motion control for a walking companion robot with a novel human robot interface

Research Article Motion control for a walking companion robot with a novel human–robot interface International Journal of Advanced Robotic Systems September-October 2016: 1–15 ª The Author(s) 2016 DOI: 10.1177/1729881416657752 arx.sagepub.com Yunqi Lv1, Xueshan Gao1, Fuquan Dai1, Yubai Liu1, Adil Shahzad1, Jun Zhao2, and Tong Zhang2 Abstract A walking companion robot is presented for rehabilitation from dyskinesia of lower limbs in this article A new human– robot interface (HRI) is designed which adopts one-axis force sensor and potentiometer connector to detect the motion of the user To accompany in displacement and angle between the user and the robot precisely in real time, the common motions are classified into two elemental motion states With distinction method of motion states, a classification scheme of motion control is adopted The mathematical model-based control method is first introduced and the corresponding control systems are built Due to the unavoidable deviation of the mathematical model-based control method, a force control method is proposed and the corresponding control systems are built The corresponding simulations demonstrate that the efficiency of the two proposed control methods The experimental data and paths of robot verify the two control methods and indicate that the force control method can better satisfy the user’s requirements Keywords One-axis force sensor, potentiometer connector, elemental motion states, mathematical model-based control method, force control method Date received: January 2016; accepted: 31 May 2016 Topic: Medical Robotics Topic Editor: Arianna Menciassi Introduction Many countries have stepped into aging societies with many ambulation dysfunction people Meanwhile, they have to face the shortage of nursing care.1 There are growing requirements in developing mechanism equipment to replace nursing in helping those people to walk Robotics is regarded as a promising technology to solve this problem.2,3 Scholars and researchers have made some contributions to developing intelligent walker robot recent years The main difficulties in developing a walker robot lie in the following three aspects: (1) robot mechanism design; (2) human–robot interface; and (3) control system based on the human–robot interface The walker robot mechanism should possess both stability and flexibility to support the partial body weight of its user and accompany the movement of the user timely With respect to stability, researchers usually enlarge the base of the walker robot or balance placement of heavy elements (e.g motors, batteries, electronics, etc.) at lower planes of the robot.3 As for flexibility, one typical type of mobile base consists of three Mecanum wheels 120 apart from each other.4,5 Another typical type of mobile base utilizes a pair of casters as front wheels and two rear wheels driven by two DC motors.6 Human–robot interface is of crucial importance for a walker robot because it directly influences the control Beijing Institute of Technology, Beijing, China China Rehabilitation Research Center, Beijing, China Corresponding author: Yunqi Lv, Beijing Institute of Technology, Beijing 100081, China Email: pkuchm@126.com Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License (http://www.creativecommons.org/licenses/by/3.0/) 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 algorithms and control effect When designing the human– robot interface, researchers need to take into account not only the functionality but also the user-friendliness because of the user’s deficiencies at cognitive and sensory levels.3 The design of human–robot interface involves two difficulties: the selected variables of body should fully reflect the motion state of the user and the sensors adopt to effectively measure the selected variables Many researchers select upper body strength to reflect the user walking motion To get abundant information for the user movement, many researchers use a six-axis force/torque sensor or tridimensional (3-D) force sensors to detect the force the user poses on the robot.4,7–12 In order to lower the cost of the walker robot, many researchers utilize relatively low-cost sensors to replace the six-axis force/torque sensor Tang and Cao used force-sensing resistors to detect the pull or push pressure that the user poses on the handlebar of the robot.13 Ye et al proposed a special arrangement of one-dimensional push–pull force sensors to measure the interactive force and torque between the human and the robot.14 Jiang and Wang used four force sensors embedded in the armrest.15 Patel et al used two strain gauges on each of the walkers handlebars to detect indicative pressure.16 Huang et al developed a pair of force grip handles using 13 force sensors for the left/right hand.17 Martins et al designed a new handlebar composing of two linear potentiometers and one rotary potentiometer to read the user’s walking intentions qualitatively.18 Some researchers select lower limbs to reflect the user motion JAIST (Japan Advanced Institute of Science and Technology) robotic walker employed a pair of rotating infrared sensors to detect the location of the user’s lower limbs and locate the user’s lower limbs in real time.5,19 Some researchers use vision-based methods to detect the user state Taghvaei et al used a depth sensor to estimate the human state.20,21 Based on the types of human–robot interface, the control algorithms