹,

Tang

Hauser

2021

IEEE Trans. Robot.

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In the article, we present an efficient optimization framework that solves trajectory optimization problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier subproblems. With timing fixed, the state variables can be optimized efficiently using convex optimization, and the timing variables can be optimized in a separate NLP, which forms a bilevel optimization problem. The challenge of obtaining the gradient of the timing variables is solved by sensitivity analysis of parametric NLPs. The exact analytic gradient is computed from the dual solution as a by-product, whereas existing finite-difference techniques require additional optimization. The bilevel optimization framework efficiently optimizes both timing and state variables which is demonstrated on generating trajectories for an UAV. Numerical experiments demonstrate that bilevel optimization converges significantly more reliably than a standard NLP solver, and analytical gradients outperform finite differences in terms of computation speed and accuracy. Physical experiments demonstrate its real-time applicability for reactive target tracking tasks.

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Alternating Minimization Based Trajectory Generation for Quadrotor Aggressive Flight

Cited by 35 publications

References 20 publications

Proactive Guidance for Accurate UAV Landing on a Dynamic Platform: A Visual–Inertial Approach

Proactive Guidance for Accurate UAV Landing on a Dynamic Platform: A Visual–Inertial Approach

Adaptive Bézier Degree Reduction and Splitting for Computationally Efficient Motion Planning

Fast UAV Trajectory Optimization Using Bilevel Optimization With Analytical Gradients

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