In this work, 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 closed-loop state sensitivity, which is extended in this work
to also include uncertainties in the initial state. The proposed
framework, which considers the sensitivity of the nominal closedloop system w.r.t. both model parameters and initial state mismatches, is exploited to compute tubes 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 closed-loop state sensitivity framework has the
important advantage of computational simplicity and minimal
assumptions (and simplifications) regarding the underlying robot
closed-loop 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 intrinsically robust and safe
trajectory 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.
