Energy-Based Adaptive Control and Learning for Patient-Aware Rehabilitation IROS2019国际学术会议论文集 1918

Energy based Adaptive Control and Learning for Patient Aware Rehabilitation Erfan Shahriari1 Dinmukhamed Zardykhan1 Alexander Koenig2 Elisabeth Jensen1and Sami Haddadin1 Abstract In this paper we propose a novel energy based control scheme for an assist as needed rehabilitation strategy which both adapts the level of support based on patient participation and allows the patient to deviate from the pre scribed motion in favor of his her safety We build an energy network model with which we can monitor the energy fl ow through the system and prescribe a threshold on stored energy We also develop an adaptive motion control law that shapes the desired trajectory in order to respect the stored energy threshold Next we show how adapting the stored energy threshold can be used to change the level of responsiveness to the patient as well as to prevent excessive energy transfer to the human by the system A criterion is defi ned for setting this energy threshold which can be further used for monitoring the patient active participation and for adapting and learning the appropriate assistance level during rehabilitation Experimental results based on implementation in MATLAB SimscapeR and on the VEMO robotic system demonstrate the feasibility of the suggested approach The presented control scheme can be applied to any system including position and torque controlled robots and does not require the use of EMG sensors or precise force measurements I INTRODUCTION Stroke has risen to become one of the top three leading causes of disability 1 In this aging society it is expected that the incidence and prevalence of stroke survivors will continue to increase Survivors are often faced with vari ous impairments including movement disabilities 2 3 Movement rehabilitation is a well established method to aid in recovery and to maximize residual functionality 4 5 but this has become a major burden due to the increasing number of patients and an increasing shortage of nurses 6 and therapists As a result robotic assistance systems have become widespread in rehabilitation hospitals to support clinicians with therapy execution 7 Initially these robotic devices were purely position con trolled leaving patients no possibility to use their residual motor functions to infl uence the movement pattern The passivity of patients induced through such control paradigms were shown to correlate with lower therapy success Active patient participation in contrast was shown to be a crucial factor for recovery 8 10 To promote active participa tion in their rehabilitation so called assist as needed con trollers have been proposed by several research groups Such control strategies give patients the possibility to infl uence the movement while providing suffi cient robotic support for correct timing and direction of the movement pattern 11 1The authors are members of Munich School of Robotics and Ma chine Intelligence Technical University of Munich Munich Germany firstname lastname tum de 2The authors are members of Reactive Robotics GmbH Munich Ger many firstname lastname reactive Fig 1 VEMO robotic system Reactive Robotics 12 Early results have been promising however assist as needed control strategy development is in its infancy and much work is still needed Recently rehabilitation has come to be of interest in the Intensive Care Unit while rehabilitation was previously initiated several weeks after stroke incidence new research suggests that Very Early Mobilization VEM defi ned as starting rehabilitation at most 72h after stroke onset signifi cantly improves recovery for severely affected patients 13 15 With VEM in the ICU assist as needed paradigms are faced with a new set of challenges as patients 1 can be uncooperative or sedated 2 might suffer from delirium which can lead to uncon trolled or even aggressive behavior 3 can execute sudden non therapy related movements including but not limited to spasticity 4 might fatigue quickly and therefore require a rela tively swift shift from low to a high support level 16 Consequently robotic systems that are suitable for treat ment of patients in the VEM stage are required to not only support patients with an adaptive assist as needed functionality but also to keep the patient safe during un predictable interactions Simple force triggered shutdowns which are typically used in commercial products to ensure safety limit therapy time and quality and require either highly conservative or patient specifi c force thresholds The former may lead to frequent and unnecessary shutdowns while the latter is diffi cult to determine A novel approach that may be able to address both of these problems is to view control from an energy perspective 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 European Union5671 This follows logically from the fact that the rehabilitation device effect on the patient can be described in the form of energy exchanged through physical interaction Thus the energy model and energy transfer will be the primary focus of our control scheme development A Problem Statement We aim to develop an energy based rehabilitation control scheme that both adapts the level of support according to the patient participation in the rehabilitation and helps ensuring patient safety by allowing them to actively deviate from the prescribed motion B Related works An adaptive rehabilitation control scheme implies an ad equate assessment of patient performance and appropriate reaction This type of assessments has been tackled with various approaches for example using EMG 17 18 or force feedback 19 20 In the latter the robot assistance was adapted based on patient active force Also many studies have used tracking performance for the evaluation of human performance such as 21 in which robot stiffness and damping were adapted based on patient self initiated trajectory tracking Moreover there have been