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Development of Force Observer in Series Elastic Actuator for Dynamic Control Yongsu Park, Student Member, IEEE, Nicholas Paine , Member, IEEE, and Sehoon Oh , Senior Member, IEEE
Abstract—Recently, a series elastic actuator (SEA) has emerged as a potential actuator system for various robotic applications where safe and precise interactive force control is required. Even though lots of research has been conducted on the mechanical/controller design and the development of applications for SEAs, the accurate force observation issue has not been highlighted much. Only the simple law, that is, the spring in an SEA can measure interactive force has been repeatedly mentioned and utilized. However, this is not true when the load-side dynamics affects the spring deformation significantly. This paper tackles this problem by demonstrating the imprecise force observation of the spring deformation and proposing two types of external force observers to address the problem. A reaction force-sensing SEA (RFSEA) is adopted in this paper, and its dynamic characteristic is analyzed in detail using the Lagrangian mechanics. Based on the analyzed dynamics, force observers are designed and verified through simulations and experiments. An XY stage driven by RFSEAs is developed so that the stage can be force controlled, and the proposed force observers are applied to this. Human interactive forces on the developed XY stage, the impedance of which is controlled in several ways, are estimated and compared with a force plate. Various experimental results validate the performance and potential of the proposed force observer for SEA systems. Index Terms—Force estimation, impedance control, load dynamics, series elastic actuator.
I. INTRODUCTION S VARIOUS robotic technologies find their way to serve humans in more directive ways, the physical interaction between robots and humans has become more significant than ever. In order to achieve safe and task achieving physical in-
A
Manuscript received January 26, 2017; revised July 9, 2017; accepted July 23, 2017. Date of publication August 25, 2017; date of current version December 15, 2017. This work was supported in part by the DGIST Start-Up Fund of the Ministry of Science, ICT and Future Planning (2017010057), and in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF2016R1A2B4016163). (Corresponding author: Sehoon Oh.) Y. Park is with the Convergence Research Center for Collaborative Robots, Daegu Gyeongbuk Institute of Science and Technology, Daegu 42988, South Korea (e-mail:
[email protected]). N. Paine is with the Apptronik Inc., Austin, TX 78758 USA (e-mail:
[email protected]). S. Oh is with the Department of Robotic Engineering, Daegu Gyeongbuk Institute of Science and Technology, Daegu 42988, South Korea (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2017.2745457
teraction, a number of research works have been conducted in various domains including mechanical hardware design [1], [2] as well as software design, such as controllers [3], [4]. It requires an inherently safe actuator system that can also provide enough power to achieve tasks, where the comprehensive design of hardware and software plays a significant role. A series elastic actuator (SEA) [5], [6] has emerged as one of the most potential actuators for various systems for safe and high-performance interaction tasks. An SEA that consists of a motor as the force source, a reduction gear, and a spring as transmission, which is attached to the load, has the following features. 1) The elongation of the spring can measure the force applied on the spring [6]. 2) The motor-side dynamics and the load-side dynamics are decoupled only through the spring [6]. 3) Precise force control can be achieved by the control of the spring deformation [7]. 4) The inherent elasticity of the spring can reduce the impacts when the system contacts humans or any rigid environments [8]. Due to these features, an SEA has been employed in various robotic applications that demand safe interaction with humans, such as exoskeleton [9], rehabilitation robot [10]–[12], humanoid robot [13], [14], [15], and haptic device [16]. In these applications, SEAs are mainly force controlled to generate the desired force through the control of spring deflection, where low impedance can be achieved, while high impedance to make an SEA stiff is relatively difficult to realize. Notice that the elongation of the spring (multiplied by the stiffness) has long been utilized as the force measurement in an SEA, which is partially true when the SEA contacts rigid environment [7]. However, when the load side of the SEA can move freely without contacting any environment, this is not the case, and the spring cannot measure the external force that is applied to the load; the spring force is affected not only by the external force, but also by the inertial force and other forces, such as damping. As the static case is not the only application of the SEA, it can be generally said that the SEA has failed to provide external force information, particularly when it generates dynamic motions under position control or impedance control [17], [18]. This point will be explored theoretically and experimentally in this paper. The estimation of external force information on an SEA system can be a significant issue [19], when it is utilized in
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Fig. 1. Experimental platform used in this paper and the contributions to be shown using the platform.
