[Paper Review] Control of Separable Subsystems with Application to Prostheses

Rachel Gehlhar, Jenna Reher+1 more|arXiv (Cornell University)|Sep 6, 2019

Prosthetics and Rehabilitation Robotics22 references4 citations

TL;DR

This paper introduces a novel framework for controlling separable subsystems in nonlinear dynamical systems, enabling model-dependent controllers for prostheses using only measurable states and inputs. By constructing an equivalent subsystem with local information, the method achieves full system stability and equivalency to a feedback linearizing controller that requires full knowledge of human dynamics—demonstrated via simulation in an amputee-prosthesis system with identical performance across controllers.

ABSTRACT

Nonlinear control methodologies have successfully realized stable human-like walking on powered prostheses. However, these methods are typically restricted to model independent controllers due to the unknown human dynamics acting on the prosthesis. This paper overcomes this restriction by introducing the notion of a separable subsystem control law, independent of the full system dynamics. By constructing an equivalent subsystem, we calculate the control law with local information. We build a subsystem model of a general open-chain manipulator to demonstrate the control method's applicability. Employing these methods for an amputee-prosthesis model, we develop a model dependent prosthesis controller that relies solely on measurable states and inputs but is equivalent to a controller developed with knowledge of the human dynamics and states. We demonstrate the results through simulating an amputee-prosthesis system and show the model dependent prosthesis controller performs identically to a feedback linearizing controller based on the whole system, confirming the equivalency.

Motivation & Objective

• To address the challenge of designing stable, model-dependent controllers for prostheses when human dynamics and states are unknown.
• To develop a general control framework for separable subsystems that guarantees stability equivalent to a full-system feedback linearizing controller.
• To enable the use of advanced nonlinear control methods—like feedback linearization—on prosthetic subsystems with limited system-level information.
• To demonstrate the feasibility and equivalence of subsystem control in a realistic amputee-prosthesis model through simulation.

Proposed method

• The paper introduces the concept of a 'separable subsystem control law' that depends only on the subsystem's own dynamics and measurable states, independent of the full system's dynamics.
• It constructs an equivalent subsystem model using measurable quantities such as global orientation, velocities, and interaction forces at the socket interface.
• A feedback linearizing control law is derived for the subsystem using Lie derivatives and relative degree analysis, ensuring equivalent behavior to a full-system controller.
• The method proves that the subsystem controller achieves the same control input and system stability as a controller designed with full knowledge of the human-prosthesis dynamics.
• The approach is validated by simulating a 65.8 kg female amputee-prosthesis model with both full-system and subsystem controllers, showing identical control inputs and state trajectories.
• The framework is extended to a heavier 90.7 kg model, confirming robustness to human parameter variations as long as force and motion data are measurable.

Experimental results

Research questions

• RQ1 Can a model-dependent controller be designed for a prosthetic subsystem without knowledge of the human dynamics or states?
• RQ2 Is it possible to construct a control law for a separable subsystem that is equivalent to a full-system feedback linearizing controller?
• RQ3 Can the stability and performance of a full amputee-prosthesis system be preserved when controlling only the prosthesis using local measurements?
• RQ4 How does the subsystem control law perform under changes in human body mass, assuming only force and motion data are available?

Key findings

• The subsystem control law achieves identical control inputs and system trajectories as a full-system feedback linearizing controller, confirming theoretical equivalency.
• The simulation results show perfect tracking of desired gait trajectories and stable periodic orbits in both knee and ankle joints across 100 walking steps.
• The controller maintains performance when human mass is increased by 24.9 kg, demonstrating robustness to human parameter variations.
• Phase portraits of the prosthesis subsystem confirm stable periodic behavior in both stance and non-stance domains.
• The method enables the use of advanced nonlinear control techniques on prostheses with formal stability guarantees, even when human dynamics are unknown.
• The framework is generalizable to other robotic systems interacting with dynamic environments, enabling model-dependent control with minimal system-level information.