several approaches in adapta tion to the patient behavior Assistance has been addressed often by adjusting the stiffness 21 22 Specifi cally in 23 the stiffness was altered to maximize patients voluntary ef fort Other approaches include a tunnel based algorithm 11 which jeopardizes the robot responsiveness by restricting the subject motions Here we propose a graceful solution based on the concept of energy which can tackle several objectives in a unifi ed manner C Contributions The proposed control and learning scheme for rehabilita tion constitutes the following contributions 1 An energy aware rehabilitation guidance approach that respects the patient s intended and unintended resis tance to the prescribed motion thus enhancing safety 2 that is combined with an energy based learning algo rithm in order to assist the patient only to the level that is necessary for successful task completion thus encouraging the patient recovery process 3 that does not require extra sensors such as EMG or accurate force measurement for human intention recognition and 4 that can be applied broadly and is also applicable for position controlled robots 5 Moreover fi rst experimental validation was carried out on the real system Future large scale patient testing is planned in future work II REHABILITATIONDEVICEMODEL While the proposed control approach can be applied broadly and is not device specifi c here we consider a reha bilitation machine consisting of a bed which can be adjusted to different verticalization angles and two robot arms for interaction with each patient leg see Fig 2 Each robot Fig 2 Mobilization bed characterized by a verticalization joint and robotic arms to move the legs through a cyclic motion The robot arm is composed of a series of motorized joints and a fi nal passive joint Note that the pictured representation of the motorized joints is arbitrary and does not affect the derived equations arm is composed of n motorized joints and a fi nal passive joint to avoid the over determination scenario and thus to respect the thigh orientation As the robot arms are assumed to be identical the following model will be derived for only one of them Considering the kinematic structure the robot end effector and joints are assumed to move only parallel to the x y plane and thus their motion can be represented in R3space consisting of the x y plane position as well as the orientation around the z axis Furthermore as the last joint is passive the Cartesian pose of the passive joint xr R3is considered for the robot control design instead of the end effector position xh R3 as shown in Fig 2 The interaction wrenches at xrand xhare referred to as Fr Fh R3 respectively referring to linear force in the x y plane and the moment around the z axis Having n motorized joints in addition to the bed orienta tion qb the coordinates of the robot up to the last joint is q Rn 1and the forward kinematics equation becomes xr f q 1 For the kinematics equation the bed orientation qbis included in q However as it is assumed that the bed orien tation is controlled by a separate actuator the corresponding input torque will not be considered for the dynamics model which is described as follows in r M q0 q0 C q0 q0 q0 g q 2 q qb q0 T 3 where M q0 C q0 q0 Rn nand g q Rnare the inertia matrix the Coriolis and centrifugal matrix and the gravity vector of the robot respectively in Rnis the input torque to the robot actuators while r Rnis the 5672 Fig 3 Energy fl ow in the system The stored energy in the controlled robot changes over time as a result of the combined effect of powers Ph Pinand Pdissassociated with the patient motion the trajectory generator and the controller damping respectively and thus the desired trajectory xd are then adapted based on the level of stored energy S compared to the maximum allowed energy Smax and the threshold Smax S This adaptation directly affects the energy input removal of the motion generator to from the system i e Pinover time wrench Frmapped on to the robot motorized joints via r JT q Fr 4 J q f q q0 5 where J q Rn 3denote the robot Jacobian matrix III ENERGY BASEDCONTROL The proposed control scheme is based on the adaptation of robot desired motion xd xd xd R3in order to shape the energy fl ow within the system and consequently to control the energy transfer between the patient and the device While respecting the cyclic trajectory with the associated amplitude designed for the specifi c rehabilitation the trajectory speed is adjusted so as to also respect an energy threshold This re shaped trajectory is then fed to an interaction motion controller to derive the input torque for the robot actuators see Fig 3 In the following fi rst the motion controller law is pre sented and afterwards an energy network of the model is derived Based on this network an energy criterion is defi ned with which the energy transfer to from the patient can be shaped Finally a motion generation law is presented which respects this energy criterion A Interactive Motion Controller As the robot is assumed to be in physical interaction with the human throughout the therapy a compliant control method such as the well known Cartesian impedance control is recommended Thus considering xd xd xd as the desired Cartesian trajectory the following law will be used in JT q M C q xd CC q q xd Dx x Kx x g q 6 x xd xr 7 where Kx Dx R3 3are the Cartesian stiffness and damping matrices respectively and MC q CC q q R3 3are the Cartesian inertia matrix and the Cartesian Coriolis and centrifugal matrix respectively These matrices are defi ned as MC q J 1 T q M q J 1 q 8 CC q q J 1 T q C q q MC q J q J 1 q 9 B Energy Flow in the System Considering 2 and 6 the closed loop dynamics be comes MC q x CC q q Dx x Kx x Fr 10 For such a robotic system a control error energy storage function can be defi ned as follows Sce 1 2 xTMC q x 1 2 xTKx x 11 Considering 10 aswellastheskew symmetryof MC q q 2CC q q it can be proven that see 24 Sce xT dFr z Pin