Control of Scalable Wet SMA Actuator Arrays

Transcription

1 Proceeings of the 2005 IEEE International Conference on Robotics an Automation Barcelona, Spain, April 2005 Control of Scalable Wet SMA Actuator Arrays eslie Flemming orth Dakota State University Mechanical Engineering an Applie Mechanics Fargo, orth Dakota 5802 USA Abstract - This paper presents a new control metho to rive an array of wet Shape Memory Alloy actuators utilizing a Matrix Manifol an Valve system (MMV). The MMV architecture allows a vast DOF robotic system to be controlle using limite number of resources. Using biological inspiration, the robotic system contains a network of bloo vessels transporting flui to the various muscle actuators. In general, an array of 2 wet actuators can be controlle by 2+2 fluiic valves, resulting in a scalable architecture. This woul allow robots to contain a vast number of actuators like the human boy, an be controlle in a scalable manner. The initial prototype contains a 4x4 array of 6 actuators controlle by 0 solenoi valves, where 25% of the actuators can be activate at any one time. Since only a subset of the actuators can be activate at any time, various methos of scheuling the resources (i.e. valves) are investigate, as well as various ways to efine the error or ifference between the esire an actual states of the array. The fluiic impeance of the system is taken into account in orer to optimize the control. Results of simulation show that new scheuler options an efinitions of error improve the performance of the system by a factor of 0 when operating the array near its maximum capacity. Inex Terms Shape Memory Alloys, actuators, scalable, biologically inspire. I. ITRODUCTIO As humanoi robots become more like the real human boy, they will become vast egree-of-freeom (DOF) systems with a nee for vast numbers of actuators to power them. While humanoi robots such as the ona P2 [] an the Sony SDR-4X [2] alreay have more than 30 inepenent actuators or DOF, the human boy has more than an orer-of-magnitue larger DOF, actuate by over 600 skeletal muscles alone. In aition, countless smooth muscles assist in the circulation of bloo by opening an closing vessels to provie energy to the boy an regulate the boy s temperature. Furthermore, each muscle is not just a single actuator, but consists of numerous segmente muscle fibers that can work in series an in parallel to prouce wie ranges of forces an isplacements. While the number of actuators is truly vast, the boy is not continuously in motion an thus only a small percentage of the muscles are active at any one time. The same will be true for vast DOF humanoi robots, which creates an opportunity to share limite resources such as components for elivery of power. Stephen Mascaro The University of Utah Mechanical Engineering Salt ake City, Utah 842 USA smascaro@mech.utah.eu In orer to accommoate hunres or even thousans of actuators in a compact boy, the actuators must have a high power to weight ratio an there must be a scalable architecture for controlling an elivering power to them. If the actuators are structure an manage correctly, a robot coul have more DOF by networking its resources. The fluiic heating an cooling of the boy has inspire similar methos for artificial muscles. Recently, the iea of a vasculate robotic flesh was propose, where a robot is imbue with a network of bloo vessels for elivering energy to embee fluiic actuators [3]. These fluiic actuators consist of compliant vessels containing Shape Memory Alloy (SMA) wires, which are contracte an extene by using combinations of electrical an fluiic power. These wet SMA actuators are capable of 200 MPa strength (800 times higher than human muscle [4]) an power to weight ratios on the orer of kw/kg (00 times greater than DC motors), while maintaining banwiths of at least 2 z. Fluiic heating is not as fast as electrical heating, but banwiths of 0.5 z have been achieve [5]. On the other han, electrical activation yiels an extremely low efficiency on the orer of 0.