Trajectory Generation for Minimum Closed-Loop State Sensitivity

Abstract

In this paper we propose a novel general method to let a dynamical system fulfil at best a control task when the nominal parameters are not perfectly known. The approach is based on the introduction of the novel concept of closedloop sensitivity, a quantity that relates parameter variations to deviations of the closed-loop trajectory of the system/controller pair. This new definition takes into account the dependency of the control inputs from the system states and nominal parameters as well as from the controller dynamics. The reference trajectory to be tracked is taken as optimization variable, and the dynamics of both the sensitivity and of its gradient are computed analytically along the system trajectories. We then show how this computation can be effectively exploited for solving trajectory optimization problems aimed at generating a reference trajectory that minimizes a norm of the closed-loop sensitivity. The theoretical results are validated via an extensive campaign of Monte Carlo simulations for two relevant robotic systems: a unicycle and a quadrotor UAV.

Online Optimal Perception-Aware Trajectory Generation

“…A better possibility is probably to leverage tools coming from the nonlinear reachability analysis instead in order to quantify how much the actuation/process noise degrades the collected information during motion. Another possibility when in presence of parametric uncertainty in the robot model is to combine the CG with a parameter sensitivity metric, such as the one proposed in [30], for taking into account at the same time state observability and robustness against model uncertainty (which could be seen as a form of process noise).…”

“…On the other hand, for the planar quadrotor, we will not change the parametrization imposed by the B-Spline. Finally, by exploiting the flatness, a feedback control law able to ensure the tracking of the planned B-Spline trajectory with desired timing law can be also simply designed (see [30] for details).…”

Robust Trajectory Planning with Parametric Uncertainties

“…An alternative point of view is to focus on the generation of feedforward trajectories with minimal state sensitivity, see, e.g., [14]- [16], but with the main limitation of working only for 'open-loop' cases. To overcome this problem, in [17] it has been proposed to plan trajectories with minimal 'closedloop' state sensitivity, which allows to take into account the coupling between the robot and its motion controller in an explicit way.…”

“…Building upon [17], in this work we introduce the novel notion of input sensitivity. To the best of our knowledge, this metric has never been considered before and we strongly † are with CNRS, Univ Rennes, Inria, IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France, e-mails: pascal.brault@irisa.fr, quentin.delamare@irisa.fr, prg@irisa.fr.…”

“…In [17], the state sensitivity method was validated by simulating several perturbed cases for only one arbitrarily chosen trajectory. In this work, we conduct an upgraded statistical analysis in a large number of initial trajectories which are then individually perturbed for assessing the validity of our method.…”