Research Article
The man-machine motion planning of rigid-flexible hybrid lower limb rehabilitation robot
Advances in Mechanical Engineering 2018, Vol. 10(6) 1–11 Ó The Author(s) 2018 DOI: 10.1177/1687814018775865 journals.sagepub.com/home/ade
Ke-Yi Wang , Peng-Cheng Yin, Hai-Peng Yang and Xiao-Qiang Tang
Abstract At present, in view of the question that the general lower limb rehabilitation training robot is only achieving motion training of lower limb’s flexion and extension. A kind of the lower limb rehabilitation robot is conceived which can achieve lower limb adduction or abduction and internal or external rotation in sports training, and it is aimed to research the robot’s structure and motion planning. When analyzing the typical movement forms of the lower limb, the relation of man–machine coordinated movement is also considered. A kind of lower limb rehabilitation training robot is conceived, which consists of the rigid mobile device and the flexible drive system. The influence coefficient method is used to analyze the kinematics of the robot. According to the rehabilitation training of man–machine cooperation relations, the trajectory planning strategy is studied. A robot configuration that meets the needs of rehabilitation motion trajectory planning is drawn by setting the parameters of the robot mechanism and simulation. According to the trajectory of the training program, the simulation analysis of the state of wire movement is carried out. The experimental study of adduction and abduction of the lower extremities was carried out, proving the effectiveness of robot mechanism. Keywords Wire traction, rehabilitation robot, adduction and abduction, internal and external rotation, motion planning
Date received: 6 March 2018; accepted: 10 April 2018 Handling Editor: Jose Antonio Tenreiro Machado
Introduction With the fast pace of modern life and lifestyle changes, from the treatment of stroke and infantile paralysis patients to muscle rehabilitation, besides early surgical treatment, recovery training is very important in the later stage.1 In recent years, it has gradually been recognized by the society that the rehabilitation training methods used to replace the traditional physical exercise therapy.2 T Noda et al.3 combined wires with the muscles of an electric cylinder to effectively increase the torque and better recover the muscles of the upper extremities. CJ Nycz et al.4 added soft cords to the upper body rehabilitation facility to provide finger and elbow movements and to imitate the function of the tendons in a biological manner. There are many developments in the structure and control of upper limb
rehabilitation robots that are not described here. Overall, this design provides an extended platform and studies the concept of soft robot rehabilitation. According to the functional of the lower limb rehabilitation training robot, it is divided into the multifunctional lower limb rehabilitation robot (LLRR) and local functional rehabilitation robot. The former robot aims at rehabilitation training for the whole lower limbs, and the latter specifically aimed at a joint or part College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin, China Corresponding author: Ke-Yi Wang, College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China. Email:
[email protected]
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage).
2 of the lower limb and targeted implementation of rehabilitation training. The rigid mechanism of robot structure often appeared in the gait rehabilitation training of the lower limbs. The Free University in Germany developed an LLRR, Mechanized Gait Trainer (MGT),5 the gait mechanism of which adopted a crank rocker mechanism, only 1 degree of freedom (DoF), single function, so it cannot achieve complex motions. Swiss Federal Institute of Technology in Zurich developed the Lokomat LLRR,6 in which the wearing device with 4 rotational DoFs is used to drive the legs of the trainers to achieve gait movement, but the whole mechanism was complex and expensive. The University of Birmingham developed a 6-DoF parallel robot to perform various rehabilitation exercises,7,8 which can simulate different foot trajectories. The research of this aspect in China also made some progress: Harbin Engineering University developed the equipment using a parallel mechanism control pedal to achieve the stepping,9 which can meet the different needs of various movements of the lower extremity, but the mechanism is large. Henan University of Science and Technology presented a new horizontal lower limb rehabilitation training robot with 4 DoFs,10 which is integrated with a traditional Chinese medicine (TCM) massage technique, but space for activities is limited. Shanghai University, Zhejiang University, and other units developed a device of lower extremity dermatoskeleton,11,12 through an electric cylinder linear drive to achieve the rotation to control the movement of the joints of the lower limbs. Sun Yat-sen University developed a 3DoF LLRR for motion recovery13 with a simple and flexible structure, which involves the