Paul Manns

Barbara Kaltenbacher, Paul Manns

In this paper, by means of a standard model problem, we devise an approach to computing approximate dual bounds for use in global optimization of coefficient identification in partial differential equations (PDEs) by, e.g., (spatial) branch-and-bound methods. Linearization is achieved by a McCormick relaxation (that is, replacing the bilinear PDE term by a linear one and adding inequality constraints), combined with local averaging to reduce the number of inequalities. Optimization-based bound tightening allows us to tighten the relaxation and thus reduce the induced error. Combining this with a quantification of the discretization error and the propagated noise, we prove that the resulting discretization regularizes the inverse problem, thus leading to an overall convergent scheme. Numerical experiments illustrate the theoretical findings.

Manish Sreenivasa, Matthew Millard, Paul Manns et al.

The coupling of human movement dynamics with the function and design of wearable assistive devices is vital to better understand the interaction between the two. Advanced neuromuscular models and optimal control formulations provide the possibility to study and improve this interaction. In addition, optimal control can also be used to generate predictive simulations that generate novel movements for the human model under varying optimization criterion.

Paul Manns, Manish Sreenivasa, Matthew Millard et al.

Designing an exoskeleton to reduce the risk of low-back injury during lifting is challenging. Computational models of the human-robot system coupled with predictive movement simulations can help to simplify this design process. Here, we present a study that models the interaction between a human model actuated by muscles and a lower-back exoskeleton. We provide a computational framework for identifying the spring parameters of the exoskeleton using an optimal control approach and forward-dynamics simulations. This is applied to generate dynamically consistent bending and lifting movements in the sagittal plane. Our computations are able to predict motions and forces of the human and exoskeleton that are within the torque limits of a subject. The identified exoskeleton could also yield a considerable reduction of the peak lower-back torques as well as the cumulative lower-back load during the movements. This work is relevant to the research communities working on human-robot interaction, and can be used as a basis for a better human-centered design process.