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Variable stiffness mechanism for human-friendly robots
Mechanism and Machine Theory 45 (2010) 880–897
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Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmt
Variable stiffness mechanism for human-friendly robots Dongjun Hyun a, Hyun Seok Yang a,*, Jungwan Park a, Youngbo Shim b a b
Department of Mechanical Engineering, Yonsei University, 134, Sinchon-dong, Seodamun-gu, Seoul 120-749, Republic of Korea Fundamental Technology Team, Samsung Electronics Co., Ltd., 416, Maetan-3dong, Yeongtong-gu, Suwon-City, Gyeonggi-do 443-742, Republic of Korea
a r t i c l e
i n f o
Article history: Received 26 June 2008 Received in revised form 6 January 2010 Accepted 6 January 2010 Available online 7 February 2010 Keywords: Variable stiffness Safety mechanism Passive compliance Human-friendly robot Head impact test HIC index
a b s t r a c t We have developed a variable stiffness mechanism (VSM) for human-friendly robots to simultaneously meet safety and performance needs. The VSM has high stiffness in normal operation mode and has low stiffness in collision mode when the load applied to the joint exceeds a critical load, specified by the physical constraints of the joint structure and an actively controlled electro magnet. We have verified the safety of the VSM by simulations and experiments using the head injury criteria index. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Numerous robot applications, such as cleaning, lawn mowing, and entertaining, are being rapidly introduced in our daily lives assisted by developments in navigation, Artificial intelligence and various sensor technologies, though most are oriented to mobile technologies, are not able to cover other personal/public demands such as caring for the handicapped or the aged or assisting human work in close proximity, among other activities. To do such physical human robot interaction (pHRI) tasks, the robot should be equipped with manipulators. However, if safety issues are not properly addressed, no matter how great the performance and function, robots will not be applicable to our daily lives. Unfortunately, it is nearly impossible to imagine a system without any problems or potential problems. This is because as the complexity of systems increases, the probability of critical problems due to defects or failures on the part of the system also increases. For this reason, engineers and scientists have been trying to design better ways to reduce failure and prevent dangerous robot action in the event of a failure. Also, making a robot with parts safe for human contact is another important research area. One of the easiest and effective safety approaches is to wrap up the part in contact with humans with a soft and thick material, though this method still has drawbacks such an increase in size and mass, dull movement, and difficulty in covering up to the end effectors, among others. The larger the mass of the robot and the faster it moves, the more dramatically increased are the thickness and stiffness demands. Therefore, we need mechanical safety devices, which can ensure a minimum level of safety under uncontrollable failure cases. Mechanical safety devices may be implemented in various forms; among them, we are interested in joint compliance. If robotic joints have favorable compliance, they have an intrinsic safety of a certain level. Such mechanisms have a very low probability of harming humans in any external environment due to their natural characteristics. It is truly a beneficial solution for safety, but when we consider its response to the input, its benefits seem diminished. Joint compliance creates delays in forces from the actuator to the link and reduces the frequency bandwidth of the * Corresponding author. Tel.: +82 2 2123 2824; fax: +82 2 364 6769. E-mail address: [email protected] (H.S. Yang). 0094-114X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2010.01.001
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system. To solve this problem, mechanisms, such as series actuators connected to each other by properly designed elastic elements, including variable transmission stiffness, have been introduced over the last two decades [4,5,13,14]. In this article, a variable stiffness mechanism (VSM) for human-friendly robots was developed to meet the need of safety and performance simultaneously, even with a compact size. A VSM is comprised of a cam and a linear motion guide. The stiffness of the joint could be freely adjusted by the cam profile, and a compact size with a 70-mm diameter and a 40mm height was achieved. The cam profile was designated to obtain high stiffness under ordinary operational conditions and to obtain low stiffness in the collision condition. We demonstrated a dynamic model of the VSM in collision situations and the safety of the robot arm equipped with VSM through a head impact test using the head of a HybridIII car crash test dummy. The robot arm of 1 DOF was used in experiments in order to minimize the effect of unmodeled dynamics. The head injury criteria (HIC) index is used for the evaluation of the experimental results. The performance of the VSM and the effect of active control by the electro magnet were verified by simulations. 1.1. Related research Andre Sharon et al. (1988) introduced the macro/micro manipulator system [16] to achieve high bandwidth force regulation and inertia reduction. This system is composed of a macro-manipulator to treat low frequency and a micro manipulator to treat high frequency, which are connected serially with a spring and damper system with a specific coefficient. Morrell and Salisbury (1995) propose a parallel coupled macro-mini actuators [7] with the proper passive characteristics providing the best potential for fast, accurate force control. Unlike previous micro–macro robots, which used actuators coupled in series, the actuators in this system are coupled in parallel using a compliant transmission. Chew et al. (2004) propose a series damper actuator (SDA) [6] for force/torque control of manipulators, legged robots, and haptic devices, among others. The SDA system incorporated a series damper instead of a series elastic component between the actuator and the load in order to overcome some of the shortcomings in the SEA. Zinn et al. (2004) propose a force control actuation approach called distributed macro-mini actuation [3], which is connected in parallel and distributed to different locations on the manipulator. Distributed macro-mini actuation reduces the effective inertia of the overall manipulator and maintains performance with small actuators collocated with the joints. Sensinger and Weir (2005) design a non-backdrivable series elastic actuator [12] to expand the application of it into a non-backdrivable transmission like a harmonic drive, although its application is limited to backdrivable transmission. Koganezawa et al. (2004) introduce an actuator with non linear elastic system (ANLES) [8] to mimic the skeletal muscular system, which is composed of a torsion spring and guide shaft to modify stiffness by constraining the effective length of the torsion spring. Yoon et al. (2003) propose a safe arm with MR-based passive compliant joints [9] to reduce unwanted vibrations due to joint compliance. The safe arm consists of a magneto-rheological (MR) rotary damper and a rotary spring for elasticity and is designed to actively vary the damping coefficient according to the relative position of an actuator and link in order to absorb impact effectively. Bicchi and Tonietti (2002) design soft robot arms [10] for an intrinsically safe interaction with humans through applying a conical compression spring and a pneumatic artificial muscle and (2005) designed for a variable stiffness actuator [11] composed of a transmission belt and 3 pulleys, of which, one is idle and the others are driven by a DC motor. Iwata et al. (1999) propose physical interference adapting a hardware system using a mechanical impedance adjuster (MIA) arm [15], which is composed of leaf spring and ball thread and is able to vary the stiffness of the joint by using an effective length for the leaf spring. Park et al. (2007) propose a safe link mechanism based on nonlinear stiffness for collision safety by using a double-slider mechanism and shock-absorbing system [17]. Park’s mechanism is based on the four bar linkage while the VSM is based on the cam mechanism. The VSM has several strengths as followings: (1) The stiffness of the VSM varies with the cam profile freely in contrast to Park’s mechanism that has only one stiffness function such as Eq. (4) in the reference [17]. For an example, the VSM can be stiffer than Park’s mechanism for better performance under the same critical impact force. (2) The stiffness of the VSM can be controlled by electromagnets. Therefore, it can eliminate the effect of the gravitational force or can enhance performance of service robots. 1.2. Evaluation of safety We use the head injury criteria (HIC) index to evaluate the safety level of the robot equipped with the VSM. The HIC index was developed by the automotive industry to assess head injuries of occupants during car accidents. It is reasonable to use the HIC Index as the evaluation method for the safety of robots, since the head is the single most critical human organ that could be most seriously harmed by a robot. For the same reason, the HIC Index was used as an evaluation tool for the safety of robots in several previous works [10]. In this section, we specify the test protocols and calculation procedures that are applied in this study to show that test results are acceptable. It is inadequate to directly compare the results of previous works because the test results are largely influenced by small differences in test conditions such as the impact region on the head, stiffness of the head fixture, contact
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speed, and the behavior of the actuator during impact. Test protocols and calculation procedures applied in this article follow, as much as possible, those of the automotive industry. The head used for the impact test is the HybridIII 50th percentile crash test dummy’s head, which is the most broadly used for automotive frontal impact tests and has authorized weight and contact stiffness of an ordinary male head. Three 7264–200s of Brüel&Kjær, which are also used for car crash tests, are used as accelerometers to measure head acceleration during the impact test. It is not only expensive but also inefficient to use a full body dummy for these small size tests in the laboratory. Hence, a head fixture is used instead of a full dummy body. The fixture of the head is a cylindrically shaped urethane rod with an 80-mm diameter and 200-mm height. The stiffness of the fixture is adjusted to 3.825 Nm/deg since neck stiffness of a seated HybridIII dummy is 3.696 Nm/deg and neck stiffness of a standing HybridIII dummy is 3.936 Nm/deg, according to the HybridIII Geometrical and Inertial Properties specified by Kaleps and Whitestone [1]. Impact direction is horizontal, and the impact region is the forehead, which has a uniform skin thickness. Fig. 1 shows the equipment and conditions of the head impact test. The HIC index is calculated by Eq. (1), where the acceleration of the head is obtained by a resultant acceleration of three axes in the g unit, and T is a 36-msec time duration. In the automotive industry, HIC36 is the most broadly used standard of head injury representation, though T is defined as the final time of impact in other articles [Antonio Bicchi ‘‘Fast and soft-arm tactics”]. HIC36 is obtained by selecting the maximum value in the all HIC36s during impact tests.
