Predictive Optimization of Assistive Force on Admittance Control-Based Mobile Walking Support System IROS2019国际学术会议论文集 2487

Predictive Optimization of Assistive Force in Admittance Control based Physical Interaction for Robotic Gait Assistance Shunki Itadera1 3 Emmanuel Dean Leon1 Jun Nakanishi2 Yasuhisa Hasegawa3 and Gordon Cheng1 Abstract In this paper we introduce our approach to walk ing assistance for elderly adults through predictive optimization of gait assistive force We focus on providing supportive interaction force to the user during walking with a robotic assistive device with an admittance controlled mobile base Appropriate physical Human Robot Interaction pHRI could be benefi cial in reducing the risk associated with immobility such as disuse syndrome by encouraging physical activities with proper assistance We propose an optimization algorithm based on a model predictive control MPC approach in order to provide desirable assistive forces according to the estimated user s state during walking Using a simplifi ed human gait model with a linear inverted pendulum we formulate the optimization of the assistive forces as a linear quadratic programming QP problem that can be suitable for real time pHRI Numerical simulations and experimental results demonstrate the feasibility of our gait support strategy in achieving appropriate compliant interactions during walking fall prevention and suitable positioning for user companion I INTRODUCTION The population ratio of elderly adults in need of help in everyday life is rapidly increasing 1 Accordingly there are growing expectations for robotic assistive devices to improve their quality of life It has been reported that walking ability could be benefi cial in promoting healthy activities of daily living and poor gait function could cause an increase in the risk of falling and disuse syndrome 2 The focus of this paper is to provide walking assistance for seniors through physical Human Robot Interaction pHRI Previously a number of assistive robots for gait support have been developed which can be largely categorized into either wearable or non wearable type devices Wearable assistive robots also called as exoskeletons are directly attached to the users lower limbs and transmit support ive force or torque to the limbs in order to assist user s joint movements 3 4 5 Such wearable robots typically adjust the users gait using pre planned motion trajectories However as the movement of the user s limb is restricted by the structure of the wearable devices attachment parts need to be carefully designed for individual users to prevent skin issues such as skin wounds and pressure sores 6 In This work is supported in part by the JSPS Overseas Challenge Program for Young Researchers 1Shunki Itadera Emmanuel Dean Leon and Gordon Cheng are with the Institute for Cognitive Systems Technical University of Munich Munich Germany shunki itadera dean gordon tum de 2Jun Nakanishi is with the Department of Mechanical Engineering Meijo University Nagoya Japan jnakanis meijo u ac jp 3Shunki Itadera and Yasuhisa Hasegawa are with Department of Micro Nano Mechanical Science and Engineering Nagoya University Nagoya Japan hasegawa mein nagoya u ac jp user gait measurement gait state estimation admittance controller predictive optimization supportswing LIPM optimizer prediction model pastprediction admittance f user non wearable assistive robot f operation force assistive force Mv p t Dv p t f t t Mv Bv f f Fig 1 A concept and a framework of the proposed walking assistance system through quasi passive pHRI based on predictive optimization of admittance control model with a simplifi ed human dynamics model addition attachment and detachment of such wearable robots structurally require assistance from several caregivers which would be time consuming for both the users and the helpers 7 On the other hand non wearable robots which are typically in the form of a robotic cane or walker composed of a mobile base and a holding handle do not impose physical restrictions on the user s limb movement thus allowing free leg movement in locomotion Such non wearable devices are generally designed to provide walking assistance from a viewpoint of offering suitable interactive forces and in formative guidance with smart sensing e g autonomous braking measuring vital information and route guidance support 8 9 10 However these assistive approaches have primarily focused on motion support based on static indices as the posture and the center of mass COM position of the user In order to take a further step and provide more effi cient gait assistance such non wearable robots are desired to be capable of providing support considering dynamic components such as the center of pressure COP and the capture point 11 In this paper we introduce a notion of quasi passive pHRI based gait assistance by combining the desirable passive compliant dynamic response of the device and providing active support when necessary at an appropriate timing In this notion the aim is to provide a suitable amount of IEEE Robotics and Automation Letters RAL paper presented at the 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 Copyright 2019 IEEE physical assistance in an active manner without interfering with user s intended natural motion according to the esti mated user s gait state Figure 1 depicts a concept and a framework of the proposed quasi passive assistance based on the predicted user s gait model We address the development of a quasi passive control architecture for a non wearable mobile robot which can support walking of elderly adults with direct gait adjustment as well as offering appropriate interactive and informative assistance In this study as an example task we aim to improve gait stability of the user and prevent falling over during walking through our proposed strategy Using a simplifi ed human gait model based on linear inverted pendulum we propose a method to optimize assistive interactive forces in an adaptive