Invariant Sets for Integrators and Quadrotor Obstacle Avoidance. Doeser, L.; Nilsson, P.; Ames, A. D; and Murray, R. M
abstract   bibtex   
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 nthorder 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.
@article{doeser_invariant_nodate,
	title = {Invariant {Sets} for {Integrators} and {Quadrotor} {Obstacle} {Avoidance}},
	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 nthorder 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.},
	language = {en},
	author = {Doeser, Ludvig and Nilsson, Petter and Ames, Aaron D and Murray, Richard M},
	pages = {8},
}
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