On the Development of a Walking Rehabilitation Device with a Large Workspace

Transcription

1 2011 IEEE Internationa Conference on Rehabiitation Robotics Rehab Week Zurich, ETH Zurich Science City, Switzerand, June 29 - Juy 1, 2011 On the Deveopment of a Waking Rehabiitation Device with a Large Workspace Cément Gossein and Thierry Laiberté Abstract Rehabiitation therapy aiming at heping a person to regain or improve the abiity to wak is a abour-intensive activity. In this context, the patient is often imited to very restricted waking spaces. This paper presents a device that can support the weight of a person waking freey over a arge workspace. The device is based on an overhead gantry mechanism combined with a cabe routing that decoupes the vertica motion from the horizonta dispacements of the person. The mechanica architecture is first presented and it is shown that the principe can be appied to the design of a competey passive device in which the portion of the weight to be supported can be adjusted. A simpified dynamic mode is aso derived in order to highight the characteristics of the device. A powered version of the device is then discussed. Finay, a prototype of a passive device buit at fu scae is presented and discussed. A video accompanying the paper iustrates the experimenta tests underway with the prototype. I. INTRODUCTION Bipeda waking is a mechanicay compex activity that invoves the coordination of many musces based on a variety of sensing inputs. Therefore, the rehabiitation of patients with waking disabiities requires earning, which can in turn transate into ong hours of exercises. Moreover, assisting a person that requires support to wak is a difficut task. If the person is assisted ony by therapists, then severa of them are needed which becomes very costy. On the other hand, if the person is supported by a harness, the waking space is usuay very imited (e.g. a treadmi is used) which is a significant drawback, especiay in advanced stages of the earning process. The deveopment of devices to assist in the rehabiitation of patients with waking disabiities has been addressed by severa research groups. Two main issues have been considered, namey the support of the patient and the guidance of his/her imbs. Most of the proposed concepts are based on a the use of a treadmi (see [1] and [2] for instance). Athough treadmis offer some advantages in terms of footprint and contro, they cannot reproduce the rea dynamics of waking because the inertia of the upper body of the patient is not incuded in the waking scenario. Other simiar devices have aso been deveoped for appications in the support of edery peope (see for instance [3]). In [4], a robotic assistive device is used to support the weight of the patient. The portion of the weight to be supported can be adjusted. However, the workspace avaiabe This work was supported by The Natura Sciences and Engineering Research Counci of Canada (NSERC) as we as the Canada Research Chair program. The authors are with the Department of Mechanica Engineering, Université Lava, Québec, Québec, Canada, G1V 0A6, gossein@gmc.uava.ca, thierry@gmc.uava.ca /11/$ IEEE 263 to the patient is imited and the foor footprint of the device is rather arge. Mobie robotic devices that foow the patient have aso been deveoped (see for instance [5] and [6]) in order to increase the workspace and aow the patient to wak naturay on a foor. However, this approach invoves a arge mobie robot that requires significant foor space and raises issues regarding the safe active contro of the robot. In other approaches, robotic patforms are attached to the feet of the user and controed directy (see for instance [7], [8] and [9]). Such systems are simiar to the use of treadmis regarding the waking simuation, athough they provide more fexibiity and aow the simuation of obstaces, stairs and others. In [10], a waking rehabiitation device based on a cabe-driven parae mechanism is proposed. This concept eads to an effective ight-weight apparatus and aows the appication of controed forces to the person. However, it aso requires the use of a treadmi with the patient waking on the spot. In [11], a robotic system suspended from a ceiing-mounted rai is proposed. This device aows the patient to wak more naturay on a foor. However, deviations from a inear path and changes of direction are not possibe. Other commercia systems based on some of the concepts mentioned above are aso avaiabe (see for instance [12] and [13]). This paper presents a new device that aims at providing a arge waking space whie supporting the weight of the patient. The proposed concept aows the user to wak freey on a foor in a directions, incuding changes of rotation, over a arge workspace. The device naturay eads itsef to a passive mechanism but can aso be impemented as an active robotic system. After presenting the basic principe of the device, its impementation as a passive mechanism or as an active robotic system is discussed. A dynamic mode is then studied to highight the design chaenges. Finay, the experimenta vaidation on a fu-scae prototype is presented and some concusions are drawn. II. MECHANICAL ARCHITECTURE A. Four-degree-of-freedom gantry mechanism The device proposed in this work is based on an overhead gantry mechanism simiar to those commony found in industria settings. Two parae rais attached to the ceiing provide the motion trave in one horizonta direction. A bridge is suspended to these rais. A troey is suspended to the bridge on a rai orthogona to the first set of rais. The troey provides the motion trave in the second horizonta direction. A vertica sider mechanism is attached to the troey and provides the third degree of freedom, i.e., vertica