HIC36 ¼ T
Z T 2:5 1 aðsÞds T 0
ð1Þ
Head acceleration data of EuroNcap frontal impact tests on a Mercedes A-Class are used to verify Eq. (1). According to the official test reports, the HIC36 of the driver was 446.9, and we obtain the result from Eq. (1). In addition, another interesting test is performed. A person who weighs approximately 100 kg hit the test equipment using a basketball with his best. Through this test we could ascertain what would be a realistic injury level of the head in the ordinary operation of a robot arm. The measured HIC36s of the tests were 9.448, 7.349, and 13.19. We found from the test results that an HIC36 of unit 10 results in severe injuries, in the case of a head hit only locally, and that the value of HIC36 increases exponentially as head acceleration increases. Fig. 2 shows the head acceleration of the EuroNcap frontal impact test on a Mercedes A-Class and head impact tests using a basketball. 2. Design of a variable stiffness mechanism (VSM) 2.1. Dynamic modeling and analysis of the collision To study the effect of joint flexibility on the safety level of robots, we first derive a dynamic model to describe the collision of a head with a single-link robot arm equipped with a flexible joint of which stiffness is constant. The head is fixed to the
Fig. 1. Head impact test equipment and conditions.
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Fig. 2. Resultant acceleration of a head.
ground through a spring and damper and has contact with a robot arm through a spring and damper as well. However, contact elements that are composed of a spring and a damper have an effect only during contact. If the sign of the distance between the head and a robot arm is negative, then the stiffness constant and damping coefficient are constant. Otherwise, the stiffness constant and damping coefficient are zero. The robot arm and rotor are connected by a spring and a damper as well. Eqs. (2)–(4) represent the dynamic model of the collision as shown in Fig. 3
kC dC kN dN ðx þ lh2 Þ ðx_ þ lh_ 2 Þ x x_ MHEAD MHEAD M HEAD M HEAD kT dT sROTOR ¼ ðh1 þ h2 Þ þ ðh_ 1 þ h_ 2 Þ þ IROTOR IROTOR IROTOR kC l dC l k dT _ T ¼ ðx þ lh2 Þ ðx_ þ lh_ 2 Þ þ ðh1 h2 Þ þ ðh1 h_ 2 Þ IARM IARM IARM IARM
€x ¼
ð2Þ
€h1
ð3Þ
€h2
ð4Þ
x represents the linear displacement of the head. kN and dN are the stiffness constant and the damping coefficient of the neck, which can be obtained easily by a linear force–displacement test and a free vibration test. MHEAD is the effective mass of the test equipment, which is composed of a HybridIII 50th percentile crash test dummy head and the fixture. l is the length of robot arm and kC and dC represent the stiffness constant and damping coefficient of the contact element. It has unique
Fig. 3. Impact model.
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characteristics such that the stiffness constant and damping coefficient depend on the penetration depth between two bodies, that is, if lh2 6 x then kC = 0 and dC = 0. h1 and h2 represent the rotor angle and link angle. sROTOR is the torque exerted by the actuator. kT and dT represent the stiffness constant and damping coefficient of the transmission element. IROTOR and IARM are the inertia of the rotor and arm. T Referring to Eqs. (2)–(4), we let q ¼ x x_ h1 h_ 1 h2 h_ 2 be the state vector. Then the state space equation is given by
q_ ¼ Aq þ Bu
ð5Þ
where A, B, and u are
2
0
6 kC þkN 6 MHEAD 6 6 0 6 A¼6 6 0 6 6 0 4 kC l IARM
1
0
0
0
þdN dMCHEAD
0
0
Cl MkHEAD
0
0
1
0
0
kT IROTOR
dT IROTOR
kT
0 Cl IdARM
0
0
kT
dT
IARM
IARM
B ¼ ½ 0 0 0 1=IARM
0 0 T ;
IROTOR
0 2 Cl kTIþk ARM
0
3
7 Cl MdHEAD 7 7 7 0 7 7 dT 7 IROTOR 7 7 1 5 2 dT þdC l IARM
ð6Þ
u ¼ sROTOR
In our simulation, we assume that the end point of the robot arm hits someone’s forehead at its maximum speed under malfunction and the actuator exerts a torque on the arm link after collision. The simulation starts at contact and therefore the initial state is qð0Þ ¼ ½ 0 0 0 xMAX 0 x MAX T . At that time, Fig. 4 shows the relation between kT and HIC36 obtained by the resultant acceleration of the head. Parameters of the simulation model are shown in Table 1. Two inflection points at kT = 200 and 20,000 Nm/rad are found from Fig. 4. The HIC36 does not decrease much despite the decrease in the transmission stiffness when it was less than 200 Nm/rad, and the HIC36 does not increase much despite the transmission stiffness increase when it is more than 20,000 Nm/rad. This means that the effective inertia to transfer the impact to the head is determined by the transmission stiffness. If the transmission stiffness is rigid, the rotor and robot arm behave like a rigid body. Likewise, if transmission stiffness is soft, then the inertia of the rotor has little effect on the HIC36. Therefore, the injury suppression mechanism through the control of transmission stiffness has an advantage in systems with large rotor inertia. 2.2. Stiffness varying mechanism with cam The design goals of the VSM are: (1) (2) (3) (4)
Adjustability of stiffness. Low stiffness of the robot arm in collision mode for safety purposes. High stiffness of the robot arm in the normal operating mode, for fast response. Minimum electric control to prevent malfunctions due to a complex system.
Fig. 4. HIC and transmission stiffness.
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D. Hyun et al. / Mechanism and Machine Theory 45 (2010) 880–897 Table 1 Parameters of the simulation model. Mass (kg) and Inertia (kg m2) Stiffness constant (N/m) Damping coefficient (N s/m) Length of the arm (m)
MHEAD = 5.09, IROTOR = 0.175, IARM = 0.14 kN = 3300, kC = 1500 dN = 12, dC = 15 l = 0.6
(5) Compact size. In this article, a mechanism that uses a cam is proposed to achieve the above design goals. Fig. 5 illustrates the concept that the horizontal stiffness constant is a function of the vertical stiffness constant and the cam angle /.
F H ¼ kV tan /y y ¼ tan /x
ð7Þ ð8Þ
F H ¼ kV tan2 /x ¼ kH x
ð9Þ
) kH ¼ kV tan2 /
ð10Þ
FH is the external horizontal force exerted from a rotor or robot arm, which moves the cam follower to the x-direction. The cam follower compresses the spring installed in the vertical direction for which the stiffness constant is kV. The cam follower moves along a cam slope with an incline of /. Therefore, the resultant stiffness constant in the horizontal direction, kH, is kV tan 2/ as shown in Eq. (10). Fig. 6 illustrates the concept that the cam profile is applied to the rotational joint. The cam profile was proposed to achieve a low stiffness for the safety of the robot arm in the collision mode and high stiffness for a simultaneous fast response of the robot arm in the normal operating mode. The adjustability of the stiffness can be obtained by varying the angle / of the cam slope freely, that is, the stiffness constant in the horizontal direction varies from 0 to infinity as / varies from 0 to 90 degrees. If the cam profile is applied to the rotational joint of radius r, the rotational stiffness constant kR is function of r and kH. Eq. (11) describes the relationship between the rotational stiffness constant and vertical stiffness constant.
kR ¼ r 2 kV tan2 /
ð11Þ
This rotational joint mechanism has a large variation of stiffness and a compact size. Furthermore, it does not need to be actively controlled by logic. Fig. 7 shows a large variation of stiffness according to the cam profile and kV.
