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Invariant Sets for Integrators and Quadrotor Obstacle Avoidance
Abstract Ensuring safety through set invariance has …
Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nth-order integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n <= 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.
al expressions for control-invariant sets.  +
Authors Ludvig Doeser, Petter Nilsson, Aaron D. Ames, and Richard M. Murray  +
Funding Formal Methods for V&V and T&E of Autonomous Systems +
ID 2019l  +
Source 2020 American Control Conference (ACC)  +
Tag dnam20-acc  +
Title Invariant Sets for Integrators and Quadrotor Obstacle Avoidance +
Type Conference paper  +
Categories Papers
Modification date
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26 May 2020 05:51:51  +
URL
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https://www.cds.caltech.edu/~murray/preprints/dnam20-acc.pdf  +
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