IROS2019国际学术会议论文集 1068

Closed loop Force Control of a Pneumatic Gripper Actuated by Two Pressure Regulators Rocco A Romeo1 Luca Fiorio1 Edwin J Avila Mireles2 Ferdinando Cannella2 Giorgio Metta1 and Daniele Pucci1 Abstract Robotic arms can perform grasping actions thanks to their dexteorus part i e the gripper Among the various categories nowadays pneumatic grippers became the most employed in industry as they have low cost and little bulkiness Despite their simplicity controlling the force applied by these grippers is not straightforward due to the dependence of such a force on the air pressure in the gripper chambers As a result it is still tricky to implement closed loop force control for pneumatic grippers This paper intends to deliver a control scheme relying on the force measurement to control pneumatic grippers The force might be measured through a commercial sensor e g a load cell and fed back to close the control loop This includes a calibration which maps the force pressure relation taking into account both desired force and length of the gripper fi ngers The control scheme exploits two different pressure regulators to precisely adjust the air pressure inside the gripper chambers i e opening and closing chambers To this aim a quadratic programming algorithm is employed The control scheme performance revealed to be good results will be shown in terms of gripper response to sinusoidal and step inputs along with the pressure force characterization I INTRODUCTION The gripper is the terminal part of a robotic arm It in cludes at least two fi ngers allowing the robotic arm to grasp items to lift and to place them in a precise point in space As the presence of robots increases in industrial environment the necessity to design effi cient grippers becomes crucial These are involved in a mass production process which due to its constant growth poses a challenge for the minimization of cycle times 1 For sure grippers performance can benefi t from the development of effective control strategies In this context electrical grippers are the easiest to control both in terms of force and position 1 As a consequence such grippers are preferred when it is required the grasp and or assembly of fragile items Being the applied torque proportional to the current supplying the gripper actuator 2 by knowing the latter it is possible to directly control the force exerted onto a grasped object Besides position sensors embedded in electrical grippers permit to fi nely manage the position of the fi ngers For instance the device developed in 3 had both force and proximity sensors However there exist cheaper solutions that are also less bulky i e pneumatic grippers Despite the diffi culty in con trolling the fi ngers of a pneumatic gripper i e they can be 1iCub FacilityDepartment IstitutoItalianodiTec nologia ViaMorego30 16163Genoa Italy Email firstname lastname iit it 2Advanced RoboticsDepartment IstitutoItalianodiTec nologia ViaMorego30 16163Genoa Italy Email firstname lastname iit it kept either fully open or fully closed their capability to apply considerable force with very short strokes along with the reduced encumbrance and cost foster their employment in the industrial scenario Moreover pneumatic grippers do not suffer from overheating due to prolonged working time 2 this constitutes another reason for choosing pneumatic grippers which indeed are dominant in the industry over electrically powered ones Pneumatic actuation is being adopted since several decades Examples include the tendon actuation of dexter ous hands 4 the actuation of a whole robotic arm 5 using a position control algorithm and a 6 DOF Degrees of Freedom robot for percutaneous intervention equipped with a pneumatic gripper 6 Although the latter featured a closed loop force control pneumatic grippers not often embed closed loop control An early attempt was made in 7 where a two fi ngered gripper was controlled by means of a proportional integral PI control The force measured by a commercial force sensor mounted between the fi ngers was used to close the loop whereas the PI continuously adjusted the input voltage of the pressure valve controlling the gripper Recently a PI controller was designed to control a pneumatic gripper closing the loop by means of the force measured by a strain gage sensor 2 Other closed loop applications include soft robotic grippers 8 9 or else different control types such as sliding mode control 10 relying on position measurement and velocity estimation Moreover the effectiveness of using a feedforward term was demonstrated in 11 as regards soft pneumatic actuators It is also possible to endow a pneumatic gripper with a force regulation mechanism 12 which does not exploit sensory information but rather regulates the grasping force which is the same for more objects through mechanical components In this paper we propose a new closed loop scheme to control the grasping force of pneumatic grippers The scheme exploits force information measured by a load cell to implement a continuous feedback and a controller based on a quadratic programming algorithm such a controller is able to yield accurate calculation of the input pressure to be sent to the pneumatic regulators actuating the gripper Besides the controller takes into account the mathematical relationship linking the pressure to the force which varies with the gripper fi ngers height Here we instrument a pneumatic gripper with custom designed fi ngers and a force sensor i e load cell and demonstrate the repeatability of the results with different input signals and on two different setups The remainder of the paper is organized as follows 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE7157 Section II briefl y describes the gripper and explains the control algorithm Section III illustrates the experimental setups and results Section IV contains the conclusion and the future work II MATERIALS AND METHODS In this Section the gripper