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Research Papers

A Synergy-Based Motor Control Framework for the Fast Feedback Control of Musculoskeletal Systems

[+] Author and Article Information
Reza Sharif Razavian

Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: rsharifr@uwaterloo.ca

Borna Ghannadi

Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: bghannad@uwaterloo.ca

John McPhee

Fellow ASME
Professor
Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: mcphee@uwaterloo.ca

1Corresponding author.

Manuscript received April 16, 2018; final manuscript received November 14, 2018; published online January 25, 2019. Assoc. Editor: Eric A. Kennedy.

J Biomech Eng 141(3), 031009 (Jan 25, 2019) (12 pages) Paper No: BIO-18-1185; doi: 10.1115/1.4042185 History: Received April 16, 2018; Revised November 14, 2018

This paper presents a computational framework for the fast feedback control of musculoskeletal systems using muscle synergies. The proposed motor control framework has a hierarchical structure. A feedback controller at the higher level of hierarchy handles the trajectory planning and error compensation in the task space. This high-level task space controller only deals with the task-related kinematic variables, and thus is computationally efficient. The output of the task space controller is a force vector in the task space, which is fed to the low-level controller to be translated into muscle activity commands. Muscle synergies are employed to make this force-to-activation (F2A) mapping computationally efficient. The explicit relationship between the muscle synergies and task space forces allows for the fast estimation of muscle activations that result in the reference force. The synergy-enabled F2A mapping replaces a computationally heavy nonlinear optimization process by a vector decomposition problem that is solvable in real time. The estimation performance of the F2A mapping is evaluated by comparing the F2A-estimated muscle activities against the measured electromyography (EMG) data. The results show that the F2A algorithm can estimate the muscle activations using only the task-related kinematics/dynamics information with ∼70% accuracy. An example predictive simulation is also presented, and the results show that this feedback motor control framework can control arbitrary movements of a three-dimensional (3D) musculoskeletal arm model quickly and near optimally. It is two orders-of-magnitude faster than the optimal controller, with only 12% increase in muscle activities compared to the optimal. The developed motor control model can be used for real-time near-optimal predictive control of musculoskeletal system dynamics.

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Figures

Grahic Jump Location
Fig. 1

The hierarchical structure of the proposed synergy-based motor control framework. The high-level controller is responsible for task space control, and outputs the task space force, Fref. The low-level F2A controller translates this force command to muscle activations, u.

Grahic Jump Location
Fig. 2

The schematic of the force-to-activation (F2A) mapping. An arbitrary force vector (black arrow, Fref) can be decomposed onto the basis set Bi to find the corresponding coefficients. The same coefficients can then be used to combine the synergies to calculate the muscle activities, u, that result in the reference force, Fref. In this illustration, the task space is 3D (p =3), and only four synergies (k =4) are shown to demonstration the concept. See online for color version.

Grahic Jump Location
Fig. 3

(a) The experimental setup includes a 2DOF haptic robot to measure force/position in the 2D task space. The arm is lifted above the table surface to support its weight and minimize friction. (b) The setup configuration in phase one of the experiment. The robot is locked in any of the nine points in the task space, and the subject has to match the target forces by pushing against the robot.

Grahic Jump Location
Fig. 4

(a) The schematic of the 3D 4DOF arm model. (b) The 3D task space, containing (x, y, z) position of the hand, and the redundant space containing the kinematic variable ϕ. Here, the rotation specified by the angle ϕ is irrelevant to the reaching task.

Grahic Jump Location
Fig. 5

A large number of optimization problems are solved off-line to obtain the synergies that are used in the simulations. In a given posture, an optimization is solved to find the optimal muscle activations that produce each of the desired task space accelerations (ades). The same process is repeated for a variety of postures.

Grahic Jump Location
Fig. 6

The 2D experimental results. The data belong to subject #2. (a) The synergies obtained by applying the NNMF to the experimentally measured EMG data. Each plot shows the activity level of the muscles in a synergy change across posture (See online for color version). (b) The basis vectors associated with the posture-dependent synergies. (c) The motion and force in the task space during the motion trials. The motion is divided into five segments (color coded). (d) The measured EMG and the reconstructed activations for the seven muscles and for each motion segment. The gray and black lines, respectively, show the measured EMG data, and the reconstructed muscle activations. Each line represents a single trial. The numbers in each plot give the calculated VAF. The bold numbers on the right and the bottom are the average for the row or column of data, respectively. The single large number on the bottom right is the average of all VAF measures.

Grahic Jump Location
Fig. 7

The 3D simulation results. (a) The synergies visualized in the task space. Each plot shows the activity level of the 15 muscles in a synergy, as the hand moves in the task space (See online for color version). The x and y axes indicate the position of the hand (cm), and the vertical axis shows the muscle share in a synergy. These plots belong to the posture where the hand's vertical position is 20 cm below the shoulder (z = −0.2 m), and ϕ = 0 deg. More detailed synergy plots are available in the Supplemental Material which is available for this paper on the ASME Digital Collection. (b) The basis vectors in the task space. The units are m/s2. These basis vectors belong to the posture (x, y, z, ϕ) = (15 cm, −20 cm, −20 cm, 0 deg). (c) The trajectory for the hand position (moving 20 cm upwards), the tracking error, and the motion in the redundant space. Two control methods are compared: an optimal controller, and the synergy-based motor control model. (d) The muscle activations resulting from the two control methods.

Grahic Jump Location
Fig. 8

The effect of number of synergies on the performance of the motor control framework. (a) The experimental results belonging to subject #2. (b) The simulation results. Because the NNMF is sensitive to the initial guesses, multiple runs of NNMF are performed. The plots show the mean and standard deviation of the results. When a small number of synergies are used, the variability is small. (a) Experiment and (b) simulation.

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