Fig. 5. Cam mechanism.
Fig. 6. The development figure of the cam profile applied to the rotational joint.
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Fig. 7. Rotational stiffness constant.
2.3. Preload adjusting mechanism with screws and electromagnets The preload is necessary to eliminate the gap between the cam follower and the cam and to compensate for gravity. If the preload affects the VSM, then the stiffness constant is at a maximum without an inclined cam angle. Since the cam follower does not move along the cam, all the components of the VSM rigidly contact. Basically, a preload of VSM is determined by the difference between the free length and the installed length of the vertical spring and is adjusted by a screw mechanism shown in Fig. 8. The preload mechanism is fixed permanently after it is adjusted. The Preload has no need to be changed when the robot arm rotates only horizontally. However, if a robot arm were to rotate vertically, as shown in Fig. 9, the preload must be adjusted according to the angle a. Most flexible joints share the same
Fig. 8. Preload adjusting mechanism by a screw.
Fig. 9. Variation of moment arm length according to link angle.
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problems of deflection in vertical operation due to joint flexibility. VSM stiffness minimizes when the external load exceeds the critical load, which is determined by the cam profile. Therefore, the external force due to the weight of the arm disturbs the critical load and the VSM behaves in an undesired way. Thus, the VSM equips a programmable preload control mechanism by electromagnets, which apply a pulling force to the cam follower toward the cam side. Electromagnets may improve robot arm performance through a pulling force control according to the robot arm speed. For example, the stiffness of the VSM may decrease in an undesired situation during which the robot arm accelerates rapidly from rest. At this time, the pulling force of the electromagnets can prevent the VSM from any unwanted sudden change of stiffness. Fig. 10 illustrates the preload control mechanism by electromagnets. Eq. (12) describes the preload determined by the screw and electromagnet mechanism. The force–displacement characteristics of the VSM are shown in Fig. 11.
F H ¼ kV tan2 /x þ kV tan /ðlFREE lADJ Þ þ F EM tan /
ð12Þ
where lFREE is the free length of the spring, lADJ is the length of the spring adjusted by the screw mechanism and FEM is the pulling force of the electromagnets. The response of the preload controlled by electromagnets is fast enough that the VSM could be adopted in a rapidly operated robot arm. 2.4. Prototype design The prototype of the VSM is composed of 3 parts, an inner-upper part, an inner-lower part, and an outer part as shown in Fig. 12. The inner-upper part is composed of 2 cam followers, 2 spring assemblies, and 2 linear motion guide (LM guide). It connects the inner-lower part and the outer part. The inner-upper part is connected to the inner-lower part with LM guides for relative linear motion as shown in Section B–B of Fig. 13, and the spring assemblies for kV, as shown in Section C–C of Fig. 13. Therefore, the inner-upper part and the inner-lower part rotate together and simultaneously move linearly from each other with an elasticity of kV. The inner-lower part is composed of two electromagnets, two linear motion shafts (LM shaft), a cross roller bearing, and an input shaft. It transfers torque input from the rotor. Two electromagnets control the preload as shown I n Section A–A of Fig. 13, and two LM shafts transfers torque from the rotor to the inner-upper part. The inner-lower
Fig. 10. Preload control mechanisms.
Fig. 11. Force–displacement characteristics of VSM.
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Fig. 12. Parts of the VSM.
Fig. 13. Overview of the VSM.
part is attached to the outer part with a cross roller bearing, and therefore, the inner-lower part does not transfer torque to the outer part directly and only rotated relative to each other. The outer part, which has a cam profile on its cylindrical outer
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wall, transfers torque from the inner-upper part to the robot arm with a determined stiffness by the cam and the cam followers. The performance properties are shown in Fig. 14. In neutral mode, the cam follower exists in the high stiffness region at the center of the cam profile. At this time, the stiffness of the VSM is close to the rigid condition; therefore, the VSM does not
Fig. 14. Performance property.
Fig. 15. Prototype of the VSM.
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degrade the performance of the robot arm. In the case of a collision, the VSM experiences a sudden load more than a critical load, which is determined by the composition of the preload and high stiffness cam profile. As a result, the cam followers move along the cam profile and the inner-upper part is separated from the inner-lower part along two LM shafts as the inner-upper part overcomes the pulling force of the springs and electromagnets. At this time, the inner-upper part undergoes the rotational motion and linear motion about the outer part simultaneously and the inner-lower part undergoes only rotational motion about the outer part and the stiffness of VSM becomes low. Fig. 15 shows the prototype of the VSM. 3. Simulations and experiments In this section, we demonstrate the effectiveness of the VSM through simulations and experiments. Safety levels and input tracking performance of the robot arm are the main considerations of the VSM. Additional applications such as gravity compensation and active preload control are addressed as well. The safety of the robot arm is evaluated by simulations with the dynamic model described in Section 2.1 and experiments with the test equipment in Section 1.2. Performance and additional applications are demonstrated by simulation only, since it is possible to obtain a reasonable result through simulation, and it is difficult to measure the accurate motion of the robot arm from an external environment without an expensive measurement system. 3.1. Safety In the simulation to evaluate VSM safety, we assume the worst case in which the robot arm hit the head at maximum speed without an emergency stop. The simulation is performed in cases of VSM and a rigid joint to evaluate the effectiveness of the VSM. We determine the inertia of the robot arm using a robot arm, which consists of a 150-W Maxon motor, gear, and an aluminum pipe since this robot arm is the most appropriate out of the robot arms available in our laboratory. The speed at collision is 4.2 m/s because the rotor is driven by a motor rotating at 7580 rpm in constant speed mode by an EPOS 70/10 Maxon motor driver. The reduction gear ratio is 3/338, and the length of the robot arm is 0.6 m. We obtain an HIC36 from the results of the simulation as shown in Table 2. The injury level on the simulation is not high enough to lead to human death or serious injury but it is sufficient to demonstrate the effectiveness of the VSM. Moreover, the injury level in the simulation was not so low that a human could not sense pain since a collision of an object as large as the head moves 50 mm in the case of a rigid joint. As shown in Fig. 16, the VSM reduces the displacement of the head from
Table 2 HIC36 of simulations and experiments. Simulation VSM Rigid joint Reduction rate
0.11 0.40 72%
Experiment 0.073 0.22
0.074 0.22
Fig. 16. Head displacement of simulation.
0.074 0.21 66%
0.075 0.22
0.075 0.22
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50 mm to 18 mm. As shown in Fig. 17, head acceleration of the VSM case differs from the acceleration of the rigid joint case by approximately 12 msec and starts to decrease at approximately 21 msec. Therefore, the duration time of the first contact in the case of VSM is shorter than that in the case of rigid joint. The second peak acceleration is found at approximately 135 msec in the case of VSM due to the constructive limit of the VSM but it does not have such an effect that it dramatically increases the extent of injury. This is because impact energy has already been spent considerably in the first impact. We have performed 5 experiments on the VSM and the rigid joint, respectively through test equipment as shown in Fig. 18. The results of the experiments are shown in Figs. 19 and 20 and Table 2. All the experimental results show a small deviation and demonstrate the effectiveness of the VSM. The VSM reduces the HIC36 values by 33% with respect to the rigid joint. Figs. 19 and 21 show that the stiffness of the VSM changes well. The cam initially stays at position r in Fig. 21. When the cam stays within the high stiffness region, measured acceleration of the VSM is nearly the same as that of the rigid joint. At the moment that the cam arrives at position s in Fig. 21, the cam moves into the low stiffness region and the time is approximately 25 msec. in Fig. 19. From this time, measured acceleration of the VSM is deviated from that of the rigid joint, and starts decreasing in contrast with the rigid joint. When the cam moves in the low stiffness region, measured acceleration of the VSM decreases or keeps low level. However, at the moment that the cam arrives at position t in Fig. 21, the cam
Fig. 17. Head acceleration of simulation.
Fig. 18. Test equipment configuration.
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Fig. 19. Head acceleration of experiments.
