Myoelectric Prosthetic Hand

Biomimetic Control of Myoelectric Prosthetic Hand Based on a

Akira Furui, Kosuke Nakagaki, And Toshio Tsuji

Abstract— Myoelectric prosthetic hands are intended to re- place the function of the amputee’s lost arm. Therefore, develop- ing robotic prosthetics that can mimic not only the appearance and functionality of humans but also characteristics unique to human movements is paramount. Although the impedance model was proposed to realize biomimetic control, this model cannot replicate the characteristics of human movements effec- tively because the joint angle always converges to the equilib- rium position during muscle relaxation. This paper proposes a novel biomimetic control method for myoelectric prosthetic hands integrating the impedance model with the concept of the λ-type muscle model. The proposed method can dynamically control the joint equilibrium position, according to the state of the muscle, and can maintain the joint angle naturally during muscle relaxation. The effectiveness of the proposed method is evaluated through simulations and a series of experiments on non-amputee participants. The experimental results, based on comparison with the actual human joint angles, suggest that the proposed method has a better correlation with the actual human motion than the conventional methods. Additionally, the control experiments showed that the proposed method could achieve a natural prosthetic hand movement similar to that of a human, thereby allowing voluntary hand opening and closing movements.

Index Terms— Prosthetics and exoskeletons, biomimetics, human-centered robotics.

I. Introduction

A study published by the cabinet office of Japan reported more than 82,000 upper-limb amputations due to accidents or disease . As a part of life support for upper-limb amputees, a myoelectric prosthetic hand is prescribed. The myoelectric prosthetic hand is controlled by inferring the amputee’s in- tentions from electromyogram (EMG), which is the electrical activity produced by muscles. As the myoelectric prosthetic hand can be manipulated voluntarily according to the muscle force exerted, there is a possibility that users would operate it as they use their hands. Hence, various related research and development have been developed in this regard.

Corresponding authors: Akira Furui and Toshio Tsuji. A. Furui and T. Tusji are with the Graduate School of Advanced Science

(E-Mail:

future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This paper is accepted for publication at the International Conference on Robotics and Automation 2021 (ICRA 2021).

Myoelectric prosthetic hands are designed to replace the function of the upper limb by replacing the lost arm. Thus, the prosthetic must realize human-like behavior that mimics the movements of the human hand in addition to its ap- pearance and operability. MyoBock is currently the most popular myoelectric prosthetic hand and enables control of two hand movements (grasp and open). Its appearance is improved by wearing a glove that resembles a human arm. In addition, the Vincent evolution 3 controls multiple fingers independently, making it possible to reproduce various types of human gripping motions. However, most myoelectric prosthetic hands studied and developed thus far use a simple proportional control to open and close the hand in response

To The Muscle Strength –. Therefore, Human Motion

characteristics have not been sufficiently considered for these myoelectric prosthetic hands, and human-like behavior has not been realized entirely.

Studies on biomimetic control of prosthetic hands have focused on reflecting the human motion characteristics in

The Prosthetic Hand –. The Authors Previously In-

troduced the impedance model-based biomimetic control

Method , To Control A Prosthetic Hand . This

model can realize natural human-like hand movements by controlling the actuators, considering the inertia, viscosity, and stiffness around the human joint. We showed that smooth movement according to the user’s EMG signals could be achieved through the experiments conducted on intact and amputee participants . However, in the impedance control, the equilibrium angle at the resting state is fixed at the origin as the equilibrium position of the spring, and in consequence, the joint angle always converges to the origin, regardless of its position. In contrast, if the actual human movement is considered, it is possible to maintain the joint angle during muscle relaxation after realizing the desired joint angle by muscle contraction. Therefore, the previously proposed impedance control is insufficient to replicate the characteristics of human movement.

For this problem, if we could develop a control system considering the movement characteristics of the muscles, it would be possible to control the equilibrium position of the joint angle dynamically, according to the contraction state of the muscles. Various theories have been proposed

To Model Muscle Dynamics –. Merton Proposed The

servo hypothesis (γ-model), assuming that the tonic stretch reflex is the primary motor control mechanism . Bizzi et al. proposed an α-model , relying on the hypothesis that the brain mainly controls the activity of α motor neurons.

Arxiv:2105.14215V1 [Cs.Ro] 29 May 2021

that the command from the central nervous system controls the threshold of the tonic stretch reflex. This model assumes that the muscle contracts when the muscle length is longer than the threshold, and conversely, when it is shorter, the muscle activity stops. The λ-model is prone to be superior to other models in that it can explain the entire voluntary movement of humans to some extent in a concise theory .