the pressure regulators the experimental setups and the control algorithm will be pre sented The name of the company manufacturing both the gripper and the regulators will not be provided due to disclosure restrictions A Pneumatic gripper and pressure regulators The pneumatic system included a gripper and two pressure regulators Fig 1 depicts the gripper section by increasing the pressure in the closing chamber the piston moves down On the contrary by increasing the pressure in the opening chamber the piston moves up The motion of the piston is converted into an opening closing motion of the gripper jaws by two levers The levers are constrained to the gripper main body by a pin joint Fig 1 Section of the pneumatic gripper The gripper action is generated by the force exerted by the piston rod on the mechanical subsystem Because of the system confi guration the displacement of the rod is the same as the displacement of the jaws These movements are perpendicular to each other and can be expressed as xR t y t 1 xL t y t 2 where xRand xLare the displacements of the right and left jaws and y is the displacement of the piston rod Both the force and the displacement are transmitted from the rod to the jaws through the levers which work as transmission The rod applies a force on the head of the horizontal arm of the lever and the lever returns the force on the jaw with the head of the vertical arm It is important to notice that the movements of the rod and the jaw are linear while the lever s movement is rotational see Fig 2 Mathematically it is necessary to consider that the force coming from the piston is divided by two since one single rod has to move two levers Fp 2 Fn Fj Fp 2 Fn Fj Fp Fig 2 Internal geometry of the gripper in fully open confi guration From the geometrical confi guration of the gripper we can infer that the transmission of the forces from the rod all the way to the jaw depends on the lever s angular position The force applied by the piston rod on the lever is always linear and its transmission to the jaw through the rotation of the lever can be analyzed as a torque In our case we can express the torque as Fnl 3 where Fnis the force normal to the lever arm and l is the length of the lever arm Considering the force exerted by the piston Fpon the levers the torque can also be expressed as Fp 2 sin l 4 Moreover the force in the jaw axis Fjcan be expressed as a function of Fnas Fj Fn sin 5 By combining 3 4 and 5 we get Fj FP 2 6 FPis also expressible as FP F F 7 where F and F are the forces from the opening and the closing chambers respectively which depend directly on the applied pressure p In general this two forces follow the same general rule expressed as F pA 8 being A the active area of the piston i e the area where the pressure insists p might either be the pressure in the closing chamber Pcor the one in the opening chamber Po It is important to mention that for the same applied pressure the piston force has different modulus when the air is either in the closing chamber or in the opening chamber due to the difference in the geometrical characteristics of the pneumatic chambers The FPis also affected by the friction generated between the jaws guides and the gripper body when the grasping force changes As regards the pressure regulation we employed a micro pressure regulator that controlled the outlet pressure by regulating two internal valves The activation of each valve is dependent on the inlet signal and the measurements of 7158 the integrated pressure sensor Each of the gripper chambers was controlled by means of a regulator hence two regulators were used The pneumatic scheme is available in Fig 3 An air source feeds the two regulators which in turn actuate the gripper equipped with a load cell More details about the generation of the gripper input pressures Pcand Powill be provided in the next Section Fig 3 Schematic of the whole pneumatic setup B Setups Three setups were designed to perform the experiments The fi rst one was the static setup In this confi guration Fig 4 the load cell was connected to two cylindrical supports by means of two spherical joints The cylinders acting as fi ngers were then connected to the gripper jaws by means of adjustable supports The spherical joints were necessary to decouple the loads on the load cell so that the cell was subject to either pure compression force or pure extension force according to the gripper action Fig 4 Static setup left panel and its section right panel The so connected jaws were not allowed to do any movement therefore the load applied on the load cell was static and it was possible to measure both the opening and closing grasping forces Further by varying the position of the adjustable supports it was possible to perform tests with the gripper jaws in different positions as well As detailed in Fig 5 the jaws had a maximum stroke of 4 mm Finally the distance R between the gripper jaws and the load cell Fig 5 Gripper section fully closed left panel and fully open right panel measurement axis was adjusted by using cylindrical supports with diverse lengths The second setup namely dynamic setup Fig 6 included a compression spring The load cell is connected on one side to one of the custom fi nger while the other side is linked to a compression spring The spring is then supported by the second custom fi nger In this case the fi ngers have an L shape and have a fl at surface When the gripper was fully open the spring had a pre compression of 1 5 mm which yielded a pre load of about 12 N This helped simulate the condition in which the gripper is already holding an item and is then demanded to increase the grip force to a one ore more desired levels Fig 6 Dynamic setup left panel and its section right panel The third setup namely gap setup Fig 7 still included the load cell which was connected on one side to one of the custom L shaped fi ngers while on the other side it was connected to a cylindrical