Safe Model Predictive Control for Robotic Manipulation and Locomotion

In last decades, robots have been increasingly used in a wide range of fields, including industrial automation and emerging applications from logistics to healthcare, agriculture and home assistance. Safe and high-performance control of robots is a crucial aspect of their deployment. Many researchers in the robotic community have converged on the idea of generating motion control law by solving an Optimal Control Problem. Even though data-driven approaches have gained popularity in recent years, model-based methods are still widely developed. Advanced techniques, like Model Predictive Control (MPC), have been successfully applied unlocking complex motions for a wide range of robotic systems, from manipulators to legged robots. Nonetheless, open problems remain, especially in terms of safety and versatility of these model-based methods. In this thesis, we address some of these challenges by proposing novel control strategies for robotic systems. We first present an innovative MPC scheme that can guarantee recursive feasibility (thus safety) under weaker assumptions than classic methods. Safety is ensured by moving a safe-set constraint backward over the horizon. If a risk of constraint violation is detected, a safe task-abortion strategy is triggered. Through simulation of different robot manipulators, we empirically show that our approach leads to fewer constraint violations than state-of-the-art methods, while maintaining good performance in terms of tracking cost and computation time. We then focus on the problem of generating versatile and stable locomotion for quadruped robots. In full-body dynamics MPC, reference trajectories are typically provided for the Center of Mass of the robot and swing feet. These references may limit the robot's adaptability to unforeseen situations. We propose a novel full-dynamics MPC formulation that does not require reference swing-foot trajectories, featuring a novel cost function targeting swing foot motion, which enables automatic online footstep location adjustments. Simulations and experiments on a quadruped robot show better push-recover capabilities with respect to state-of-the-art methods. Finally, we tackled the problem of pre-defined footstep timings in bipedal locomotion. This is a critical issue in the design of walking controllers, as it may lead to undesired behaviors, such as limping or even falling down, when the robot faces external disturbances. We propose to apply the hybrid framework to the Linear Inverted Pendulum Model, such that the foot switches are triggered based on the Center of Mass position. We define tracking error coordinates induced by our hybrid model, using a concept similar to reference spreading, and prove local asymptotic stability using a saturated feedback controller. Then, we show the applicability of the proposed framework though full-body model simulations, showing its advantages compared to standard MPC with pre-defined footstep timings. In conclusion, this thesis addresses critical challenges in robotic control by advancing model-based methods to enhance safety, versatility, and adaptability across a variety of robotic systems. By introducing novel MPC strategies, we achieve improved safety with fewer constraint violations and enable more responsive and stable locomotion for quadruped and biped robots. These contributions demonstrate the potential of innovative control frameworks to overcome limitations in traditional approaches, paving the way for more robust and reliable robotic systems in dynamic and unpredictable environments.