Master’s Thesis: Optimal Periodic Orbit Stabilization Applied to Elastic Bipedal Locomotion

In nature there is a huge variety of locomotion strategies. Horses use multiple different gaits to accomplish locomotion at different velocities in an energy efficient way. When they accelerate while walking, they switch naturally to trotting and at even higher speeds to galloping for a more energy efficient gait. A similar behavior can be observed for humans and terrestrial birds, which utilize walking and running depending on the velocity to save energy. Humans profit hugely from the compliant muscle tendon system, such that up to 75% of the positive work generated around the ankle is contributed by the tendons while running. In particular, the tendons store energy after touch down while vertically decelerating and release this energy when vertically accelerating.

Comparable compliant structures gain more attention in robotics. However, leveraging elastic elements to ensure an efficient and continuous energy conversion along the gait is still an open research topic. In fact, optimal energy conversion as well as efficiency are considered to be among the most important current engineering problems [Van der Schaft]. The goal of the thesis is to find and stabilize an energy efficient gait, which utilizes the elastic elements.

Nonlinear optimization is a very powerful numerical tool for trajectory planning and will be used within the thesis to search for an efficient gait of an elastic biped. The resulting periodic orbit should be rendered asymptotically stable using linear optimal control in transverse coordinates. A solution to the optimal control problem can be obtained by already existing algorithms to solve the periodic Riccati equation. The control strategy should be validated in numerical simulations and in experiments.

Your Qualification: 

• Strong background in robotics, control and optimization theory
• Experience in C++ programming (trajectory optimization),
• Ability to learn basics in Python and Julia language (hardware interface and PRE solver interface)

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] Utilizing the Natural Dynamics of Elastic Legged Robots for Periodic Jumping Motions Fabian Beck; Maximilian Rehermann; Johann Reger; Christian Ott International Conference on Humanoid Robots, 2022

[2] On Energy Conversion in Port-Hamiltonian Systems Arjan van der Schaft; Dimitri Jeltsema Conference on Decision and Control, 2021

[3] Constructing Transverse Coordinates for Orbital Stabilization of Periodic Trajectories Maksim Surov; Sergei Gusev; Leonid Freidovich American Control Conference, 2020