In this paper we extend the previously introduced notion of closed-loop state sensitivity by introducing the concept of input sensitivity and by showing how to exploit it in a trajectory optimization framework. This allows to generate an optimal reference trajectory for a robot that minimizes the state and input sensitivities against uncertainties in the model parameters, thus producing inherently robust motion plans. We parametrize the reference trajectories with Béziers curves and discuss how to consider linear and nonlinear constraints in the optimization process (e.g., input saturations). The whole machinery is validated via an extensive statistical campaign that clearly shows the interest of the proposed methodology.

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.

No abstract

In this paper we consider the problem of letting an aerial robot exploiting its contact with the environment in order to enhance its motion possibilities, in a way reminiscent of legged robots exploiting contact forces for locomotion purposes. As a representative and initial case study, we consider a quadrotor equipped with a 1-DOF arm able to hook at some pivot points, and needing to perform a maneuver from an initial hooked configuration to a final hooked configuration while passing though a free-flight phase between the two anchor points. To this end, we propose a dynamical modeling able to capture the various phases (hooked, free-flying) together with an optimization framework for generating optimal motion plans compatible with actuation constraints. Simulation results illustrate the effectiveness of the approach and the promising potential in terms of more advanced maneuvers.