%, while fluiic activation has theoretical efficiencies reaching 3% [5]. eat conuction with Peltier Moules has also resulte in banwiths of 0.5 z [6], but is also inefficient. Since SMA actuators are so compact, creating SMA bunles [7] an arrays [8] is a natural extension. In aition, wet SMA actuator arrays have been esigne an implemente where networks of fluiic valves are use to irect hot an col water to any actuator in the array [9]. The architecture allows 2 actuators to be controlle with 2 valves. In aition, new control methos have been propose to share the available resources among the actuators requiring attention at any given time. The performance of the wet SMA array has been simulate assuming ieal conitions, however many of the real fluiic characteristics of the system were ignore, such as the effects of the varying fluiic resistance an capacitance of the network. In this paper, we exten this work by eveloping matrix control methos tailore for use with fluiic or wet actuator arrays, specifically ealing with the fluiic impeance of the system. We will evelop answers to the questions of how to best efine a measure of performance for the array as a whole, an how to optimize that performance in the light of the varying fluiic impeance. Finally, the control methos are implemente an verifie on an experimental prototype X/05/$ IEEE. 350

2 II. DESIG COCEPTS A. Wet SMA Actuators Fluiic heating an cooling of SMA wires appears to be an ieal metho to active them, but there are challenges to be aresse. The elivery of water to each actuator is affecte by the fluiic resistance of vessels an valves the efficiency is affecte by the heat lost to the environment. To reuce the amount of heat lost, it woul be ieal to reuce the surface area of the flui vessels. On the other han, the fluiic resistance is a function of imensions of the vessels an larger imension woul reuce the resistance. If a one to one ratio of actuator to control valve were use, the power to weight ratio an cost woul suffer. By eveloping new network architectures, the ratio of valves to actuators can be ecrease, an allow more actuators to be place in a compact volume. The wet SMA actuator consists of an SMA wire that is suspene in a hollow compliant capillary vessel that is able to accommoate the strain prouce by the SMA when heate an allows flui to encompass the wire. Each en of the wire an capillary is connecte to a manifol that allows flui to pass through the capillary an transfer the mechanical connection to the exterior of the actuator. B. Matrix Manifol an Valve (MMV) System etworke Actuation Architecture (AA) has been propose where multiple actuators are riven by a single switch (in this case a fluiic valve). Taking avantage of the fact that not all of the actuators in the system must be active at the same time, the AA can greatly reuce the number of valves in the system; therefore significantly ecreasing the size, the weight an the cost of the new system [2]. A Matrix Manifol an Valve (MMV) system is built on the basis of AA an arranges the wet SMA actuators in an -by- array. The structure of the MMV is scalable, such that 2+2 valves route the hot an col flui an can activate any of the 2 the actuators in the array iniviually. The array can also have multiple valves open allowing multiple actuators to be riven at the same time. The control commans to the system can be esigne to maximize the performance of the system as a whole. Row valves provie flui to each row of the array (all actuators in a row have the same source line) an the exit en of the actuator is connecte to its respective column valve (all actuators in a column have the same return) as seen in Fig. Turning a single row an column shoul exclusively activate the actuator at the intersection. To ensure that no flui can flow backwars an take an alternate path through the array, influencing other actuators, every actuator requires a check valve. Multiple actuators in a single row or column can be simultaneously activate, as well as certain subsets of the matrix. An aitional 3-way valve has been installe to select between the hot an col source an a secon 3- way valve is use to return the hot an col to the appropriate reservoir. This recycles the energy not absorbe by the actuators to maximize the efficiency. Fig. 2 shows the implementation of a 4x4 actuator array, which is 00 mm x 00 mm x 200 mm in size. There are 6 silicone rubber capillaries of.6 mm inner iameter with 0.25 iameter SMA wire insie. There are 0 solenoi valves that control the flui flow an a check valve at the en of each actuator. Fig. System iagram of wet SMA actuator arrays using matrix manifol an valve structure Fig. 2 Implementation of wet SMA actuator array When multiple actuators are activate, the fluiic resistance of the array changes, an thus the flow rates within each actuator are subject to change epening on how many actuators are open. Since the controller must take into account the time it takes for flui to propagate through the actuators, these changing resistances complicate the constraints on the controller. For our implementation, the valves are connecte to a constant pressure source (70kPa). Due to various fluiic resistances, the flow rates when 2 valves are open compare to 4 valves are not equivalent, but the scheuler can accommoate to allow just enough time for the flui to propagate through the system, given the equivalent fluiic resistance of the array. 35

