Optimization-based methods for stable and robust motion generation and control in mobile robots

While Robotics is seeing an ever-increasing adoption in both industrial and service applications, truly autonomous robots are still far from being widespread. One of the limiting factors is in the availability of adaptable, performant and robust control methods to generate complex motions for such systems. At the moment, Model Predictive Control (MPC) stands out among the most promising techniques to fill this gap. In fact, with its ability to minimize a cost function while respecting a set of constraints that represent physical and operational limitations of a system, MPC is capable of outperforming classic approaches, and its predictive nature makes it adaptable to a large range of tasks. This thesis presents a series of motion generation methods based on Model Predictive Control with the aim of improving over the current methodologies in two aspects: the first being the treatment of systems that exhibit a non-minimum phase behavior and thus pose the challenge of generating motions that are stable; the second being the robustness against uncertainties in the model parameters, which will inevitably make the robot deviate from the planned trajectory. The first part presents IS-MPC (Intrinsically Stable MPC), demonstrating its effectiveness in the stable inversion of non-minimum phase systems. We showcase the applications of IS-MPC in stabilizing balancing robots performing non-trivial navigation and loco-manipulation tasks, and in preventing the jackknife phenomenon in autonomous Tractor-Trailer vehicles. The second part of the thesis addresses the problem of robustifying motions against parametric uncertainties, focusing on aerial robots. We make use of the recent notion of closed-loop sensitivity and explore its application for robust flight control in Quadrotors with an experimental validation. We also present a novel computationally efficient Robust MPC scheme, named ST-MPC (Sensitivity-aware Tube MPC), for controlling nonlinear systems affected by parametric uncertainties, demonstrating its effectiveness through an extensive simulation campaign. The contributions of this thesis extend to both stability and robustness in motion generation, offering valuable insights and practical applications across diverse robotic systems.