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Invariant Sets for Integrators and Quadrotor Obstacle Avoidance

Doeser, Ludvig and Nilsson, Petter and Ames, Aaron D. and Murray, Richard M. (2020) Invariant Sets for Integrators and Quadrotor Obstacle Avoidance. In: 2020 American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 3814-3821. ISBN 9781538682661. https://resolver.caltech.edu/CaltechAUTHORS:20200730-143943975

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Abstract

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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.23919/acc45564.2020.9147872DOIArticle
ORCID:
AuthorORCID
Nilsson, Petter0000-0001-8748-6936
Ames, Aaron D.0000-0003-0848-3177
Murray, Richard M.0000-0002-5785-7481
Additional Information:© 2020 AACC.
Record Number:CaltechAUTHORS:20200730-143943975
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200730-143943975
Official Citation:L. Doeser, P. Nilsson, A. D. Ames and R. M. Murray, "Invariant Sets for Integrators and Quadrotor Obstacle Avoidance," 2020 American Control Conference (ACC), Denver, CO, USA, 2020, pp. 3814-3821, doi: 10.23919/ACC45564.2020.9147872
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104674
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:31 Jul 2020 14:11
Last Modified:20 Nov 2020 23:57

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