hip, knee, and ankle joints, and it can also be adjusted to fit for the different heights of patients, but it is very bulky. Beihang University designed a 3-RPR (revolute pair– prismatic pair–revolute pair) parallel mechanism to fully accommodate the motion of the human knee joint and obtain the trajectory of the lower limb.14 However, its training model is single and the organization is huge. University of Waterloo samples and analyzes the joint angles of the five leg movement models,15 laying the groundwork for rehabilitation research by other scholars, which is very useful and important. As mentioned above, the main research of the rehabilitation robot is the human gait movement, but the training of muscular strength of the medial thigh muscle group is not obvious. Because the lower limb motion is a multi-muscle group and coordinated motion of multiple joints, the combined action of these movements to the lower extremity is bound to make the movement in space not only three-dimensional motion, but also rotational motion. This requires that the moving platform of traction lower extremity motion has as many degrees of freedom as possible to meet the multi functional
Advances in Mechanical Engineering training requirements. Referring to the lower limb of the human body with a 6-DoF kinematics model, lower limb rehabilitation training is achieved by driving the lower end of the metatarsal. In order to meet the needs of the rehabilitation training path, this article proposes a kind of rigid–flexible hybrid adduction and abduction rehabilitation robot which especially helps patients with medial thigh muscle group exercise rehabilitation training. Meanwhile, the robot mechanism and trajectory planning are analyzed and the results prove the feasibility and effectiveness of the robot.
Robot kinematics analysis According to the implementation of lower limb adduction and abduction of training forms and the specific location of the lower limb control point, referring to the lower limb of the human body kinematics model, the motion form of the control point can be clearly defined, so as to determine the robot’s mechanism. This article presents a rigid–flexible hybrid robot, and its system is composed of four groups of rigid–flexible hybrid chains and a pedal. Rigid–flexible hybrid chain mechanism consists of a fixed linear slide and a direct current (DC) torque motor which drives the wire and winch on the frame. Linear slide is used to change the position of the flexible wire wheel and the pedal is pulled by the four wires. The other end of the wire is connected with the winch driven by the DC torque motor through the passing wheel, and a force sensor is installed in the middle of each wire, as shown in Figure 1 (the suspension system is shown in the figure, which in this article is not the focus of discussion, hence it is not explained). The 3D model of the organization is shown in Figure 2.
Pedal kinematics modeling Referring to a kinematic model of 6 DoFs of the human body’s lower limb16 and according to the trajectory of the rehabilitation process of the lower limb control points with changing the joint angle, the position of the pedal center point in the abduction and adduction movements is solved. Relative to the basic coordinate system of the robot, the position of the pedal center point is changing with the change of the joint angle17 P = up T H + O
ð1Þ
where P is the coordinate of the pedal center point in the world coordinate system, H is the angle of the lower limb joint in the human body coordinate system, O is the position of the origin of the human body coordinate system in the world coordinate system, and up T is the coordinate transformation matrix of the Denavit– Hartenberg (D-H) model of the human lower limb.
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Figure 1. Robot model: (a) The training model of robot, (b) The main view of robot, and (c) The top view of robot.
Figure 3. Block diagram of the transformation matrix. Figure 2. Wire-driven lower limb rehabilitation robot 3D model.
Because the joint in the D-H model of the human lower limb is rotary, based on the method of solving the singular transformation matrix, the velocity mapping relationship of the human lower limb control points of the pedal center point is derived
According to 0n T = 0n T (q1 , q2 , . . . , qn ) and 0i T = 0 i1 i T (0 T = I), the following recurrence formula i1 T can be obtained 0
0_ iT
d i1 _i = i1 0 T_ i1 i T + i1 0 T i1 i T_ = i1 0 T_ i1 i T + i1 0 T iT q dqi = i1 0 T_ i1 i T + i1 0 T i1 i TQi q_ i = i1 0 T_ i1 i T + 0 TQi q_ i i
_ P_ = up T_ H + up T H
ð2Þ
ð3Þ
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Figure 4. Wire distribution: (a) master view and (b) top view.
among (00 T_ = O). The recurrence formula can be further solved as follows 0€ iT
= i1 0 T€ i1 i T + i1 0 T_ i1 i T_ + 0i T_ Qi q_ i + 0i TQi q€i ð4Þ = i1 0 T€ i1 i T + i1 0 T_ i1 i TQi q_ i + 0i T_ Qi q_ i + 0i TQi €qi (00 T€
among = O). The block diagram of the two recurrence formulas is shown in Figure 3. Hence, the acceleration of the pedal center point P€ can be obtained.
