Constrained Trajectory Optimization for Hybrid Dynamical Systems

Hybrid dynamical systems, such as quadruped robots, humanoids and aerial manipulators, pose unique control challenges due to their coexistence of continuous and discrete dynamics and in response to these challenges, this thesis presents a novel control algorithm for hybrid dynamical systems. Based on the iterative linear quadratic regulator algorithm adapted for hybrid systems through the use of the saltation matrix, we further extend the approach to effectively accommodate state and input constraints. Our methodology integrates both an Interior Point method and an Augmented Lagrangian method to ensure the generation of trajectories within the safe operational set, thereby enhancing system stability and safety. Subsequently, comprehensive evaluations of the proposed control algorithms are conducted across various simulation environments, providing comparative analysis between the different constraint-handling techniques in terms of success rate and computational complexity of the solutions. Through this work, we aim to contribute to the advancement of control methodologies for hybrid dynamical systems.