are used accordingly Many available control algorithms have been employed in walker robot control systems Admittance control algorithm and variant of admittance-based control algorithm are widely used in the walker robot.4,7,8,10,11,13 Fuzzy control is also widely used.12,15,18,22 Other control algorithms such as learning algorithm,23 smooth control,24 and Bayesian Networks mode16 are also adopted to the walker robot Although more and more functions (e.g.: fall prevention,25,26 obstacle avoidance,27 health monitoring,8 and outdoor guidance28) are attached to the walker robot, many walker robot are not designed according to a clear requirement from the target group To archive a goal of real-time precise accompany in displacement and angle between the user and the robot, further researches are still required The precise motion control highly depends on the design of HRI Researchers have developed various kinds of HRI for walker robots and verified their effectiveness, however, there is still some space for improvement First, the sixaxis force/torque sensors or 3-D force sensors are required International Journal of Advanced Robotic Systems to remove noise (Kalman filters19 and G-h filters12), and the responding time would be extended, which has a great impact on the user comfort Second, it is difficult to build a mathematical model between the sensors outputs and the user’s postures or gestures during gait,12,18 therefore, it is not easy for motion control Third, the costs of six-axis force/torque sensors or 3-D force sensors contribute little to the extension of walker robots Finally, the upper body strength may not be the most suitable variable to detect for reflecting the motion of the user Because many patients display upper-limb discoordination symptoms after stroke.29 The lower limbs can reflect the user motion effectively, but the sensors on the lower limbs would put burden on the user, especially for the dyskinesia of lower limbs The main purpose of this article is to present our walking companion robot and its motion control algorithms This article is organized as follows The section ‘‘Walking companion robot design’’ describes the integrated design and kinematics of walking companion robot In the section ‘‘Motion control for different motion states,’’ we analyze how the human–robot interface distinguishes the different motion states and propose two motion control methods In the section ‘‘Stability analysis of motion control,’’ we analyze the stability of control systems The simulation results of the two motion control methods are provided in the section ‘‘Simulation results and analysis.’’ The section ‘‘Experiments’’ presents experimental results Finally, the conclusions and future work are given in the section ‘‘Conclusion and future work.’’ Walking companion robot design A survey of target group requirements for a satisfactory walker robot was made in China rehabilitation research center (CRRC) Based on the results of the survey, their requirements are summarized as follows: (1) a kind of flexible mechanical structure that can give user a sense of security; (2) as few operation rules as possible, especially operation rules for upper limbs; and (3) light weight and low cost In addition, other researchers’ conclusion of walker robot should be taken into consideration To make the user feel relaxed during walking, the input forces to drive the robot should be small in all conditions For the user, the required operation force should be small, better no more than 20 N.30 Based on the above analysis, we design a walking companion robot Mechanical structure of walking companion robot Mechanical structure design In order to use more security, we design four enclosed layers mechanical structure for different functions (namely top layer, middle layer, lower layer, and bottom layer) The sketch and photo of the robot are shown in Figure The user enters the robot via four doors in the back of four layers To give user support and protection, the top layer is designed The motion of waist is selected to detect the motion of the user, and thus the Lv et al Figure Walking companion robot prototype * G user can be decomposed into Y direction and the direction along with the user body RT Fcy Fty Ft Ftz Fcz Guser−H tension * Fccollision Guser * Figure Stability analysis when user falls down middle layer is designed with human–robot interface fixed in this layer To meet different height requirements of the users, the heights of the top and middle layers are adjustable The bottom layer is the mobile chassis Considering the movement characteristics of the users, the bottom layer should have a translation freedom in Y-axis and a rotation freedom in Z-axis Therefore, two-wheeled differentialdriven structure is adopted in the bottom layer Stability analysis of mechanical structure The robot should be stable when the user falls down A threshold value V max is set for the robot velocity (V) When V ! V max , the robot should slow down and serve as a stable handler for the user The break should not be too sudden to hit the user nor too slow to have a long breaking distance The force analysis in this case is shown in Figure There are four categories of force considered: the gravity * * of the user (G user ), the gravity of the robot (G robot ), collision * * force (F c ), and tension (F t ) * F c can be decomposed into Z and Y directions * * (1) The tension is * * F t ¼ k᭝ d (3) * (4) As we assume the feet of the user would not slip, we can know that the supporting force and friction force are made even by the counter force from the ground The force in Y direction can be calculated as following Grobot * * G userB ẳ N user ỵ f RB F c ẳ F cy ỵ F cz * The force in the direction along with the user body * is countervailed by the supporting force (N user ) and fric* tion ( f ) force h Guser−B * G user ẳG userB ỵ G userY (2) Since there is a breaking distance when the robot slows * * down, ᭝ d ! 