2 Y Z X Bridge Troey Y Z X Bridge x θ y Vertica Actuation and Baancing Troey End effector z Payoad Fig. 1. Schematic representation of the 4-dof gantry structure. Fig. 2. Cabe routing for the weight compensation mechanism. transation. Finay, a revoute joint with a vertica axis can be added in order to aow the end body to rotate freey around a vertica axis. Aternativey, the vertica sider and the rotation can be repaced by a cabe hoist. The four degrees of freedom of the mechanism correspond to the so-caed Schönfies motions or SCARA motions. The kinematic architecture of the gantry mechanism is iustrated schematicay in Fig. 1. One advantage of an overhead gantry mechanism is that it does not occupy any of the foor space. B. Weight compensation The overhead gantry mechanism described in the preceding subsection provides the degrees of freedom required to aow a person to wak freey in a directions, incuding a rotation around a vertica axis. However, the vertica degree of freedom must provide a force to baance the weight (or part of the weight) of the person. In other words, the main objective of this mechanism is to be abe to foow the person with an overhead support and compensate part of its weight. One effective means of supporting the weight of the person is to use an adjustabe counterweight mounted on the vertica sider mechanism. However, mounting the counterweight directy on the vertica sider woud significanty increase the inertia of the moving bodies of the mechanism, thereby eading to a arge inertia in the horizonta directions. In a passive system, this inertia woud be highy detrimenta because it woud require the person to drag a significant additiona mass. Therefore, it is desired to move the counterweight away from the person and mount it on the fixed frame. A cabe transmission using the routing iustrated in Fig. 2 can be used to move the counterweight to a fixed ocation. This arrangement basicay connects the counterweight to the person via a cabe transmission that cances out the horizonta motions. Additionay, it is noted that the tota ength of cabe in the routing is constant and therefore no spoo is required. The motion of the counterweight is competey decouped from the horizonta motions which means that horizonta motions of the mechanism eave the counterweight at rest. A motion of the counterweight is induced ony when a 20 kg Fig kg 80 kg Adjustabe weight compensation mechanism. 100 kg vertica motion of the end-effector takes pace. Therefore, the counterweight does not contribute to the horizonta inertia. The weight compensation mechanism must be adjustabe in order to accommodate variations on the weight of the user. Moreover, for a given user, the portion of the weight to be compensated may vary depending on the person s condition. It may aso be desirabe to change this parameter during a working session in order to test different waking conditions or vary the stimui. Therefore, the counterweight is mounted on a rotating ever. Siding the counterweight aong the ever and ocking it in different positions provides a simpe and effective means of adjusting the weight compensation. The adjustabe compensation mechanism is iustrated in Fig. 3. It is cear from the above that the proposed device is wesuited for a passive assistive waking mechanism. Indeed, horizonta motions are provided by the bridge and troey gantry mechanism which can be designed to induce imited friction and does not require arge forces to be activated. Aso, because of the cabe transmission, the counterweight is mounted on a fixed pivoting ever and does not contribute to increasing the inertia in the horizonta directions. Finay, the adjustment of the mass to be compensated is easiy performed by moving the counterweight aong the ever arm. III. DYNAMIC MODELLING A dynamic mode is derived in order to determine the forces required to acceerate the mechanism when performing waking exercises. One can write f = f r + A(p) p + b(p, ṗ) + c(p) (1) where f is the externa force vector defined as f = [f x f y f z τ] T, (2) 264

3 f r is the friction force vector defined as f r = [f rx f ry f rz τ r ] T, (3) p is the Cartesian position vector defined as p = [x y z θ] T, (4) in which x, y, z and θ are the position components in a directions, where θ is the rotation around the vertica axis, ṗ is the Cartesian veocity vector and p is the Cartesian acceeration vector defined as [ ṗ = ẋ ẏ ż θ ] T [ θ] T, p = ẍ ÿ z. (5) Matrix A describes the inertia of the system which can be written as M A = 0 M M 33 0 (6) I z with M 11 = m 1 + m 2 + m 3 + m h (7) M 22 = m 2 + m 3 + m h (8) and where m 1, m 2, m 3 and m h are respectivey the mass of the bridge, the mass of the troey, the mass of the endeffector and the mass of the human subject whie I z is the inertia of the end-effector pus the human subject around the vertica axis. Vector b represents the so-caed centrifuga and Coriois terms b = [0 0 B 3 0] T, (9) whose components are a zero except for the vertica motion for which there is a noninear reationship between the motion of the end-effector and the counterweight. Vector c represents the terms arising from the potentia energy of the system and can be written as c = [0 0 C 3 0] T, (10) whose components are a zero except for the vertica motion, which invoves gravitationa potentia energy. The expressions for M 33, B 3 and C 3 wi be given after the kinematics of the baancing system is estabished. The geometry of the baancing system is described in Fig. 4. It can be seen that with From the reationships z = ρ o ρ (11) ρ o = h 2 + ( o ) 2. (12) ρ sin φ = o cos ψ (13) h ρ cos φ = sin ψ (14) and eiminating φ, one can obtain ρ as ρ = h o + 2 2(h sin ψ + o cos ψ). (15) 265 Fig. 4. m + m 3 h z φ h ρ o ρ m Geometry of the baancing system. The time derivative of eq. (11) gives c o ż = (h cos ψ o sin ψ) ψ. (16) ρ In order to simpify the dynamic modeing and provide more insight, the foowing approximations are introduced. The engths o and are assumed to be approximatey equa, h is assumed to be significanty arger than o and, and ψ is kept reativey sma, say ess than 30 degrees. As a resut, ange φ is sma and cos φ 1. Then, eq.(11) is approximated by z = sin ψ (17) and eq.(16) is approximated by ψ ż = ψ cos ψ (18) The dynamic mode is obtained using the Lagrangian approach ( ) d (T V ) (T V ) = f z f rz (19) dt ż z The kinetic energy T is T = 1 2 (m 3 + m h )ż I c ψ 2 (20) where I c is the inertia of the counterweight around its pivot. The potentia energy V is V = m c gc sin ψ (m 3 + m h )gz = ( m cc c m 3 m h )gz (21) where m c is the mass of the counterweight. The resut can then be incuded in eq. (1) which gives M 33 = m 3 + m h + I c 2 cos 2 ψ (22) B 3 = ż2 I c tan ψ 3 cos 3 (23) ψ ( mc c ) C 3 = m 3 m h g. (24) In the mechanica architecture described in the preceding section, the troey is mounted on the bridge and the vertica

4 sider is mounted on the troey. Therefore one has, by inspection of eqs.(7) and (8), M 11 > M 22 (25) Hence, considering eqs.(6) and (25), it is cear that the inertia is not equa in the two horizonta directions. This is a drawback of the bridge and troey arrangement. In a passive system, it means that the spurious inertia fet by the user wi not be the same depending on the direction of waking. Therefore, it is important that the design of the mechanism aims at minimizing m 1. Ceary, a masses shoud be minimized but the atter has the most impact on the performance of a passive device. Simuations can be performed based on the simpified dynamic mode presented above in order to estimate the performances in terms of the horizonta forces required for waking. However, at ow veocities, friction may be dominant and shoud therefore be estimated in a practica design. Approximating the counterweight as a point mass, its inertia around the fixed pivot, noted I c in the above equations, can be written as I c = m c c 2. (26) The baancing ratio, noted γ, is defined as the ratio of the static moment of the counterweight with respect to the fixed pivot over the static moment generated by the payoad on the pivot. In other words, when γ is equa to 1, the payoad is exacty baanced. From eq.(24), one obtains m c c γ = (m 3 + m h ). (27) The inertia ratio, noted α, is defined as the ratio of the effective inertia of the counterweight over the inertia of the payoad. A sma vaue of α is desirabe in order to minimize the spurious inertia. From eqs.(22) and (26), one obtains α = m c c 2 2 cos 2 ψ(m 3 + m h ) = cγ cos 2 ψ. (28) It can be observed that by using a arger counterweight mounted coser to the pivot, the tota inertia associated with the vertica motion is reduced. This is so because the mass of the counterweight required to obtain static baancing increases ineary with the ever arm whie the inertia increases quadraticay. Therefore, in practice a arge counterweight mounted cose to the pivot is preferabe and wi ead to smaer spurious inertia (smaer vaues of α). It can aso be observed that it is preferabe to keep the ever around the horizonta configuration in order to avoid excessive inertia. This is obtained if the ever is sufficienty ong compared to the tota vertica dispacement. Aso, from eq.