Research Papers

A Novel Theoretical Framework for the Dynamic Stability Analysis, Movement Control, and Trajectory Generation in a Multisegment Biomechanical Model

[+] Author and Article Information
Kamran Iqbal1

Department of Systems Engineering, University of Arkansas at Little Rock, 2801 South University Avenue, Little Rock, AR 72204kxiqbal@ualr.eduNewman Laboratory for Biomechanics and Human Rehabilitation, Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02319-4307kxiqbal@ualr.edu

Anindo Roy

Department of Systems Engineering, University of Arkansas at Little Rock, 2801 South University Avenue, Little Rock, AR 72204anindo@MIT.eduNewman Laboratory for Biomechanics and Human Rehabilitation, Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02319-4307anindo@MIT.edu


Corresponding author.

J Biomech Eng 131(1), 011002 (Nov 18, 2008) (13 pages) doi:10.1115/1.3002763 History: Received February 06, 2006; Revised August 29, 2008; Published November 18, 2008

We consider a simplified characterization of the postural control system that embraces two broad components: one representing the musculoskeletal dynamics in the sagittal plane and the other representing proprioceptive feedback and the central nervous system (CNS). Specifically, a planar four-segment neuromusculoskeletal model consisting of the ankle, knee, and hip degrees-of-freedom (DOFs) is described in this paper. The model includes important physiological constructs such as Hill-type muscle model, active and passive muscle stiffnesses, force feedback from the Golgi tendon organ, muscle length and rate feedback from the muscle spindle, and transmission latencies in the neural pathways. A proportional-integral-derivative (PID) controller for each individual DOF is assumed to represent the CNS analog in the modeling paradigm. Our main hypothesis states that all stabilizing PID controllers for such multisegment biomechanical models can be parametrized and analytically synthesized. Our analytical and simulation results show that the proposed representation adequately shapes a postural control that (a) possesses good disturbance rejection and trajectory tracking, (b) is robust against feedback latencies and torque perturbations, and (c) is flexible to embrace changes in the musculoskeletal parameters. We additionally present detailed sensitivity analysis to show that control under conditions of limited or no proprioceptive feedback results in (a) significant reduction in the stability margins, (b) substantial decrease in the available stabilizing parameter set, and (c) oscillatory movement trajectories. Overall, these results suggest that anatomical arrangement, active muscle stiffness, force feedback, and physiological latencies play a major role in shaping motor control processes in humans.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Schematic of the four-link biomechanical model over stationary BOS. In the figure, mi and li(i=1,2,3) represent the mass and length of the leg, thigh, and HAT segments, respectively; ki is the location of segment COM, Ii is the moment of inertia of the segment; θi are the segment angles measured from the horizontal; lf and mf are the length and mass of the foot; τi are the ankle, knee, and hip torques; Fx,Fy are the horizontal and vertical ground reaction forces (GRFs); and g is the acceleration due to gravity.

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Figure 2

Conceptual block diagram of the human musculoskeletal-proprioceptive system with position, velocity, and force feedback. In the figure, G̃I represents the linearized skeletal dynamics; G̃m represents the muscle model; R̃ represents the muscle moment arm matrix; G̃c represents the neural PID controllers; G̃GT represents the GTO model; G̃1 and G̃1∗ represent the MS model with position and velocity inputs; Δ̃m and Δ̃g represent the MS and GTO loop delays; K̃θp and B̃θp represent the passive joint stiffness and viscosity; K̃ms and B̃fv represent the active muscle stiffness and viscosity; θ̃∗ represents the intended joint angles; θ̃ represents the instantaneous joint positions underlying movement; and M̃e represents an external perturbation.

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Figure 3

Schematic illustrating family of stabilizing neural PID controllers in the 3D controller parameter space. Each stabilizing proportional gain, Kp, defines a convex region or half-plane in the integral-derivative Ki-Kd parameter space. The loci of convex planes constitute the stabilizing controller space that is valid for both trajectory tracking and disturbance rejection problems.

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Figure 4

The controller design methodology for stability characterization illustrated via flow chart. The ranges of the stabilizing knee and hip PID controller gains are chosen via internal stability considerations; the ranges of the stabilizing ankle controller gains are chosen by the intersection of closed-loop stability and internal stability.

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Figure 5

Predicted joint kinematics for the ankle, knee, and hip DOF for the four-segment musculoskeletal model in response to a third-order S-shaped input trajectory (τ=100 ms): (a) movement trajectories, zero steady-state error illustrates dynamic stability for the tracking problem; (b) bell-shaped velocity profiles; (c) smooth biphasic acceleration profiles; (d) joint toques; and (e) muscle forces. The maximum muscle forces are bounded within the maximum isometric forces that the muscles are capable of generating.

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Figure 6

Sensitivity and dynamic stability investigation in the case of the four-segment musculoskeletal model with respect to impaired proprioception and model nonlinearities in response to a third-order S-shaped input trajectory (τ=100 ms): (a) 50% reduction in spindle gains, (b) 90% reduction in spindle gains resulting in predicted trajectories that become oscillatory, (c) removal of force feedback that results in ringing in joint position profiles (time is in milliseconds), (d) removal of physiological latencies, and (e) comparison of the movement trajectories for the linear (solid) and nonlinear (dashed) models.



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