0, the tension F t can be neglected * G userÀY ¼ G user RT h (5) RT and RB are the radius of top layer and bottom layer, respectively The breaking distance can be set to RB RB ¼ at 2 (6) V max ẳ at (7) F ẳ FT ỵ FC ẳ m user a (8) Torque of robot M robot ¼G robot  RB (9) M userÀY ¼ G user RT (10) Torque of user Torque of collision force MFcz ¼Fcz RB RT ị (11) MFcy ẳFcy h (12) The stability of the robot should satisfy the following conditions M robot ỵ MFcz ỵ Mtz ! MFcy ỵ Mty ỵ M userY (13) International Journal of Advanced Robotic Systems that is YF Grobot RB ỵ Fcz RB RT ị ! Fcy h ỵ Guser RT (14) The values of RB ; RT ; h1 ; and h affect the user’s comfort and cannot be altered merely based on the considerations for the robot stability Therefore, we increase Grobot by putting battery and balance weights on the bottom layer After consulting the experienced doctors and nurses in rehabilitation center, we estimate the values of parameter RB ; RT ; h1 ; and h as RB ¼ 0:55 m; RT ¼ 0:4 m; h1 ¼ ½0:8 m; 1:1 mmŠ; h ¼ ½1 :2m; :5mŠ Referring to the medical literatures,31–33 we set the user physical parameters m user ¼ 90 kg, V max ¼ 0:6 m=s G robot ! t ¼ 2RB =V max ¼ 1:833 s (15) a ¼ V max =t ¼ 0:3273 m=s (16) FC ¼ muser a ¼ 29:4599N (17) Fcy h ỵ G user RT Fcz RB RT ị ẳ 73 :0675kg RB YB Figure Installation position of two force sensors Middle layer Supporting Z Rotation axis pedestal X Y (18) Finally, we have the robot weight at a minimum of 73.0675 kg The robot weight is about 75.5 kg (including the battery pack, motors, and other electronic components), and thus the robot can be stable when the user falls down Self-reset potentiometer Force sensor Human–robot interface design Figure Potentiometer connector structure Human–robot interface plays a critical part because it is the basic of the motion control of a robot Walking companion robot human–robot interface consists of the force–sensor interface and the potentiometer connector The target group includes many hemiplegic patients who display upper-limb discoordination symptoms after stroke.29 Therefore, the waist strength responses the motion intent of them more efficient than the upper body strength does The force sensor interface employs two one-axis force sensors Detecting upper body strength requires the user to put his hand in specific armrest during the whole walking process, which is dissatisfactory according to the above survey To detect the interactive force between the user and the robot, a new arrangement of two one-axis force sensors is proposed The installation position of two one-axis force sensors is shown in Figure One end of elastic string is tied to the waist of the user and the other end of the string is connected a oneaxis force sensor When the user begins to move, the output of one-axis force sensor will reflect the motion intent of user To cover the shortage of one-axis force sensor, a novel potentiometer connector installed between the force sensor and the middle layer is designed The mechanical structure is shown in Figure The one-axis force sensor is connected to the rotation axis by screw threads The selfreset potentiometer is steadily connected with supporting pedestal When the user is turning, the one-axis force sensor and potentiometer will rotate in Z-axis The output of one-axis force is the actual one-axis force on the string The output of potentiometer can reflect the direction of rotation Electronics implementation The hardware schematic is shown in Figure Kinematics of walking companion robot Due to the limitation of motor driver, we can get output values of absolute turns of motors (nL ; nR ) rather than relative turns of motors Considering the processing speed of stm32F103ZET6, only absolute turns of motors and force sensor readings are output in the control programs The transition algorithms (transform absolute turns of motors to the robot trajectory) are as follows The absolute positions of two wheels posL and posR are nL kr nR posR ¼ 2pr wheel kr posL ¼ 2pr wheel where kr is the reduction ratio (19) Lv et al L(k + 1) Force sensors Potentiometer D L Liner amplifier +1 ) α Stm32 CAN bus Serve motor driver Serve motor driver R(k ) W (k + 1) DL (k ) CAN bus Singlechip (k W (k ) D R L(k ) DR (k ) (k +1 ) α R(k + 1) Figure Transition algorithm in motion state II Serve Reducer motor Encoder Encoder Serve Reducer motor D angle robot ¼ arccos Right drivering wheel Left drivering wheel 2ðR Dị dR k ỵ 1ịị ! 