(23), it can be seen that the effect of I c is imited if ψ and ż are kept sma. IV. POWERED ASSISTIVE DEVICE Athough the device described above eads naturay to a passive mechanism, it is aso possibe to introduce actuation in order to improve the performances and reduce the spurious forces to be provided by the user due to the inertia and friction in the mechanism. To this end, actuators coud be 266 incuded directy on the joints of the gantry mechanism. However, this approach woud further increase the inertia of the moving components. In order to circumvent this probem, cosed-oop bet-driven transmissions are used. Severa cosed-oop transmissions were proposed in [14] for appication in four-dof gantry mechanisms. The transmissions used here are based on the arrangements proposed in the atter reference. First, it is observed that because of the mechanica architecture of the grantry device, the inertia induced by the mechanism around the vertica axis of rotation is rather negigeabe. Therefore, this degree of freedom is eft passive and no actuation is required. Then, it is pointed out that the cabe routing used to attach the payoad to the counterweight can be used to ocate the actuator providing the vertica motion on the base. Indeed, the actuator for the vertica motion can be mounted directy at the counterweight. Finay, the horizonta motions (bridge and troey) are considered. Actuation is most reevant for these degrees of freedom since they are more ikey to produce undesirabe effects on the user. The actuation of the bridge is based on the cosed-oop transmission iustrated in Fig. 5-eft. In this figure, the bridge is represented by a rectange and the pueys by circes. The s mark the paces where the bet is attached to the bridge and the square around one of the circes denotes that the corresponding puey is actuated. As it can be observed on the figure, the ength of the cosed oop is constant and therefore no spoo is needed. Aso, the forces appied on the bridge are we baanced and provide stabiity. The actuation of the troey is based on the cosedoop transmission iustrated in Fig. 5-right. Simiary to the preceding routing, the cosed oop for the actuation of the troey aso has a constant ength and does not require a spoo. Moreover, it is pointed out that the two transmissions are competey decouped. In other words, a motion of one of the actuators does not have any impact on the other degree of freedom and vice-versa. One important advantage of decouping is that no antagonistic forces are generated, which makes the contro easier and which reduces the power required at the actuators. Using the above actuation schemes, it is possibe to actuate the horizonta motions of the gantry mechanism and compensate for the inertia and friction in these directions by tracking the motion of the torso of the person. V. EXPERIMENTAL VALIDATION A passive 3-dof version of the concept described above was impemented experimentay for demonstration purposes. The mechanism buit in the aboratory shown in Fig. 6 is based on a device that was deveoped for other appications (payoad manipuation). The main modification is the addition of a chair as an interface between the human subject and the end-effector. Therefore, athough it provides a proof of concept, the experimenta set-up is not taiored to the appication described here. First, the mechanism has ony three degrees of freedom and does not aow rotations around the vertica axis, which is definitey a imitation

5 θ1 θ 2 Fig. 5. Cosed-oop bet-driven transmissions. Left: for the actuation of the bridge motion. Right: for the actuation of the troey motion. for waking devices. Additionay, the inertia of the bridge, troey and end-effector coud be significanty reduced since the prototype mechanism was deveoped for arger payoads. Despite the aforementioned imitations, the experimenta impementation performs rather we, as shown in the accompanying video. In particuar, it can be observed that the gravity compensation is effective and we decouped from horizonta motions. It is observed that for arge baancing ratios (γ > 0.8), the static forces between the human subject and the foor are so sma that it is difficut to perform horizonta acceerations by waking. The user tends to jump when trying to appy more force on the foor. It is aso observed that for sma baancing ratios (γ < 0.2) the prototype coud not aways foow the user, i.e., the chair separates from the subject when arge upwards acceerations are performed. In order to avoid this phenomenon, the unoaded device (without the person) shoud be abe to perform arge upward acceerations. In other words, with m h = 0, C 3 shoud be as arge as possibe compared to M 33. The use of a chair aowed to adapt a system intended for another appication. However, the waking motion was not fuy natura and comfort was imited. It is cear that a better interface, such as a harness, shoud be used in the future. Horizonta motions are aso we demonstrated, athough it is cear that friction and inertia shoud be reduced in a rea impementation of the concept. As mentioned above, such a reduction shoud be possibe in a design based on reaistic requirements. In order to verify the dynamic mode aong the vertica motion, position mesasurements were performed. Numerica differentiation of the position was then performed in order to obtain the veocity and acceeration. The resuts obtained can then be compared with the acceeration computed from eq.