Thus, the theory has been used as a major motion control theory for several decades. This paper proposes a biomimetic control method for myoelectric prosthetic hands based on the impedance prop- erty of muscle and the concept of the λ-model. The pro- posed method can reflect human motor characteristics to the movement of the prosthetic hand by dynamically controlling the equilibrium angle of the joint according to the state of contraction/relaxation of the muscle. In the experiments, the effectiveness of the proposed method is verified through simulations and control experiments.

A. Impedance Control Model

First, based on impedance control , the characteristics of joint motion is represented by the tension balance between flexors and extensors (Fig. 1). The equation of motion around each joint j (j = 1, 2, . . . , J) of the prosthetic hand is

(1)

where Ij, Bj(αj), and Kj(αj) are the inertia, viscosity, and

J Are The Joint Angle And Its

equilibrium angle for stiffness element only. Furthermore, τjf and τje are the joint torque generated by the flexor and extensor, respectively. The change in the characteristics associated with muscle activity is expressed by defining the stiffness and viscosity as functions of the muscle contraction level αj (0 ≤αj ≤1).

Of The Complete System Can Be

calculated as the joint angle θj when ¨θ and ˙θ = 0.

B. Model Requirements

From (4), the torque τj(t) and the equilibrium angle θ0 of the joint angle can be varied adaptability to control the equilibrium angle of the model dynamically, according to the muscle contraction state. This study designs these variables to build a control model satisfying the following specifications.

• Specification 1: When the muscle relaxes, the equi- librium position is maintained at the value just before relaxation.

−

Fig. 1. Biomimetic impedance control based on the musculoskeletal model of human joint. (a) The characteristics of joint motion can be represented by the tension balance between flexors and extensors. By reflecting the impedance characteristics of human joints, natural and smooth control of the prosthetic hand can be achieved.

• Specification 2: Continuity of the equilibrium posi- tion is maintained even when the direction of motion changes from flexion to extension or extension to flex- ion.

When designing the model, it is desirable to consider all the muscle information for the joint movement. However, various muscles act when a person performs a complicated operation, such as flexing their fingers, and it is thus difficult to estimate all the muscle information on the joint motion from the EMG signals. Therefore, we switch the muscle contraction level depending on the classified motion as

Αje(T)

(Extension motion) .

(5)

Furthermore, the torque τjf, τje can be expressed as a

Is The Maximum Value Of Each Predetermined

torque, and the subscript i ∈{f, e} indicates flexor and extensor. Henceforth, we omit (t) to indicate a function of time, except when highlighting the temporal context.

C. Invariant Condition During Muscle Relaxation

We first design a model satisfying the specification 1. In the model design, we adopt the concept of the λ-model , which is a model of human muscle movements. The λ-model assumes that the brain achieves motion by controlling the muscle length x, while the intensity of the motor commands determines the threshold λ of the muscle length. Motion conditions of the muscle are formulated as follows: x −λ > 0.

(7)

The muscle is active if the condition of (7) expression is satisfied; otherwise, the muscle activity is stopped, and the current state is maintained. Here, the muscle activity level s in the λ-model is defined as a function of the muscle length x and threshold λ. Moreover, the muscle activity level is assumed to be a simple linear function that can be written

Command

Fig. 2. Invariant condition during muscle relaxation based on the concept of the λ-model. The silent and activation areas are provided by the muscle contraction level threshold eλ. The torque is generated only when the current muscle contraction level is in the activation area.

where G and h are constants. Equation (8) can be rewritten

X −Λ = 1

G(s −h).

(9)

Here, we assume that the constant G is the maximum value smax of s, and s/G in (9) can be regarded as the muscle contraction level αji. Furthermore, if the constant h/G is regarded as the threshold value eλji of the muscle contraction level, from the conditional expression (7), the muscle length x can be replaced by the muscle contraction level αji, and the muscle length threshold λ can be replaced by the muscle contraction level threshold eλji. Subsequently, the muscle activity condition in the control model is defined as follows: αji −eλji > 0.