2ðR À DÞ (23) The coordinate of robot COG in the k ỵ 1(th) sampling period is Figure Electronics implementation L(k+1) The relative angle of robot is Wðk ỵ 1ị ẳ ẵxW k ỵ 1ị; yW k ỵ 1ịT ẳ ẵxW kị ỵ dW k ỵ 1ị sinD angle robot ị; W(k+1) (24) yW kị ỵ dW k þ 1Þ cosðD angle robot ފT R(k+1) Figure shows transition algorithm in motion state II L(k) W(k) R(k) dL k ỵ 1ị DL k ỵ 1ị DL kị ẳ ẳ dR k ỵ 1ị DR kị DR k ỵ 1ị D R DL k ỵ 1ị ỵ DR k ỵ 1ị ẳ DL kị ỵ DR kị ẳ D Figure Transition algorithm in motion state I (25) (26) Suppose Figure shows the trajectory of robot in one sampling period The actual paths for robot center of mass (COG) and two driven wheels are arcs Because the sampling period is too short, the arcs can be seen as straight lines We use Lkị ẳ ẵxL kị; yL kịT , W kị ẳ ẵxW kị; yW kịT , and Rkị ẳ ẵxR kị; yR kịT to denote the coordinate in the k(th) sampling period of left driven wheel, robot COG, and right driven wheel, respectively dL k ỵ 1ị, dW k ỵ 1ị, and dR k ỵ 1ị are used to denote the relative displacement of left driven wheel, robot COG, and right driven wheel, respectively, in one sampling period dL k ỵ 1ị ẳ posL k ỵ 1ị posL kị dR k ỵ 1ị ẳ posR k þ 1Þ À posR ðkÞ (20) dL ðk þ 1Þ R ẳ dR k ỵ 1ị R D (21) D dW k ỵ 1ị ẳ dR k ỵ 1ị dL k ỵ 1ị ẳl dR k ỵ 1ị (27) Dl lỵ1 (28) then we can get DL kị ẳ DR k ỵ 1ị ẳ DR kị ẳ (22) D lỵ1 DL k ỵ 1ị ẳ Dl lỵ1 dW k ỵ 1ị D=2 DR k ỵ 1ị l ẳ ẳ dR k ỵ 1ị DR kị ỵRD RD D lỵ1 dW k ỵ 1ị ẳ l1 dR k ỵ 1ị (29) (30) (31) (32) (33) International Journal of Advanced Robotic Systems Δdy R0YF Δangle user Y motion state I dyuser > Δ angleuser = R 0YB Δ dy user O motion state II Δ dyuser = Δ angleuser ≠ X Figure Interactive force analysis in motion state Figure Coordination definition of the robot system a ¼ arccos User next position User last position  2  2 dL k ỵ 1ịị ỵ DL kị DL k ỵ 1ị 2DL kịdL k ỵ 1ị (34) The coordinate of robot COG in the k ỵ 1(th) sampling period is W k ỵ 1ị ẳ ẵxW k ỵ 1ị; yW k ỵ 1ịT ẳ ẵxW kị ỵ dW k ỵ 1ị cosaị; yW kị (35) T ỵdW k þ 1Þ sinðaފ Motion control for different motion states Recognition of elemental motion state The doctors and nurses in CRRC demanded that the robot can help patients to walk slowly on flat path and suggested two common elemental motion states of human (as shown in Figure 8) Motion state I occurs when user is going straight Motion state II occurs when user is rotating in one spot (clockwise rotation or counterclockwise rotation) The reference frame O-XY is built to introduce a concept: relative motion variables A set of relative motion variables in a sampling period (denoted by Ddy user Dangle user Ddy robot Dangle robot ) was adopted to evaluate the relative displacement or angle of user and robot The human–robot interface would generate corresponding output when user begins to move So the motion state can be indicated by the interaction force between the user and the robot The outputs of two one-axis force sensors in initial state (the moment when user begin to walk with the help of robot) are F0YB ; F0YF and the real-time outputs of the two one-axis force sensors (FYB ; FYF DFYB ¼ FYB À F0YB ; DFYF ¼ FYF À F0YF ) are used to evaluate variation of the one-axis force sensors PF and PB are the voltage values of front and back potentiometers in real-time PMF and PMB are the midpoint voltage values of front and back potentiometers A rule-based method is used to recognize the current motion state Fuzzy threshold rules are summarized from general knowledge and described as follows Rule set (rule-based method) If DFYF > and DFYF and FYB > FYF , then Ddy user > 0; Dangle user ¼ If DFYB > and DFYF > and FYB % FYF and PF > PMF and PB > PMB , then Ddy user > 0; Dangle user > If DFYB > and DFYF > and FYB % FYF and PF < PMF and PB < PMB , then Ddy user > 0; Dangle user < Mathematical model-based control method The first proposed motion control method was the mathematical model-based control (MMBC) Here, we introduced a concept: calculated motion variable Calculated motion variables (consists of Ddy ðkÞ and gðkÞ) depend on sampling time and can be calculated from sampled sensors data based on the mathematical model between sensors outputs and calculated motion variable Motion state I We first built the mathematical model in motion state I Figure shows the interactive force analysis in motion state I The mathematical model between force sensor data and calculated motion variable is shown in equation (36)       R0YF À Ddy À RS FYF RYF À RS ¼ kf ¼ kf R0YB ỵ Ddy RS FYB RYB RS (36) where Ddy ẳ Ddy user ỵ otị (37) otị is a combination of sensor noises and user individual difference; RYB and RYF are the length of the two elastic strings in real-time; Rs is original length of two elastic strings; kf is elasticity coefficient of the string; R0YB and R 0YF are the initial state length of the two elastic strings The corresponding control block diagram is shown in Figure 10 Because there is possibility that DFYF ¼ 0, sensor YB is selected as the control system input Based on equation (36), Ddy can be considered as the desired displacement increment for robot and can be calculated as equation (38) Lv et al FYB Math model Δ dy ΔθLd , ΔθRd Inverse kinematics + – ΔθL , ΔθR τL , τR eL , eR Δ dy robot Kinematics Robot PID Controller L&R Figure 10 MMBC block diagram MMBC: mathematical model based control (38) (39) The torque of the right and left driving wheels is   IL tL ẳ eL PL ỵ ỵ DL S s   (40) IR tR ẳ eR PR ỵ ỵ DR S s The actual angular displacements DyL ; DyR can be estimated by mobile robot dynamics34 * * * _ ỵ F qị _ t ẳ M v_ ỵ V qịv * (41) * _ is the centripetal and where M is the inertia matrix, V ðqÞ * _ is a vector of frictional forces, t is the Coriolis matrix, F qị torque vector q ẳ ẵdx dy angle robot yr yl ŠT The robot actual displacement is User waist next position DyL ỵ DyR ịr wheel (42) Motion state II Clockwise rotation at one spot was taken as example in the following analysis of motion state II The interactive force analysis in motion state II is shown in Figure 11 The mathematical model in motion state II is shown in equation (43) Because the two sensors have a rotation freedom in Z-axis, the outputs