數(shù)控銑床二維精密工作臺設(shè)計

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Tradeoffs of the design are discussed,especially in the areas of human safety and control bandwidth.The arm is used to demonstrate pancake cooking (pouringbatter, flipping pancakes), using the intrinsic compliance of thearm to aid in interaction with objects.I. INTRODUCTIONMany robotic manipulators are very expensive, due tohigh-precision actuators and custom machining of compo-nents. We propose that robotic manipulation research canadvance more rapidly if robotic arms of reasonable perfor-mance were greatly reduced in price. Increased affordabilitycan lead to wider adoption, which in turn can lead tofaster progressa trend seen in numerous other fields 1.However, drastic cost reduction will require design tradeoffsand compromises.There are numerous dimensions over which robotic armscan be evaluated, such as backlash, payload, speed, band-width, repeatability, compliance, human safety, and cost, toname a few. In robotics research, some of these dimensionsare more important than others: for grasping and object ma-nipulation, high repeatability and low backlash are important.Payload must be sufficient to lift the objects under study.Human-safety is critical if the manipulator is to be used inclose proximity to people or in classroom settings.Some areas of robotics research require high-bandwidth,high-speed manipulators. However, in many research set-tings, speed and bandwidth may be less important. Forexample, in object manipulation, service robotics, or othertasks making use of complex vision processing and motionplanning, large amounts of time are typically required forcomputation. This results in the actual robot motion requiringa small percentage of the total task time. Additionally, inmany laboratory settings, manipulator motions are oftendeliberately slowed to give the programmers time to respondto accidental collisions or unintended motions.In this paper, we present a robotic arm with similarperformance on many measures to high-end research roboticMorgan Quigley, Alan Asbeck, and Andrew Ng are with the Departmentof Computer Science, Stanford University, Stanford, CA 94305, USAmquigley, aasbeck, angcs.stanford.eduFig. 1.The low-cost compliant manipulator described in this paper.A spatula was used as the end effector in the demonstration applicationdescribed in this paper. For ease of prototyping, lasercut plywood was usedas the primary structural material.arms but at a drastically lower single-unit parts cost of $4135.A shipped product must include overhead, additionaldesign expenditures, testing costs, packaging, and possiblytechnical support, making a direct comparison with the partscost of a research prototype rather difficult. However, wedocument the parts cost of our manipulator in order to givea rough idea of the possible cost reduction as compared tocurrent commercially-available manipulators.Our experiments demonstrate that millimeter-scale re-peatability can be achieved with low-cost fabrication tech-nologies, without requiring the 3-d machining processestypically used to construct robotic manipulators.A set of requirements were chosen to ensure the arm wouldbe useful for manipulation research:Human-scale workspace7 Degrees of freedom (DOF)Payload of at least 2 kg (4.4 lb.)Human-safe: Compliant or easily backdrivable Flying mass under 4 kgRepeatability under 3 mmMaximum speed of at least 1.0 m/sZero backlashTo meet these requirements at the lowest possible cost,a new arm design was developed. The arm uses low-coststepper motors in conjunction with timing belt and cabledrives to achieve backlash-free performance, trading off thecost of expensive, compact gearheads with an increased armvolume. To achieve human safety, a series-elastic design was2011 IEEE International Conference on Robotics and AutomationShanghai International Conference CenterMay 9-13, 2011, Shanghai, China978-1-61284-385-8/11/$26.00 2011 IEEE6051used, in combination with minimizing the flying mass of thearm by keeping the motors close to ground. The resultingprototype is shown in figure 1.A brief outline of this paper is as follows. Section II givesan overview of other robotic arms used in robotics research.Section III gives an overview of the design of the arm, anddiscusses tradeoffs with its unique actuation scheme. SectionIV discusses the series compliance scheme, and sections V,VI, and VII discuss the sensing, performance, and control,respectively. Section VIII discusses application of the roboticarm to a pancake-making task, followed by a conclusion.II. RELATED WORKA. Robotics research armsThere are a number of robotic arms used in robotics re-search today, many with unique features and design criteria.In this section, we discuss some recent widely-used and/orinfluential robotic arms.The