Control of a Power Assisted Lifting Device

Transcription

1 Proceedings of the RAAD th International Workshop on Robotics in Alpe-Adria-Danbe Region eptember 1-13, 212, Napoli, Italy Control of a Power Assisted Lifting Device Dimeas otios a, Kostompardis Panagiotis b and Aspragathos Nikos c Department of Mechanical Engineering & Aeronatics, University of Patras Patra, Greece a demeasfotis@gmail.com, b kost@mech.patras.gr c asprag@mech.patras.gr Abstract. In this paper, two control schemes for a power assisted lifting device are presented. ch a device can be sed to hoist a heavy object in cooperation with a hman by redcing the operator s brden. The proposed system incldes an admittance controller that establishes the desired dynamic relationship between the applied force to the object and the motion, while an inner control loop reglates the velocity of the object. or the adaptation to a variety of loads, an online adaption controller is implemented based on a neral network with backpropagation training. Alternatively, a gain schedling PID controller is designed for the inner loop. This controller measres the object weight and tnes the gains with predefined rles. The performance of these two adaptation methods is demonstrated on an experimental setp and the reslts are illstrated and discssed at the end of this manscript. Keywords. Power Assist, Admittance Control, Neral Network Control, PID Gain chedling 1. Introdction A power assist system can be sed to facilitate the maniplation of a heavy object by a hman operator with a considerable redction of the reqired force. This system has a wide range of applications in indstry and healthcare e.g. in the maniplation of heavy parts in assembly lines, in rehabilitation throgh physiotherapy etc. The last five decades many researchers have worked on power assist systems. Lee (Lee et al., 1999) developed a power assisted mobile robot arm, based on impedance control (Hogan, 1985), that follows the operator s motion and attenates the load force. The same control method was also sed on a mobile robot arm to assist a hman operator to carry a long object (Hayashibara et al., 1999). Later, a hybrid control framework was proposed that nifies impedance and admittance control (Ott et al., 21). According to Ott, the mapping of force inpts to motion otpts provides very good performance when the environment is soft bt reslts in poor accracy when the environment is stiff. rther research on power assist systems was made on a bridge crane (Miyoshi & Terashima, 24) that controls the velocity of the object in the vertical direction in proportion to the applied force based on and robst control. Doi installed a power assist system in the vertical direction of a pnematic powered crane sing a PD controller (Doi et al., 28). Osamra implemented a power assist system with an ideal plant model and a PD controller on a horizontal slide door to provide comfortable operational feeling (Osamra et al., 27). or force control problems, neral networks have been widely sed (Lin & Tzeng, 1999). Alternatively, the neral network techniqe has been combined with impedance control as an addition in order to improve the controller robstness (Jng & Hsia, 1998). The majority of the systems mentioned above, calclate the assisting force according to the applied force by the ser. The force is either received from the maniplation of the force sensor, which is a pretty straightforward techniqe with many advantages, or indirectly from the maniplation of the object itself. The latter incorporates a loadcell within the sspension system that withdraws the need of a handle and facilitates the intitive handling of an object by the operator. In this paper, a single degree-of-freedom power assist system is developed that can be sed for moving objects in the vertical direction. Admittance control is implemented to establish a relationship between the imposed forces and the motion of the object. To ensre that or object reaches the desired velocity that derived from the admittance controller, a neral network controller with online training is designed that adapts to the variable plant parameters, 1

2 nlike most of the systems mentioned above, which perform nder certain parameters or bondaries. A gain schedling PID was also implemented for the velocity control instead of the neral network controller. A set of objects with different weights were sed on an experimental setp to investigate the performance of the designed controllers in hoisting/lowering and adaptation. 2. ystem Description The proposed system (see ig. 1) consists of an electric motor that is mechanically copled with a drm. Rotation of the motor shaft cases a wire rope to wrap arond the drm and move the object that is attached to the edge along the vertical direction. The position of the object is calclated from a rotary encoder installed at the drm shaft. Using a nmeric differentiation, the velocity of the object is calclated. or the force measrement we selected to mont a loadcell between the rope and the sspended object and let the operator maniplate the object itself rather than se a handle. As a reslt, the operator wold maniplate the object in a more physical manner. The measred force consists of three main components; the weight of the object, the hman force and the inertial forces. We assme that the wire rope is always tensed and that its spring constant is very high. The mass of the loadcell is very small and it has no significant effect on the system dynamic response. object is considered known and is compensated 1 by the static friction T that appears in the drive system. The walls of the gide that are illstrated in ig. 2 are not parts of the actal plant bt were designed in order to model the static friction in the drive system. The motion of the mass can be expressed by the following eqation: - (1) Later it will be demonstrated that the effects of friction forces can be neglected. The known component of gravitational force mg can be nmerically removed from the measred force and the can be given by the eqation: - (2) In order to obtain an accrate measrement of the hman force, the term shold be as small as possible ( ), otherwise it cold affect the dynamic response. ig. 2. ingle degree-of-freedom model m mg T 3.1. Admittance Control To achieve power assisting movement, a desired relationship between the inpt force and the otpt velocity shold be established. Both impedance and admittance control have the ability to establish sch a relationship. In common implementations of impedance control the external force is measred and is commanded sch that the following eqation of the motion is enforced: (3) ig. 1. Layot of control system 3. Design of the Controller or the controller design let s assme a simplified single degree of freedom system in which a mass interacts with the environment (see ig. 2). The mass of the object and displacement are m and x, respectively, and the actator force and external measred force are and. The weight of the This is a typical linear second-order relationship where is the deviation from a reference trajectory. The parameters, and represent the desired inertia, damping and stiffness respectively. In or system we do not want to inclde a restoring force so we set in order to ensre that the actator force will be zero when the ser does not apply. By setting and in (3), we get: 1 This assmption is valid only when. A large static friction T can be achieved with a high transmission ratio. In different case when, a breaking system is reqired. 2