of them are the actual oneaxis force on the string     FYF RYF À RS ¼ kf FYB RYB À RS q 2 R R ỵ a acosgị ỵ a singị 0YF S C B ẳ kf @ q A 2 R 0YB ỵ a acosgị ỵ a singị RS (43) R0YF a a γ a R width Figure 11 Interactive force analysis in motion state II In the equation, g ¼ Dangle user þ oðtÞ,oðtÞ is a combination of sensor noises and user individual difference The calculated motion variable g can be considered as the desired angle increment for robot and can be calculated based on equation (43)  2 FYF 2 BR0YF ỵ aị ỵ a K ỵ RS C B C f g ¼ acosB C @ A 2aR0YF ỵ aị DdY robot ẳ length b Rlength Ddy DydL ¼ DydR ¼ r wheel User waist last position RYF The user always moves faster than the robot and the motion control system should response as soon as possible, so the classic and simple Proportion Integration Differentiation (PID) controller is adopted The desired angular displacements of the right and left driving wheels are R 0Y F FYB R0YB ỵ Rs kf R0YB Ddy ẳ 2  FYF BR length ỵ a K þ RS B f ¼ acosB @ 2aR length (44) C C C A where R length ẳ R0YF ỵ a ẳ R0YB ỵ a ẳ length (45) a is estimated based on Chinese elder average waistline The control system in motion state II is similar to which in motion state I except the inverse kinematic and kinematic module The desired angular displacements of the right and left driving wheels are DydL ¼ gR width DydR ¼ ÀgR width (46) The robot actual angle is D angle robot ¼ DyL r wheel À DyR r wheel 2R width (47) International Journal of Advanced Robotic Systems F0YB + e – Δdydrobot PID ΔθLd , ΔθRd Inverse kinematic External controller + – ΔθL , ΔθR τL , τR e0 PID Internal controller Robot Δdyrobot Kinematic + – Calculation FYB Δ dyuser Figure 12 FC method in motion state I FC: force control Defect analysis of MMBC system In MMBC system, there are two main deviations as follows Calculation for force value F In calculation of calculated motion variable, force value F(N) must be handled first Force value F is calculated from sampled Analog/Digital converter (A/D) voltage data, that is, V AD ¼ k liner  F Because there are unavoidable deviations in one-axis force sensor output, linear amplifier, and voltage division circuit, k liner cannot be measured precisely and the calculated F would be in deviation Parameters determination in mathematical model The parameters R0YB ; R0YF , and a are relevant to personal waistline and different from person to person So those parameters in experiment program are different from the realistic parameters Finally, for the existence of the unavoidable deviation, the calculated motion variable (Ddy or g) would be in deviation Furthermore, the two deviations are difficult to be eliminated by improving the controllers So another control system needs to be developed to avoid the deviation In the experiment of force control (FC) system, we plan to use sampled AD voltage data (mV) instead of the calculated force value in order to avoid inaccurate force value calculation due to the sensor So FC method may be more likely to achieve the accurate control than MMBCS Above analyses of two control strategies are just rough analyses and theoretical inference, experimental verifications are required to determine the pros and cons FC method To overcome the disadvantages of MMBC method, a FC system is proposed, which not rely on mathematical model and avoided too much imprecise calculation The force sensor data serve as the feedback of the control system rather than the input of control system The FC basic concept is: when the real-time force sensor data equals to the initial state force sensor data, it indicates that robot moves at the same pace or rotate at the same angle with user The robot is seen as a stable system and the motion of user is seen as the disturbance, the initial output of the force sensor is seen as the reference input The control objective is to make the realtime output of force sensors equal to the initial one-axis force sensor data by adjust the motion of robot Motion state I The control block diagram of FC method is shown in Figure 12 In motion state I, the reference input of the system is the back force sensor data in initial state F0YB Based on the FC basic concept, the deviation signal of FC system is e ¼ F0YB À FYB (48) When the user begins to move, e < The desired displacement of robot can be get through PID external controller   ki E þ kd E s Ddydrobot ¼ Àe kp E þ s (49)   ki E E E ¼ ÀðF 0YB FYB ị kp ỵ ỵ kd s s The desired angular displacements of the right and left driving wheels are DydL ¼ DydR ¼ Ddydrobot r wheel (50) The actual angular displacements can be esti DyL ; DyR  I mated by internal controller tL ¼ tR ¼ e kp I ỵ ksi ỵ 34 kd I sÞÞ and mobile robot dynamic model The displacement of user is taken as a disturbance signal for the system The real-time back force sensor data FYB is the feedback of control system and can be calculated as   FYB ẳ kf R0YB ỵ Ddy robot Ddy user ịị À RS (51) Motion state II Clockwise rotation at one spot is also taken as example for FC system There is only a small difference between states II and I The desired angle of robot can be got through PID external controller   ki E ỵ kd E s (52) D angledrobot ẳ e kp E ỵ s The desired angular displacements of the right and left driving wheels are DydL ¼ angledrobot R width DydR ¼ À angledrobot R width (53) The robot actual angle is D angle robot ¼ DyL r wheel À DyR r wheel 2R width (54) Lv et al The real-time back one-axis force sensor data FYB is the feedback of control system and can be calculated