Optimal behaviours of a system to perform a specific task can be achieved by exploiting the coupling between trajectory optimization, stabilization and design optimization.
The main objective of this thesis work is to analyze a novel co-optimization approach, which aims to improve the optimization results applicability to real world systems.
This methodology has shown interesting advantages for underactuated systems, which are systems that have fewer actuators than degrees of freedom and thus require to make use of the passive dynamics to compensate for their lack of control inputs.
Two co-design algorithms, namely Robust Trajectory Control (RTC) and RTC with Design optimization (RTCD), have been concieved, implemented and evaluated. While the first method optimizes the trajectory behavior and the cost matrices of a stabilizing Time-Varying LQR (TVLQR) controller by fixing the model parameters, the second algorithm adds a further optimization layer where a design optimization is performed.
Both aim to maximize the system's robustness, measured by a time-varying Lyapunov-based Region Of Attraction (ROA} analysis. This analysis provides an intuitive representation of the controller's robustness to off-nominal states and can also result with a formal guarantee of stability for the entire stabilized trajectory.

The proposed algorithms have been tested on two different underactuated systems: the torque-limited simple pendulum and the cart-pole. The experiments demonstrate an increased volume of the stabilizable state-space region, indicating improved robustness. Extensive simulations of off-nominal initial conditions have further validated the results, and real system experiments have shown an improved sensitivity to torque disturbances.

This last presentation aims to show the most recent achievements in this direction. The extension of the above mentioned algorithms to the Cart-pole system and the results of real world experiments will be the main focus. Given the observed results, conclusions and future plans of this thesis work will be outlined.