Fig. 20. Head displacement of experiments.
collides with the wall of the case, and then measured acceleration of the VSM makes a sharp peak at approximately 135 msec. Despite the sharp peak, measured HIC36s of the VSM are still lower than those of the rigid joint. The sharp peak can be reduced easily by attaching a soft stopper at the wall of the case. The VSM can equip with the soft stopper easily. As shown in Figs. 22 and 23 and Table 2, the results of simulations and experiments do not correspond to cases of the VSM and the rigid joint, respectively. However, from the view point of contact duration at first contact and the magnitude of head displacement and approximate behavior, the simulations describe the dynamic behavior of experiments well. Therefore, the dynamic model of collision and simulation is valid. Differences between simulations and experiments arise from the backlash of the reduction gear, nonlinear characteristics of the contact materials, and unmodeled dynamics, such as local vibration of the robot arm. Fig. 24 shows the test equipment. 3.2. Performance One of the design goals of the VSM is to achieve a high stiffness for the fast response of the robot arm in the normal operating mode. In this simulation, we compare a soft joint, rigid joint, and VSM to demonstrate how fast the VSM responds. The stiffness constant of the soft joint is considered to be 200 Nm/rad because the stiffness constant must be less than 200 Nm/
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Fig. 21. Illustration of varying stiffness according to cam position.
Fig. 22. Comparison of head acceleration with simulations and experimental data.
rad to achieve safety of the robot arm as shown in Fig. 4. The stiffness constant of the rigid joint is considered to be 5000 Nm/ rad because the stiffness constant must be greater than 5000 Nm/rad to minimize the effect of compliance between the rotor and the robot arm. The rotor of the soft joint, rigid joint, and VSM drive the robot arm with uniform sinusoidal input torque. Figs. 25–29 show the response of the robot arm to the sinusoidal input. The results of the rigid joint can be regarded as a standard of performance since the performance of the rigid joint is the best. The motion of the soft joint and the VSM follow the rigid joint case very well at 1 Hz. However, the soft joint starts to disperse at 5 Hz and becomes uncontrollable at 15 Hz. The VSM follows the rigid joint up to 15 Hz considerably and starts to disperse at 20 Hz. Therefore, it is reasonable to assume that the response of the VSM is approximately 4 times faster than that of the soft joint. 3.3. Additional applications The prototype of the VSM is equipped with two electromagnets of 15 mm in diameter and 30 mm in length, which can produce 40 N pulling forces continuously and 60 N temporarily. The maximum force of this active controlled preload can be
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Fig. 23. Comparison of head displacement with simulations and experimental data.
Fig. 24. Test equipment.
Fig. 25. Angular displacement and velocity at 1 Hz.
easily increased by enlarging the diameter of the VSM, since the pulling force of the electromagnet increases dramatically as the diameter of the electromagnet increases. In this simulation, we demonstrated the effectiveness of the active controlled
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Fig. 26. Angular displacement and velocity at 5 Hz.
Fig. 27. Angular displacement and velocity at 10 Hz.
Fig. 28. Angular displacement and velocity at 15 Hz.
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Fig. 29. Angular displacement and velocity at 20 Hz.
Fig. 30. Effectiveness of actively controlled preload.
preload simply by improving the simulation results presented in Section 3.2. The increase in the preload of the VSM degrades the safety of the robot arm but improves performance. Therefore, it is necessary to control preload actively to achieve the required safety and performance of the robot arm. The control strategy is to increase the preload when the speed of the robot arm is low and decrease the preload when speed is high since the robot arm is less dangerous at low speeds. This strategy is referred to as [10]. As shown in Fig. 30, the robot arm, in the case of a controlled preload, does not become uncontrollable even though the torque exerted from the rotor increases.
4. Conclusions and future work We have proposed a variable stiffness mechanism (VSM) to achieve simultaneous safety and performance of the robot arm. Five design goals suggested in the Section 2.2 were satisfied by the VSM. The adjustability of stiffness means how easily stiffness can be changed and means how largely the range of stiffness can be changed. The stiffness of the VSM can be changed freely and largely by the cam angle and the installed spring. The fact that the VSM makes the stiffness of the robot arm high in normal operating mode and makes the stiffness of the robot arm low in collision mode is demonstrated by experiments and simulations. The VSM has no need to be controlled electrically or can have a simple controller separated from the complex main control system. The prototype of the VSM has a compact size with a 70-mm diameter and a 40-mm height, which is slightly larger than a tennis ball.
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The safety of the VSM is evaluated by both simulations and experiments. The performance of the VSM is confirmed by simulations. The VSM, equipped with an electromagnet to control the preload, is suggested to extend its application to various fields such as the vertical motion applications and high frequency operation applications. In the future, we will study a multi-DOF manipulator equipped with a VSM through simulations since the dynamic model in this article describes physical systems well. To apply the VSM to multi-DOF manipulator, the cam profiles adequate to the respective joints and gravity compensation for vertical motion joints will be needed. Acknowledgement This research is supported by the Mechatronics and Manufacturing Technology Center of Samsung Electronics Co. References [1] Stanley H. Backaitis, Harold J. Mertz, HybridIII: The First Human-Like Crash Test Dummy (1994) 687–707. [3] Michael Zinn, Bernard Roth, Oussama Khatib, J. Kenneth Salisbury, A new actuation approach for human-friendly robot design, International Journal of Robotics Research 23 (4–5) (2004) 379–398. [4] Alin Albu-Schäffer, Christian Ott, Gerd Hirzinger, A unified passivity-based control framework for position, torque and impedance control of flexible joint robots, International Journal of Robotics Research 26 (1) (2007) 23–39. [5] Hun-Ok Lim, Kazuo Tanie, Human safety mechanisms of human-friendly robots: passive visco-elastic trunk and passively movable base, International Journal of Robotics Research 19 (4) (2000) 307–335. [6] Chee-Meng Chew, Geok-Soon Hong, Wei Zhou, Series damper actuator: a novel force/torque control actuator, International Conference on Humanoid Robots 2 (2004) 533–546. [7] J.B. Morrell, J.K. Salisbury, Parallel coupled actuators for high performance force control: a micro–macro concept, International Conference on Intelligent Robots and Systems 1 (1995) 391–398. [8] K. Koganezawa, Y. Shimizu H. Inomata, T. Nakazawa, Actuator with non linear elastic system (ANLES) for controlling joint stiffness on antaonistic driving, in: Proceedings of the 2004 IEEE International Conference on Robotics and Biomimetics, 2004, pp. 51–55. [9] S.-S. Yoon, S. Kang, S.-J. Kim, Y.-H. Kim, M. Kim, C.-W. Lee, Safe arm with MR-based passive compliant joints and visco-elastic covering for service robot applications, IEEE/RSJ International Conference on Intelligent Robots and Systems 3 (2003) 2191–2196. [10] A. Bicchi, G. Tonietti, Design, realization and control of soft robot arms for intrinsically safe interaction with humans, in: Proceedings of the IARP/RAS Workshop on Technical Challenges for Dependable Robots in Human Environments, 2002, pp. 79–87. [11] Giovanni Tonietti, Riccardo Schiavi, Antonio Bicchi, Design and control of a variable stiffness actuator for safe and fast physical human/robot interaction, in: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 2005, pp. 526–531. [12] Jonathon W. Sensinger, Richard F. ff. Weir, Design and analysis of a non-backdrivable series elastic actuator, in: Proceedings of the 2005 IEEE Ninth International Conference on Rehabilitation Robotics, 2005, pp. 390–393. [13] G.A. Pratt, M.M. Williamson, Series elastic actuators, intelligent robots and systems 95. Human Robot Interaction and Cooperative Robots, in: 1995 IEEE/RSJ International Conference on Proceedings 1(5–9) (1995) 399–406. [14] Björn Jensen, Nicola Tomatis, Laetitia Mayor, Andrzej Drygajlo, Roland Siegwart, Robots meet humans – interaction in public spaces, IEEE Transactions on Industrial Electronics 52 (6) (2005) 1530–1546. [15] Hiroyasu Iwata, Hayato Hoshino, Toshio Morita, Shigeki Sugano, A physical interference adapting hardware system using MIA arm and humanoid surface covers, in: Proceedings of the 1999 IEEERSJ International Conference on Intelligent Robots and Systems, 1999, pp. 1216–1221. [16] Andre Sharon, Neville Hogan, David E. Hardt, High bandwidth force regulation and inertia reduction using a macro/micro manipulator system, in: Proceedings of the IEEE International Conference on Robotics and Automation, 1988, pp. 126–132. [17] Jung-Jun Park, Byeong-Sang Kim, Jae-Bok Song, Hong-Seok Kim, Safe link mechanism based on nonlinear stiffness for collision safety, Mechanism and Machine Theory (2007).