as q  R0YB ỵ a À acosðD angle user À D angle robot ÞÞ þ ðÀa sinðD angle user À D angle robot ÞÞ À RS FYB ¼ kf Stability analysis of motion control The stability is also important for a control system The stability of two control methods is analyzed as following Stability analysis of MMBC method The math model module in MMBC method does not influence the stability of the system, so it is not taken into consideration in the analysis of system stability Stability analysis of MMBC system (motion state I) The closeloop transfer function of the system is GðsÞ ẳ 2kp ỵ 2kd s r 2wheel ms2 ỵ 2kd s ỵ 2kp where m is the mass of the robot The characteristic equation of the system is r 2wheel ms2 ỵ 2kd s ỵ 2kp ẳ The roots of characteristic equation are qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Àkd + kd À 2r 2wheel mkp s 1;2 ¼ r 2wheel m (56) (57) The sufficient and necessary condition of regional stable for the system is s 1;2 < or s 1;2 possess a negative real part The controller parameters should satisfy the following equations (58) or (59)  kd > (58) kd À 2r 2wheel mkp < ( kd > q kd ỵ kd 2r 2wheel mkp < ỵ GK sị ẳ (55) Stability analysis of MMBC system (motion state II) The closeloop transfer function of the system is Gsị ẳ r 2wheel Is2 2R width kp ỵ kd sị ỵ 2R width kd s ỵ 2R width kp where I is the moment of inertia of the robot The characteristic equation of the system is r 2wheel Is2 ỵ 2R width kd s ỵ 2R width kp ẳ (60) The roots of characteristic equation are qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ÀR width kd + ðR width kd Þ À 2r 2wheel IR width kp s 1;2 ¼ (61) r 2wheel I The sufficient and necessary condition of regional stable for the system is s 1;2 < or s 1;2 possess a negative real part The controller parameters should satisfy equation (62) or (63)  kd > (62) ðR width kd Þ À 2r 2wheel IR width kp < ( kd > q (63) R width kd ỵ R width kd Þ À 2r 2wheel IR width kp < Stability analysis of FC method Stability analysis of FC system (motion state I) The open-loop transfer function for the closed-loop control system is GK sị ẳ (59) 2kf kpI þ kdI sÞðkpE þ kdE sÞ r 2wheel ms2 þ 2kd I s ỵ 2kp I The characteristic polynomial is   r 2wheel m ỵ 2kf kdI kdE ịs ỵ kf kpI kdE ỵ kdI kpE ị þ kd I s þ 2kf kpI kpE þ 2kp I r 2wheel ms2 ỵ 2kd I s ỵ 2kp I The poles of the system are   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kf kpI kdE ỵ kdI kpE ị ỵ kd I + ẵkf kpI kdE ỵ kdI kpE ị ỵ kd I 2kpI kf kpE ỵ 1ịr 2wheel m ỵ 2kf kdI kdE ị s 1;2 ẳ r 2wheel m ỵ 2kf kdI kdE (64) (65) The sufficient and necessary condition of regional stable for the system is s 1;2 < or s 1;2 possess a negative real part 10 International Journal of Advanced Robotic Systems The controller parameters should satisfy the following equation (66) or (67) ( kf ; kpE ; kdE ; kpI ; kdI > I I E I E ½kf ðkp kd ỵ kd kp ị ỵ kd 2kpI kf kpE ỵ 1ịr 2wheel m ỵ 2kf kdI kdE Þ < ( kf ; kpE ; kdE ; kpI ; kdI > ffi  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  À kf kpI kdE ỵ kdI kpE ị ỵ kd I ỵ ẵkf kpI kdE ỵ kdI kpE ị ỵ kd I 2kpI kf kpE ỵ 1ịr 2wheel m þ 2kf kdI kdE Þ < (66) (67) Stability analysis of FC system (motion state II) The open-loop transfer function for the closed-loop control system is GK sị ẳ 0:24R width kpE ỵ kdE sịkp I ỵ kd I sị r 2wheel Is2 ỵ 2R width kd I s þ 2R width kp I The characteristic polynomial is ỵ GK sị ẳ   r 2wheel I ỵ 0:24R width kdI kdE ịs ỵ 2R width kd I ỵ 0:24R width kpI kdE ỵ kdI kpE ị s ỵ 2R width kpI ỵ 0:12kpE ị r 2wheel Is2 ỵ 2R width kd I s ỵ 2R width kp I The poles of the system are   2R width kd I ỵ 0:24R width kpI kdE ỵ kdI kpE ị s 1;2 ẳ 2r 2wheel I ỵ 0:24R width kdI kdE ị q ẵ2R width kd I ỵ 0:24R width kpI kdE ỵ kdI kpE ị 8r 2wheel I ỵ 0:24R width kdI kdE ịR width kpI ỵ 0:12kpE ị + 2r 2wheel I ỵ 0:24R width kdI kdE ị (68) (69) The sufficient and necessary condition of regional stable for the system is s 1;2 < or s 1;2 possess a negative real part ( kf ; kpE ; kdE ; kpI ; kdI > (70) ½2R width kd I ỵ 0:24R width kpI kdE ỵ kdI kpE ị 8r 2wheel I ỵ 0:24R width kdI kdE ịR width kpI ỵ 0:12kpE ị < > > < kf ; kpE ; kdE ; kpI ; kdI >  À 2R width kd I þ 0:24R width ðkpI kdE þ kdI kpE Þ þ > qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > : ½2R I E 2 I E I I E I E width kd ỵ 0:24R width kp kd ỵ kd kp ị 8r wheel I ỵ 0:24R width kd kd ịR width kp þ 0:12kp Þ <  Simulation results and analysis MMBC system Simulink (include in MATLAB R2009a) is utilized to conduct the simulations in order to verify the efficiency of the two control algorithms The simulation results of MMBC system (motion states I and II) are shown in Figures 13 and 14 The user relative motion variables (Ddy user and Dangle user ) is time-varying, and thus we build a force sensor input signal with acceleration and deceleration The calculated motion variable (Ddy and g) signal also has acceleration and deceleration corresponding The signal variables of relative robot motion (Ddy robot and Dangle robot ) need to coincide with the variables signal of calculated motion (Ddy and g) The fitting degree between the two lines in Figures 13 and 14 shows that the MMBC method works as expected (71) The controller parameters (motion state I) in simulation are kp ¼ 1000; ki ¼ 0; kd ¼ 1, which can satisfy equation (58) The controller parameters (motion state II) in simulation are kp ¼ 700; ki ¼ 0; kd ¼ 10, which can satisfy equation (62) FC system The simulation results of the FC system (motion states I and II) are shown in Figures 15 and 16 We also use a signal with acceleration