Proceedings of 2017 IEEE International Conference on Mechatronics and Automation August 6 - 9, Takamatsu, Japan
An Innovative Bio-Robot Imitating the Cervical Spine Behaviors During the Rotation-Traction Manipulation Jian Li, Guancheng Li,Zhen Chen and Xuefei Mao
Minshan Feng and Liguo Zhu
Liwei Shao
School of Automation Beijing Institute of Technology Beijing, China { yellowlightlee & bit_lgc}@163.com {chenzhen76 &mxf14}@bit.edu.cn
Wangjing Hospital Chinese Academy of Traditional Chinese Beijing, China
[email protected] Research Institute of BIT in Zhongshan
should be taken into account primarily. Mechanical principle and control strategy could be applied to solve biomechanical problems due to fact that the living tissue has the loadtransmitting mechanism [6]. The biomechanical behaviors have been studied from two aspects such as in vivo and in vitro [7], [8], [9]. On the one hand, the desired mechanical parameters such as displacement, velocity, acceleration and external force are directly measured using dedicated sensor systems. On the other hand, during the RT process, a suitable control scheme is indispensable for regulating the contact force between the robot and physician to simulate the actual movement of neck and interactive force. The impedance control is widely applied for its simplicity and acceptable performance, which controls the robot to interact with the environment compliantly by establishing a virtual mass-springdamper system [10], [11]. Based on the actual biomechanical behavior and humanrobot interaction trait, this paper designs the clinical simulation robot with excellent electromechanical system and appropriate control strategy. Moreover, the RT manipulation simulation robot consists of torso and neck. In our previous research, the combination of a nonlinear spring and an electromagnetic clutch was designed to capture the biomechanical behaviors of cervical spine robot during the RT manipulation. There are two contributions in this work. Firstly, the neck motion and interactive force could be simulated by the position-based force tracking impedance control. Secondly, the robot could evaluate the accuracy of the force in direction and amplitude during the RT process. The rest of this paper is organized as follows. An innovative mass-spring electromagnetic clutch model is proposed to capture the biomechanical features of the cervical spine in Section 2. The proposed impedance control scheme is described and its simulation and tracking performance are analyzed in the subsequent section. Moreover, experiments are implemented to verify the effectiveness of the cervical spine robot system.
Abstract - This article demonstrates an innovative humanoid robot applied in the Rotation-Traction (RT) manipulation practice and evaluation process. A mass-spring mechanical system with an electromagnetic clutch was designed to emulate the cervical spine and a 3DOF non-planar model with impedance control algorithm is built to replace the neck part. The robot could imitate the entire dynamic response of human cervical spine in the RT manipulation process. Test results reveal that the cervical spinal robot can faithfully replicate the biomechanical properties of the human cervical spine during RT manipulation and it is helpful in training and evaluating interns. Index Terms - robotics; adaptive impedance control; rotationtraction manipulation; cervical spine model; biomechanical;
I. INTRODUCTION Cervical spondylosis is a common disease of cervical spine, which is part of the aging process and affects most people [1]. More specifically, 95% of patients by the age of 65 are suffering from degenerative disorders of the spine [2]. However, most surgical approaches are still controversial and can cause undesired side effects [3]. Together with drug therapy, cervical traction as a nonsurgical regimen constitutes the mainstay of the treatment [4]. RT manipulation is an important TCM (Traditional Chinese Medicine) nonsurgical manner for cervical spondylosis, which has the characteristic of simple and fast operation and effective therapeutic modalities. Cervical spondylosis could affect the intervertebral disks, vertebrae, facet joints and ligamentous structures encroach even spinal cord while RT manipulation is an effective remedy to improve these symptoms [1], [5]. In medical field, clinical experience is the most precious asset for physician, the lack of which could cause inadvertent errors, resulting in medical malpractice events ranging from soft tissue contusion to serious spine injury. Therefore, a device which could simulate the biomechanical characteristics and substitute for real human spine is of necessity during RT manipulation. As automation, control theory, mechanical technique and medical technology continue to integrate, robotics is an emerging comprehensive technology which can be applied in clinical medicine area. With the aim of simulating the human cervical spine, the accurate biomechanics characteristics
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[email protected] II. CERVICAL SPINE MODELLING AND MECHANICAL DESIGN As the living tissues possess the linearly viscoelastic characteristic, the normal contact force is modelled by parallel or/and serial combination of linear springs and linear dashpots [13], [14], [15]. Considering the RT manipulation process, the 1614
biomechanics of cervical spine is captured by a nonlinear spring positioned in parallel with linear dashpots [12]. However, the spine consists of skin, muscle, cartilage and ligaments so that the effectiveness of linear dashpots is less significant. Moreover, an electromagnetic force limiter emulates the facet-sliding phenomenon during the jerky action and generates the spiky acceleration.