3 (4) where. By comparing Eq. (1) with the desired behavior in Eq. (4), we can derive the impedance control law which gives the force applied by the actator. This method will not be sed, since it reqires a very good estimation of the plant parameters. In or system, it is qite time consming to calclate the dynamics becase these are changing, by lifting a variety of objects. As an alternative, admittance control is considered. In contrast with the impedance control, admittance control accepts force inpts and yields motion otpts and implements an atomatic control system that imposes the actating force indirectly to the plant. This procedre fits better to power assist systems. Admittance control also provides high level of accracy in non-contact tasks. V r = Admittance V d + - Velocity Control ig. 3. Block diagram of control system In the block diagram of ig. 3, the control system is illstrated. It consists of the main control loop for the admittance control and an inner loop for the velocity controller. The main control loop is described by Eq. (4). The reference velocity is set to zero as a necessary condition for the object to remain still when no is applied. When, then and the admittance control law can be rewritten as follows: Motor h Plant V nmodeled parameters are treated as distrbances and are diminished. The mass m of the object is a parameter that has great impact in the plant dynamics and cannot be considered as a distrbance. ince we want or system to perform nder a variety of loads an adaptive controller mst be designed. Neral Network Controller. ince the system dynamics depend on the object weight, a eedforward Neral Network (NN) velocity controller is implemented, as shown in ig. 4. The NN is composed of three layers with the configration (2-6-1), i.e. two linear nerons (L) in the inpt layer, six in the hidden and one in the otpt respectively (see ig. 5). A sigmoid fnction (), which is bonded in magnitde between -1 and 1, is sed for the nerons in the hidden and otpt layers. The well-known backpropagation (Wasserman, 1989) training algorithm is sed for the online adaptation of the network s weights and thresholds b, which are set randomly in the beginning. The velocity error ( - is sed in the backpropagation part and is also fed back to the inpt of the NN together with the previos one [kt-t] in order to close the controller s loop. V r = Admittance V d + - NN ig. 4. Block diagram with neral network velocity control b Motor h Plant V (5) The transformation of Eq. (5) in the discrete time domain sing a sampling period T s and expressed in terms of V d, describes the admittance control law that is sed for the experimental implementation: V e [kt] V e [kt-t] L L Inpt Layer b Otpt Layer - (6) 3.2. Velocity Controller In series with the admittance controller a velocity controller is placed, as shown is ig. 3. The velocity controller inpts the error between the desired velocity that derived from the admittance controller and the measred velocity V from a feedback loop and otpts a voltage to drive the motor. As a reslt, the actating force is derived indirectly from the velocity controller and any ig. 5. Neral network configration PID Gain chedling. The second velocity controller is a gain schedling PID (see ig. 6). The gains of the controller are calclated for a pair of different weights (1kg & 3kg) according to the Ziegler-Nichols method with no overshoot rles. More sample weights cold be sed or greater deviation between them if or experimental setp had Hidden Layer 3