and deceleration to simulate the user’s relative motion In Figures 15(a) and 16(a), the fitting degree between two lines shows that the signal variables of the robot relative motion (Ddy robot and Dangle robot ) can coincide with the variables signal of user relative motion Lv et al 11 (Ddy user and Dangle user ) In Figures 15(b) and 16(b), the small difference between the force signal in real time and in initial state (F0YB À FYB ) can verify the control effect and the FC method The controller parameters (motion state I) in simulation are kpE ¼ 100; kiE ¼ 0; kdE ¼ 0:1 and kpI ¼ 1000; kiI ¼ 0; kdI ¼ which can satisfy equation (66) The controller parameters (motion state II) in simulation are kpE ¼  108 ; kiE ¼ 0; kdE ¼ 0:5 and kpI ¼ 700; kiI ¼ 0; kdI ¼ 10, which can satisfy equation (71) 0.1 0.05 –0.05 Calculated motion variable(displacement) Relative robot motion variable(displacement) 10 20 30 Time (s) Figure 13 Simulation result of MMBC system (motion state I) MMBC: mathematical model-based control Angle (radian) 0.25 0.2 0.15 0.1 0.05 Calculated motion variable (angle) Robot motion variable (angle) 0.5 1.5 2.5 Time(s) 3.5 4.5 Relative displacement (m) Figure 14 Simulation result of the MMBC system (motion state II) MMBC: mathematical model-based control 0.08 0.06 0.04 0.02 User relative displacement Robot relative displacement 0 10 20 Experiments Before the overall experiment, the proportionality coefficient k liner from sampled AD data (mV) to force value (kg) is measured about 700–750 k liner varies between each power on and cannot be measured precisely as expected To verify the control algorithms, a participant is asked to go straight (motion state I) and rotate in one spot (motion state II), while the samplings of the relevant data are taken The experiment photos are shown in Figure 17 The first problem for the overall experiment is how to acquire the ground truth path For mobile robot location, many scholars acquire robot ground truth path by motion capture system (VICON motion system35 and top-down camera tracking system (UGV) 36 ), global positioning Front force sensor output (N) Displacement (m) 0.15 30 3.602 3.601 3.6 3.599 3.598 3.597 3.596 Front force sensor output in real-time Front force sensor output in initial state 10 20 Time (s) Time (s) (a) (b) 30 0.3 Robot relative angle User relative angle Angle (radian) 0.25 0.2 0.15 0.1 0.05 0 Front force sensor output (N) Figure 15 A simulation result of FC system (motion state I) FC: force control 3.6 Front force sensor output in real-time Front force sensor output in initial state 3.6 3.6 3.6 3.6 3.6 Time (s) Time (s) (a) (b) Figure 16 Simulation results of FC system (motion state II) FC: force control 12 International Journal of Advanced Robotic Systems Potentiometer connector 4.5 high And low adjustable One-axis force sensor Y axis (m) 3.5 Motor Baterry 2.5 1.5 Path of FC method Reference path Path of MMBC method Start point Finish point Figure 17 Photos of field experiment 0.5 37 system (GPS and the combination of radio frequency identification (RFIR) and encoder,38 but that is actually unnecessary for a walker robot For the walker robot location, most researchers calculate the ground truth paths by motor turns.4,8,28 Researchers use simple concepts like best-fit line4 and desired path8 to represent the user ground truth path We use best-fit line to represent the user path in this article The comparison method and best-fit line concept are introduced as follows: To quantitatively evaluate the coincidence between the motion of robot and the user’s walking intention, we assume a metric that is given by DIFð robot; userÞ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N 2  2 (72)  X ẳ xR iị xfit iị ỵ yR iị yfit iị DIF (robot and user) Motion state I Motion state II In the experiment of motion state I, a patient was asked to go straight along the reference path with the help of walking companion robot The distance from the starting point to the finishing point is 4.6 m As shown in Figure 18, the differences between the two paths and the reference path are small and can meet the needs of user The path of MMBC method has an error in terminal point in Y-axis (which is about 0.05 m) The path of FC method also has an error in terminal point in Y-axis (which is about 0.008 m) that verifies the deviation analysis of MMBC method This fact was further proven by calculating the average values of DIF(robot,user) see Table 1) The angles of robot with two control methods are shown in Figure 19 The errors in angle of the robot with two control methods are also small Both –3 × 10 MMBC method FC method 0.02295 0.02180 0.02141 0.01802 MMBC: mathematical model based control; FC: force control × 10 –3 Force control method Math model based control method –2 –4 –6 Motion state I Table Comparison of DIF(robot,user) using different control methods Angle of robot (radian) the point set of the motion path Note that the best-fit line should be obtained according to the given motion state, which reflect the user’s motion state.4 X axis (m) Figure 18 Paths comparison for two control methods (motion state I) i¼1 where N is the  data number of a motion path of the robot;  xR ðiÞ; yR ðiÞ is the ith point in the robot motion path;   xfit ðiÞ; yfit ðiÞ is the ith point of the best-fit line through –2 10 Time (s) 15 20 Figure 19 Angle of robot with two control methods (motion state I) the errors in displacement (X-axis) and angle increase with time Those errors are time-accumulated errors, which