Fr = 4 Fh tan α
(3) = 4k [σ + R(1 − cos α )] tan α . Therefore, the stiffness of the nonlinear spring is obtained dF R +σ K = r = 4k − 1 3 dx R α cos . (4) 1+ σ R = 4k 3 2 2 2 (1 − x R ) According to (4), the stiffness of the nonlinear device corresponds with the preloaded distortion spring stiffness and curvature radius. The electromagnet imitates the facet-sliding phenomenon during the jerky action, where the attractive force must lie between the maximum preloaded force and the maximum applied force [12]. The electromagnetic force in the air gap is computed by Bg2 Aa . (5) Fem = 2 μ0 where Bg represents the magnetic flux density in the air gap,
A. Rectilinear Nonlinear Spring and Electromagnet Model The nonlinear spring device is composed of an axially symmetric slide curvilinear support surfaces and four springbearing-roller sets placed in radial symmetry as shown in the Fig. 1(a). With the cam rollers pressing tightly against the curvilinear surfaces, the slider could move up and down along its guide rod. Several curvilinear surfaces with different curvatures could be tangentially joined together to form the support surfaces. F(t) Helical Spring
Linear Bearing
Cam Roller
Supporting Surface
(a)
Initial Position x dx
Aa represents the corresponding cross-sectional area and μ0 is the permeability of free space. During the jerky action, the dynamic of the spine model is described as following: F (t ) = ( M + m)( x + g ) + μ1 x + Fspring ( x) + Fem (6)
Slider
Front view
where, M denotes the gross mass of the head and slider, m represents the armature mass which could be neglected. Besides, Fspring and Fem are restoring force of the nonlinear
Undeflected Position of Roller R
spring and electromagnetic force, respectively. In addition, g represents the gravitational acceleration, x denotes the
r
displacement of the nonlinear spring and μ1 is the damping coefficients of the guide rod.
(b) Force analysis Fig. 1 Front view and force analysis of the nonlinear spring
B. Mechanical implementation Fig. 2 displays the rear view of the real robot and schematic diagram of the torso part consisting of the nonlinear spring and electromagnet. The slider could only slip vertically along the guide rods. Besides, the cam roller are pressed tightly against the support surfaces by the helical spring which has a preloaded deformation adjusted by a hand wheel.
In each instantaneous state, the support surface possesses a curvature radius R. The force analysis on a cam roller is displayed in the Fig. 1(b), where Fh represents the restoring force from the helical springs, Fn and Fv are normal and tangential components of the support force, respectively. Here, r denotes the radius of the cam roller and x represents the displacement of the slider related to the reference position. Moreover, m gives the mass of the slider and head and k is the stiffness of the spring. Besides, F (t ) stands for the external force and the deflected angle α is calculated by x α = arcsin( ) . (1) R The spring deformation is s = R (1 − cos α ) x . Correspondingly, the restoring force of the helical spring is Fh = k (σ + s) = k [σ + R (1 − cos α ) ] , (2) where σ represents the preload distortion of linear spring. As the mass of nonlinear spring is not dominant, the resilient force, excluding the gravity bias, satisfies the equation
(a)
Rear view
(b) 3D model of mechanism structure
Fig. 2 The rear view of the real robot and the 3D model of the nonlinear spring mechanism with the electromagnet
The neck part consists of a 3-DOF non-planar structure and a head. The head fixed on the pedestal could rotate and pitch independently even be lifted vertically along the guide rods, which could imitate human head movements. Each
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θ e which is the difference between actual joint angle θ and desired joint angle θ d .
revolute joint is actuated by a DC brush motor, which is equipped with a harmonic reducer. Moreover, the joint torque is measured by the torque sensor and the position is measured by the encoder. The 3D and physical model is shown in the Fig. 3.