various interactive systems. For instance, in the rehabilitation robot application [10], the force generated by a patient during rehabilitation can be measured and utilized for the diagnosis. Also, the estimation of the force exerted on the slave/master robot is important in haptic applications to obtain environmental information for the stability analysis. A method to account for this problem is to reduce the inertia/mass of the load side [20] so that the force measured through the spring can be directly approximated as the external force by reducing the dynamic effect of the load side. However, this approach constrains the freedom of an SEA design, which also leads to the limitation of SEA applications. As an SEA accomplishes high performance force control by tactfully associating the motor force/torque and elastic force, many researchers have proposed various mechanical designs of SEAs, seeking for appropriate combinations and configurations of motor, gear, and spring. In each case, the force measured by spring deformation implies different physical meanings, e.g., it can represent the action force to the load, while it can represent the reaction force to the ground. Therefore, it is necessary to provide a methodology that can be applied to a variety of SEA designs to estimate external force affecting the SEA system. This paper addresses this force estimation problem in an SEA system, and proposes external force observers (EFOs). Among numerous types of SEAs, a reaction force-sensing SEA (RFSEA) [21] is employed as the target system of the force estimation, since the dynamics of RFSEA is complicated, and the spring deformation is affected not only by the load dynamics, but also by the spring dynamics. Two types of force observer are designed for the SEA, and its accuracy is verified compared with a load cell. As the application of this force observer, a force-controlled sliding platform— a linear XY stage that is driven only by SEAs—is developed, and its impedance is controlled. As mentioned previously, the spring deformation in this case cannot measure the force acting on the platform, which will be shown later. The proposed force observer is applied to this platform, and the force estimation performance during impedance control is validated. Fig. 1 illustrates the contribution points along with the system proposed in this paper: The dynamics of an RFSEA, including the load dynamics, is derived, and force observers are designed based on that. An XY stage that is fully driven and controlled by RFSEAs are developed, and the performance of the proposed observers is validated using the stage.
Fig. 2.
Configuration of an RFSEA.
Fig. 3. Two different configurations of (a) conventional FSEA and (b) RFSEA.
II. DYNAMICS ANALYSIS OF RFSEA In this research, an RFSEA is utilized as the target of force observation and SEA application. Fig. 2 shows the configuration of an RFSEA, where the spring is connected between the stator of the motor and the ground. This is the most significant difference from other SEAs (which can be called force-sensing SEA, FSEA), where the stator section of the motor is directly fixed to ground base, and the elastic element is placed between the motor output and the load. Due to this characteristic, the motor itself is floating with regard to ground base in an RFSEA, and the spring deformation measures rather the reaction force from the motor than the force to the load. This difference is illustrated in Fig. 3. Due to this unique characteristic, an RFSEA can achieve the screw-moving mechanism in an SEA, which can lead to compact size of the actuation system. The other difference of RFSEAs from other conventional SEAs is well discussed in [21], and in spite of this mechanical advantage of an RFSEA, its dynamics has not been clearly explored due to its complicated design. The dynamics, however, needs to be clarified for the design of force observer, in this research. A. Modeling of RFSEA Using Conventional Two-Mass Dynamic Model In general, the dynamics of SEA is modeled as a two-mass system, when the load side is not fixed but moving [22], [23]. Fig. 4 illustrates the block diagram of the two-mass dynamic model. Note that, in this model, the dynamics of an SEA is described as a Multi-Input-Multi-Output (MIMO) system, where two inputs are the motor torque (τm ) and the external force (Fext ), and three outputs are the motor angle (θm ), the load angle/position (xl ), and the spring deformation (xs ). The dynamic relationship between the inputs and the outputs is derived and
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Fig. 4. Block diagrams of an SEA system. P m (s) represents the motor dynamics (P m (s) = J s 2 1+ B s ), P l (s) is the load dynamics (P l (s) = m
m
1 ), and P s (s) is the spring and motor stator dynamics (P s (s) = M l s2 + B l s 1 ), where Jm , M l , and M s represent the inertia/mass of M s s2 + B s s+ K s the motor, the load, and the spring, respectively, while B m , B l , and B s
mean the damping coefficients of the motor, the load, and the spring, respectively. K s is the stiffness constant, and N m is the reduction gear ratio. (a) Conventional two-mass system to describe the dynamics of FSEA. (b) Novel dynamic model to describe the dynamics of RFSEA.