(10)

Here, we introduce a function expressing the active state of the muscle using the activity condition (10) as follows:

(12)

where C+ is a function expressing the active state of the

I = 1 When Αji

is equal to or less than the threshold eλji. We consider that the joint angle varies when the muscular activity condition is satisfied and is maintained when the muscle is in an inactive state, according to the concept of the λ-model (Fig. 2). Then,

Ji (T −∆T) Is The Equilibrium Angle Before The

sampling time ∆t. Subsequently, we preform the control using muscle in- formation only in the flexion direction or extension direc- tion based on the constraint condition mentioned above. A separate model is defined for each direction, and control is achieved by switching between models. Under this condition, when a model is applied in a specific direction, the muscle contraction in the other direction is zero. Therefore, when the control is performed based on (13) and (14), the torque and the equilibrium position are discontinuous before and after switching the models. The continuity of the equilibrium position can be maintained by complementing the muscle contraction level in the other direction with the muscle contraction level in the classified direction. In cases other than co-contraction, it is assumed that one muscle contraction level gradually decreases as the other muscle contraction level increases. Based on this assumption, when the flexion direction is classified, the muscle contraction level αje in the extension direction is expressed using the muscle contraction

(15)

where Ae is a constant. Here, substituting (15) into (13) and expressing torque in the flexion direction, the control model

Ae(1 −Αjf)

(Flexion direction).

(16)

Similarly, when the extension direction is classified, the muscle contraction level αjf in the flexion direction is expressed using the muscle contraction level αje in the

(17)

where Af is a constant. Thus, the control model in the

(Extension Direction). (18)

From the above equations, considering the muscle activity condition based on the λ-model for muscle motion, we can construct a model that maintains the equilibrium position of the joint angle even when the muscle relaxes.

D. Continuity Condition for Switching of the Motion Direc-

Tion

We next consider the continuity of the equilibrium position at the time of changing the model to satisfy the specification 2. We consider that a model is applied in the extension direction at time te and then in the flexion direction at time te + ∆t. At this time, the equation of motion of the model

Je

αje(te).

(19)

The equation of motion of the model in the flexion direction applied at te + ∆t immediately thereafter is given as Ij ¨θj + Bj(αjf(te + ∆t)) ˙θj + Kj(αjf(te + ∆t))θj

Je

Ae(te + ∆t)(1 −αjf(te + ∆t)).

(20)

The equilibrium positions of (19) and (20) must be equal to maintain continuity at the time the model switches. Here, we assume that the state of motion is the steady state ( ¨θj, ˙θj = 0) just before switching the direction of motion.

Je

Ae(te + ∆t)(1 −αjf(te) + ∆t)}.

(22)

Solving the above equations for Ae and organizing it by substituting in equation (16), we obtain the following torque τjf expression, when the flexion direction is determined.

= Αjf(Te + ∆T) Is The Muscle

contraction level in the flexion direction immediately after switching. Similarly, when the model is applied in the flexion direction at time tf and there is a switch to the model in the extension direction at time tf + ∆t, the torques τjf and τje in the extension direction can be written as follows:

= Αje(Tf + ∆T) Is The Muscle Con-

traction level in the extension direction immediately after switching. Finally, using (1), (23), and (24), the control model for the direction i ∈{f, e} is obtained as follows:

Ji

.

A. Methods

Numerical simulation using artificial data was conducted to study whether the control model satisfies the design specifications. For simplicity, the number of joints was j = 1, and the change in the equilibrium angle θeq was confirmed

Ij: [Kgm2], B1, B3: [Nms/Rad], K1, K3: [Nm/Rad]

for the two types of input signals.

Otherwise

.

2

if 5 ≤t ≤30 s .

(31)

Here, αf and αe were assumed to be the muscle contrac- tion level obtained from the flexor and extensor muscles, respectively. The threshold eλi was defined as the maximum value of the muscle contraction level in the classification section. In addition, the section where αf > αe represents the classification section of the flexor muscle while the section where αf < αe represents the classification section of the extensor muscle. In this experiment, only the muscle contraction level of the classified muscle was used as the input of the control model. The impedance parameters were set to the values of the wrist joints (Table I) measured in a previous study .

B. Results And Discussion

Fig. 3 shows the artificially generated muscle contraction level αi and the equilibrium angle θ0 of the joint obtained from the numerical simulation for (a) Input 1 and (b) Input 2. The direction of joint extension is defined as positive, and the shaded area in the figure represents the section of muscle relaxation.

In Fig. 3, when flexors are classified, the equilibrium angle transitions into a negative direction. In contrast, when extensors are classified, the equilibrium angle transitions into a positive direction. When considering the muscle re- laxation section, the equilibrium angle was maintained at the same level as before muscle relaxation. Furthermore, the equilibrium angle changes continuously and smoothly

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