Barrett WAM 2, 3 is a cable-driven robot knownfor its high backdrivability and smooth, fast operation. It hashigh speed (3 m/s) operation and 2 mm repeatability.The Meka A2 arm 4 is series-elastic, intended for humaninteraction; other, custom-made robots with series-elasticarms include Cog, Domo, Obrero, Twendy-One, and theAgile Arm 5, 6, 7, 8, 9. The Meka arm and Twendy-One use harmonic drive gearheads, while Cog uses plane-tary gearboxes and Domo, Obrero, and the Agile Arm useballscrews; the robots all use different mechanisms for theirseries elasticity. These arms have lower control bandwidth(less than 5 Hz) due to series compliance, yet that hasnot appeared to restrict their use in manipulation research.Several human-safe arms have been developed at Stanfordusing a macro-mini actuation approach, combining a series-elastic actuator with a small motor to increase bandwidth10, 11.The PR2 robot 12, 13 has a unique system that uses apassive gravity compensation mechanism, so the arms floatin any configuration. Because the large mass of the arm isalready supported, relatively small motors are used to movethe arms and support payloads. These small motors providehuman safety, as they can be backdriven easily due to theirlow gear ratios.The DLR-LWR III arm 14, Schunk Lightweight Arm15, and Robonaut 16 all use motors directly mountedto each joint, with harmonic drive gearheads to providefast motion with zero backlash. These arms have somewhathigher payloads than the other arms discussed in this section,ranging from 3-14 kg. They are not designed for humansafety, having relatively large flying masses (close to 14kg for the DLR-LWR), although demonstrations with theDLR-LWR III have been performed that incorporate a distalforce/torque sensor that uses the arms high bandwidth toquickly stop when collisions are detected.Of the robotic arms discussed previously, those that arecommercially available are all relatively expensive, with end-user purchase prices well above $100,000 USD. However,there are a few examples of low-cost robotic manipulatorsused in research. The arms on the Dynamaid robot 17are constructed from Robotis Dynamixel robotics servos,which are light and compact. The robot has a human-scaleworkspace, but a lower payload (1 kg) than the class of armsdiscussed previously. Its total cost is at least $3500 USD,which is the price of just the Dynamixel servos. In videosof it in operation, it appears to be slightly underdamped.The KUKA youBot arm is a new 5-DOF arm for roboticsresearch 18. It has a comparatively small work envelope ofjust over 0.5 m3, repeatability of 0.1 mm, and payload of0.5 kg. It has custom, compact motors and gearheads, and issold for 14,000 Euro at time of writing.B. Robot arms using stepper motorsMany robot arms have been made using stepper motors.Pierrot and Dombre 19, 20 discuss how stepper mo-tors contribute to the human-safety of the Hippocrate andDermarob medical robots, because the steppers will remainstationary in the event of electronics failure, as compared toconventional motors which may continue rotating. Further-more, they are operated relatively close to their maximumtorque, as compared to conventional motors which mayhave a much higher stall torque than the torque used forcontinuous operation.ST Robotics offers a number of stepper-driven roboticarms, which have sub-mm repeatability 21. However, theseare not designed for human safety. These are also rela-tively low-cost, for example the R17 arm (5-DOF, 0.75mworkspace, 2 kg payload) is listed for $10,950 USD. Severalother small, non-compliant robots were made in the 1980s-1990s used for teaching were also driven by stepper motors22. For example, the Armdroid robotic arm is 5-DOF andhas 0.6m reach; it uses steppers with timing belts for gearreduction, then cables to connect to the rest of the arm 23.III. OVERALL DESIGNThe arm has an approximately spherical shoulder and anapproximately spherical wrist, connected by an elbow. Thejoint limits and topology were designed to enable the robot toperform manipulation tasks while being mounted near table-height, as opposed to anthropomorphic arms, which musthang down from the shoulder and require the base of thearm to be mounted some distance above the workspace.The shoulder-lift joint has nearly 180 degrees of motion,allowing the arm to reach objects on the floor and alsowork comfortably on tabletops. A summary of the measuredproperties and performance of the arm is shown in table I.TABLE IMEASURED PROPERTIES OF THE ARMLength1.0m to wristTotal Mass11.4 kgMoving Mass2.0 kgPayload2.0 kgMax. speed1.5 m/sRepeatability3 mm6052Fig. 2.Actuation scheme for each of the proximal four DOF.A. Actuation schemeFigure 2 shows the actuation scheme for the proximal fourDOF. These joints are driven by stepper motors, with speedreduction accomplished