discussed in [22]. This two-mass dynamic model can be adopted as the model of RFSEA; dynamics analysis and the parameter identification can be performed based on the model. In order to verify the dynamic model, the frequency response function (FRF) of an RFSEA is measured using a fast Fourier transform (FFT) analyzer (Ono Sokki, CF9400) and compared with the theoretical model. The load side was not fixed during the measurement, and thus three outputs, i.e., the motor angle, the spring deformation, and the load position, were measured differently. The parameters for the model were identified to fit the measured FRF. Fig. 5 shows the comparison, where three FRFs (from the motor torque to the three outputs) are displayed. The two-mass dynamic model can match well with two FRFs, of the motor angle and of the spring deformation, with the resonance frequency located at 9.53 Hz. On the other hand, the FRF of the load position presents a different match; there is an antiresonance around 17 Hz in the measurement, while the model cannot include the antiresonance. In addition, the estimated load mass (34 kg) derived to fit the FRF measurement is very different from the actual load mass (21.87 kg). B. Modeling of RFSEA Using Unlumped Mass Model The most significant reason for the failure of the two-mass dynamic model to represent the dynamics of RFSEA, in particular, the load dynamics is due to the fact the dynamic model cannot describe the dynamics of the motor stator/housing that is floating with regard to ground. To observe the external force precisely, it is important to capture the dynamic characteristics of the load side. Therefore, a novel dynamic model for an RFSEA is proposed in this section. A similar problem was investigated in [24]; the paper proposed to utilized unlumped mass model to precisely model the reaction dynamics of SEA, which decopules the inertia of the motor and the inertia/mass of the transmission. However, the discussion in [24] only covers the static case where the load
Fig. 5. FRF result with respect to each outputs using conventional two-mass system modeling (dotted red line: estimated FRF, and solid blue line: measured FRF). (a) FRF from motor current to motor velocity. (b) FRF from motor current to spring deformation. (c) FRF from motor current to load position.
side contacts only high-impedance environments. This research provides more comprehensive solution that can also cover dynamic conditions. In order to incorporate the dynamics of the motor stator, an unlumped model for RFSEA is proposed, as shown in Fig. 6, where Ms , Jm , Bs , and Bm are the inertias and the damping coefficients of the motor stator and the rotor of the motor, respectively.
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Notice that the general torque inputs here are the motor torque τm and the external force Fext to the load, which is to be estimated. By eliminating the constraint force λ, the final equations of motions can be derived as follows: ¨l + Bl x˙ l + Ms x ¨s + Bs x˙ s + Ks xs Fext = Ml x
(10)
−1 τm = Jm θ¨m +Bm θ˙m − Nm (Ms x ¨s + Bs x˙ s + Ks ).(11)
Fig. 6.
Unlumped dynamic model of SEAs. (a) FSEA. (b) RFSEA.