manner in order to provide appropriate physical support by adjusting user s zero moment point ZMP trajectory We formulate a model predictive control problem as a linear quadratic program ming which is suitable for real time implementation on the robot We fi rst present numerical simulations to demonstrate that the proposed assistive strategy is capable of adjusting user s ZMP trajectory during walking for the purpose of gait stability improvement Then we present hardware experi mental results in providing walking assistance through our quasi passive pHRI in order to demonstrate the feasibility of the proposed architecture using a mobile base manipulator robot II QUASI PASSIVE PHRIFORWALKINGASSISTANCE This section presents an overview of our objective and approach to the proposed quasi passive pHRI based walking assistive device see Fig 1 As mentioned above we take advantage of both passive control based assistance and desirable active support at an appropriate timing First we address technical considerations of quasi passively controlled non wearable walking assistive devices Then we discuss our target users control objectives and the proposed methodol ogy for human robot interaction via admittance control A Technical Considerations In this study in order to provide effective walking assis tance we consider the following desirable functionalities for mobile gait assistive devices 1 Operability The user should be able to operate the gait assistive device intuitively This functionality is moti vated from the viewpoint of passive control approaches for non wearable robotic walkers providing appropriate physical interaction 2 Supportability Assistive devices are required to safely adjust user s gait while providing active physical support This functionality has been addressed in the viewpoint of active control approaches for wearable gait assistive systems However compared with wearable walking assistive devices which are directly attached to the user s limbs non wearable robots are likely less capable of transmitting external assis tive forces or torques effi ciently to the user in order to adjust the user s gait Therefore it would be desirable to devise an effective control strategy for non wearable devices to provide suitable assistive forces in an adaptive manner based on the online prediction of the gait of individual users B Target Users and Control Objectives The potential users of our proposed gait assistive system will be elderly adults with reduced mobility living at home or in a nursing facility in need of physical assistance during walking or even when standing still to keep their balance For example specifi c cases could include patients who have lower middle level of primary nursing care requirements such as osteoporosis stroke and Parkinson s disease In general such patients with locomotor disability have dif fi culty in keeping their balance during walking even with the support of a walker In order to reduce the risk of falling over our control objective for the assistive device is to provide adaptive physical support to increase stability margin during walking by appropriately adjusting the user s ZMP or equivalently COP When the ZMP is at the edge of the support polygon it is known that the foot starts to rotate leading to the loss of balance Therefore in this case if the resultant ZMP with physical assistance is close to the reference ZMP it can be considered that the gait is more robust with larger ZMP margin As will be discussed below by the proposed strategy the robot is controlled so that the user s ZMP is kept away from the edge of the footprint of the user via model predictive control C Physical Interaction via Admittance Control In our framework as a hardware system we consider a walker type robotic mobile platform as illustrated in Fig 1 A prototype of such a robotic walker is currently under development towards planned use in clinical experiments with seniors in nursing facilities This prototype will be equipped with sensory systems including a laser range fi nder LRF and a force sensor The LRF is to be used to measure the relative position between the robot and the legs of the user and the force sensor is to be used to measure the interaction force The base of the robot is composed of omni directional wheels whose horizontal movement is controlled using the following admittance controller in order to achieve desirable physical interaction between the robot and the user Mv p Dv p f 1 where p x y Tis the vector of the horizontal robot handle position f fxfy Tis the vector of the user s operation force applied to the handle and x y Tis the vector of the gait assistive forces provided by the robot In the following section this gait assistive force vector will be optimized to provide suitable physical support to the user Mvand Dv are defi ned by Mv diag mvx mvy Dv diag dvx dvy 2 where mvxand mvy are the virtual mass coeffi cients dvx and dvy are the virtual damping coeffi cients Note that in the absence of the assistive force 0 in 1 the robot acts as passive dynamics governed by the admittance control model with the virtual mass and damping coeffi cients Therefore in terms of operability mentioned in Section II A this passive behavior would be helpful in achieving intuitive and easy to use interface to the users In order to address supportability we fi nd it useful to optimize the magnitude and the direction of the assistive forces in an adaptive and active manner for providing suitable physical support III OPTIMIZATIONAPPROACH In this section we present an optimization approach to fi nding a suitable assistive force in 1 within our quasi passive pHRI framework As an example we consider the task of improving gait stability i e fall prevention during walking through physical interaction The goal of this task is to provide appropriate supportive force depending on the user s balance state supportability while presenting desirable passive compliant dynamics of the robot during walking operability