Real-Time Finite Element Methods for Controlling Flexible Biomechatronic Systems

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The rise of biomechatronics has enabled the development of novel interventions not only in the areas of healthcare and rehabilitation but also in the areas of human factors and ergonomics. Examples range from surgical robotics to exoskeletons that are used to improve healthcare outcomes as well as from active-controlled garments to morphing seats capable to adapt to one's posture to minimize discomfort. Such systems are generally studied within the realm of multibody systems. When elastic deformations of structural members are considered, these systems are often modeled as flexible multibody systems, for example, to control a soft surgical robot or to reduce stress on the human musculoskeletal system during interactions with a robotic device. However, elasticity complicates the design of the control system, making most existing control methods obsolete when dealing with nonlinear geometrical and material effects. The finite element method (FEM) is the standard approach in studying complex systems; however, its use in real-time control is rather rare due to its large computational load. Consequently, there is a paucity of theoretical approaches able to use finite element analysis for the control of systems. The goal of this research program is to address this gap of knowledge in order to extend FEM towards real-time control systems, especially for controlling flexible biomechatronic systems. To fulfill the above objective, the proposed research program consists of three pillars, including (1) instrumentation and calibration (2) real-time FEM solver, and (3) control law. The first pillar will develop optimization-based methods for model calibration, and computer vision-based sensing mechanisms to measure system states in real-time FEM-based settings. The second pillar will focus on computationally efficient algorithms for fast solving of finite element problems, by using quasi-Newton methods and parallelization on graphical processing units (GPUs). The third pillar will explore the design of control laws for finite element models using online constrained optimization and Lyapunov methods, followed by sensitivity analysis of the control system with respect to design parameters and modeling and measurement errors. The proposed research program is anticipated to address present challenges associated with the control of flexible biomechatronic systems and will lead to the design of novel wearable devices and soft robotic systems, especially in medicine and ergonomics. This will support several Canadian industry sectors, including healthcare, aerospace, automotive, and manufacturing.