Position Sensor
+ +
Inverse kinematics
-
Position Controller
+
Robot
Kinematics
Position Control Loop Impedance Control
Envrionment Stiffness
Force Sensor
Fig.4 The framework of the position based impedance control
According to the controller structure, the position of endeffector is obtained by
Fig. 3 The 3D and physical model and of the cervical spine robot
Xd = Xr +
III. ADAPTIVE IMPEDANCE CONTROL APPLIED IN THE SIMULATION ROBOT
F , M d s 2 + Bd (θ ) s + K d (θ )
(10)
which has a characteristic of compliance. The biodynamic effect of human neck could be simulated by selecting appropriate parameter values, namely Bd (θ ) and K d (θ ) . However, it is difficult to choose the appropriate value to establish an accurate mode.
A. Position-based Impedance Control(PBIC) During the RT manipulation process, the physician tracts the patient’s head upwardly with his/her forearm tightly against patient’s mandible. To address the interactive task, the hybrid force-position control is applied to robotics for the first time [16]. Instead of controlling forces and motions in orthogonal directions, the impedance control strategy provides a unified framework controlling a manipulator both in freespace and in compliant motion [10]. The mass-damper-spring relationship between the external force F and position X is the core of the impedance controller. The desired impedance equation of the simulation robot can be expressed as (7) M d ( Xr - X ) + Bd ( X r - X ) + K d ( X r - X ) = F
B. Indirect Adaption Force Tracking Impedance Control In order to imitate the tactile feedback of interact force during the RT manipulation process, the force tracking impedance control within PBIC is suggested. As the traditional impedance control lacks the force tracking capability [17], the improved target impedance function is obtained [18] M d E + Bd E + K d E = Fe − Fd , (11) where Fd and Fe are the desired and actual contact force. Although the force tracking problem can be solved through modification of the impedance formulation, there are other problems related to unknown environment such as environment stiffness and environment position. From a practical viewpoint, it is assumed that the robot is equipped with perfect position control loop. We can consider each Cartesian variable independently and replace the upper-case vectors by lower-case scalars. Commonly, the environment is represented by a linear spring with stiffness k e , and hence the measured contact force is f e = ke ( x − xe ) [19]. Under this assumption, the force tracking error is given by
where K d ， Bd ， M d are 3 × 3 user-specified symmetric and positive definite inertia, damping and stiffness matrices of the system. Moreover, F represents a 3 × 3 force vector on behalf of the force acted on the end-effector, and X , X r are 3×1 vectors denoting the actual position and reference position [17]. Define E = X d − X , E = X d − X and E = Xd − X , (7) can be simplified as: M d E + Bd E + K d E = F . (8) After the Laplace transformation, (8) could be rewritten as (9) ( M d s 2 + Bd s + K d ) E ( s ) = F ( s ) .
e e = f r − f e = f d + ke xe − ke xr + 2 . ms bs k + +
(12)
The steady-state force tracking error is obtained as
It is noted that in the viscoelastic model of human neck, the stiffness and damping is non-linear, and it is difficult to establish an accurate model. Therefore, the stiffness and damping parameters are expressed by K d (θ ) and Bd (θ ) . The framework of PBIC is displayed in Fig. 4. Here, X r is the reference position of the end-effector and e
ess =
k [ f d + ke ( xe − xr )] . k + ke
(13)
Now from (13), we could conclude that when the reference position trajectory is chosen precisely as xr = xe +
represents the position deviation caused by the external force Fext measured by force sensor. In addition, θ d represents a commanded joint angle calculated by the position of the end-effector X d , based on the inverse kinematics formula. Then the input of the position controller is the angle error
fd ke
(14)
then we have ess = 0 . In other words, if we know the precise location of the environment xe and the exact value of the environment stiffness k e , we can generate the position trajectory according to (14).
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The indirect adaptive control strategy estimates the environmental parameters on-line and the required reference position is generated based on the estimations [19]. Assuming that the estimated value of the environment stiffness and position are kˆe and xˆe , respectively. Therefore, the estimation
t
m( x − xr ) + b( x − xr ) + k ( x − xr ) = k p e f + ki e f dτ + kd e f (22) 0
There are two independent PID controllers which are used to accelerate the convergence of the actual contact force to the desired value. According to (12), the actual position x can be obtained by x = xe + ( f r − e ) ke . Substituting the actual position and its first and second order derivatives into the new target impedance model yields the force error differential equation.
of the contact force fˆe is obtained fˆe = kˆe ( x − xˆe ) = kˆe x − kˆx .