Contents lists available at ScienceDirect
Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmt
Variable stiffness mechanism for human-friendly robots Dongjun Hyun a, Hyun Seok Yang a,*, Jungwan Park a, Youngbo Shim b a b
Department of Mechanical Engineering, Yonsei University, 134, Sinchon-dong, Seodamun-gu, Seoul 120-749, Republic of Korea Fundamental Technology Team, Samsung Electronics Co., Ltd., 416, Maetan-3dong, Yeongtong-gu, Suwon-City, Gyeonggi-do 443-742, Republic of Korea
a r t i c l e
i n f o
Article history: Received 26 June 2008 Received in revised form 6 January 2010 Accepted 6 January 2010 Available online 7 February 2010 Keywords: Variable stiffness Safety mechanism Passive compliance Human-friendly robot Head impact test HIC index
a b s t r a c t We have developed a variable stiffness mechanism (VSM) for human-friendly robots to simultaneously meet safety and performance needs. The VSM has high stiffness in normal operation mode and has low stiffness in collision mode when the load applied to the joint exceeds a critical load, specified by the physical constraints of the joint structure and an actively controlled electro magnet. We have verified the safety of the VSM by simulations and experiments using the head injury criteria index. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Numerous robot applications, such as cleaning, lawn mowing, and entertaining, are being rapidly introduced in our daily lives assisted by developments in navigation, Artificial intelligence and various sensor technologies, though most are oriented to mobile technologies, are not able to cover other personal/public demands such as caring for the handicapped or the aged or assisting human work in close proximity, among other activities. To do such physical human robot interaction (pHRI) tasks, the robot should be equipped with manipulators. However, if safety issues are not properly addressed, no matter how great the performance and function, robots will not be applicable to our daily lives. Unfortunately, it is nearly impossible to imagine a system without any problems or potential problems. This is because as the complexity of systems increases, the probability of critical problems due to defects or failures on the part of the system also increases. For this reason, engineers and scientists have been trying to design better ways to reduce failure and prevent dangerous robot action in the event of a failure. Also, making a robot with parts safe for human contact is another important research area. One of the easiest and effective safety approaches is to wrap up the part in contact with humans with a soft and thick material, though this method still has drawbacks such an increase in size and mass, dull movement, and difficulty in covering up to the end effectors, among others. The larger the mass of the robot and the faster it moves, the more dramatically increased are the thickness and stiffness demands. Therefore, we need mechanical safety devices, which can ensure a minimum level of safety under uncontrollable failure cases. Mechanical safety devices may be implemented in various forms; among them, we are interested in joint compliance. If robotic joints have favorable compliance, they have an intrinsic safety of a certain level. Such mechanisms have a very low probability of harming humans in any external environment due to their natural characteristics. It is truly a beneficial solution for safety, but when we consider its response to the input, its benefits seem diminished. Joint compliance creates delays in forces from the actuator to the link and reduces the frequency bandwidth of the * Corresponding author. Tel.: +82 2 2123 2824; fax: +82 2 364 6769. E-mail address: [email protected] (H.S. Yang). 0094-114X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2010.01.001
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system. To solve this problem, mechanisms, such as series actuators connected to each other by properly designed elastic elements, including variable transmission stiffness, have been introduced over the last two decades [4,5,13,14]. In this article, a variable stiffness mechanism (VSM) for human-friendly robots was developed to meet the need of safety and performance simultaneously, even with a compact size. A VSM is comprised of a cam and a linear motion guide. The stiffness of the joint could be freely adjusted by the cam profile, and a compact size with a 70-mm diameter and a 40mm height was achieved. The cam profile was designated to obtain high stiffness under ordinary operational conditions and to obtain low stiffness in the collision condition. We demonstrated a dynamic model of the VSM in collision situations and the safety of the robot arm equipped with VSM through a head impact test using the head of a HybridIII car crash test dummy. The robot arm of 1 DOF was used in experiments in order to minimize the effect of unmodeled dynamics. The head injury criteria (HIC) index is used for the evaluation of the experimental results. The performance of the VSM and the effect of active control by the electro magnet were verified by simulations. 1.1. Related research Andre Sharon et al. (1988) introduced the macro/micro manipulator system [16] to achieve high bandwidth force regulation and inertia reduction. This system is composed of a macro-manipulator to treat low frequency and a micro manipulator to treat high frequency, which are connected serially with a spring and damper system with a specific coefficient. Morrell and Salisbury (1995) propose a parallel coupled macro-mini actuators [7] with the proper passive characteristics providing the best potential for fast, accurate force control. Unlike previous micro–macro robots, which used actuators coupled in series, the actuators in this system are coupled in parallel using a compliant transmission. Chew et al. (2004) propose a series damper actuator (SDA) [6] for force/torque control of manipulators, legged robots, and haptic devices, among others. The SDA system incorporated a series damper instead of a series elastic component between the actuator and the load in order to overcome some of the shortcomings in the SEA. Zinn et al. (2004) propose a force control actuation approach called distributed macro-mini actuation [3], which is connected in parallel and distributed to different locations on the manipulator. Distributed macro-mini actuation reduces the effective inertia of the overall manipulator and maintains performance with small actuators collocated with the joints. Sensinger and Weir (2005) design a non-backdrivable series elastic actuator [12] to expand the application of it into a non-backdrivable transmission like a harmonic drive, although its application is limited to backdrivable transmission. Koganezawa et al. (2004) introduce an actuator with non linear elastic system (ANLES) [8] to mimic the skeletal muscular system, which is composed of a torsion spring and guide shaft to modify stiffness by constraining the effective length of the torsion spring. Yoon et al. (2003) propose a safe arm with MR-based passive compliant joints [9] to reduce unwanted vibrations due to joint compliance. The safe arm consists of a magneto-rheological (MR) rotary damper and a rotary spring for elasticity and is designed to actively vary the damping coefficient according to the relative position of an actuator and link in order to absorb impact effectively. Bicchi and Tonietti (2002) design soft robot arms [10] for an intrinsically safe interaction with humans through applying a conical compression spring and a pneumatic artificial muscle and (2005) designed for a variable stiffness actuator [11] composed of a transmission belt and 3 pulleys, of which, one is idle and the others are driven by a DC motor. Iwata et al. (1999) propose physical interference adapting a hardware system using a mechanical impedance adjuster (MIA) arm [15], which is composed of leaf spring and ball thread and is able to vary the stiffness of the joint by using an effective length for the leaf spring. Park et al. (2007) propose a safe link mechanism based on nonlinear stiffness for collision safety by using a double-slider mechanism and shock-absorbing system [17]. Park’s mechanism is based on the four bar linkage while the VSM is based on the cam mechanism. The VSM has several strengths as followings: (1) The stiffness of the VSM varies with the cam profile freely in contrast to Park’s mechanism that has only one stiffness function such as Eq. (4) in the reference [17]. For an example, the VSM can be stiffer than Park’s mechanism for better performance under the same critical impact force. (2) The stiffness of the VSM can be controlled by electromagnets. Therefore, it can eliminate the effect of the gravitational force or can enhance performance of service robots. 1.2. Evaluation of safety We use the head injury criteria (HIC) index to evaluate the safety level of the robot equipped with the VSM. The HIC index was developed by the automotive industry to assess head injuries of occupants during car accidents. It is reasonable to use the HIC Index as the evaluation method for the safety of robots, since the head is the single most critical human organ that could be most seriously harmed by a robot. For the same reason, the HIC Index was used as an evaluation tool for the safety of robots in several previous works [10]. In this section, we specify the test protocols and calculation procedures that are applied in this study to show that test results are acceptable. It is inadequate to directly compare the results of previous works because the test results are largely influenced by small differences in test conditions such as the impact region on the head, stiffness of the head fixture, contact
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speed, and the behavior of the actuator during impact. Test protocols and calculation procedures applied in this article follow, as much as possible, those of the automotive industry. The head used for the impact test is the HybridIII 50th percentile crash test dummy’s head, which is the most broadly used for automotive frontal impact tests and has authorized weight and contact stiffness of an ordinary male head. Three 7264–200s of Brüel&Kjær, which are also used for car crash tests, are used as accelerometers to measure head acceleration during the impact test. It is not only expensive but also inefficient to use a full body dummy for these small size tests in the laboratory. Hence, a head fixture is used instead of a full dummy body. The fixture of the head is a cylindrically shaped urethane rod with an 80-mm diameter and 200-mm height. The stiffness of the fixture is adjusted to 3.825 Nm/deg since neck stiffness of a seated HybridIII dummy is 3.696 Nm/deg and neck stiffness of a standing HybridIII dummy is 3.936 Nm/deg, according to the HybridIII Geometrical and Inertial Properties specified by Kaleps and Whitestone [1]. Impact direction is horizontal, and the impact region is the forehead, which has a uniform skin thickness. Fig. 1 shows the equipment and conditions of the head impact test. The HIC index is calculated by Eq. (1), where the acceleration of the head is obtained by a resultant acceleration of three axes in the g unit, and T is a 36-msec time duration. In the automotive industry, HIC36 is the most broadly used standard of head injury representation, though T is defined as the final time of impact in other articles [Antonio Bicchi ‘‘Fast and soft-arm tactics”]. HIC36 is obtained by selecting the maximum value in the all HIC36s during impact tests.