Wire kinematics modeling
Pix , Piy , Piz
T
T = R ri + Px , Py , Pz
ð5Þ
where R is the transformation matrix of the pedal coordinate system Pxp yp zp , which is relative to the base coordinate system Oxyz, and is given by 2
cos a R = 4 sin a 0
sin a cos a 0
3 2
cos b 0 05 4 0 sin b 1
3
0 sin b 1 0 5 ð6Þ 0 cos b
When ri = PPi , the direction vector of the point Pi in the pedal coordinate system is relative to the origin P of the coordinate system. Therefore, when the wheel point Bi and Pi relative to the fixed coordinate system are known, then Li = Pi Bi and the length li of each wire can be obtained as follows
ð7Þ
The derivation of equation li2 = Li LTi to get wire speed is as follows Li l_i = vPi Bi = u i vPi Bi li
ð8Þ
where ui = ½Pix Bix , Piy Biy , Piz Biz =jPi Bi j represents the unit direction vector of the wire i and vPi Bi indicates the speed of the wire i, vPi Bi = vPi vBi . When the speed P_ = ½ vx vy vz vx vy vz T of the center of the pedal is known, vPi can be expressed as vPi = GPPi P_
As can be seen from the configuration of the rigid-flexible hybrid robot (shown in Figure 1), the projection of the flexible wire of the robot on xoy plane and xoz plane is shown in Figure 4, and the posture change rule of the center point of the foot pedal can be obtained through the human-machine training track analysis,then the coordinate of the traction point ½Pix , Piy , Piz of the pedal can be obtained
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi li = (Bix Pix )2 + (Biy Piy )2 + (Biz Piz )2
ð9Þ
where GPPi represents the speed transformation matrix between the center point P of the pedal and the connecting point of each wire, given by GPPi = ½i 3 ri , j 3 ri , k 3 ri , i, j, k 2 R3 3 6
ð10Þ
Here, the x-axis direction unit vector for i is given by i = ½ 1 0 0 T ; the y-axis direction unit vector for j is j = ½ 0 1 0 T ; the z-axis direction unit vector for k is k = ½ 0 0 1 T . This can be pushed l_i = ui GPPi P_ ui vBi = Ji P_ ui vBi
ð11Þ
where Ji is the first-order influence coefficient of the wire i to the moving platform, Ji = ui GPPi . That is J = ½J1 , J2 , J3 , J4 . When the velocity of each end of the wire is known, the first derivative of the velocity is obtained, then the acceleration of the wire movement can be obtained; the derivation of 2li l_i = L_ i LTi + Li L_ Ti again 2li€li + 2l_i2 = €i LT + 2L_ i L_ T + Li L €T is available, that is L i i i
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Figure 5. The trajectory projection of the center of the moving platform: (a) XY surface projection and (b) XZ surface projection.
