Demonstrating the Safety and Performance of a Velocity Sourced Series Elastic Actuator

Transcription

1 008 IEEE International Conference on Robotic and Automation Paadena, CA, USA, May 19-3, 008 Demontrating the Safety and Performance of a Velocity Sourced Serie Elatic Actuator Gordon Wyeth, Member, IEEE Abtract Actuator with deliberately added compliant element in the tranmiion ytem are often decribed a improving the afety of the actuator at the detriment of the performance. We how that our variant of the Serie Elatic Actuator topology, the Velocity Sourced Serie Elatic Actuator, ha well defined performance characteritic that make for improvement in afety and performance over conventional high impedance actuator. The improvement in performance wa principally achieved by having tight velocity control of the DC motor that act a the mechanical power ource for the actuator. Reult for performance are given for point to point tranition time, while reult for afety are baed on empirical aement of the Head Injury Criterion during colliion. T I. INTRODUCTION he new field of human-centered robotic addree the many challenge in creating cloe interaction between human and robot, including direct contact between robot and human. Current tandard for robot afety prohibit uch contact, pecifying failafe robot encloure that keep human completely out of the robot workpace at all time, and removing the poibility of direct interaction. The iue of robot afety i being addreed by a range of trategie that operate to either prevent colliion or to minimize the harm caued by colliion. Many reearcher are invetigating the ue of compliance in the tranmiion ytem of robot actuator a a mean of reducing force during an accidental impact ([1],[],[3],[4]). A compliant tranmiion ytem coupled with light weight mechanical deign reduce the mechanical impedance of the manipulator. Mot robot ue high impedance actuator typical of indutrial robot arm. When a high impedance robot collide with an obtacle, the force are large and rie quickly, maximizing the likelihood of injury. Torque Command + - Controller Motor Torque Feedback (from pring diplacement) Figure 1: Serie Elatic Actuator topology. Gearbox Spring oad Manucript received September 14, 007. Gordon Wyeth i with the School of Information Technology and Electrical Engineering, Univerity of Queenland, Bribane, 407, Autralia (phone: ; fax: ; wyeth@itee.uq.edu.au). To achieve a low impedance deign it i imperative to decouple the high moment of inertia of the motor een through the gearbox which can create a high impact load. The Serie Elatic Actuator (SEA) deliberately introduce compliance via a pring between the motor-gearbox and the load, and o ha intrinic low impedance. However, it i widely held that the SEA ha bandwidth limited to about one-third of the fundamental frequency, and that attenuation of flexible mode ocillation can be difficult to achieve [5]. Thi paper how that it i poible to produce high performance from an SEA, well beyond one-third of the fundamental frequency, while retaining the inherent afety given by the actuator low effective inertia and tiffne. The improvement in performance i principally achieved by having tight velocity control of the DC motor that act a the mechanical power ource for the actuator. Thi variant of the SEA, the Velocity Sourced SEA (VS-SEA), ha well defined performance characteritic that help to define trajectorie that are both achievable and afe. The paper review the principle of the Velocity Sourced SEA, and than give a decription of a prototype device and it controller. The afety of the VS-SEA i evaluated by a erie of quantitative meaurement of the Head Injury Criteria (HIC) [6], a tandard ued in automotive afety. Performance i compared with a high impedance actuator ytem baed on the ame DC motor and gearbox for point to point time trial conducted within the afe peed limit of the repective device. II. PREVIOUS SEA STUDIES The control and implementation of Serie Elatic Actuator have been approached from a number of perpective. In [7], the concept i firt introduced in the form of an electric motor in erie with a pring. The pring in thi model wa a beam with a cro-haped cro ection. Deflection in the beam wa meaured uing train gauge. The motor wa controlled uing current control a the input to the motor, making the motor an effective torque ource. The compenation cheme ued both feedback from the train gauge, and feedforward from the deired torque input to calculate a deired current for the motor. While the implementation demontrated many of the deirable characteritic of a Serie Elatic Actuator, there were a number of undeirable characteritic in the deign. Backlah in the gearbox introduced ome undeirable and unpredictable reonance in the cloed loop repone, and friction effect limited the effectivene in providing large /08/$ IEEE. 364