HIC36 ¼ T
Z T 2:5 1 aðsÞds T 0
ð1Þ
Head acceleration data of EuroNcap frontal impact tests on a Mercedes A-Class are used to verify Eq. (1). According to the official test reports, the HIC36 of the driver was 446.9, and we obtain the result from Eq. (1). In addition, another interesting test is performed. A person who weighs approximately 100 kg hit the test equipment using a basketball with his best. Through this test we could ascertain what would be a realistic injury level of the head in the ordinary operation of a robot arm. The measured HIC36s of the tests were 9.448, 7.349, and 13.19. We found from the test results that an HIC36 of unit 10 results in severe injuries, in the case of a head hit only locally, and that the value of HIC36 increases exponentially as head acceleration increases. Fig. 2 shows the head acceleration of the EuroNcap frontal impact test on a Mercedes A-Class and head impact tests using a basketball. 2. Design of a variable stiffness mechanism (VSM) 2.1. Dynamic modeling and analysis of the collision To study the effect of joint flexibility on the safety level of robots, we first derive a dynamic model to describe the collision of a head with a single-link robot arm equipped with a flexible joint of which stiffness is constant. The head is fixed to the
Fig. 1. Head impact test equipment and conditions.
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Fig. 2. Resultant acceleration of a head.
ground through a spring and damper and has contact with a robot arm through a spring and damper as well. However, contact elements that are composed of a spring and a damper have an effect only during contact. If the sign of the distance between the head and a robot arm is negative, then the stiffness constant and damping coefficient are constant. Otherwise, the stiffness constant and damping coefficient are zero. The robot arm and rotor are connected by a spring and a damper as well. Eqs. (2)–(4) represent the dynamic model of the collision as shown in Fig. 3
kC dC kN dN ðx þ lh2 Þ ðx_ þ lh_ 2 Þ x x_ MHEAD MHEAD M HEAD M HEAD kT dT sROTOR ¼ ðh1 þ h2 Þ þ ðh_ 1 þ h_ 2 Þ þ IROTOR IROTOR IROTOR kC l dC l k dT _ T ¼ ðx þ lh2 Þ ðx_ þ lh_ 2 Þ þ ðh1 h2 Þ þ ðh1 h_ 2 Þ IARM IARM IARM IARM
€x ¼
ð2Þ
€h1
ð3Þ
€h2
ð4Þ
x represents the linear displacement of the head. kN and dN are the stiffness constant and the damping coefficient of the neck, which can be obtained easily by a linear force–displacement test and a free vibration test. MHEAD is the effective mass of the test equipment, which is composed of a HybridIII 50th percentile crash test dummy head and the fixture. l is the length of robot arm and kC and dC represent the stiffness constant and damping coefficient of the contact element. It has unique
Fig. 3. Impact model.
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characteristics such that the stiffness constant and damping coefficient depend on the penetration depth between two bodies, that is, if lh2 6 x then kC = 0 and dC = 0. h1 and h2 represent the rotor angle and link angle. sROTOR is the torque exerted by the actuator. kT and dT represent the stiffness constant and damping coefficient of the transmission element. IROTOR and IARM are the inertia of the rotor and arm. T Referring to Eqs. (2)–(4), we let q ¼ x x_ h1 h_ 1 h2 h_ 2 be the state vector. Then the state space equation is given by
q_ ¼ Aq þ Bu
ð5Þ
where A, B, and u are
2
0
6 kC þkN 6 MHEAD 6 6 0 6 A¼6 6 0 6 6 0 4 kC l IARM
1
0
0
0
þdN dMCHEAD
0
0
Cl MkHEAD
0
0
1
0
0
kT IROTOR
dT IROTOR
kT
0 Cl IdARM
0
0
kT
dT
IARM
IARM
B ¼ ½ 0 0 0 1=IARM
0 0 T ;
IROTOR
0 2 Cl kTIþk ARM
0
3
7 Cl MdHEAD 7 7 7 0 7 7 dT 7 IROTOR 7 7 1 5 2 dT þdC l IARM
ð6Þ
u ¼ sROTOR
In our simulation, we assume that the end point of the robot arm hits someone’s forehead at its maximum speed under malfunction and the actuator exerts a torque on the arm link after collision. The simulation starts at contact and therefore the initial state is qð0Þ ¼ ½ 0 0 0 xMAX 0 x MAX T . At that time, Fig. 4 shows the relation between kT and HIC36 obtained by the resultant acceleration of the head. Parameters of the simulation model are shown in Table 1. Two inflection points at kT = 200 and 20,000 Nm/rad are found from Fig. 4. The HIC36 does not decrease much despite the decrease in the transmission stiffness when it was less than 200 Nm/rad, and the HIC36 does not increase much despite the transmission stiffness increase when it is more than 20,000 Nm/rad. This means that the effective inertia to transfer the impact to the head is determined by the transmission stiffness. If the transmission stiffness is rigid, the rotor and robot arm behave like a rigid body. Likewise, if transmission stiffness is soft, then the inertia of the rotor has little effect on the HIC36. Therefore, the injury suppression mechanism through the control of transmission stiffness has an advantage in systems with large rotor inertia. 2.2. Stiffness varying mechanism with cam The design goals of the VSM are: (1) (2) (3) (4)
Adjustability of stiffness. Low stiffness of the robot arm in collision mode for safety purposes. High stiffness of the robot arm in the normal operating mode, for fast response. Minimum electric control to prevent malfunctions due to a complex system.
Fig. 4. HIC and transmission stiffness.
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MHEAD = 5.09, IROTOR = 0.175, IARM = 0.14 kN = 3300, kC = 1500 dN = 12, dC = 15 l = 0.6
(5) Compact size. In this article, a mechanism that uses a cam is proposed to achieve the above design goals. Fig. 5 illustrates the concept that the horizontal stiffness constant is a function of the vertical stiffness constant and the cam angle /.
F H ¼ kV tan /y y ¼ tan /x
ð7Þ ð8Þ
F H ¼ kV tan2 /x ¼ kH x
ð9Þ
) kH ¼ kV tan2 /
ð10Þ
FH is the external horizontal force exerted from a rotor or robot arm, which moves the cam follower to the x-direction. The cam follower compresses the spring installed in the vertical direction for which the stiffness constant is kV. The cam follower moves along a cam slope with an incline of /. Therefore, the resultant stiffness constant in the horizontal direction, kH, is kV tan 2/ as shown in Eq. (10). Fig. 6 illustrates the concept that the cam profile is applied to the rotational joint. The cam profile was proposed to achieve a low stiffness for the safety of the robot arm in the collision mode and high stiffness for a simultaneous fast response of the robot arm in the normal operating mode. The adjustability of the stiffness can be obtained by varying the angle / of the cam slope freely, that is, the stiffness constant in the horizontal direction varies from 0 to infinity as / varies from 0 to 90 degrees. If the cam profile is applied to the rotational joint of radius r, the rotational stiffness constant kR is function of r and kH. Eq. (11) describes the relationship between the rotational stiffness constant and vertical stiffness constant.
kR ¼ r 2 kV tan2 /
ð11Þ
This rotational joint mechanism has a large variation of stiffness and a compact size. Furthermore, it does not need to be actively controlled by logic. Fig. 7 shows a large variation of stiffness according to the cam profile and kV.