€li = ui (aPi aBi ) +
:
vTPi Bi vPi Bi li2
ð12Þ
li
where aPi represent the acceleration of each point Pi on the pedal. The generalized acceleration of the center point P of the pedal is P€ = ½ex , ey , ez , ax , ay , az T T aPi = GPPi P€ + P€ Hi P€
ð13Þ
where Hi is the second-order influence coefficient, which is the matrix of Hi 2 R6 3 6 3 3 , that is 2
i 3 (i 3 ri ) j 3 (i 3 ri ) 6 i 3 (j 3 ri ) j 3 (j 3 ri ) Hi = 6 4 i 3 (k 3 ri ) j 3 (k 3 ri ) ½03 3 3 3 3
k 3 (i 3 ri ) k 3 (j 3 ri ) k 3 (k 3 ri )
3 ½03 3 3 3 3 7 7 2 R6 3 6 3 3 5 ½03 3 3 3 3
ð14Þ The motion state of the wire can lay the foundation for dynamic analysis and selection of the drive motor.18,19
Man–machine training trajectory planning strategy In the lower limb of the human body model, a rehabilitation training mode is set, which is a special passive adduction and abduction for patients; then this mode corresponds to the lower limb function of the joint angle as follows 8 u1 = 45 sin (2:7t 0:34) 15 > > > > u2 = 10 sin (2:7t) > > < u3 = 20 u4 = 0 > > > > u = 45 > > : 5 u6 = 10 sin (2:7t)
ð15Þ
where u1 is the lower extremity hip adduction and abduction angle in degrees; u2 is the internal rotation and external rotation angle of the hip joint in the lower limbs in degrees; u3 is the lower limb hip flexion and extension angle in degrees; u4 is the lower limb knee flexion and extension angle in degrees; u5 is the lower limb ankle flexion and extension angle in degrees; u6 is the lower limb ankle adduction and abduction angle in degrees; and t is the lower limb training time in seconds. According to the standard of human body parameter20, the length parameter of human lower limb thigh and lower leg is set up, that is: L1 = 420 mm, L2 = 390 mm. According to the formula (1), the position of the origin O of human body coordinate system in the world coordinate system is O = [850, 1000, 2650]T. Training patterns corresponding to the center point of the trajectory of the moving platform are available, as shown in Figure 5. The training strategy has the following features: in the XY plane projection (see Figure 5(a)), its trajectory is similar to a part of parabola, the mobile platform center along the X-axis displacement between 200 and 1300 mm and along the Y-axis displacement between 300 and 700 mm. In the XZ plane projection (see Figure 5(b)), the motion trajectory shows symmetrical distribution, and the dynamic range of motion platform center along the Z-axis is very small (2415 to 2410 mm). The purpose of simplifying the robot control program can be achieved through the planning of the dynamic platform around the Z-axis of the rotation law (i.e. the movement of a in Figure 6) and simplify the robot kinematics analysis. In Figure 6, when the motion trajectory is at the right side of the lowest point B(xs , yPmin ), the motion law of the lead screw nut mechanism 1 is B1y = yPmin , so we can know that the movement rule of the lead screw nut mechanism 2 is
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ð23Þ
The generalized velocity equation of the center point of the moving platform can be obtained vP = v P x
v Py
vPz
vPx
vPy
vPz
T
ð24Þ
In the same way, the angular acceleration is e Pz = a €= 8 2 a _ 2(Px d)sec2 a tan aa_ 2 aPx tan a Py 2vPx sec aa > > , Px \xs > < (Px d)sec2 a > > a 2vPx sec2 aa_ 2Px sec2 a tan aa_ 2 aPx tan a > : Py , Px x s Px sec2 a
Figure 6. Trajectory planning of moving platform.