Compared to the model of the conventional FSEA shown in Fig. 6(a), it is clear that the proposed model, shown in Fig. 6(b), can explicitly represent the dynamics of the motor housing also including the stiffness Ks of the spring. C. Derivation of RFSEA Dynamics Notice that there exist three degrees of motions in this model, which are the motor angle θm , the load position xl , and the spring deformation xs . However, these motions are kinemati−1 = xl , and thus, there are only cally constrained as xs + θm Nm two degrees of freedom in the motion of an RFSEA (also of FSEA, too). In order to solve the dynamics of RFSEA taking the degrees of freedom and the constraint into account, Lagrangian mechanics is employed, where the kinematic energy (T ), the potential energy of spring (V), the energy dissipation by damping friction (D), and the kinematic constraint (C) are considered as follows: 1 1 1 2 Ml x˙ 2l + Ms x˙ 2s + Jm θ˙m 2 2 2 1 V = Ks x2s 2
T =
−1 C = xs − xl + Nm θm
1 1 1 2 Bl x˙ 2l + Bs x˙ 2s + Bm θ˙m 2 2 2 L = T − V + λC
D=
(1) (2) (3) (4) (5)
where physical variables are as shown in Fig. 6. Based on this definition, the dynamics of RFSEA can be derived using the Lagrangian mechanics as follows: d ∂L ∂D ∂L + = Fi (6) − dt ∂ x˙ i ∂xi ∂ x˙ i where Fi is generalized force input. As there are three variables, θm , xl , and xs , three equations of motions are derived as follows: Ms x ¨s + Ks xs + λ + Bs x˙ s = 0 Ml x ¨l − λ + Bl x˙ l = Fext −1 Jm θ¨m + Nm λ + Bm θ˙m = τm .
(7) (8) (9)
The derived dynamic model can be depicted using the block diagram shown in Fig. 4(b). Compared to the conventional FSEA shown in Fig. 4(a), the spring stiffness Ks is replaced by Ps−1 (s) = Ms s2 + Bs s + Ks in the RFSEA. This difference implies that the force connecting the motor and the load is not only the spring force, but also the inertial and damping force of the motor stator, which shows that the proposed unlumped model shown in Fig. 6(b) is more adequate to describe the dynamics of RFSEA. The transfer functions to describe the dynamic relationship between the two inputs and the three outputs can be derived as (12) based on the derived dynamics: ⎤ ⎡ P (P +P ) −1 Pm Pl Nm m s l ⎤ ⎡ D (s) D (s) θm ⎥
⎢ ⎥ τm −1 ⎥ ⎢ ⎢ Nm Pm Ps Ps Pl ⎥ ⎢ (12) ⎣ xs ⎦ = ⎢ − D (s) ⎥ F D (s) ⎦ ext ⎣ xl −2 −1 Pm ) P l (P s +N m Nm Pm Pl D (s)
D (s)
where the common denominator is given as −2 Pm (s) + Pl (s) + Ps (s). D(s) = Nm
(13)
D. Experimental Verification of the Proposed Dynamic Model In order to verify that the proposed dynamic model can properly describe the motion of RFSEA, FRF is calculated based on the proposed model and compared with the measurement. Fig. 7 shows the results, which shows the proposed model can match all the FRF measurement. Unlike the conventional two-mass model, the unlumped model can present the antiresonance in the load motion response, as shown in Fig. 7(c). This can be attributed to the point that Ms and Bs are included in the model resulting in zeros in the dynamics from the motor torque to the load angel, which can be verified by the transfer function in (12) from τm to xl . The mechanical parameters are identified from the measure FRF. Table I presents the comparison of parameters identified using the conventional two-mass model and the proposed unlumped dynamic model. Notice that the identification of the load mass Ml using the proposed model is close to the actual mass (21.87 kg). III. OBSERVER DESIGN FOR EXTERNAL FORCE ESTIMATION As discussed above, the force measurement based on the spring deformation does not coincide with the external force, when the load side is moving dynamically, in particular. In this section, a force observer is designed based on the dynamics model of SEAs to address this problem.
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TABLE I ESTIMATED PARAMETERS Parameter Jm Bm Ml Bl Ms Bs Ks Nm
Fig. 8.
