Robust Co-design for Underactuated Systems

An approach to obtain an optimal behaviour of a system to achieve a specific task is via an interplay between trajectory optimization, stabilization and design optimization.
To find a structured way to deal with this co-optimization is the main objective of the thesis work.
The sim-to-real gap represent a very important issue in the robotics research field, that becomes even more challenging when dealing with underactuated systems.
So, as a further contribution, the idea is to define the robustness feature as an objective of the whole process.
The Region of attraction (RoA) analysis, that had been introduced in my thesis exposé, has been used to express the robustnessto off-nominal statesin an optimization cost.
Unfortunately, this process often requires a computational time that is not suitable for an optimization problem and it does not specifically reason about parameters and modelling uncertainties.
Hence, a robust trajectory optimization has been implemented with an analytical and differentiable cost function that approximated the invariant funnels.
This last objective function permits also the inclusion if uncertainties in the dynamics equations in a rather straightforward way.
Thanks to the measure given by these tools an interplay between trajectory optimization and trajectory stabilization has been obtained for the torque-limited simple pendulum system.
This process fix the model parameters and defines the trajectory and the stabilizing linear controller that minimize the given cost.
Acomplete robust co-design optimization has also been formulated in order to include design parameters in the overall optimization.Different trials show an improvement of the RoA volume.
Given the observed results, future plans and final goals for the thesis work will be presented.