Optimal Control for Applications in Medical and Rehabilitation Technology: Challenges and Solutions

Abstract

This paper gives an overview of the mathematical background and possible applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of appropriate medical devices. One particular challenge in this area is the formulation of suitable subject-specific models of motions for healthy and impaired humans including skeletal multibody dynamics and potentially neuromuscular components, and their combination with models of the technical components. The formulation of hybrid multi-phase optimal control problems arising in this context involves non-standard elements such as the open- or closed loop stability of the dynamic motion. Efficient methods for the solution of optimal control and inverse optimal control are discussed and particular difficulties of this problem class are highlighted. In addition, we present several example applications of these methods in the development of mobility aids for geriatric patients, the optimization-based design of exoskeletons, the analysis of running motions with prostheses, the optimal functional electrical stimulation of hemiplegic patients, as well as stability studies for different types of movement.