(15)
φ kˆ − k Defining φ = k = e e , and differencing estimated φx kˆx − k x
t me + (b + ke kd )e + (k + ke k p )e + ke ki edτ = mfr 0
+ bfr + kf r − ke (mxr + bxr + kxr ) + kke xe
contact force and ideal value yields fˆe − f e = [ x − 1]φ .
(16)
Then the steady state force error is obtained as (24).
Our task is to devise a scheme for adjusting kˆe and xˆe based on the force error so that fˆ → f when t → ∞ . e
s →0
Obviously, if the numerator equals to zero with a non-zero denominator, the system is stable. Then the trajectory of the end-effector is obtained as
Supposing fˆe → fe could be well achieved and thus f e → f r . The update law is derived by the Lyapunov-based approach. As to the (12), the following positive quadratic Lyapunov function is specified V = φ T Pφ (17) where P represents a symmetric positive-definite constant matrix. Assuming φ is specified as x
X r ( s) =
e
(18)
-
e
+
Robot
Ke Impedance Control
η2 )dt (21) η1 kˆe 0 From a practical point of view, the contact force measured by sensor is often a noisy signal and as a result, the differentiation of it is undesired. As e = f r − f e = f d − ke ( x − xe）has been obtained, considering the variation rate of xe is very small in the RT manipulation process, which could be neglected. Therefore, e = fr − fe = fr − ke x where f r is artificially specified time-varying reference force imitating the actual tactile sense. The impedance function acts as a second order low pass filter and the force signal is converted to the position signal. The framework of the PBIC consists of outer force loop and inner position loop. As the controlled force is generated by position trajectory, the larger the inner loop gains, the faster the actual force approaches the desired value [22]. In order to modify the contradiction brought by lager inner loop gain and improve the robustness, the force error is supposed to be modified. The novel improved impedance target function with the PID compensator to the force error e f is suggested. t
Position Controller Position Control
( fˆe − f )( xxˆe +
Trajectory Designer
Parameter Estimation
Adaptive Control
-
Force Sensor
+
Fig. 5 The framework of indirect adaptive force tracking impedance control
C. Force Tracking Simulation For simplicity, the model used in the simulation is a single joint and the following initial conditions are specified, where q (0) = q (0) = 0 . Initially, the desired environment information is selected as X e = 0.1 and K e = 30 . In addition, the desired force is Fd = t 2 and the parameters of the adaptive law are selected as η1 =50 and η 2 =4 . Ke (N/m)
η1
(25)
Position Sensor
(19)
Therefore, the underlying asymptotically stable conditions for the system is derives. Direct calculation of (18) yields the complete indirect adaptive time varying force tracking schemes [20]. t (20) kˆe (t ) = kˆe (0) − η1 x ( fˆe − f e )dt 0 xˆe (t ) = xˆe (0) +
Fr ( s ) kx + 3 e2 . ke ms +bs +ks
According to the adaptive law, the environment stiffness and position could be estimated based on the force error. With the estimates, the desired force could be specified as timevarying, which could imitate the interactive force during the RT manipulation process. The framework of indirect adaptive force tracking impedance control is shown in the Fig. 5 where the input of position control X c is equal to the actual position X according to our assumption.
and differentiating (17) along (18) yields the negative semidefinite function x V = 2φ T Pφ = −2φ T ( fˆe − f e ) . −1 2 = −2( fˆ − f ) ≤ 0
(ms 4 + bs 3 + ks 2 )( Fr ( s ) − ke X r ( s ) + kke xe s ) (24) s →0 ms 3 + (b + ke kd ) s 2 + (k + ke k p ) s + ke ki
ess = lim sE ( s ) = lim
e
φ = − P ( fˆe − f e ) , −1
(23)
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Self-positioning
Preload Procedure
Jerky Action
Restitution
Fig. 8 The whole RT manipulation process in the experiment Fig. 6 The identificaiton of envrioment parameters
Table I COMPARISON OF PARAMETER VALUES FOR CORRECT MANIPULATION AND EVALUATION CRITERIA. Preload Jerky Max Force(N) Force(N) Force(N)
The identification accuracy of the two environmental parameters could be seen in Fig. 6. At the starting of the identification, the performance is not satisfying. The identification curve could be modified by changing the parameters of η1 and η 2 . The parameters of the impedance controller are selected as m = 10 , b = 40 and k = 40 , which represents a critically damped second-order manipulator environment system. The contact force increases rapidly within 0.5 second. The force tracking error is mostly due to the corresponding trajectory tracking performance, which has been illustrated in the above figures. The Fig. 7 demonstrates an admirable transient and steady force tracking performance, which illustrates the efficacy of the proposed force control scheme in time-varying force tracking.