Two-Mass model
Unlumped Dynamic Model
0.64e− 5 kg·m2 0.6e− 4 N · m · s/rad 34 kg 350 N · s/m N/A N/A 141 350 N/m 7854
0.64e− 5 kg·m2 0.6e− 4 N · m · s/rad 22 kg 200 N · s/m 10 kg 100 N · s/m 141 350 N/m 7854
Structure of an EFO.
searchers have developed a force observer for flexible systems using the two-mass dynamic model [27], which can be applied to an SEA system with some modification. Here, a force observer to estimate external force is designed for an RFSEA based on the derived dynamic model; external force Fext can be calculated as follows based on (10):
Fˆext = Ql (s) Pl−1 (s)xl + Ps−1 (s)xs (14) where Ql (s) is a low-pass filter to make the observer proper and also to reduce high-frequency noise. In this paper, Ql (s) is designed as a second-order low-pass filter as in (15) with the cut-off frequency set to ωc = 25 Hz, and Pl (s) and Ps (s) are second-order systems: Ql (s) =
ωc2 . s2 + 2ωc s + ωc2
(15)
The structure of the proposed EFO is represented in Fig. 8. B. Steady-State Kalman Filter (KF) to Estimate External Force
Fig. 7. FRF result with respect to each outputs using unlumped twomass system modeling (dotted red line: estimated FRF, and solid blue line: measured FRF). (a) FRF from motor current to motor velocity. (b) FRF from motor current to spring deformation. (c) FRF from motor current to load position.
A. External Force Observer Force estimation based on the dynamic model of a system has been proposed from the 90 s [25], and now is widely utilized as force sensorless control [26]. However, these approaches are for rigid actuator systems that do not take into consideration the elasticity of the system significantly. Recently, several re-
The force observer designed as in (14) requires second-order time derivatives, which can lead to very noisy observation result. Even though low-pass filters can reduce the noise level, it also deteriorates the observation performance by limiting the bandwidth. To address this problem, a state observer can be designed for force observation. Since the dynamics of RFSEA is derived as in (10) and (11), a state-space model can be built for the state observer. Based on (10) and (11), the states to be observed is defined as T (16) x = θm xs θ˙m x˙ s Fext . Notice that the external force Fext should be included as a state to be observed. The input to the system is the motor torque,
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and the outputs are the motor angle and the spring deformation measurements that are represented as T u = τm , y = θm xs . (17) With these definitions, the state-space model of RFSEA is given as follows: x˙ = Ax + Bu
(18)
y = Cx + Du
(19)
⎡
0
0
α
0
0
0
α
0
⎤
⎢0 ⎢ 1⎢ ⎢0 A= α⎢ ⎢ ⎣0
a1
a2
a3
a5
a6
a7
0⎥ ⎥ ⎥ a4 ⎥ ⎥ ⎥ a8 ⎦
0
0
0
0
0
B= C= D=
T 1 0 0 b1 b2 0 α
1 0 0 0 0 0
0
1 0 T 0
0
0
(20)
(21)
(22) (23)
where each element is given as a1 = Ks Ml Nm
(24)
a2 = −(Ml Ms +
2 Bm Ml Nm
+
2 Bm Ms Nm )
(25)
a3 = −Nm (Bl Ms − Bs Ml )
(26)
a4 = −(Nm (2Ml + Ms ))
(27)
2 a5 = −(Jm Ks Nm + Ks Ml )
(28)
a6 = −Bl Jm Nm + Bm Ml Nm
(29)
2 2 a7 = −(Bs Ml + Bl Jm Nm + Bs Jm Nm )
(30)
a8 =
2 Jm Nm
+ 2Ml
(31)
2 b 1 = Nm (Ml + Ms )
(32)
b2 = −(Ml Nm )
(33)
2 2 α = Ml Ms + Jm Ml Nm + Jm Ms Nm .
(34)
Then, a linear state observer is designed as x ˆ˙ = Aˆ x + Bu + L(y − yˆ)
(35)
where L is the observer gain determined as the optimal gain of the KF with the covariance matrices set to ⎤ ⎡ 1 0 0 0 0 ⎢ 0 e−12 0 0 0 ⎥ ⎥ ⎢ ⎥ ⎢ −7 ⎢ 0 0 ⎥ 0 e (36) Q = ⎢0 ⎥ ⎥ ⎢ −2 ⎣0 0 ⎦ 0 0 e
R=
0
0
e17
0
0
e−5
0
.