3 III. COTRO A. Scheuler The propose MMV system has minimize the valves to 2+2 with the ability of controlling 2 actuators iniviually. With the ability of the MMV system to rive actuators at the intersections of the active rows an columns, a variety of combination of valves can be turne on. The SMA wire ictates that this is a ternary system (ot / Col / one) an requires at least one more control valve to switch between the hot an col water sources. The SMA actuator is an analog evice, that can take on any position between fully contracte to fully extene an to achieve this, each actuator may be riven with a hot water (contract), col water(expan), or remain steay with no water. In orer to maximize the response of the system, it is not esirable to control a single actuator an even less esirable to rive them in a sequential orer. A scheuler must take the reference commans (I) an maximize the control commans (OUT). In previous work [9], we propose that the control comman activate one row an any number of columns. This has been expane to inclue multiple rows an columns an this woul activate the actuators at the intersections. The final element that ictates the control comman is the esire source of water (ot/col or /C). The scheuler ientifies the maximum error (E) an then selects the row(r), column(c) an hot/col valves that correlates to the errors. [ R, C, / ] = arg Max[ E i, / i Ri Ri Cj Cj Bkl Bkl () The total errors are etermine by the following equations; ientifying the rows, columns an high or low power source. igh Error e = ( x ) if ( x ) > 0 e = (2) e = 0 if ( x ) 0 ow Error e = ( x ) if ( x ) < 0 e = (3) e = 0 if ( x ) 0 Total ow Error - Row (i) j= E E Ri = e Column (j) E Cj = e Bkl i= il ] (4) (5) Box (i,j,l,k) E = e + e + e + e (6) kj - for all i,j,k,l where i < k an j < l kl Total igh Error E Row (i) j= E Ri = e Column (j) E Cj = e Bkl i= il (7) (8) Box (i,j,l,k) E = e + e + e + e (9) - for all i,j,k,l where i < k an j < l Multiple factors can influence the overall response of the MMV system. It has been propose that the actuators be mechanically connecte to one another in series or in parallel to achieve higher force or isplacement. It may be more esirable to rive the column actuators or the row actuators, epening on how they are mechanically connecte. These are examine in the moeling foun in the next section an this will influence the overall response of the system. B. Error selection The scheuler is structure to maximize the control comman; in turn reucing the error in the actual system to that of the esire. In previous work [9], two methos were use to etermine the error that woul be input to the scheuler. The first efinition of error was focuse on the position of the actuator an the secon insure that no actuator was ignore for an extene amount of time. These have been re-examine an improvements have been ientifie when other efinitions of error are use. For now, the system is being analyze as iniviual binary actuators with no relationship to one another. Each actuator receives a time stampe reference comman an these are store in a queue, so an actuator may have multiple reference commans waiting for the scheuler to aress them. This structure allows for a variety of errors to be efine an the following ones will be explore in the moeling section of this paper.. Position Error the error between the esire an actual position. 2. Delay the time ifference between the current time an that of the reference comman s time stamp. 3. Delay Square the elay multiplie by the absolute value of the elay, insuring the irection is preserve 4. Sum of the Delays the sum of all the elay for reference commans within the queue. 5. Queue length This is the number of reference commans in queue. These are only a few of the errors that can be efine an there is the possibility that they coul be use together in some weighte fashion. Once the scheuler aresses the reference comman, it is remove form the queue. kj kl 352

