Safe and Robust Planning for Uncertain Robots: A Closed-Loop State Sensitivity Approach

Abstract

In this letter, we detail a comprehensive framework for safe and robust planning for robots in presence of model uncertainties. Our framework is based on the recent notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-loop state sensitivity</i>, which is extended in this work to also include uncertainties in the initial state. The proposed framework, which considers the sensitivity of the nominal closed-loop system w.r.t. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">both</i> model parameters and initial state mismatches, is exploited to compute <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tubes</i> that accurately capture the worst-case effects of the considered uncertainties. In comparison to the current state-of-the-art for safe and robust planning, the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-loop state sensitivity</i> framework has the important advantage of computational simplicity and minimal assumptions (and simplifications) regarding the underlying robot <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-loop</i> dynamics. The approach is validated via both extensive simulations and real-world experiments. In the experiments we consider as case study a nonlinear trajectory optimization problem aimed at generating an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">intrinsically robust and safe trajectory</i> for an aerial robot for safely performing an obstacle avoidance maneuver despite the uncertainties. Simulation and experimental results further confirm the viability and interest of the proposed approach.