(1). The parameters of the prototype are as foows: = 1.0m, o = 0.96m, h = 2.2m, m 3 = 12kg and m h = 70kg. For reasons reated to other appications of the prototype, the range of motion of the ever is 15 o < ψ < 30 o. As a resut, a person in a standing position with their feet on the foor corresponds to z = 0.31m or ψ = 18 o. Aso, the vaue of φ is comprised between 1 o and 1 o for 80% of the range of motion, with a maximum of 3 o. Therefore, the geometric 267 Fig. 6. Passive 3-dof assistive waking device buit in the aboratory. approximation used for the reation between z and ψ is appicabe. From measurements taken with a dynamometer, the friction is estimated to be approximatey f rz = 20N. Six baancing cases are studied. They are presented in Tabe I. Typica experimenta curves are potted in Fig. 7. Since the forces appied by the person on the foor are not known, the mode can be verified ony during the free-faing trajectory of the person jumping in the air. For the ast two cases given in the tabe, since the baancing ratio is sma, it is possibe to manuay throw the chair downwards and measure the acceeration of the unoaded device. However, it is difficut for the person to stay in the air ong enough to obtain effective measurements with the setup used. TABLE I THE SIX BALANCING CASES. THE ACCELERATIONS z ARE CALCULATED AROUND THE POINT WHERE THE VELOCITY IS ZERO. THE CORRESPONDING MEASURED VALUES ARE GIVEN IN PARENTHESES. Case m c c γ α z z (ψ = 0) with person chair ony (kg) (m) (m/s 2 ) (m/s 2 ) C (1.8) -5.6 C (2.0) -9.4 C (4.0) -4.2 C (4.4) -6.6 C (-2.2) C (-3.0)

6 Position (m) and Veocity (m/s) Veocity Position Time (s) 3 2 Acceeration (m\s2) Time (s) appication is ceary iustrated in the accompanying video, where the effect of gravity compensation is demonstrated using eaping motions that are characteristic of astronauts evoving in a ow-gravity environment. VII. CONCLUSION This paper presented a waking rehabiitation device that aows a person to wak freey on a foor over a arge workspace. The basic principe of the device consists of a cabe-routing system that foows the user in order to provide gravity compensation without hindering waking motions. The device naturay eads itsef to a passive mechanism but can aso be impemented as an active robotic system. Using a dynamic mode, it was shown that a rea impementation can be deveoped based on reaistic requirements. Aso, it was shown that the baancing principe based on the use of a counterweight can be expoited to minimize the spurious inertia. Finay, the experimenta vaidation on a fu-scae prototype provided design hints. Athough there were some imitations on the experimenta impementation, the prototype and the accompanying video ceary demonstrate the potentia of the concept in a context of rehabiitation. Fig. 7. Exampe of measured position, veocity and acceeration aong z. Acceeration curves obtained from eq.1 are potted during free-faing. The steps in the curves correspond to the change of direction of the friction force. The sight changes at the ends of the curves are due to the variation of ψ. From the six cases studied, the effect of the baancing ratio (γ) on the acceeration is very cear. Aso, the effect of the inertia ratio (α) is significant, especiay on the unoaded device. Therefore, it is of interest to minimize the inertia in order to obtain better performances during the upwards acceeration (user pushing up). The effect of friction, which pushes against the direction of motion, is sma but visibe. It is noted that, with the setup used, the free fa of the person occurs around ψ = 0 o and the upwards acceeration of the chair occurs around ψ = 25 o. A arge vaue of ψ produces an increase of the effective inertia (see eq. (22)). Therefore, it is advantageous to keep ψ sma to minimize this effect. For instance, in a future impementation, the baancing ever wi be designed such that it is horizonta when the person is standing. Simuations with and without taking into account B 3 were performed, and the resuts were aways very cose for the present setup. Therefore, the effect of the veocity which rarey exceeded 1m/s in the experiments on the effective inertia seems to be very sma. VI. OTHER APPLICATIONS The concept presented in this paper can aso be used in other appications such as the deveopment of training faciities for astronauts (see [15] for instance). By propery adjusting the baancing ratio, the device can emuate the gravity fied of other panets or the moon and the trainees can wak in a arge workspace without being hindered by foormounted mechanisms. Aso, the device does not require the use of springs, which raise safety and reiabiity issues. This 268 REFERENCES [1] M. Bouri, Y. Stauffer, C. Schmit, Y. Aemand, S. Gnemmi, R. Cave, P. Metraier and R. Brodard, The WakTrainer: A Robotic System for Waking Rehabiitation in IEEE Int. Conference on Robotics and Biomimetics, pp , [2] S. Jezernik, G.Coombo, T. Keer, H. Frueh and M. Morani, Robotic orthosis Lokomat: a rehabiitation and research too, Neuromoduation: Technoogy at the Neura Interface, Vo. 6, No. 2, pp , [3] J. Jang, S. Yu, J. Han and C. Han, Deveopment of a waking assistive service robot for rehabiitation of edery peope, in Service Robot Appications (Takahashi, ed.), In-Tech, August [4] N. Siddiqi, F. Gazzani, J. Des Jardins and E.Y.S. 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