Fig. 5. Cam mechanism.
Fig. 6. The development figure of the cam profile applied to the rotational joint.
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Fig. 7. Rotational stiffness constant.
2.3. Preload adjusting mechanism with screws and electromagnets The preload is necessary to eliminate the gap between the cam follower and the cam and to compensate for gravity. If the preload affects the VSM, then the stiffness constant is at a maximum without an inclined cam angle. Since the cam follower does not move along the cam, all the components of the VSM rigidly contact. Basically, a preload of VSM is determined by the difference between the free length and the installed length of the vertical spring and is adjusted by a screw mechanism shown in Fig. 8. The preload mechanism is fixed permanently after it is adjusted. The Preload has no need to be changed when the robot arm rotates only horizontally. However, if a robot arm were to rotate vertically, as shown in Fig. 9, the preload must be adjusted according to the angle a. Most flexible joints share the same
Fig. 8. Preload adjusting mechanism by a screw.
Fig. 9. Variation of moment arm length according to link angle.
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problems of deflection in vertical operation due to joint flexibility. VSM stiffness minimizes when the external load exceeds the critical load, which is determined by the cam profile. Therefore, the external force due to the weight of the arm disturbs the critical load and the VSM behaves in an undesired way. Thus, the VSM equips a programmable preload control mechanism by electromagnets, which apply a pulling force to the cam follower toward the cam side. Electromagnets may improve robot arm performance through a pulling force control according to the robot arm speed. For example, the stiffness of the VSM may decrease in an undesired situation during which the robot arm accelerates rapidly from rest. At this time, the pulling force of the electromagnets can prevent the VSM from any unwanted sudden change of stiffness. Fig. 10 illustrates the preload control mechanism by electromagnets. Eq. (12) describes the preload determined by the screw and electromagnet mechanism. The force–displacement characteristics of the VSM are shown in Fig. 11.
F H ¼ kV tan2 /x þ kV tan /ðlFREE lADJ Þ þ F EM tan /
ð12Þ
where lFREE is the free length of the spring, lADJ is the length of the spring adjusted by the screw mechanism and FEM is the pulling force of the electromagnets. The response of the preload controlled by electromagnets is fast enough that the VSM could be adopted in a rapidly operated robot arm. 2.4. Prototype design The prototype of the VSM is composed of 3 parts, an inner-upper part, an inner-lower part, and an outer part as shown in Fig. 12. The inner-upper part is composed of 2 cam followers, 2 spring assemblies, and 2 linear motion guide (LM guide). It connects the inner-lower part and the outer part. The inner-upper part is connected to the inner-lower part with LM guides for relative linear motion as shown in Section B–B of Fig. 13, and the spring assemblies for kV, as shown in Section C–C of Fig. 13. Therefore, the inner-upper part and the inner-lower part rotate together and simultaneously move linearly from each other with an elasticity of kV. The inner-lower part is composed of two electromagnets, two linear motion shafts (LM shaft), a cross roller bearing, and an input shaft. It transfers torque input from the rotor. Two electromagnets control the preload as shown I n Section A–A of Fig. 13, and two LM shafts transfers torque from the rotor to the inner-upper part. The inner-lower
Fig. 10. Preload control mechanisms.
Fig. 11. Force–displacement characteristics of VSM.
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Fig. 12. Parts of the VSM.
Fig. 13. Overview of the VSM.
part is attached to the outer part with a cross roller bearing, and therefore, the inner-lower part does not transfer torque to the outer part directly and only rotated relative to each other. The outer part, which has a cam profile on its cylindrical outer
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wall, transfers torque from the inner-upper part to the robot arm with a determined stiffness by the cam and the cam followers. The performance properties are shown in Fig. 14. In neutral mode, the cam follower exists in the high stiffness region at the center of the cam profile. At this time, the stiffness of the VSM is close to the rigid condition; therefore, the VSM does not
Fig. 14. Performance property.
Fig. 15. Prototype of the VSM.
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degrade the performance of the robot arm. In the case of a collision, the VSM experiences a sudden load more than a critical load, which is determined by the composition of the preload and high stiffness cam profile. As a result, the cam followers move along the cam profile and the inner-upper part is separated from the inner-lower part along two LM shafts as the inner-upper part overcomes the pulling force of the springs and electromagnets. At this time, the inner-upper part undergoes the rotational motion and linear motion about the outer part simultaneously and the inner-lower part undergoes only rotational motion about the outer part and the stiffness of VSM becomes low. Fig. 15 shows the prototype of the VSM. 3. Simulations and experiments In this section, we demonstrate the effectiveness of the VSM through simulations and experiments. Safety levels and input tracking performance of the robot arm are the main considerations of the VSM. Additional applications such as gravity compensation and active preload control are addressed as well. The safety of the robot arm is evaluated by simulations with the dynamic model described in Section 2.1 and experiments with the test equipment in Section 1.2. Performance and additional applications are demonstrated by simulation only, since it is possible to obtain a reasonable result through simulation, and it is difficult to measure the accurate motion of the robot arm from an external environment without an expensive measurement system. 3.1. Safety In the simulation to evaluate VSM safety, we assume the worst case in which the robot arm hit the head at maximum speed without an emergency stop. The simulation is performed in cases of VSM and a rigid joint to evaluate the effectiveness of the VSM. We determine the inertia of the robot arm using a robot arm, which consists of a 150-W Maxon motor, gear, and an aluminum pipe since this robot arm is the most appropriate out of the robot arms available in our laboratory. The speed at collision is 4.2 m/s because the rotor is driven by a motor rotating at 7580 rpm in constant speed mode by an EPOS 70/10 Maxon motor driver. The reduction gear ratio is 3/338, and the length of the robot arm is 0.6 m. We obtain an HIC36 from the results of the simulation as shown in Table 2. The injury level on the simulation is not high enough to lead to human death or serious injury but it is sufficient to demonstrate the effectiveness of the VSM. Moreover, the injury level in the simulation was not so low that a human could not sense pain since a collision of an object as large as the head moves 50 mm in the case of a rigid joint. As shown in Fig. 16, the VSM reduces the displacement of the head from
Table 2 HIC36 of simulations and experiments. Simulation VSM Rigid joint Reduction rate
0.11 0.40 72%
Experiment 0.073 0.22
0.074 0.22
Fig. 16. Head displacement of simulation.
0.074 0.21 66%
0.075 0.22
0.075 0.22
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50 mm to 18 mm. As shown in Fig. 17, head acceleration of the VSM case differs from the acceleration of the rigid joint case by approximately 12 msec and starts to decrease at approximately 21 msec. Therefore, the duration time of the first contact in the case of VSM is shorter than that in the case of rigid joint. The second peak acceleration is found at approximately 135 msec in the case of VSM due to the constructive limit of the VSM but it does not have such an effect that it dramatically increases the extent of injury. This is because impact energy has already been spent considerably in the first impact. We have performed 5 experiments on the VSM and the rigid joint, respectively through test equipment as shown in Fig. 18. The results of the experiments are shown in Figs. 19 and 20 and Table 2. All the experimental results show a small deviation and demonstrate the effectiveness of the VSM. The VSM reduces the HIC36 values by 33% with respect to the rigid joint. Figs. 19 and 21 show that the stiffness of the VSM changes well. The cam initially stays at position r in Fig. 21. When the cam stays within the high stiffness region, measured acceleration of the VSM is nearly the same as that of the rigid joint. At the moment that the cam arrives at position s in Fig. 21, the cam moves into the low stiffness region and the time is approximately 25 msec. in Fig. 19. From this time, measured acceleration of the VSM is deviated from that of the rigid joint, and starts decreasing in contrast with the rigid joint. When the cam moves in the low stiffness region, measured acceleration of the VSM decreases or keeps low level. However, at the moment that the cam arrives at position t in Fig. 21, the cam
Fig. 17. Head acceleration of simulation.
Fig. 18. Test equipment configuration.
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Fig. 19. Head acceleration of experiments.