4 bigger payload. This method incldes offline adaptation by compting the gains with linear interpolation at the beginning of the process dring the initialization. V r = Admittance V d + Gain chedling Initial PID gains V e ig. 6. Block diagram with gain schedled PID velocity control 4. Experimental Evalation 4.1. etp Or experimental setp (see ig. 7) consists of a DC motor with high ratio gearbox for non-backdrivability along with a self-made hoist. The maximm lifting/lowering velocity is.6m/s and the capacity is 6kg. The rotational speed of the motor is controlled with plse width modlation (PWM) method throgh a motor driver and is expressed as a percentage of the rated rotational speed. The mass of the loadcell is eqal to.15kg and does not inflence the dynamic response of the system. Both the motor and the sensors are connected to a personal compter with Phidget interfaces. The compter is a common laptop with 2.1GHz CPU clock that acts as a controller. The commnication between the compter and the external interfaces is performed via niversal serial bs (UB) with sampling period T s =8ms. ig. 7. Experimental setp - PID Motor Plant In order to switch to power assisted motion, an initialization process mst take place at the beginning. The object weight is measred at eqilibrim point and is removed from the inpt motor winch encoder wire rope loadcell load h V signal to compensate the gravity. In addition, the appropriate gains are calclated in the gain schedling PID controller. To implement the admittance controller the following parameters are sed: The mass indicates the desired mass for or power assisted system. This vale refers to the desired behavior of the system and shold be accomplished regardless of the actal object weight. The parameter represents the viscos damping in which the desired mass moves and indicates the sensitivity of or system to external forces. Assming, a small external stimlation wold case the object to move indefinitely becase no frictional forces are modelled. The actal frictional forces on the plant wold be perceived as distrbance and wold be compensated by the velocity control system. A desired damping factor of 15Ns/m indicates that in order to move an object with speed.6m/s (rated speed), the reqired force is: To verify this assmption three different objects weighting 1kg, 2kg and 3kg are selected and a constant force eqal to.9n is applied to them in both directions, by adding and removing a mass eqal to.9kg. Then, the velocity of the object in each experiment is plotted and the reslts are sed to investigate the performance between the two controllers in the transient and the steady states. It is expected that the object shold move with a speed eqal to.6m/s PID Gain chedling To begin with, the PID is implemented in digital form along with the admittance controller (Eq. (6)). The gains of the controller are calclated in the system initialization. or the integral term an antiwindp tracking is added to avoid instability de to the satration of the otpt velocity. or three different masses a constant force eqal to.9n is applied for approximately two seconds in each direction casing the lowering (negative vales of velocity) and the hoisting (positive vales of velocity) of the object respectively (see ig. 8). The experiments are condcted nder a constant force becase we want to investigate the performance of the controllers nder the same conditions. The gains for the mass of 2kg reslted from interpolation, while the other two objects coincide with the gain vales obtained by the Ziegler-Nichols tning. The criteria for the evalation of the control methods are the qality of the response rate, the response smoothness and the overshooting. In ig. 9, a smmarized graphical representation of the experiments is presented. The system response is very fast in both directions, specifically in the acceleration of the load. Dring deceleration (when 4

5 the external force is removed) a small delay appears which becomes more evident with the increase of the load. Another notable remark is that the velocity in both directions differs from the rated one and between the different weights mainly becase of the existence of the gravitational component as an external torqe to the motor. The ripples are attribted to residal vibrations de to the flexibility of the system strctre. ig. 8. External force profile that was sed in the experiments ig. 9. Velocity of object for lowering and lifting with gain schedling PID control ig. 1. Velocity of object for lowering and lifting with neral network control niformity of the velocity among the different weights and especially dring the transient state. The responses at the acceleration and deceleration of the object are very similar and meet the desired specifications. Dring the steady state, the deviation of the average velocity from the expected one appears for the same reason as in the PID schedling, de to the gravitational component. The ripples are considerably less and occr only dring the steady state PID vs. Neral Network Before we come to a conclsion a comparison between the two velocity controllers shold be made. Therefore, for each load of the experiments demonstrated in ig. 9 and 1, the velocity graphs of the gain schedled PID and the neral network are overlaid in three figres. tarting from the object with mass m=1kg, we can see in ig. 11 that both controllers accelerate in steady state at the same time. The PID controller cases mch less ripple than the neral network and more steady velocity, bt it needs longer time for the object to stop after the lifting. In ig. 12, comparative reslts for the object of m=2kg are demonstrated. In this case we can also derive valable information for the performance of the PID with gains that reslted from interpolation. Both controllers respond very fast, while the PID cases small leaps of the velocity dring deceleration. Unlike the previos graph, appeared in ig. 11, here the PID controller also cases more ripples than the neral network. or the heaviest object of or experiment with m=3kg we can clearly see (ig. 13) that the neral network otperforms the PID gain schedling. The latter cases even bigger leaps dring deceleration and more intense ripples, while the neral network responses very fast and with very little oscillation of the velocity. mmarizing the reslts, the schedling PID controller even thogh it performs better in small loads, it cases ndesirable effects in greater loads. On the other hand, the performance of the neral network controller is not affected by the increase of the load and has better adaptability in rejecting distrbances. It can be conclded that the neral network as a velocity controller has better generalization than the PID gain schedling and shold be preferred in power assist systems where heavy objects are carried Neral Network Controller bstitting the PID controller with the neral network, the same series of experiments are condcted. In this case, the weights and thresholds of the neral network are adapted online. As it is illstrated in ig. 1, the neral network as a velocity controller demonstrates better 5

