Flatness of musculoskeletal systems under functional electrical stimulation

Area of Science:

• Biomedical Engineering
• Control Systems Theory
• Rehabilitation Robotics

Background:

• Controlling musculoskeletal systems with functional electrical stimulation (FES) is challenging due to complex, nonlinear dynamics.
• Existing musculoskeletal models are difficult to control and invert, hindering precise FES applications.

Purpose of the Study:

• To investigate the feasibility and application of flatness-based control for musculoskeletal systems.
• To explore flatness properties of a dynamic knee joint model controlled by quadriceps FES.

Main Methods:

• Developed a mathematical framework to analyze the flatness properties of musculoskeletal models.
• Applied differential flatness theory to a two-input knee joint model under quadriceps FES.
• Conducted open-loop simulations to validate the flatness-based control approach.

Main Results:

• Mathematically proved that a two-input musculoskeletal system (e.g., knee joint) is differentially flat.
• Identified muscle stiffness and knee joint angle as flat outputs for the two-input system.
• Demonstrated that single-input musculoskeletal systems are not flat, limiting control strategies.
• Open-loop simulations showed perfect tracking for a perfect model, but highlighted limitations with parameter errors (4% deviation).

Conclusions:

• Flatness-based control is a promising technique for FES of musculoskeletal systems, particularly for multi-input configurations.
• The findings provide crucial insights for developing advanced FES control strategies, moving beyond single-input limitations.
• Closed-loop control should be considered for robust FES applications when model uncertainties exist.