ð25Þ B3y =
d(Py B1y ) + Px B1y Px
ð16Þ
€ sin a + 2b_ cos aa_ b sin aa_ 2 + b cos a€ a ð27Þ eP x = b
When the movement track is in the left side of B(xs , yPmin ), the movement rule of the lead screw nut mechanism 2 is B3y = yPmin ; then the displacement law of the screw nut mechanism 1 is known as the rule d(Py B3y ) + B3y (d Px ) B1y = d Px
ð17Þ
Moving platform around the z-axis of the local coordinate system PxP yP zP angle is 8 Py ymin > > > , P x xs arctan < d Px ð18Þ a= > P ymin > > arctan y , Px .xs : Px The rotation angle variation law of the moving platform around the z-axis of the local coordinate system PxP yP zP should be consistent with the rotation (internal or external) of the lower limbs, that is b = 10 sin (2:7t)
ð19Þ
Thus, the position and pose equation of the center point of the moving platform is obtained P = ½ b sin a
b cos a
a
Px
P z 2 T
Py
ð20Þ
The angular velocity of the center point relative to the base coordinate system of the robot can be obtained by the rotation law of the moving platform 8 vPy + vPx tan a > > < (Px d)sec2 a vPz = a_ = v vPx tan a > > : Py Px sec2 a
Px \xs ð21Þ P x xs
vPy = b_ cos a b sin aa_
€ cos a 2b_ sin aa_ b cos aa_ 2 b sin a€ a ð26Þ eP y = b
ð22Þ
The generalized acceleration equation of the center point of the moving platform is aP = ePx
eP y
eP z
a Px
aPy
aPz
T
ð28Þ
From the man–machine trajectory planning training and kinematics analysis of the moving platform, the speed and acceleration of the screw nut mechanism and moving platform center point had the following relationship 8 vPy d > > , vB3y = 0, Px \xs < vB1y = d Px v d > > : vB1y = 0, vB3y = Py , P x xs Px
ð29Þ
Further calculations can be obtained 8 aPy d > > , aB3y = 0, Px \xs < aB1y = d Px a d > > : aB1y = 0, aB3y = Py , P x xs Px
ð30Þ
At this point, when determining the strategy of the lower limb rehabilitation training, the motion law of the robot can be planned.
Simulation analysis Kinematics simulation analysis of robot pedal By man–machine training trajectory analysis, it consumes a long time to perform a complete lower limb adduction and abduction in patients with motor dysfunction, taking into account the safety of patients. For this purpose, the training mode is set up which completes a set of training mode at the frequency of 2.7 Hz in the whole adduction and abduction movement, and
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Figure 9. Length variation law of wire.
Figure 7. Velocity variation law of the moving platform center.
Figure 10. Velocity variation law of wire.
Figure 8. Acceleration variation law of the moving platform center.
then the running state of the mobile platform center P in adduction and abduction training is simulated. The relationship between the speed of the moving platform center and the training time is shown in Figure 7. The relationship between the acceleration of the moving platform center and the training time is shown in Figure 8. As can be seen from Figure 7, the center of the moving platform had the largest velocity (about 21500 to 1500 mm/s) along the X-axis, the medium velocity (about 21000 to 1000 mm/s) along the Y-axis, and the minimum velocity (in 6 10 mm/s) along the Z-axis. From Figure 8, acceleration is similar to velocity on the three axes (x, y, z) in the law changing, and the center of the moving platform had the largest acceleration (about 24000 to 4000 mm/s2) along the X-axis, the centered acceleration (about 22000 to 4000 mm/s2) along the Y-axis, and the minimum velocity (in 6 500 mm/s) along the Z-axis. By comparing the motion law of point P movement in Figure 3, the correctness of the velocity and acceleration model of the center point of the moving platform is verified, which lays a foundation for the solution of the wire length, velocity and acceleration in the next step.
Figure 11. Acceleration variation law of wire.
Robot kinematics simulation analysis wires Inverse kinematics of a rigid–flexible hybrid robot are simulated and analyzed in the MATLAB environment, and then the motion law of length, velocity, and acceleration of the four wires of the driving moving platform can be obtained, which is changing with time. The simulation results are shown in Figures 9–11. As can be seen from Figures 9–11, the length of the four wires varies in the range of 200–1300 mm, the velocity of the four wires changes between 21500 and 1500 mm/s, and the acceleration of the four wires changes between 25000 and 20,000 mm/s2. It can be seen that the length of the wire is in the large range in the whole rehabilitation training process; however, its speed and acceleration remain in the low speed range.
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Figure 12. Strategies for recovery of adduction or abduction exercise.