are too small to effect use’s comfort In Figure 20, the big difference between front force sensor output and back force sensor output indicated the user is in motion state I The back force sensor output in MMBC system was no more than 16 N (as shown in Figure 20(b)), while in FC system was no more than 12 N (as shown in Figure 20(a)) These met with the requirements from the previous survey The controller parameters (MMBC method) in field experiment are kp ¼ 950; ki ¼ 0; kd ¼ 0:8, which can satisfy equation (58) 13 16 1000 Force sensor output (N) Force sensor output (mV) Lv et al Back force sensor Front force sensor 800 600 400 200 Back force sensor output in real-time Front force sensor output in real-time 12 0 10 15 20 10 Time (s) Time (s) (a) (b) 15 20 Figure 20 Force sensor outputs of two control systems (motion state I) 0.01 Angle of robot (radian) Path of MMBC method Rotation spot Path of FC method Y axis (m) –0.01 –0.02 –0.03 –0.05 –0.05 –0.04 Force control method Mathematical model based control method Time (s) –0.04 –0.03 –0.02 –0.01 X axis (m) 0.01 0.02 0.03 Figure 21 Paths comparison for two control method (motion state II) The controller parameters (FC method) in field experiment are kpE ¼ 80; kiE ¼ 0; kdE ¼ 0:1 and kpI ¼ 950; kiI ¼ 0; kdI ¼ 0:8 which can satisfy equation (66) Figure 22 Angle of robot with two control methods (motion state II) The controller parameters (MMBC method) in field experiment are kp ¼ 800; ki ¼ 0; kd ¼ 10, which can satisfy equation (62) The controller parameters in field experiment are kpE ¼  108 ; kiE ¼ 0; kdE ¼ 0:5 and kpI ¼ 800; kiI ¼ 0; kdI ¼ 10, which can satisfy equation (71) Feedbacks from the participants Motion state II In the experiment of motion state II, a patient was asked to rotate in one spot Figure 21 shows the paths with two control methods in motion state II The error in displacement is acceptable for user Obviously, the error of path with FC method was small than the error of path with MMBC method This fact was further proven by calculating the average values of DIF (robot and user; see Table 1) Data in Figure 22 shows the angle of robot The angle of MMBC method has an error in terminal point (which is about 5 ) The angle of FC method has an error in terminal point (which is about 2 ) Figure 23 shows the small difference between front and back force sensor, which can indicate the user is in motion state II The back force sensor output in MMBC system is no more than 12 N (as shown in Figure 23(a)), while output in FC system is no more than 11 N (as shown in Figure 23(b)) These made user comfortable from the previous survey Twenty patients in CRRC were asked to use the walking companion robot According to the feedbacks from these participants, we summarized the following conclusions as shown in Table These feedbacks verify the previous theoretical analysis of the two control strategies Conclusion and future work This article proposed a new walking companion robot, which is different from the existing walker robot in mechanical structure and human–robot interface Two motion control methods of this robot were studied based on online estimating user motion state The main contribution of this study is to design a novel human–robot interface which has the advantages of low noise and low cost Based on the human–robot interface, an online inference algorithm for user motion state and two 14 International Journal of Advanced Robotic Systems 800 Back force sensor Front force sensor Force sensors outputs in real time (mV) Force sensors outputs in real time (N) 12 0 Back force sensor Front force sensor 600 400 200 0 Time (s) Time (s) (a) (b) Figure 23 Force sensor outputs of two control systems (motion state II) Table Feedbacks from 20 participants Experimental objective Mechanical structure Human–robot interface MMBC method FC method Force sensor potentiometer connector Motion state I Motion state II Motion state I Motion state II Satisfaction Dissatisfaction No opinion 17 18 19 16 18 18 1 12 1 2 MMBC: mathematical model-based control; FC: force control motion control methods was proposed The inference algorithm and the two motion control methods were simple so that the robot can respond quickly when the user moves The simulation and experiments verified the effectiveness of the proposed algorithms The comparison of the two control methods was made using other researchers’ methods The comparison indicated that the FC method can better satisfy the user than the MMBC method Still, this robot could be better if we can fulfill the following requirements in future work: First, the two elemental motion states were not plenty for human motion, whereas they are just our first steps We can further add more elemental motion states for control Second, the detection and prevention against falling down should be added in the robot Falling down could be lethal for the users and thus it is essential to add this function 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 Funding The author(s) received no financial support for the research, authorship, and/or publication of this article References Spitzer WJ and Davidson KW Future trends in health and health care: implications for social work practice in an aging society Soc Work Health Care 2013; 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Taghvaei S, Hirata Y and Kosuge K Comparative study of visual human state classication; An application for a walker robot In: 2012 4th IEEE RAS & EMBS International Conference on Biomedical Robotics