Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Constrained Trajectory Optimization for Hybrid Dynamical Systems

Pietro Noah Crestaz, Gokhan Alcan, Ville Kyrki

TL;DR

This work addresses constrained trajectory optimization for hybrid dynamical systems by extending Hybrid iLQR with two constraint-handling strategies. It introduces Discrete Barrier State (DBaS-HiLQR), an interior-point approach that embeds safety constraints into the state, and Augmented Lagrangian (AL-HiLQR), a penalty-based method that allows temporary constraint violations during optimization. Through simulations on a two-dimensional bouncing-ball hybrid system, the study shows that AL-HiLQR better handles infeasible initial trajectories and complex constraint configurations, while DBaS-HiLQR offers faster convergence in feasible settings. The results provide a framework for constrained, yet computationally efficient, trajectory optimization in hybrid systems, with future work pointing to real-time deployment and learning-based constraint adaptation.

Abstract

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.

Constrained Trajectory Optimization for Hybrid Dynamical Systems

TL;DR

This work addresses constrained trajectory optimization for hybrid dynamical systems by extending Hybrid iLQR with two constraint-handling strategies. It introduces Discrete Barrier State (DBaS-HiLQR), an interior-point approach that embeds safety constraints into the state, and Augmented Lagrangian (AL-HiLQR), a penalty-based method that allows temporary constraint violations during optimization. Through simulations on a two-dimensional bouncing-ball hybrid system, the study shows that AL-HiLQR better handles infeasible initial trajectories and complex constraint configurations, while DBaS-HiLQR offers faster convergence in feasible settings. The results provide a framework for constrained, yet computationally efficient, trajectory optimization in hybrid systems, with future work pointing to real-time deployment and learning-based constraint adaptation.

Abstract

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.

Paper Structure

This paper contains 10 sections, 19 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Definition
  4. Hybrid iLQR
  5. DBaS-HiLQR
  6. AL-HiLQR
  7. Experimental Results
  8. Test Case 1: Feasible starting rollout trajectory
  9. Test Case 2: Infeasible Starting Rollout Trajectory
  10. Conclusion

Figures (4)

  • Figure 1: Constrained hybrid iLQR computes optimal trajectories for hybrid dynamical systems, avoiding obstacles while respecting dynamic constraints.
  • Figure 2: Statistical comparison of DBaS-HiLQR and AL-HiLQR performance in randomly generated scenarios with feasible starting trajectories, in terms of success rates and convergence iterations.
  • Figure 3: Example trajectories generated by DBaS-HiLQR and AL-HiLQR, highlighting the conservative updates of DBaS-HiLQR versus the ability of AL-HiLQR to navigate tighter spaces.
  • Figure 4: Trajectories generated by the AL-HiLQR algorithm, demonstrating adaptation to obstacles introduced during hybrid transitions and showcasing the algorithm's ability to replan and adjust to new constraints.