by timing belts and cable circuits,followed by a series-elastic coupling. Using only timing beltsand cable circuits in the drivetrain results in low friction,minimal stiction, and zero backlash. This enables the armto make small incremental motions (less than 0.5mm), andthere is no gearing to damage under applied external forces.Combined with stepper motors, which have high torqueat low speeds, this leads to a low-cost but relatively highperformance actuation scheme. A downside to this schemeis that the reduction mechanisms occupy a relatively largevolume, making the proximal portion of the arm somewhatlarge.Using a two-stage reduction of timing belt followed bycable circuit accomplishes not only a larger gear reductionthan a single stage, but also enables the motors to be locatedcloser to ground. The motors for the two most proximal DOFare grounded, and the motors for the elbow and upperarm rolljoints are located one DOF away from ground. By placing therelatively heavy stepper motors close to ground, the flyingmass of the arm is greatly reduced: below the second (lift)joint, the arm is 2.0 kg. For comparison, a typical adulthuman arm is about 3.4 kg 24.The two-stage reduction scheme leads to coupling betweenthe motions of joints 1 and 2, and joints 2, 3, and 4. However,this coupling is exactly linear and can easily be estimated as afeedforward term in software. The routes of the timing beltsand cables can be seen in figure 3. After the timing beltsand cable circuits, the proximal four DOF have series elasticcouplings between the cable capstan and the output link,discussed in section IV. These are used to provide intrinsiccompliance to the arm, as well as providing force sensing(section V).The distal three DOF are driven by Dynamixel roboticsRX-64 servos. These joints do not have compliance asidefrom limiting the torques. However, the compliance of theproximal four DOF allows the end effector to be displacedin Cartesian space in three dimensions, barring kinematicsingularities where only two dimensions will be compliant.B. Tradeoffs of using stepper motorsUsing stepper motors as actuators has a number of ad-vantages. Stepper motors excel at providing large torquesat low speeds, which is the target regime of the arm. Theyrequire a relatively low gear reduction, which can be accom-plished with timing belts and cable drives. In the prototypeFig. 3.Cable routes (solid) and belt routes (dashed) for the shoulder lift,shoulder roll, and elbow joints. All belt routes rotate about the shoulder liftjoint. The elbow cables twist about the shoulder roll axis inside a hollowshaft. Best viewed in color.Fig. 4.Compact servos are used to actuate the distal three joints.manipulator discussed in this paper, the effective reductionswere 6, 10, 13, and 13, respectively, for the first four joints.DC motors, for comparison, generally require a significantlylarger gear reduction through a gearbox that would be eithersusceptible to backlash or moderately expensive.The stepper motors also act as electromagnetic clutches,improving safety if large forces are accidentally applied atthe output. If a force is applied that causes a stepper toexceed its holding torque, the stepper motor will slip and thearm will move some distance until the force is low enoughthat the stepper can re-engage. The stepper holding torque isapproximately 60% more than the maximum moving torque(and hence the maximum payload of the arm), large enoughto avoid needlessly slipping but small enough to make thearm human-safe.However, there are a few downsides of the steppers actingas an electromagnetic clutch. First, if a stepper motor slips,the arm may need to be re-calibrated. The arm uses joint-6053angle encoders for state estimation, so closed-loop positioncontrol can still be done even after a slip, but force sensingwill be miscalibrated (see section V). Second, the arm maymove suddenly after a stepper motor slip. The arm onlyslips if relatively large amounts of force are applied, andafter a slip the steppers initially provide little resistance.The moving arm may collide with other objects or people;this is mitigated by making the arm as light as possible.Adding backshaft encoders to the stepper motors wouldenable tracking of the motor position even during rotor slips,and enable faster stoppage of a slipping motor. Whether ornot the additional cost is justified depends on the task and theanticipated frequency of unintended high-speed collisions.As envisioned, stepper slips occur only as a final layerof safety, and thus are not anticipated to be a frequentoperational mode.C. Hybrid SEA/non-SEA actuation schemeThe actuation scheme of the proposed manipulator usesseries-elastic actuators (SEA) in the proximal 4 DOF, butnon-series-elastic actuation for the distal 3 DOF. The band-width of the distal 3 DOF is