2 force bandwidth. In [8], the author note potential for improvement in the electronic deign of the ytem. The SEA wa reviited in detail in [9] again with the uppoition that the motor i to be controlled a a torque ource. The effect of friction and backlah are better quantified, and ome guideline for pring election are introduced. The actuator themelve formed the bai of the acuator for ale through Yobotic. ater work [] however decribe imilar problem to thoe een by Williamon. III. VEOCITY SOURCED SEA In thi paper, we change the paradigm for SEA deign by treating the motor a a velocity ource rather than a a torque ource. Thi idea i uggeted in [9]. The reaon that thi idea become attractive i that a tight velocity control of the motor can overcome ome of the undeirable effect of the motor and the gearbox and provide a conitent platform for the outer SEA controller. The principle of a velocity controlled SEA i hown in Figure. The motor ha velocity feedback from an encoder that form a tight loop for controlling the motor and gearbox. The velocity controller i tuned with no load attached, baed on the aumption that the pring decouple any highfrequency torque diturbance on the SEA output, and that a well tuned velocity controller hould be able to deal with low-frequency torque diturbance. With thi tight velocity control loop in place, the motor can be treated a an effective velocity ource, implifying the deign of the SEA controller for the outer torque loop. Torque Command + - SEA Controller + - Speed Controller Speed Feedback (from encoder) Torque Feedback (from pring diplacement) Figure : The inner velocity loop in the velocity ource SEA help to overcome problem with non-linearitie and tiction. A. Dynamic of a Velocity Sourced SEA With the motor acting a a velocity ource, the equation of motion aociated with the SEA can be written. The pring deflection θ i a function of the motor peed ω m and the poition of the load θ : ωm θ θ (1) Auming that the load ha inertial propertie, J, and i being controlled only by the actuator, that i, that there are no other torque ource affecting the load, then the poition of the load i determined from the output torque applied to the load T : 1 θ T () J Motor Gearbox Spring oad But the torque applied to the load T i due olely to the deflection of the pring θ by: T K θ (3) By combining (1), () and (3) we find the open loop tranfer function from motor velocity to SEA output torque i given by: T K (4) ω K m + J where T i the output torque applied to the load, ω m i the peed of the motor, J i the inertia of the load and K i the pring contant. If the velocity ource i a DC motor in a cloed loop with PI compenation, the cloed loop motor tranfer function will have the form: ωm B d (5) ω + A + B where A and B are ome contant derived from the choice of zero placement and gain in the PI controller to achieve fat rie time and little overhoot. Thee pole will be much fater than the imaginary pole of the velocity to torque tranfer function. B. Chooing a Control Strategy Placing the motor and erie elatic element tranfer function in erie give the open loop tranfer function that mut be compenated by the SEA controller: T BK (6) ωd K ( + A + B)( + ) J To create a ytem that will be of Type 1 with repect to a torque input (no teady tate error for a contant torque) the compenator mut have two pole at the origin. Chooing two low frequency, complex zeroe tend to attract the reonant pole of the SEA to thoe zeroe, cancelling the reonance. Thi compenator ha the form: ωd K SEA( + C + D) (6) Te where C and D are choen to attract the reonant pole under feedback, and the gain K SEA can be determined from a root locu plot. In the following ection, we will demontrate a cae tudy of the deign of a controller after decribing the implementation of our VS-SEA. IV. IMPEMENTATION We have built a prototype VS-SEA to tet the concept uitability for ue in human-robot interaction application. The following ection outline the deign of the prototype including the hardware and the controller. The effect of aturation are addreed, and the ytem for trajectory generation explained. The high impedance reference ytem ued for comparion i decribed. A. Hardware Deign The deign treat the elatic element a a modular 3643