0
e20 (37)
Fig. 9. Simulation results of external force estimation using the conventional two-mass dynamic model. The upper graphs are the estimated forces, and the lower graphs are the estimation error. (Actual: actual external force, EFO: external force observer, KF: steady-state Kalman filter, and Spring: spring force). (a) Case 1: no motor torque added. (b) Case 2: motor torque added.
C. Validation of the Proposed Observer Using Simulation Simulations are conducted to explore the performance of the proposed force observers. The following three points are mainly verified through simulations: 1) accuracy of the proposed force observers; 2) the difference between the external force observer (EFO) in Section III-A and the steady-state Kalman filter (KF) in Section III-B; 3) how the proposed dynamics can enhance observation performance. Force observations are simulated with a sinusoidal external force with a frequency of 1 Hz and a magnitude of 50 N·m given to an RFSEA. To clarify the performance of force observations, two situations are simulated: one is when only the external force is applied to the RFSEA (Case 1), and the other is when the motor torque (a sinusoidal signal with a frequency of 8 Hz and a magnitude of 0.0552 N·m) is also applied with the external force (Case 2). All the parameters are presented in Table I, and the cut-off frequency and the covariance matrix are the same as in Sections III-A and III-B. At first, the EFO and KF are designed based on the conventional two-mass dynamic model [in Fig. 4(a)], and Fig. 9 illustrates the force observation result. The observation results are compared with the actual external force (Actual) and the spring force (Spring) in the upper graphs, and the estimation errors are given in the lower graphs. In Case 1, where the load is almost stationary, the estimation error does not exceed the maximum 2 N, whereas the error becomes much larger in Case 2 as the load moves dynamically by the applied motor torque. The results verifies that the accurate dynamic model is necessary for the force observer design, and thus shows the significance of the precise dynamic model shown in Fig. 4(b). Fig. 10 shows the simulation results of the force observer designed using the dynamic model of Fig. 4(b). Compared with
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Fig. 10. Simulation results of external force estimation. The upper graphs are the estimated forces, and the lower graphs are the estimation error. (Actual: actual external force, EFO: external force observer, KF: steady-state Kalman Filter, and Spring: spring force). (a) Case 1: no motor torque added. (b) Case 2: motor torque added.
TABLE II SPECIFICATIONS OF FORCE-CONTROLLED XY STAGE Volume Weight Maximum continuous force Maximum speed Maximum load capacity
500 × 500 × 200 mm3 54 kg 797.4 N 0.213 m/s 700 kg
Fig. 9, the estimation error (in particular, the lower right graph) decreases with the proposed force observer. The force estimation using the spring deformation (spring force calculated as Fˆs = Ks xs ) is also depicted in Fig. 10, which becomes erroneous too when the load is in dynamic motions. To further explore the performance, the resolutions of the encoders are accurately simulated in this simulation: 20 000 counts per revolution for the motor-side encoder and 13-b resolution for the spring-side encoder. The lower graphs in Fig. 10 show the comparison of the estimation errors of EFO and KF. An EFO shows a more noisy observation result, whereas a KF can give an observation result with less noise. This large noise in EFO results is attributed to the two-time derivative calculation of EFO. KF can address this issue and provide better observation performance, as is validated in the simulation.
Fig. 11. Experimental setup: XY stage driven by SEAs. (a) Picture of the XY stage. (b) Inner structure of the XY stage.
Fig. 12. Block diagram for the SEA control. Fs is the spring force, C ff (s) and C fb (s) are the feedforward and feedback controller for spring force control, respectively. P n (s) and Q(s) are the nominal model of SEA and Q filter for the disturbance observer [22]. Z (s) is the desired impedance.