To this end we employ model predic tive optimization of the assistive force in an adaptive manner with a simplifi ed human gait model based on linear inverted pendulum With this assumption we formulate this model predictive optimization problem in terms of a linear quadratic programming QP problem which will be suitable for real time implementation on the robot A Problem Setup and Assumptions As shown in the concept of our gait assistance framework in Fig 1 the user walks with the robotic walker by holding its handle In order to simplify the formulation we introduce the following assumptions 1 We assume that the user grasps the handle of the robot near the hip position which is a common way of holding onto a standard walker Therefore user s horizontal body position can be represented as the robot handle position p which can be regarded as the acting point of the assistive force on the user s center of gravity COG 2 As a human gait model we employ a simplifi ed linear inverted pendulum model LIPM see Fig 2 which is often used in gait pattern generation in humanoid robots 12 among the many proposed in the study of human walking 13 In this paper the height of the user s hip position is assumed to be constant at zo 1 0m 3 The user s intended walking velocity is assumed to be constant i e the operation force f const in 1 and the time derivative of f is zero such that f 0 3 Figure 2 illustrates these assumptions on the human model and robot control model considered in this paper With these assumptions it is possible to estimate the user s posture sim ply by measuring the foot positions and make the complex optimization problem tractable as discussed in the sequel B Optimization Criteria In order to satisfy our purpose of physical gait assistance in terms of both operability passive component and support ability active support we combine the following optimiza tion criteria One is to minimize the assistive forces generated pstppzmp admittance control model LIPM user x y z assistive device Mv Bv f Fig 2 Assumptions on the human model and the controller used in this study LIPM human gait model and admittance control model for the robot base by the robot i e preserving the passive virtual admittance dynamics of the robot The other is to improve gait stability by guiding the user s ZMP toward its desirable position with the assistive force where the difference between the reference ZMP pzmp rand the actual ZMP position pzmpis minimized To achieve this goal we consider the following cost function composed of the weighted sum of these two criteria J tf t0 TW1 pzmp pzmp r TW2 pzmp pzmp r dt 4 where W1 is the positive defi nite and W2is the positive semi defi nite weighting matrix and t0and tfare the initial and the fi nal time respectively With the LIPM assumption 2 in Section III A the ZMP position pzmp can be defi ned as pzmp p z o g p 5 where g is gravitational acceleration and zois the constant height of the user s COG Furthermore with the assumption 1 in Section III A the ZMP of the user can be represented as pzmp p zo g M 1 v Dv p f 6 including physical human robot interaction and the admit tance control model 1 Note that in this model considering the physical support by the robot the ZMP will be located within the support polygon constituted by the user s footprint and the robot base In addition by providing the assistive force the user s ZMP can be adjusted accordingly In the cost function 4 we defi ne the reference ZMP trajectory pzmp rdepending of the user s gait cycle as pzmp r pslsingle stance phase pbdouble support phase 7 where pslis the center of the current footprint of the user s stance leg and pbis the user s body position which is regarded as the center of the two leg positions The objective of this reference ZMP trajectory design is to keep the user s ZMP away from the edge of the footprint in order to reduce the risk of falling over If we reformulate and discretize the dynamics given in 1 and 6 together with the assumption 3 we can obtain the following equation in the matrix form as xk 1 Axk Buk 8 where A R10 10and B R10 2are the state and input matrices respectively xkis the augmented state vector and uk is the input vector at k th discrete time step defi ned as x pT p T fTpT zmp T u 9 respectively Note that since the system A B is found to be uncon trollable we cannot derive a linear optimal feedback control law using a linear quadratic regulator approach However motivated by an example presented in 14 we formulate this optimization problem using a model predictive control MPC framework to derive an open loop optimal control law for this system in a receding horizon manner C Model Predictive Optimization In this section we solve an optimal control problem defi ned by the discrete time dynamics 8 and the cost function 4 based on the MPC framework We consider the prediction horizon steps of N and impose upper and lower bounds on the state and control input The MPC problem to fi nd the optimal control law u can be formulated as u arg min xk uk N k 0 xk xr TQ xk xr uT kRuk subject toxk 1 Axk Buk xmin xk xmax umin uk umax x0 x 10 where xkis the state vector of the model at k th prediction step xris the reference vector of xk N is the prediction horizon ukis the control output vector and Q 0 and R 0 are the weighting matrices x is the measured current state of x The state reference vector is taken as the reference ZMP position as defi ned in 7 and the upper and lower bounds of the state and the output vectors are defi ned as xr 0T0T0TpT zmp r T xmin 1 1 0 5 0 1 fx fy T xmax 1 0 5 0 1 fx fy T umin 20 10 T umax 20 10 T 11 where fxand fyare measured current operation force These bounds are chosen empirically with a pilot test on our actual robotic platform see Section V A In this paper TABLE I NOMINAL PARAMETER SET OF THE ADMITTANCE CONTROL MODEL Parameter Defi nitionValueUnit mvxVirtual horizontal frontal mass15 0kg dvxVirtual horizontal frontal damper40 0Ns m mvyVirtual horizontal lateral mass30 0kg dvy