4 IV. Moeling an Results A. Moeling an Constraints The propose system was moele with MATAB an the reference comman an control commans are riven by the uty ratio, error selection an control selection. The system starts in a zero/col state, in the extene position. Each actuator is commane to change states (contract / expan) with a probability equal to the uty ratio. The uty ratio is efine as the average percentage of the actuators that change states in a single cycle. The change state comman is given a time stamp an store in a queue. The error is compute from the reference queue an sent to control selection. Once the actuator is selecte an the control comman is sent, the reference comman is remove from the queue. The control comman consists of three elements: rows, columns, an hot/col. Acknowleging that size an power limits are both constraints that must be aresse, the simulation of the 4x4 array limits the number of actuators that can change states at any one time to 4. The moeling takes the stance that time between reference commans is equal to the time for the flui to propagate through the array when a x4 subset of actuators is aresse. The constraint that at most four actuators can change states uring one control comman suggests three primary configurations that maximize the array structure. The first propose is activating one row an any combination of column valves. The secon is the transverse of the first; one column an any combination of row valves are selecte. The final metho is to turn two rows an two columns on; the intersection of these woul active the four corners of a box. The columns an row o not nee to be ajacent, so rows an 4 an columns 2 an 3 coul be turne on. Multiple Rows/ Single Column ( 2 ) () 2 Rows / 2 Columns )] 2 [ ( (2) 2 Since the control selection is ternary, there are twice as many control commans as that of a binary system. The possibilities may be reuce if the power source can not support that number of actuators an aitional possibilities coul be available if the restriction that more than 4 actuators at once is remove (2 rows by 3 columns, etc). B. Results To examine the propose scheuling an error selection, a table of ranom reference commans was generate an use for all moeling results presente. As seen in figure 4, the 4x4 MMV system exhibits instability as the uty ratio approaches 25% or /. This is expecte with the control comman being limite to activate four actuators at once. Total Delay Square 6 x Cycles Fig. 4 Total elay square vs. cycles (uty ratio = 0.25). Queue ength an Sum Delay errors prouce similar response at this uty ratio. 26% 25% 24% Fig. 3 Possible Scheuling Structure If the scheuler is limite to only activate any of the actuators in a single row or column an the 4 corners of a box, the number of possible control commans that are available for the scheuler are: Single Row / Multiple Columns ( 2 ) (0) Average Queue Reference Commans Row Row / Column Row / Column / Box Fig. 5 Scheuler Selection: Average queue reference commans vs. uty ratio 353

5 Fig. 5 shows that using the Row/Column/Box scheuler significantly improves the response to the reference commans. The 36 aitional control comman possibilities from the box structure result in a reuction of a factor of approximately 0 in the average queue reference commans as the uty ratio approaches 25%. Fig 6 emonstrates similar results as the average total elay square for the Box/Row/Column is about 00 times smaller than that of the Row an Row/Column Scheulers Average Total Delay Square Row Row / Column Row / Column / Box Fig. 6 Scheuler Selection: Average total elay square vs. uty ratio. Average Total Delay Square Delay Square Sum Delay Queue ength Fig. 7 an 8 both emonstrate that the performance of the system improves when the efinition of error is efine as the number of commans in the queue rather than as a function of the time stamp. The ifference seems to isappear at lower uty ratio, but when the system is operating near capacity, it is clearly better to efine the error as the queue length rather than the elay square. This is significant since up until now, the elay square was use to efine the error [9]. Experimentally implementing this system raises esign concerns when operating multiple actuators simultaneously. Even though water is provie by a constant pressure source, the flow rates from the various configurations are not uniform ue to the changes in valve an vessel resistance. Experiments emonstrate that the impeance of the array is ominate by the resistance of the solenoi valves. Fig. 9 shows equivalent resistances when the various allowable combinations of valves are opene. When a single actuator is active (x), the equivalent resistance is nearly