IV. EXPERIMENTS USING FORCE-CONTROLLED XY STAGE A. SEA-Driven XY Stage In this research, a novel XY stage that is driven by two SEAs is developed. Fig. 11 shows the picture and the inner structure of the developed XY stage, where two RFSEAs actuate the upper plate in the x- and y-direction independently. The detailed specification of the XY stage is presented in Table II.
The XY stage is controlled in three ways in the following force observation experiments: 1) open loop control 2) zero force control 3) impedance control Fig. 12 shows the block diagram of the controller utilized for the experiments.
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Fig. 13. Force estimation performance in Case 1 and Case 2 (Actual: actual external force, EFO: external force observer, KF: steadystate Kalman Filter, and Spring: spring force). (a) Without motor torque. (b) With motor torque. TABLE III RMS VALUES OF EACH ERROR
Spring force (Spring) EFO KF
Case 1
Case 2
5.325 N 8.079 N 6.591 N
28.654 N 8.304 N 8.292 N
In the open-loop control, the motor torque (τm in Fig. 11) is set regardless of the load position xl . During zero force control, the reference Fsr for the spring force Fs is set to 0. During impedance control, the reference Fsr is set as a function of the load position xl . Force observation performance is verified through the experiments under these three control strategies. Any type of force control and impedance control can be designed, since the proposed force observer can be designed independently from the force controller. In this paper, the modelbased force control proposed in [22] and [28] is utilized as the inner force control. B. Force Observation Experiment External force applied to the XY stage is estimated utilizing the proposed force observers. Experiments are conducted under several different conditions. At first, experiments under the same conditions of the simulations discussed in Section III-C are conducted; the same motor torque pattern as in Fig. 9 is applied, which is the open-loop control. External forces are applied to the plate with and without motor torques. Fig. 13 shows the result, where “Actual” represents the external force measured by the load cell (CAS, SBA-100). The result verifies that the spring force (Spring) can indicate the accurate external force (Actual) amount when there is no additional motor torque, however, it failed to show the external force information when motor torque is applied. Meanwhile, the proposed observers (EFO and KF) can estimate accurate external force values regardless of the motor torque conditions. The root mean square (rms) of the observation errors are compared in Table III, which shows that the proposed force observers show better observation performance when the load is moving. Next, external force is observed while the XY stage is controlled to provide small resistive force by zero force control (the force reference for the force control is set to zero). Experiments are conducted under two conditions: 1) External force is given
Fig. 14. Force estimation performance under zero force control (Actual: actual external force, EFO: external force observer, KF: steady-state Kalman Filter, and Spring: spring force). (a) Slow load motion. (b) Fast load motion.
to drive the stage at a slow velocity (slow load motion), and 2) relatively large external force is applied to drive the stage at a high velocity (fast-load motion). Fig. 14 shows the results, where the upper graphs show the force observation results and the lower graphs show the velocity of each case. Close investigation of the result clarify the characteristics of the proposed observer. Spring force (Spring) still exhibits wrong force information in both cases; the estimation error of Spring force around 2–2.5 s is 7–8 N in the upper left graph in Fig. 14. Notice that the velocity of the stage at that time is around 0.038 m/s, and taking the viscous friction coefficient 200 N·s/m into account, the force estimation error of Spring force can be attributed to the damping force of the plate. The Spring force cannot reflect this dynamic characteristic, whereas the proposed observer can. In the fast load motion case, Spring force exhibits largest estimation error around 320 ms, where the error reaches around 29 N. Notice that the velocity at that moment is almost zero while the decceleration is highest, which is around 1.29 m/s2 . The multiplication of the decceleration and the mass of the load (22 kg) generates the force amount almost same as the estimation error 29 N. This aspects also verifies that the proposed observers can estimate the external force taking the dynamic characteristic of the load into account, which the force estimation based on the spring deformation fails to. C. Application for Human Force Measurement While Stepping The developed XY stage can be utilized to measure the human interactive force on ground (or ground reaction force) while he/she is walking. The ground reaction force is usually measured using force plates. Compared to this force plate, the proposed XY stage can provide various programmable ground impedance characteristics by impedance control of the stage.
