Research in Optimization

Inspired on the one hand by the assumption of inherent optimality principles in natural processes and on the other hand by the desire to optimize performance of technical systems (using different performance indicators), model-based optimization and optimal control represent the key methods for our research, both in biomechanics and robotics. We combine model-based and model-free methods for increased efficiency and precision and perfom comparisons with machine learning approaches based on similar models to take the largest benefit from th advantages of each method. 

Our research includes the following topics:

Mathematical models of humans, robots and their interactions:  

Detailed and realistic models of humans, robots and their interactions are crucial for model-based optimization and control, but also for machine learning in simulation. Our models of the human body include mechanical, muscular and neural components and take subject specific parameters into account (e.g. recognizing age, gender and ability-based movement differences as well as individual movement specifics). Physical properties of robots can be transformed into mathematical models considering all their realistic kinematic and dynamic limitations. For mobility assistance robots, in partciular wearable robotics, combined models of humans and robots are established, including interaction forces and torques. Our research includes the development of the modeling tools themselves, measurement approaches to identify model characteristics and the development for specific models in all the cases mentioned.

Optimization/optimal control algorithms:  
We need efficient algorithms for the optimization-based analysis process of human movement and for the design of intelligent robotic systems and for motion generation, exploiting the above models for:

• Model-based optimization / optimal control algorithms for motion analysis and potentially parameter identification based on experimental data 

• Model-based optimization / optimal control algorithms for motion synthesis to generate motions for situations that have not been previously studied in experiments, and  

• Inverse optimal control methods that identify the underlying objective function of a recorded experimental motion, assuming that movement is optimal and based on a set of potential candidate objective functions. 

We will seek to improve our understanding, increase the efficiency of our algorithms to treat even larger data sets, automate problem formulation and data handling, and improve our interfaces so that non-experts can use our tools in their daily research. 

Combining optimization with model-free approaches 

We explore the combination of model-based optimization with model-free approaches in two different ways: (a) We generate training data based on a set of optimal control solutions to learn movement primitives or train neural networks as a simplified representation of the complex solutions, which allow us to generate new trajectories in a flexible and rapid manner, and (b) We combine nonlinear model-predictive control and reinforcement learning to exploit model knowledge of the underlying physics, but also compensate for the model-plant mismatch. We apply these methods in both humanoid and assistive robotics.   

Explorations of data driven approaches for motion classification and component description

In some applications, such as motion classification based on very few sensors as well as the description of components of the human body or a robot for which no good models exist, we are investigating the use of model-free machine learning approaches. Systematic comparisons of the predictions of different ML algorithms and parameter setting are performed for vast test data sets. We are interested to find out reliable settings for particular applications, and ultimately want to use the knowledge to develop more explicit models of these processes or combine the black box components with physically modeled components into predictive simulations.