Master’s Thesis: Optimal Control for a Multibody System in Free-Flight Solved with Collocation and GPUs

Nonlinear optimization provides very powerful numerical tools for solving trajectory planning problems for applications in robotics. The typical problem statement involves dealing with nonlinear motion constraints, such as robot dynamics and collision avoidance. The tools available for solving such problems have the drawback of generally not being online-capable, due to their large computational burden.  The goal of this work is to leverage GPU technology for increasing the computational efficiency of the numerical resolution process.

The system of interest involves a robot during a flight phase. This system may represent a humanoid robot during running (the flight phase is between the stance phases on the right and left foot) or it may represent a robotic spacecraft operating in outer space, where the dynamics is governed by the felt weightlessness.

This work will start by partly reformulating an existing multibody dynamic library of the Institute (LucaDynamics) to improve its numerical efficiency for the problems of interest. The following step will comprise applying the method of collocation, which is one of the standard methods for parameterizing an optimal control problem to obtain a nonlinear program, to the control problems of interest. This method will be compared to existing implementations of different methods. The first implementation in C++ or FORTRAN will then be extended with the use of a GPU architecture, in order to analyze the potential benefit in the computational speed-up that can derive from it.

Your Qualification: 

• Strong background in multibody dynamics, optimal control and optimization theory
• Experience in C++ programming (trajectory optimization)
• Experience in OpenMP and CUDA programming

Your Start:

The thesis will be conducted at the Institute of Robotics and Mechatronics in Oberpfaffenhofen. Envisioned starting date April 2024. We give preference to severely disabled applicants if they are professionally suitable.

References:

[1] Garofalo, G., Ott, C., and Albu-Schäffer, A., “On the closed form computation of the dynamic matrices and their differentiations”, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) November 3-7, 2013

[2] Garofalo, G., Henze, B., Englsberger, J., Ott, C., “On the inertially decoupled structure of the floating base robot dynamics”, IFAC-PapersOnLine, 48(1), 322-327, 2015

[3] Lampariello, R. Hirzinger, H., "Generating Feasible Trajectories for Autonomous On-Orbit Grasping of Spinning Debris in a Useful Time", IEEE/RSJ International Conference on Intelligent Robots and Systems 2013 (IROS 2013), Tokyo, Japan, November 2013

[4] Chretien, B., Escande, A., Kheddar, A., “GPU Robot Motion Planning Using Semi-Infinite Nonlinear Programming”, IEEE Transactions on Parallel and Distributed Systems, Vol. 27, No. 10, Oct. 2016