Fig. 20. Head displacement of experiments.
collides with the wall of the case, and then measured acceleration of the VSM makes a sharp peak at approximately 135 msec. Despite the sharp peak, measured HIC36s of the VSM are still lower than those of the rigid joint. The sharp peak can be reduced easily by attaching a soft stopper at the wall of the case. The VSM can equip with the soft stopper easily. As shown in Figs. 22 and 23 and Table 2, the results of simulations and experiments do not correspond to cases of the VSM and the rigid joint, respectively. However, from the view point of contact duration at first contact and the magnitude of head displacement and approximate behavior, the simulations describe the dynamic behavior of experiments well. Therefore, the dynamic model of collision and simulation is valid. Differences between simulations and experiments arise from the backlash of the reduction gear, nonlinear characteristics of the contact materials, and unmodeled dynamics, such as local vibration of the robot arm. Fig. 24 shows the test equipment. 3.2. Performance One of the design goals of the VSM is to achieve a high stiffness for the fast response of the robot arm in the normal operating mode. In this simulation, we compare a soft joint, rigid joint, and VSM to demonstrate how fast the VSM responds. The stiffness constant of the soft joint is considered to be 200 Nm/rad because the stiffness constant must be less than 200 Nm/
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Fig. 21. Illustration of varying stiffness according to cam position.
Fig. 22. Comparison of head acceleration with simulations and experimental data.
rad to achieve safety of the robot arm as shown in Fig. 4. The stiffness constant of the rigid joint is considered to be 5000 Nm/ rad because the stiffness constant must be greater than 5000 Nm/rad to minimize the effect of compliance between the rotor and the robot arm. The rotor of the soft joint, rigid joint, and VSM drive the robot arm with uniform sinusoidal input torque. Figs. 25–29 show the response of the robot arm to the sinusoidal input. The results of the rigid joint can be regarded as a standard of performance since the performance of the rigid joint is the best. The motion of the soft joint and the VSM follow the rigid joint case very well at 1 Hz. However, the soft joint starts to disperse at 5 Hz and becomes uncontrollable at 15 Hz. The VSM follows the rigid joint up to 15 Hz considerably and starts to disperse at 20 Hz. Therefore, it is reasonable to assume that the response of the VSM is approximately 4 times faster than that of the soft joint. 3.3. Additional applications The prototype of the VSM is equipped with two electromagnets of 15 mm in diameter and 30 mm in length, which can produce 40 N pulling forces continuously and 60 N temporarily. The maximum force of this active controlled preload can be
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Fig. 23. Comparison of head displacement with simulations and experimental data.
Fig. 24. Test equipment.
Fig. 25. Angular displacement and velocity at 1 Hz.
easily increased by enlarging the diameter of the VSM, since the pulling force of the electromagnet increases dramatically as the diameter of the electromagnet increases. In this simulation, we demonstrated the effectiveness of the active controlled
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Fig. 26. Angular displacement and velocity at 5 Hz.
Fig. 27. Angular displacement and velocity at 10 Hz.
Fig. 28. Angular displacement and velocity at 15 Hz.
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Fig. 29. Angular displacement and velocity at 20 Hz.
Fig. 30. Effectiveness of actively controlled preload.
preload simply by improving the simulation results presented in Section 3.2. The increase in the preload of the VSM degrades the safety of the robot arm but improves performance. Therefore, it is necessary to control preload actively to achieve the required safety and performance of the robot arm. The control strategy is to increase the preload when the speed of the robot arm is low and decrease the preload when speed is high since the robot arm is less dangerous at low speeds. This strategy is referred to as [10]. As shown in Fig. 30, the robot arm, in the case of a controlled preload, does not become uncontrollable even though the torque exerted from the rotor increases.
4. Conclusions and future work We have proposed a variable stiffness mechanism (VSM) to achieve simultaneous safety and performance of the robot arm. Five design goals suggested in the Section 2.2 were satisfied by the VSM. The adjustability of stiffness means how easily stiffness can be changed and means how largely the range of stiffness can be changed. The stiffness of the VSM can be changed freely and largely by the cam angle and the installed spring. The fact that the VSM makes the stiffness of the robot arm high in normal operating mode and makes the stiffness of the robot arm low in collision mode is demonstrated by experiments and simulations. The VSM has no need to be controlled electrically or can have a simple controller separated from the complex main control system. The prototype of the VSM has a compact size with a 70-mm diameter and a 40-mm height, which is slightly larger than a tennis ball.
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The safety of the VSM is evaluated by both simulations and experiments. The performance of the VSM is confirmed by simulations. The VSM, equipped with an electromagnet to control the preload, is suggested to extend its application to various fields such as the vertical motion applications and high frequency operation applications. In the future, we will study a multi-DOF manipulator equipped with a VSM through simulations since the dynamic model in this article describes physical systems well. To apply the VSM to multi-DOF manipulator, the cam profiles adequate to the respective joints and gravity compensation for vertical motion joints will be needed. Acknowledgement This research is supported by the Mechatronics and Manufacturing Technology Center of Samsung Electronics Co. References [1] Stanley H. Backaitis, Harold J. Mertz, HybridIII: The First Human-Like Crash Test Dummy (1994) 687–707. [3] Michael Zinn, Bernard Roth, Oussama Khatib, J. Kenneth Salisbury, A new actuation approach for human-friendly robot design, International Journal of Robotics Research 23 (4–5) (2004) 379–398. [4] Alin Albu-Schäffer, Christian Ott, Gerd Hirzinger, A unified passivity-based control framework for position, torque and impedance control of flexible joint robots, International Journal of Robotics Research 26 (1) (2007) 23–39. [5] Hun-Ok Lim, Kazuo Tanie, Human safety mechanisms of human-friendly robots: passive visco-elastic trunk and passively movable base, International Journal of Robotics Research 19 (4) (2000) 307–335. [6] Chee-Meng Chew, Geok-Soon Hong, Wei Zhou, Series damper actuator: a novel force/torque control actuator, International Conference on Humanoid Robots 2 (2004) 533–546. [7] J.B. Morrell, J.K. Salisbury, Parallel coupled actuators for high performance force control: a micro–macro concept, International Conference on Intelligent Robots and Systems 1 (1995) 391–398. [8] K. Koganezawa, Y. Shimizu H. Inomata, T. Nakazawa, Actuator with non linear elastic system (ANLES) for controlling joint stiffness on antaonistic driving, in: Proceedings of the 2004 IEEE International Conference on Robotics and Biomimetics, 2004, pp. 51–55. [9] S.-S. Yoon, S. Kang, S.-J. Kim, Y.-H. Kim, M. Kim, C.-W. Lee, Safe arm with MR-based passive compliant joints and visco-elastic covering for service robot applications, IEEE/RSJ International Conference on Intelligent Robots and Systems 3 (2003) 2191–2196. [10] A. Bicchi, G. Tonietti, Design, realization and control of soft robot arms for intrinsically safe interaction with humans, in: Proceedings of the IARP/RAS Workshop on Technical Challenges for Dependable Robots in Human Environments, 2002, pp. 79–87. [11] Giovanni Tonietti, Riccardo Schiavi, Antonio Bicchi, Design and control of a variable stiffness actuator for safe and fast physical human/robot interaction, in: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 2005, pp. 526–531. [12] Jonathon W. Sensinger, Richard F. ff. Weir, Design and analysis of a non-backdrivable series elastic actuator, in: Proceedings of the 2005 IEEE Ninth International Conference on Rehabilitation Robotics, 2005, pp. 390–393. [13] G.A. Pratt, M.M. Williamson, Series elastic actuators, intelligent robots and systems 95. Human Robot Interaction and Cooperative Robots, in: 1995 IEEE/RSJ International Conference on Proceedings 1(5–9) (1995) 399–406. [14] Björn Jensen, Nicola Tomatis, Laetitia Mayor, Andrzej Drygajlo, Roland Siegwart, Robots meet humans – interaction in public spaces, IEEE Transactions on Industrial Electronics 52 (6) (2005) 1530–1546. [15] Hiroyasu Iwata, Hayato Hoshino, Toshio Morita, Shigeki Sugano, A physical interference adapting hardware system using MIA arm and humanoid surface covers, in: Proceedings of the 1999 IEEERSJ International Conference on Intelligent Robots and Systems, 1999, pp. 1216–1221. [16] Andre Sharon, Neville Hogan, David E. Hardt, High bandwidth force regulation and inertia reduction using a macro/micro manipulator system, in: Proceedings of the IEEE International Conference on Robotics and Automation, 1988, pp. 126–132. [17] Jung-Jun Park, Byeong-Sang Kim, Jae-Bok Song, Hong-Seok Kim, Safe link mechanism based on nonlinear stiffness for collision safety, Mechanism and Machine Theory (2007).