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types are compared with the force measurement by a force plate (AMTI, OR6-7-OP), on which the subject performs the same stepping. The comparison among these results indicate that the proposed observer provides similar force observation results to the force plate measurement even with different impedance settings. Analysis of force patterns in detail, e.g., why the rise of the human force is steeper and why there is a second peak in the low ground impedance case, should be conducted with some helps of biomechanics, which is beyond the scope of this paper. However, it can be validated that the proposed force observer and the developed XY stage can provide successful force observation while providing different ground impedances. V. CONCLUSION The paper proposed the following three points. 1) Accurate dynamic model for RFSEA is derived. 2) Two types of force observer are designed based on the derived dynamic model. 3) Force-controlled XY stage is developed using RFSEAs, and the proposed force observer is applied to the XY stage to precisely estimate interactive forces with humans. The experimental result validated that the proposed observer can successfully estimate external force taking into account the dynamic characteristics of the load, which the force estimation using the spring deformation cannot do. In-depth analysis of human force on the developed XY stage and its application to human gait analysis are future works. Fig. 15. Ground reaction force estimation performance comparing with force plate. (a) Force measurement and estimation. (b) Velocity of the plate.
The proposed force observer allows accurate measurement of human force while providing various ground impedances. To verify the performance, a healthy subject (male, 70 kg, 170 cm) stands on the XY stage and performs stepping. Ground impedance of the XY stage is realized by setting force reference F r for RFSEAs as r ¨l{x,y } + Bg x˙ l{x,y } + Kg xl{x,y } = Z{x,y } (s) F{x,y } = Mg x (38) where xl{x,y } is the position of the stage in the x- and y-direction. The following three types of impedances are set: 1) low impedance case, where Mg = 100, Bg = 700, and Kg = 2000; 2) middle impedance case, where Mg = 100, Bg = 1000, and Kg = 8000; and 3) high impedance case, where Mg = 100, Bg = 3000, and Kg = 100 000. These parameters set in Z(s) in Fig. 12 to generate the spring force reference Fsr . Fig. 15 shows the estimated lateral forces (Fx in Fig. 1) generated by the subject when he steps and the velocities of the plate produced by those forces. The KF is utilized for the estimation here. The estimation results under three different impedance
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PARK et al.: DEVELOPMENT OF FORCE OBSERVER IN SERIES ELASTIC ACTUATOR FOR DYNAMIC CONTROL
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Yongsu Park (S’15) received the B.S. degree in mechanical system engineering from Hansung University, Seoul, South Korea, in 2015, and the M.S. degree in robotics engineering from the Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu, South Korea, in 2017. He is currently a researcher at the Convergence Research Center for Collaborative Robots, DGIST. His current research interests include human–robot interaction applications, and the development of human force assist algorithms.
Nicholas Paine (S’12–M’16) received the B.S, M.S., and Ph.D. degrees in electrical engineering from The University of Texas at Austin, Austin, TX, USA, in 2008, 2010, and 2014, respectively. He received the Virginia & Ernest Cockrell, Jr. Fellowship in Engineering from 2008 to 2012. He is currently the Chief Technology Officer at Apptronik Inc, Austin, TX, USA. His research interests include design and control of high-power high-efficiency actuation for dynamic articulated robots.
Sehoon Oh (S’05–M’06–SM’16) received the B.S., M.S., and Ph.D. degrees in electrical engineering from The University of Tokyo, Tokyo, Japan, in 1998, 2000, and 2005, respectively. He was an Assistant Professor at The University of Tokyo until 2012, a Visiting Researcher at the University of Texas at Austin from 2010 to 2011, a Senior Researcher at the Samsung Heavy Industries, and a Research Professor in the Department of Mechanical Engineering, Sogang University. He is currently an Assistant Professor at the Daegu Gyeongbuk Institute of Science and Technology, Daegu, South Korea. His research interests include the development of human-friendly motion control algorithms and assistive devices for people. Dr. Oh received the Best Transactions Paper Award from the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS in 2013.