ouble that of the x4 case, so the total flow is almost halve, but since there is only one actuator, the flow per actuator is increase. Therefore, even though we only activate a single actuator, less time is require for the flui to propagate through the array, an thus the rate of actuation (number of actuators aresse per unit time) is not much less than the x4 case. Table summarizes the experimentally etermine flow rates for each case an their corresponing actuation rates Fig. 7 Error Selection: Average queue reference commans vs. uty ratio. Average Queue Reference Commans Delay Square Sum Delay Queue ength Fig. 8 Error Selection: Average total elay square vs. uty ratio Fig 9 Equivalent Fluiic Resistances Table : Theoretical activation rate (actuation per cycle) Configuration Theoretical Flow Rates Actual Flow Relative Propagation Actuation Rate (Actuations/Time) (m/min) Rates (m/min) Time x T /T x T.33/T x T.44/T x T.6/T 2x T.79/T 354

6 The result is that the new scheuler uses a variable sampling rate that epens on the number of actuators being aresse, where previously the sample rate was constant [9]. The above simulations reflect this new type of scheuling. IV. COCUSIOS This paper presente the control logic to rive an array of wet SMA actuators utilizing a Matrix Manifol an Valve (MMV) system. This architecture results in a vast DOF system that minimizes the number of valves an optimizes the use of them. The 6 wet SMA actuators assemble in the 4x4 array (200mm x 00mm x 00mm) can prouce actuation forces of up to 60 when connecte in parallel an achieve isplacements of 64mm of isplacement connecte in series. 0 valves are use to rive the 4x4 system, but a 0x0 array of 00 actuators woul require only 22 valves. In general, an array of 2 actuators can be controlle by 2+2 valves, resulting in a scalable architecture. Results of simulations show that the new scheuler options an efinition of error improve the performance of the system, especially as the uty cycle approaches the limit of / for an array of 2 actuators. Specifically, the new Row/Column/Box scheuling performs 0 times better than the ol Row scheuler, an efining the error in terms of queue length is better than the time elay square. In future work, we will investigate what happens when > 4, an how the application (e.g. are the actuators connecte mechanically in series or parallel) might affect the control strategy, an verify experimentally. These methos coul be use to create biologically inspire robots where a central vascular system (heating, cooling, an pumping) coul provie the resources necessary to rive multiple arrays of wet SMA actuators locate throughout an articulate boy with vast DOF. REFERECES [] K. irai, M. irose, Y. aikawa, an T. Takenaka, The evelopment of ona humanoi robot, Proceeings of the 998 IEEE International Conference on Robotics an Automation, vol. 2, pp [2] T. Ishia, Y. Kuroki, an J. Yamaguchi, Mechanical system of a small bipe entertainment robot, Proceeings of the 2003 IEEE/RSJ Intl. Conference on Intelligent Robots an Systems, vol. 2, pp [3] S. Mascaro an. Asaa, Wet shape memory alloy actuators for active vasculate robotic flesh, in Proceeings of 2003 IEEE International Conference on Robotics an Automation. [4] I.W. unter an S. afontaine, A comparison of muscle with artificial actuators, in Proceeings of the 992 IEEE Soli-State Sensor an Actuator Workshop, pp [5] O.K. Reiniotis, D.C. agouas-dimitris,.y. Jun, R.D. Allen, Fuel-powere compact SMA actuator, in Proceeings of the 2002 SPIE Conference on Smart Structures an Materials, vol. 4698, pp [6] B. Selon, K. Cho,. Asaa, Segmente Binary Control of Shape Memory Alloy Actuator Systems using the Peltier Effect, Proceeing of the 2004 IEEE International Conference on Robotics an Automation, pp [7] K. De aurentis, A. Fisch, J. ikitczuk, C. Mavroiis, Optimal Design of Shape Memory Alloy Wire Bunle Actuators, Proceeings of the 2002 IEEE International Conference on Robotics & Automation, pp [8] R. Mukherjee, T. F. Christian, R. A. Thiel, An actuation system for the control of multiple shape memory alloy actuators, Sensors an Actuators A: Physical, vol. 55, no. 2-3, 996. [9] S. Mascaro, K. Cho,. Asaa, Design an control of vast DOF wet SMA array actuators, Proceeings of the 2003 International Conference on Intelligent Robots an Systems, vol. 2, pp [0] K. Cho, S. Au,. Asaa, arge-scale servo control using a matrix wire network for riving a large number of actuators, Proceeings of the 2003 IEEE International Conference on Robotics an Automation, pp