3 component that might be ued with a range of motor ytem, a are other tranmiion element uch a gearboxe. The elatic element (illutrated in Figure 3) i 10 mm in diameter, and 98.5 mm in length, compriing a body 36 mm long, with 5 mm of output haft and 37.5 mm of input haft. With four pring, the element provide a rotational pring contant of 138 Nm/rad, although the deign can ue le pring or accommodate a range of pring ize. The pring are alway in compreion and remain linear in their behavior. The deflection enor i a critical element in the deign, a noie or quantization in the angle meaurement impact ytem performance dramatically. We have employed a Philip KMZ-41 Magnetic Field Senor in a 150 ka/m field, achieving an abolute poition meaurement with 0.01 of reolution. TABE I PROPERTIES OF MOTOR USED TO DRIVE THE VS-SEA. Property Value Nominal voltage 4 V Terminal reitance.07 Ω Terminal inductance 0.6 mh Torque contant Nm/A Back EMF contant V/rad Max peed 859 rad/ Max continuou torque Nm Rotor inertia kg.m Reflected gear head inertia kg.m Gear ratio 156:1 Coulomb friction (at output) 10 mnm Coefficient of vicou friction N/mm pring Magnetic Angle Senor 19N/mm pring Permanent Magnet Bearing Figure 4: The velocity ourced SEA in it tet rig. The prototyping board i a preamplifier for the magnetic field enor. Figure 3: Exploded view of the Serie Elatic element ued in the VS- SEA. The elatic element i actuated by a Maxon RE35 90W 4V motor with an integrated GP4C 156:1 planetary gear head and a HED CPT encoder. The motor / gear head / encoder ha the relevant characteritic lited in Table 1 below. For thee experiment, the element drive a 5 kg link with length 0.6 m and a moment about the actuator drive axi of 0.6 kg/m. The dimenion are typical of the combined propertie from the houlder of an arm ued in human-robot interaction. It i ignificantly heavier than other tudie [4], [1], but i perhap truer to the achievable ma if the arm i to be equipped with a dexterou gripper. Control i performed by a cutom motor drive board with a 5 MHz 3 bit microcontroller, with ening and power electronic. The motor drive are rated to 60V at 5A, but can provide up to 0 A peak. Power i drawn from laboratory upplie uing a 4 V bu. The control ytem i implemented a a dicrete time digital ytem, baed on the enuing continuou time deign. The ample rate for the dicrete ytem i 3.6 khz. B. Controller Deign With the prototype ytem configured a decribed above the ytem ha open loop tranfer function in the form of equation (6) with the following value: T /156. (7) ωd ( )( + 30) Uing the control trategy decribed in ection III B we tried a number of complex zero poition near the reonant pole. Uing a root locu plot we choe zeroe at -10 ± 6.5j and a gain of 300 giving the compenator tranfer function: ωd 300( ) (8) T e The final cloed loop tranfer function for torque command i: 8 T ( ) (9) Td ( + 374)( )( ) Note that, a oberved by Robinon [9], the tranfer function can be independent of the pring tiffne. Any change in pring tiffne can be offet by an equal and oppoite change in the controller gain. Note alo that the bandwidth of the linear ytem ha ignificantly exceeded the reonance of the compliant ytem, but it i important to verify that that i the cae with the non-linearitie mot 3644

4 notably motor aturation in the implemented ytem. C. Effect of Saturation In conidering the effect of aturation on the implemented ytem, it i important to think of the motor a a velocity ource with the principle role of controlling the length of the pring between motor and load that in turn control torque (1). Conidering jut the fat-acting movement aociated with the motor and pring rather than the teady tate peed of the load, one can write: T J ωm ω (10) K K That i, the peed of the motor define the rate of change of torque which in turn define the jerk of the load. The maximum peed of the motor i the key aturation effect that define the performance of the VS-SEA. The implication from thi obervation are twofold. Firtly, the VS-SEA can not ource a tep change in torque, but, given a tight velocity loop around the motor with fat rie time, will lew torque at a near contant rate of change. For a fixed load, thi implie a limit to the jerk of the trajectory of the load. Secondly, the jerk value i readily dicernable from the VS-SEA parameter, and if the load trajectory i planned with that limited jerk capability in mind then the controller will continue to operate in a linear and predictable fahion. D. Trajectory Generation The trajectory generation ytem take arbitrary velocity command tream and convert them to torque command that repect the torque limit of the motor impoed by thermal contraint and the torque lew limit impoed by the limit to motor peed (a decribed above). τ ff f ( ωd, ωmax, ω MAX ) (11) The computed torque i baed on etimate of load inertia and loe. To prevent a build-up of error from error in etimate or noie, the torque profile i upplemented by feedback control from a pring-damper virtual model. The velocity profile i integrated to create a deired angle θ D for the joint, which i compared to the link angle θ derived by umming the angle of the motor θ M (from the encoder) with the angle of the pring θ S (from the torque enor). The controller ha a pring contant K of 0 N / rad and a damper contant K d of 1 N / rad. The torque command to thevs-sea i calculated by: θ err θ D ( θ M + θ S ) τ K θ + K (1) θ + τ d err E. High-Impedance Reference Sytem For the purpoe of comparative tudy, a high impedance actuator ytem wa implemented baed on the ame hardware a the Velocity Sourced SEA. Thi actuator ha the SEA element removed, allowing the motor to directly drive the link. With the peed controller implemented with well tuned PI compenation (P 100, I 5000) the cloed loop tranfer function i: S err ff 6 ωm( ) ( + 50) (11) ωd ( ) ( + 664)( + 64)( ) Trajectorie are generated by upplying a tream of deired velocitie at the ytem ampling rate (3.6 khz). The nature of the trajectorie ued i decribed in the relevant experiment. V. EXPERIMENT SETUP A. Etablihing Safe imit Safety i aeed uing the Head Injury Criterion (HIC) [6], a method for aeing the injury probability baed on the acceleration of the head during an impact. The HIC i defined a:.5 t 1 HIC max a( t) dt ( t t1) (1) t t1 t t1 t1 where a(t) i the linear acceleration at centre of the head (notionally the brain) and i a maximum duration et to limit the time extent over which an impact can be conidered (et to 15 m). An HIC limit of 100 ha been variouly quoted a a uitable limit for interactive robot [5], [1]. The head i modeled a a 5 kg pherical ma on a low friction urface with a firm, elatic covering. Colliion occur normal to the urface of the head and parallel to the low friction urface. The covering ha a pring contant of ~10 kn/m and damping of ~100 N/rad. The 5 kg link trike the head at 0.5 m along the link length. Tet were made over a range of velocitie and compliance B. Etablihing Performance Performance i etablihed by uing the trajectory generator to execute.5, 45, 90 and 180 rotation of the link tarting and topping at ret. The maximum peed of rotation i et to afe limit for the given ytem compliance baed on reult from HIC teting. The maximum acceleration ω MAX i fixed at 1 rad/ which correpond to the maximum torque ability of the motor for the fixed load. The jerk of the trajectory i et to uit the compliance between the motor and gearbox baed on: K ω IMIT ω MAX β (13) J where β i a dicounting factor that allow for motor peed to be ued driving the load, and ω IMIT i the maximum peed of the motor at the gearbox output haft (5.5 rad/). In the following tet β 5%. VI. RESUTS A. Safety veru Speed The afety wa aeed for the VS-SEA over a range of colliion peed uing the Head Injury Criterion. The Head Injury Criterion wa alo aeed for the high impedance actuator for the ame et of colliion peed. The reult in Figure 5 indicate an upper bound on afe peed of 3.3 m/ 3645

5 for the VS-SEA compared to m/ for the high impedance actuator (baed on a limit of HIC of 100). HIC VS-SEA Hi-Z ink peed (rad/) Figure 5: HIC value for a range of link peed for the VS-SEA and the high impedance (Hi-Z) actuator. An HIC of 100 i generally conidered the limit for afe operation of an interactive robot. B. Safety veru Compliance The HIC wa alo aeed for a range of pring compliance. The compliance of our VS-SEA deign i eaily changed by removing pring from elatic element. A outlined in the controller deign ection, the gain in the controller wa adjuted to compenate the change in compliance. With a ingle pring, the compliance i 34 Nm/rad, repreenting a four fold decreae in compliance. When the controller gain i increaed four-fold to compenate, there i negligible impact of the afety of the SEA a meaured by the HIC. Thi i contrat to the finding of [1], mot probably a the pring tiffne i too low to reach the teeper part of the HIC / tiffne curve. C. Performance Performance wa aeed by executing trajectorie over.5, 45, 90 and 180 uing firt the VS-SEA and then the high impedance actuator. The VS-SEA trajectorie were limited in jerk baed on (13) to 316 rad/ 3 (uing all four pring). The reult are hown in Figure 6. Comparing the velocity profile of the two actuator for a 90 turn (Figure 7) reveal the expected difference between the two actuator the VS-SEA ha a higher afe top peed, but take longer to reach that peed that explain the reult of Figure 6. Over hort angle, the high impedance actuator perform better, but for angle of greater than 30 the VS-SEA outperform the tiff actuator. From the reult preented here, our prototype VS-SEA could benefit from a tiffer pring allowing higher jerk without impacting the afe peed. The compromie would be a lo of torque reolution from the pring diplacement enor. Time (m) VS-SEA Hi-Z Angle (degree) Figure 6: Time to execute a afe movement acro a variety of angle for the VS-SEA and the high impedance actuator. Angular peed (rad/) VS-SEA Meaured VS-SEA Command Hi-Z Meaured Hi-Z Command Time () Figure 7: Velocity profile for the VS-SEA and the high impedance actuator, howing commanded and meaured velocity, for a 90 rotation. The plot in Figure 7 how the velocity derived from the digitally filtered derivative