Supervisor: Prof. Ville Kyrki (firstname.lastname@example.org)
Advisor: Dr. Gökhan Alcan (email@example.com)
Keywords: differential dynamic programming, state constraints, input constraints, constrained optimization, safe control.
Differential Dynamic Programming (DDP) is one of the most successful trajectory optimization methods, in which a large optimization problem is decomposed into smaller optimization sub-problems iteratively. This is the most important advantage of DDPs over collocation-type methods. Even though the key advantage of collocation methods over DDPs is their ability to handle state and control constraints, there exist some recent studies to employ state and/or control constraints in a DDP framework as well.
In this thesis, an extensive investigation of constrained DDP methods will be performed and the major selected ones will be implemented in a simulation environment for trajectory optimizations of different robots such as a simple point robot, 2D car-like robot, 3D quadrotor robot, and cart-pole system. In this context, the methods will be compared in terms of convergence speed, computational complexity, sensitivity to initializations, and parameter selections.
- Related literature review,
- Design of the simulation environment for different robots such as simple point robot, 2D car-like robot, 3D quadrotor robot and cart-pole system,
- Implementation of the major selected constrained DDP methods in these simulation environments,
- Comparisons of the methods in terms of convergence speed, computational complexity, sensitivity to initializations and parameter selections.
Pre-requisites: Python(high), numerical optimization (medium)
Tools: OpenAI Gym, OSQP
Start: Available immediately
- G. Alcan, and V. Kyrki. “Differential Dynamic Programming with Nonlinear Safety Constraints Under System Uncertainties“, arXiv:2011.01051, 2021.
- Z. Xie, C. K. Liu and K. Hauser. “Differential Dynamic Programming with Nonlinear Constraints“. IEEE International Conference on Robotics and Automation, pp. 695-702, 2017.
- Y. Aoyama, G. Boutselis, A. Patel and E. A. Theodorou. “Constrained Differential Dynamic Programming Revisited“. arXiv:2005.00985, 2020.