punch The second fi nger supported two Belleville washers As the jaws were fully open there was a gap of 3 4 mm between the washers and the punch When the gripper jaws closed the punch hit the washers and the load cell measured the grasping force This condition is the one that best replicates the real working scenario of the gripper Specifi cally during pick and place operations the gripper action is characterized by 3 different phases 1 Free stroke the gripper jaws close without generating any load on the object 2 Hit and load there is the contact between the fi ngers and the object which is now grasped The impact is critical for the object as it might provoke its damage depending on the velocity of the jaws and on the impact force 3 Release and open the grasping force is gradually 7159 Fig 7 Gap setup left panel and its section right panel reduced until the gripper jaws reopen releasing the object in its new position C Control algorithm The gripper was controlled by means of a closed loop architecture It can be modeled as a system that takes in input a couple of pressures Pcand Po and produces a grasping force as output The control scheme is depicted in Fig 8 The loop was closed on the force information which was measured by the load cell between the fi ngers The latter Fm and the desired force Fdwere the input of the controller The resulting output provided the input pressures Pin1and Pin2to the pressure regulators connected to the closing and opening chamber The regulators then produced corresponding pressures Pcand Po which actuated the pneumatic gripper To design the controller we assumed that the force Fg exerted by the gripper can be expressed as the difference between the forces generated by the two gripper chambers That is Fg Fo Fc 9 Both Foand Fcwere found to be linear functions of the pressure in the gripper chambers Fo c1oPo c2o Fc c1cPc c2c 10 By combining 9 and 10 one has Fg AP b 11 where P PcPo T A c1cc1o and b c2o c2c At this point we defi ned the variable F as the sum of the desired force and of a proportional term Fp F Fd K Fd Fm 12 in which Fp K Fd Fm That is Fpfeatures a gain K multiplying the error between desired force Fdand measured force Fm At each control loop iteration the controller had to solve the following quadratic programming problem P argmin P 1 2kF Fg P k2 f P s t 0 P 10 13 where P Pin1Pin2 and the interval 0 10 contains the values that the pressure regulator can accept in input The minimization of the cost function with the difference between the value of F and the theoretical gripper force Fgguaranteed that the measured force Fmfollows the trend of the desired force Fd To improve the effectiveness of this process a regularization term i e f P was added f P argmin P 1 2kP P0k 2 s t 0 P 10 14 In this manner the controller minimizes both cost functions to fi nd the two elements of P but imposing P0as the mean value of the two pressures Pin1and Pin2 By means of few algebraic passages the problem expressed by 13 and 14 reduces to P argmin P 1 2 PTH P PTZ s t 0 P 10 15 whence H ATA I Z RAT P0 R Fd K Fd Fm b 16 The parameter was chosen empirically i e 0 1 P0was set to 1 Bar so as when the gripper was required to reopen a Fig 8 Scheme of the closed loop control algorithm 7160 small non null pressure was sent to the opening chamber It is worth noticing that the matrix A and the coeffi cient b vary with the fi nger height as anticipated in Section I Indeed assuming that the object is being grasped between the distal parts of the fi ngers the force applied is smaller for longer fi ngers Consequently the force pressure calibration curve will be different for e g a fi nger of 20 mm with respect to w r t a fi nger of 40 mm as detailed in Section III The controller has to take into account this phenomenon by including different A and b per each fi nger length The whole control architecture was developed in a Lab VIEW environment all the sensor data were acquired at a sampling frequency of 100 Hz and the pressure regulators were piloted at the same frequency To this aim a NI 6343 data acquisition device was used Initial simulations were performed by means of Matlab and Simulink III EXPERIMENTAL RESULTS AND DISCUSSION In this Section the experimental results describing the gripper performance will be illustrated A Gripper characterization First we introduce the force pressure characterization that led to the determination of A and b The relationship Pff f F R was identifi ed by using the static setup presented in Section II The force F was measured in compression and extension while applying a pressure to the pneumatic chambers of the gripper from 1 to 7 Bar For the extension the opening chamber was controlled for the compression it was controlled the closing chamber instead Two diverse position of the gripper jaws were tested 25 full stroke i e 1mm and 75 full stroke i e 3 mm The aim was to observe whether there were signifi cant discrepancy in the measured force and to check if the performance of the gripper was affected by the position of the jaws Results are plotted in Fig 9 both for compression and extension with R ranging from 20 mm to 60 mm The forces measured for both 25 and 75 full stroke confi gurations do not show considerable difference Nonetheless the length of the cylindrical supports has a big infl uence this phenomenon is clearer at highest pressures When the pressure is set to 1 Bar the difference between 20 mm and 60 mm cylinder length is less than 20 for both opening and closing forces On the other hand when the applied pressure is 7 Bar the difference in the measured force between the aforementioned cylinder lengths is about 30 for the closing force and 24 for the opening force Further when working in compression smaller forces were recorded w r t the extension This difference is mainly due to the internal design of the gripper see Section II Note that the compression forces were plotted with absolute value for ease of compar