]> 2026-07-09T11:41:46+00:00 Invariant Sets for Integrators and Quadrotor Obstacle Avoidance 0 en 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. Ludvig Doeser Petter Nilsson Aaron D. Ames and Richard M. Murray NCS 2019l 2020 American Control Conference (ACC) dnam20-acc Conference paper 2021-09-05T02:04:15Z 2459462.5862847 Invariant Sets for Integrators and Quadrotor Obstacle Avoidance Title 102 en Title