Master Thesis on “Safe Constrained Differential Dynamic Programming”

Supervisor: Prof. Ville Kyrki (ville.kyrki@aalto.fi)
Advisor: Dr. Gökhan Alcan (gokhan.alcan@aalto.fi)

Keywords: differential dynamic programming, state constraints, input constraints, constrained optimization, safe control.

Project Description

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.

Deliverables

  • 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.

Practical Information

Pre-requisites: Python(high), numerical optimization (medium)
Tools: OpenAI Gym, OSQP
Start: Available immediately

References