Constrained Trajectory Optimization for Hybrid Dynamical Systems

Hybrid dynamical systems pose significant challenges for effective planning and control, especially when additional constraints such as obstacle avoidance, state boundaries, and actuation limits are present. In this letter, we extend the recently proposed Hybrid iLQR method [1] to handle state and input constraints within an indirect optimization framework, aiming to preserve computational efficiency and ensure dynamic feasibility. Specifically, we incorporate two constraint handling mechanisms into the Hybrid iLQR: Discrete Barrier State and Augmented Lagrangian methods. Comprehensive simulations across various operational situations are conducted to evaluate and compare the performance of these extended methods in terms of convergence and their ability to handle infeasible starting trajectories. Results indicate that while the Discrete Barrier State approach is more computationally efficient, the Augmented Lagrangian method outperforms it in complex and real-world scenarios with infeasible initial trajectories.