Those meet many requirements, including the large range of motion, velocity and acceleration curve smoothing, and little impact on the moving platform, which guarantees the requirement of device security in the training process. As can also be seen from the figure, in the former 0 (T =4), the length variation amplitude of the wires 3 and 4 is larger than the length of the wires 1 and 2; in the meantime, the speed of the wires 3 and 4 is positive and that of the wires 1 and 2 is negative, which shows that the moving platform moves away from the initial position and toward the direction of the wires 1 and 2. In (T =4) (T =2), the length variation amplitude of the wires 3 and 4 is still larger than that of the wires 1 and 2, but the speed of the wires 3 and 4 is negative and that of the wires 1 and 2 is positive, which shows that the moving platform is moving in the direction of the initial position and far away from the wires 1 and 2. In this period, the trend of wire 1 is consistent with the trend of wire 2 about velocity variation, but the amplitude of wire 1 is significantly smaller than that of wire 2, and wire 3 is consistent with wire 4 in the amplitude and the trend of velocity variation. These are clearly reflected in the length and the acceleration curve of the wires 1 and 2 as well as the wires 3 and 4, because it is mainly caused by the combined effect of the relative rotation of the moving platform around the Zp-axis and the motion planning of the screw nut mechanism in the trajectory planning. In (T =2) T , the variation factors of the length, velocity, and acceleration of each wire are the same as in the first half of the cycle.
Experiments of rehabilitation robot The test adopts the rehabilitation mechanism only to simulate the rehabilitation movement of adduction or abduction of the human body (the physical structure is only used for adduction and abduction (i.e. two ropes are required), while the internal–external rotation requires four ropes (not discussed)). In addition to the rigid and flexible lower limb rehabilitation mechanism,
Figure 13. Experimental object frame.
the main equipment is associated with its control equipment, including the thunder control system and the corresponding drivers, encoders, power supplies, and so on. The overall rehabilitation control strategy is shown in Figure 12. After the rehabilitation control strategy is determined, the corresponding physical object is built and the driver performance parameters are debugged to match the motor parameters. The physical diagram is shown in Figure 13. In adduction or abduction exercise, the joint angle function is presented above and not repeated. The corresponding man–machine trajectory planning is carried out, and the point (875, 0, 500) is the starting point and MATLAB simulation is carried out. The motion change curves of the wires 1 and 2 and the screw motors 1 and 2 are shown in Figures 14–17. After the trajectory planning is finished, the whole system is programmed with C#, and the control interface and control program are written. The results of the run are shown in Figure 18.
Conclusion 1.
Aiming at the general problem of lower limb rehabilitation training robot, that is, only flexion and extension exercise training of the lower
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Figure 14. Length variation law of wire 1.
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Figure 17. Position variation law of screw motor 2.
2.
Figure 15. Length variation law of wire 2.
3.
4.
Figure 16. Position variation law of screw motor 1.
limb, the LLRR configuration is set up, which can also achieve lower limb exercise training of
adduction or abduction and internal or external rotation. Referring to the human body kinematics model of the lower limb, the structure of the LLRR is established, which is the rigid– flexible hybrid model. According to the rigid–flexible hybrid structure of the LLRR, the kinematic model of the pedal is established in the situation of fully considering the human lower limb movement track. Then the mapping relation between the joint movement of the lower limb and the pedal movement is obtained. Meanwhile, the kinematic model of wire traction is established, and the first- and second-order influence coefficient matrix of the wire traction system is obtained. These provide a foundation for the analysis of system dynamics and prototype development. Based on the training need of the abduction or adduction and internal or external rotation, a training model is set up. According to the kinematic characteristics of the pedal center point and analysis of the trajectory planning strategy of man–machine training, the position, velocity, and acceleration of the slider of the two groups’ lead screw mechanism are solved. This work provides the basis for the development of follow-up lower limb rehabilitation training strategy. Based on training patterns of adduction or abduction and internal or external rotation and planning strategy of man–machine, the speed and acceleration of the pedal center point and the length, speed, and acceleration of the wire are simulated and analyzed. Then the validity of the trajectory planning strategy of man–machine training is verified, which laid the foundation for the next step in robot controlling.
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Figure 18. Control system operation interface.
Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
4.
Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project was supported by the National Natural Science Foundation of China (51405095), Postdoctoral Scientific Research Fund of Heilongjiang (LBH-Q15030), and Fundamental Research Funds for the Central Universities (HEUCF180701).
ORCID iD Ke-Yi Wang
5.
6. https://orcid.org/0000-0001-8577-0554
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