somewhat higher than thebandwidth of the proximal 4 DOF, permitting a restricted setof higher-frequency motions. This is similar to that describedin 25, which employs a macro-mini actuation scheme forthe most proximal DOF and conventional actuators for themore distal DOF.In our scheme, the lower three DOF still get most ofthe benefits of the series-elastic upper arm, including theability to control forces by modulating a position. The maindownside of this as compared to a full series-elastic schemeis that the gears in the distal DOF are more affected by shockloads, since (in the worst case) the mass of the entire arm ispast the series compliance.D. Arm inertia and series elastic stiffnessOne important tradeoff with a series-elastic robot arm isthe arm inertia and series elastic stiffness. Consider a one-DOF arm with moment of inertia I kg m2 driven by a rotaryjoint with torsional stiffness kN m/radian. The arm willoscillate at its natural frequency, which is f0=12pk/I.If the arm has a low inertia or the series elastic coupling isstiff, the motor driving the arm may not have enough torqueor bandwidth to compensate for this oscillation. Pratt andWilliamson suggest increasing the arms inertia to eliminatethis effect 26; other options are to reduce the springconstant; include damping in the series-elastic coupling; orincrease bandwidth by decreasing the motor gear reduction,at the cost of a lower payload. For human-safe robotic armswith low inertia, this issue can be significant.In our arm, considering the elbow joint, the natural fre-quency is around f0= 5.1 Hz, with k= 86 N m/radianand I = 0.083 kg m2. This is close to the bandwidth of themotors with our current gear reduction.E. Low-cost manufacturingSeveral methods were used to achieve a low-cost design.The total cost of all of the stepper motors was $700. AnTABLE IICOST BREAKDOWN OF THE ARMMotorsSteppers$700Robotics servos$1335Electronics$750Hardware$960Encoders$390Total$4135alternative with comparable speed/torque performance isto use DC brushed motors with planetary gear reduction.Although they are available for a comparable price, theirinexpensive gearheads exhibit more than 1 degree of back-lash. High-performance gearheads or brushless motors wouldincrease the cost by a factor of at least two. For example,a single zero-backlash harmonic drive actuator costs over$1000 USD, and a brushless planetary gearmotor of sufficienttorque and 0.75-degree backlash costs $500 USD.Lasercutting 5-ply plywood was used for most of thestructure in the current prototype. The lasercutter used (BeamDynamics OmniBeam 500, 500 Watts) can produce toler-ances of 0.025mm, and excellent results were also achievedwith an Epilog Legend Helix 24 (45 Watt) laser cutter.Dovetailing of the wood pieces was done, enabling themto be press-fit together, and flanged bearings and shaftswere also press-fit into holes. It is unknown how the woodstructure will respond to large temperature and humidityvariations, but in a typical lab environment these are heldrelatively constant. Wood is an excellent material for rapidprototyping, and is rigid enough to meet the repeatabilitydesign requirements. In the future, we intend to make thecomplete structure out of folded sheet metal for a moredurable structure. The lower arm of the robot was made offolded sheet metal as a first step in this direction. Foldedmetal structures cannot be made to the precision of custom-machined parts, but calibration techniques can be used tocompensate for manufacturing errors.The other technique used to keep costs low was to avoidall custom machining except for the lasercut structure; allother parts were off-the-shelf. A breakdown of the parts costfor the robot is shown in table II. Not included in this listare the costs of laser cutter time and assembly time; lasercutting would take 2.5 hours and assembly would take around15 hours for additional copies of the arm.IV. SERIES COMPLIANCEThe robot uses a compliant coupling in the proximal fourjoints. This provides increased human safety, allows the armto be compliant even though the stepper motors are notbackdrivable, and is used for force sensing as the deflectionacross the compliance is measured.A diagram of the compliant coupling is shown in figure 5.Its operation is similar to the elastic couplings described in27, 28, 29. At the joint, a capstan used in the cablecircuit (labeled 1 in figure 5) is suspended via bearings onthe same shaft as the output link (2). The capstan is then6054Fig. 5.Diagram of the series compliance. Left, compliant coupling withno external forces. Right, an applied force causes rotation.Fig. 6.Stiffness of the elbow. Some hysteresis is exhibited due to thepolyurethane in the series compliance. The joint was quasi-statically movedthrough 70% of its normal operating range.connected to the outpu