xT rFr z Pr xTDx x z Pdiss 12 where Pin Pr Pdiss R are the power input to the system by a motion generator the power input from the environment to the system and the power dissipated by the controller damping respectively These variables are defi ned as follows Pin xT dFr 13 Pr xT rFr 14 Pdiss xTDx x 15 Considering Fig 2 the power fl ow for the robot end effector can be written similarly The total end effector energy consists of kinetic and potential energy such that See 1 2 xT eeMee xee meeg T 0 xee 16 where xee R3is the end effector center of mass pose g0 0 g0 0 Tis the gravity vector in world coordinates and mee R and Mee R3 3are the mass and inertia matrix of the end effector respectively The latter matrix is defi ned as Mee diag mee mee Izz ee 17 5673 in which Izz ee R is the last component of the end effector inertia tensor Considering Newton s second law and the sum of forces on the end effector it can be shown that See xT rFr z Pr xT hFh z Ph 18 Now defi ning the overall storage function S R 0as S Sce See 19 and considering 12 and 18 it can be written that S Pin Ph Pdiss 20 where Phis the power being injected to the system from the human and defi ned as Ph xT hFh 21 Fig 3 shows the schematic interpretation of 20 which is the key point in our proposed rehabilitation control approach C Energy Bounding A common use of energy based system modeling is to in vestigate the system stability via passivity analysis However these models have additional benefi ts such as describing the fl ow of energy between two independent systems This is of particular interest when one of those systems is unpre dictable such as in the case of a human Here we propose applying the derived energy models to bound the energy transferred from the device to the human and to modulate the responsiveness of the device to human motion Based on 20 it can be deduced that the controlled robot is passive w r t the ports h xd Fri and h xh Fhi Therefore for the overall system stability it is necessary to passify the effect of the aforementioned ports on the system One way to do so is to augment a virtual energy tank for the ports As described in 25 designing the virtual tank boils down to bounding S Thus if S is guaranteed to be always bounded the overall system stability can be ensured Another conclusion from 20 is that the energy fl ow between the device and human is directly dependent on S A high value of S can be interpreted as a large amount of stored energy which may be transferred to the patient whenever Ph 0 According to 21 this may occur when the generated motion is against the patient applied force The amount of possible energy transfer from the device to the patient can be limited to a safe range by bounding the stored energy S As deduced from the above statements there exists an absolute upper limit bound on S which fulfi lls both the stability and chosen safety requirements Thus an arbitrary limit Smax may be defi ned with the range between 0 and this upper bound The exact choice of Smaxaffects the responsiveness of the device to differences between the patient motion and the desired motion of the device This can be explained as follows According to 11 and 19 and given that See Sr S is primarily driven by the magnitude of the tracking error variables x and x These values in turn can only be reduced from the control end by changing the desired trajectory in accordance with the patient motion Thus in practice the result of selecting a smaller value of Smaxis that the device becomes more responsive to the interaction with the patient Fig 4 as a function of S Note that while S is always assumed to be positive when Pin 0 the left side of the plane is considered D Energy based Motion Generator The process of bounding the energy of the described system is complex S cannot be controlled directly because according to 20 21 it is a function of the unpredictable human motion i e S f xh Fh However considering 13 S can be controlled indirectly or shaped via Pin by adapting xd using S Smax as a reference It must also be considered that energy shaping should not change the prescribed trajectory pattern or amplitude input by the therapist but only the speed of the desired motion The trajectory pattern input can theoretically take on any form However for purposes of demonstration a smooth sinusoidal function xd 0 5A 1 cos 2 22 xd A sin 2 23 is proposed where A R 0are the desired cyclic motion amplitude and frequency The periodic phase 0 1 is the motion progress within a cycle and is determined at each time t via Z t t0 dt0 24 where t0is the starting time of the cyclic motion Considering 22 and 23 by adapting while respecting the prescribes amplitude the desired velocity and ultimately the energy of the entire system may be shaped Moreover the phase value may also be used to identify when one leg has completed a full motion cycle and to trigger the motion of the opposite leg This prevents independent and chaotic motion profi les of the legs with respect to each other The desired motion adaptation law for smoothly adjusting becomes pif Smax S Pin 0 1 p 1 2 1 cos Smax S S if Smax S S Smax Pin 0 1if S Smax S 1 n 1 2 1 cos Smax S S if Smax S S 0 nif Smax S Pin 0 25 5674 where Smax S is the threshold for S at which the energy shaping begins and pand nare the maximum allowed positive and negative values respectively The default value for is 1 When S surpasses the allowed threshold the adjustment of depends on the direction of Pin If Pin 0 meaning that the device is pumping energy into the system at the time that the energy threshold is surpassed then is decreased to slow the desired motion or even to reverse it If Pin fso as to give more power to the learning factor Fig 5 shows an overall description of the approach in cluding the impedance controller energy observer trajectory generator and learning V EXPERIMENTALVALIDATION The previously described control schemes were imple mented in simulation and on a testbed in order to experi mental