Physician
250
152
335
Standard
230.3±48.8
173.5±54.5
362.1±74.4
We can see that the maximal preloaded force, jerky force and maximal force of the test RT manipulation all fall into the allowable ranges. Exactly, this RT manipulation is not qualified because the jerky action time of the standard process is between 90 milliseconds and 130 milliseconds [12]. The jerky action here is not qualified.
Fig. 9 The amplitude of the external force in the RT manipulation
There are two peaks existing in the force-time waveform and the second peak is much higher than the first. The traction force increases gradually at first, and subsequently decreases to a certain extent in the retraction for the jerky action. The acceleration of the RT manipulation process is illustrated in the following figure. The head acceleration jumps positively to its maximum in response to the maximal applied force then decreases rapidly when the exerted force disappears. The jerky action is the key component in the whole process, which could be described as a high-speed, low-amplitude, one-dimension impulse motion.
Fig. 7 The time-varying force tracking performance of indirect adaptive impedance control
IV. EXPERIMENTAL VERIFICATION AND ANALYSIS Experiments were implemented to verify whether the cervical spine robot could reproduce the biomechanical properties of the human cervical spine, and to evaluate the performance during RT manipulation training.
A. Force Amplitude Detection of RT Manipulation The whole RT treatment process can be partitioned into four steps: head self-positioning, preload procedure, jerky action and restitution [12]. The integrated process is shown in the Fig. 8, which is manipulated by a volunteer. Biomechanics is analyzed when external forces are exerted by the physiologist [7]. A large amount of tests on volunteers with different ages, genders and weights have been done by Wang Jing hospital, which have obtained the eligible acceleration, displacement and force versus time evolution curves during the standard RT manipulation process [12]. The test data which are plotted in the Fig. 8 and the standard data range are illustrated in the Table 1.
Fig. 10 The variation of acceleration in the RT manipulation
B. Force Direction Detection of RT Manipulation When an upward external force is imposed on the head, it can be decomposed into two perpendicular axes. If the direction of the force is not appropriate, it dose great harm to the patient’s stiff cervical spine. For example in Fig. 11, the direction of the external force Fext 2 is not vertical upward like
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the Fext1 , both of the two decomposed forces can be vertical to the link 2, which will generate a rotation trend on joint 1.
Equipment and Technology of Automation Research and Development Platform under Grant 2016F2FC007.
Fext1
REFERENCES
Fext2
y1
[1] x1
Joint2
[2]
θ2
z1
Link1 y0
z0 θ1 Joint1
Link2
.
[3]
x0
Fig. 11 Force schematic when external force on the robot
The following figure shows the joint torque detected during the RT manipulation process. During the preload and jerky action, the head is applied by the external force. Distinctly, the joint 2 is rotated by a horizontal component force which is beyond the range, so is improper for RT manipulation.
[4] [5]
[6] [7] [8]
[9]
[10] [11]
[12]
Fig. 12 The torque of each joint during the RT manipulation process
V. CONCLUSIONS
[13]
In this paper, the biomechanical properties of spine in the RT manipulation is revealed based on the spine model which consists of two parts. The rectilinear nonlinear spring is proposed to capture the stiffness variation of the cervical spine due to the large strain. The electromagnet is set to imitate the sliding phenomenon occurred during the jerky action of the RT manipulation. In addition, the indirect adaptive force tracking impedance strategy is applied to the neck part, which simulates the actual interactive force and then verified by MATLAB simulation. Finally, the cervical spine robot system is implemented. The experimental results show that the cervical spine robot can faithfully replicate the biomechanical properties of the human cervical spine during the RT manipulation. In the one hand, it could evaluate the pace and amplitude of the force. On the other hand, the direction of the force can also be detected.
[14]
[15]
[16]
[17]
[18] [19]
[20]
ACKNOWLEDGMENT This work is supported by National Nature Science Foundation of China under Grant 81473694 and major project of Zhongshan city under Grant 2016A1027, and Intelligent
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