of the encoder and pring length meaurement for the VS-SEA, and the digitally filtered derivative of the encoder for the high impedance actuator. The greater noie in the VS-SEA encoder ignal i attributable to the added noie from the derivative of the magnetic enor. The offet in magnitude in both encoder ignal i due to quantization error in the digital filter. D. Energy Conumption Some obervation on energy uage were made by uing high fidelity imulation. The VS-SEA mut rapidly add energy to pin up the armature in order to meet jerk demand, and then low it again when jerk drop to zero. Both operation require current from the bu, and ignificant energy i wated both mechanically (½J a ω) and electrically (I R a ). Table how the etimated energy uage and armature temperature rie baed on imulation reult. While it may be poible to capture and re-ue the energy in the pinning armature with uitable power electronic, the I R loe leading to temperature rie in the armature cannot be overcome when uing the velocity ource approach. The value of the gain in afe performance hould be weighed againt the extra energy ued. 3646

6 TABE II ENERGY USAGE OVER A 90 TURN Meaure VS-SEA High Impedance Integral of intantaneou electrical power (J) Temperature rie in rotor ( K) E. Qualitative Obervation The VS-SEA i generally robut in it behavior, provided that it i driven within it limit. For example, during teting, the VS-SEA wa often run with the link removed. With only the output plate a load inertia, the VS-SEA wa quite table while commanded to produce zero torque. Motion could be tarted or topped by a light rub of the output plate with the finger. The VS-SEA i imilarly table againt tiff load (the output plate i held till) when torque are commanded. The VS-SEA doe not alway behave well when puhed outide it limit in either commanded peed, acceleration or jerk. It may be prudent to ue anti-windup on the variou integrator in the controller to get a more graceful degradation in performance when limit are exceeded. [3] D. W. Robinon, J. E. Pratt, D. J. Paluka, and G. A. Pratt, "Serie Elatic Actuator Development for a Biomimetic Walking Robot," preented at IEEE/ASME Int'l Conf. On Adv. Intelligent Mechatronic, [4] M. Zinn, O. Khatib, B. Roth, and J. K. Salibury, "A New Actuation Approach for Human-friendly Robot Deign," International Journal of Robotic Reearch, vol. 3, pp , 004. [5] M. Zinn, O. Khatib, B. Roth, and J. K. Salibury, "Playing It Safe," IEEE Robotic and Automation Magazine, vol. 11, pp. 1-1, 004. [6] J. Newman, "Head injury criteria in automotive crah teting," preented at 4th Stapp Car Crah Conference, [7] G. A. Pratt and M. M. Williamon, "Serie Elatic Actuator," preented at International Conference on Robotic Sytem (IROS), [8] M. M. Williamon, "Serie Elatic Actuator," in Department of Electrical Engineering and Computer Science. Boton: Maachuett Intitute of Technology, [9] D. W. Robinon, "Deign and Analyi of Serie Elaticity in Cloedloop Actuator Force Control," in Department of Mechanical Engineering: Maachuett Intitute of Technology, 000. [10] G. Tonietti, R. Schiavi, and A. Bicchi, "Deign and Control of a Variable Stiffne Actuator for Safe and Fat Phyical Human/Robot Interaction," in International Conference on Robotic and Automation. Barcelona, Spain: IEEE, 005. VII. CONCUSION The VS-SEA provide enhanced afety over a conventional gear-motor actuator, and improve afe performance time for mot operation. By treating the motor that drive the VS-SEA a a velocity ource, the compliance in the drive train i een a a limit in the rate of change of torque. By factoring that limit in the rate of change into trajectory generation, the VS-SEA can produce fat, reliable and afe trajectorie for a range of load. The VS-SEA ha all of the ide benefit of an SEA alo, mot notably a low cot torque enor that facilitate torque baed control and other afety benefit uch a colliion detection. The VS-SEA performance appear comparable to other more mechanically complex device uch a DM [5] and VST [10], although a tudy with a lighter link ma would be required for a fair comparion. The chief diadvantage of the VS-SEA i that it ue over twice the energy of it high impedance counterpart, which may not be an acceptable tradeoff againt the afe performance gain. ACKNOWEDGMENT I would like to thank Dr Geoffrey Walker for hi contribution in preparing the electronic for the VS-SEA, and hi comment on the project and thi paper. REFERENCES [1] A. Bicchi and G. Tonietti, "Fat and Soft-Arm Tactic: Dealing with the Safety-Performance Tradeoff in Robot Arm Deign and Control," IEEE Robotic & Automation Magazine, pp. -33, 004. [] G. A. Pratt, P. Willion, C. Bolton, and A. Hofman, "ate Motor Proceing in ow-impedance Robot: Impedance Control of Serie Elatic Actuator," preented at Proc of American Control Conference, Boton, MA,