6 Velocity of object (m/s) External force (N) ig. 11. Velocity of object (m=1kg) for lowering and lifting with PID gain schedling and NN ig. 12. Velocity of object (m=2kg) for lowering and lifting with PID gain schedling and NN speed. We want to stdy the actal force that is applied by the operator and the corresponding velocity response in order to investigate the performance of proposed synthesis of the admittance and the velocity controllers. In ig. 14, the external force with the PID gain schedling controller is presented. The force that is applied at the beginning of the movement tends to be more than.9n mainly becase the operator takes into accont the dynamics of the actal mass. Very qickly, the operator learns the dynamics of the power assisted system and adjsts the force. This explanation is demonstrated better by the variation of the force in ig. 16 where the neral network controller is implemented. The ripples of the external force at the end of each movement are cased from remaining oscillations of the object and are being rejected by the admittance controller. The noise of the inpt force signal is also rejected and as a reslt it is shown that the admittance controller also acts as a low pass filter. The reslt of the applied force is the velocity of the object that is illstrated in ig. 15 for the PID gain schedling controller and in ig. 17 for the neral network. These figres are similar to ig. 12 from the previos experiments. Both controllers respond very fast with the neral network having slightly better performance dring the transient state. The rippling effect is less evident in the PID gain schedling and is nnoticeable dring operation for both controllers ig. 13. Velocity of object (m=3kg) for lowering and lifting with PID gain schedling and NN 4.5. Maniplation by Hman In this section, the performance of the controllers in the maniplation of an object by a hman operator is presented. The prpose of these experiments is to demonstrate the power assist system nder real conditions inclding the hman factor. The differences from the previos experiments are that the system interacts with the hman and that the applied force is not constant bt depends on the operator. A medim weight eqal to 2kg is selected and a force is applied in order to lower it in a certain distance (.1m) and then hoist it at the initial position. or the admittance controller the same parameters are sed ( ). According to these vales, a force eqal to.9n is reqired in order the object to reach the maximm -2-3 ig. 14. Applied force by hman for lowering and lifting with PID gain schedling,8,6,4,2 -,2 -,4 -,6 -,8 -,1 ig. 15. Velocity of object for lowering and lifting with PID gain schedling 6

7 Velocity of object (m/s) External force (N) ig. 16. Applied force by hman for lowering and lifting with NN,8,6,4,2 -,2 -,4 -,6 -,8 ig. 17. Velocity of object for lowering and lifting with NN 5. Conclsion In this paper, a control method for a power assist system was developed sing admittance control in series with an inner velocity controller. The experiments that were condcted proved that the admittance controller established the desired relationship between the external forces and motions. or the velocity reglator, a gain schedling PID and a neral network controller were implemented. Both of them managed to attain the velocity provided by the admittance controller althogh they did not have knowledge of the plant dynamics. In the effort to adapt to the different object weights, the neral network controller proved to be more appropriate, specifically in higher loads. The online training of the neral network cold also adapt better to distrbances in contrast with the PID gain schedling that tned its gains only at the beginning of the process. On the maniplation of the object by a hman operator, or system performed the cooperative motion very well and or power assisted design was verified. The neral network in the cooperative motion had a slightly better performance than the PID gain schedling. or frther elaboration of the crrent stdy, the implementation of the designed controllers in a 6 degrees-of-freedom robot is planned not only in the vertical direction bt in 3D space, along with the experimentation with greater loads. 6. References Doi, T., Yamada, H., Ikemoto, T., & Natarani, H. 28. imlation of pnematic hand crane type power assist system. Jornal of robotics and mechatronics, Vol.2(6), pp Hayashibara, Y., Tanie, K., & Arai, H Assist system for carrying a long object with a hman - Analysis of a hman cooperative behavior in the vertical direction. Proceedings of the 1999 IEEE/RJ Int. Conf. on intelligent robots and systems, pp Hogan, N Impedance control: An approach to maniplation, part I - theory. AME Jornal of Dynamic ystems, Measrement and Control, vol. 17, pp Jng,., & Hsia, T. C Neral Network Impedance orce Control of Robot Maniplator. IEEE Transactions on Indstrial Electronics, pp. vol. 45(3), pp Lee, H., Takbo, T., Arai, H., & Tanie, K Control of mobile maniplators for power assist systems. Proc. of 1999 IEEE Int. Conf. on systems, Man and Cybernetics (MC'99), Vol. 4, pp Lin,., & Tzeng, Neral network force control for indstrial robots. Jornal of Intelligent and Robotic ystems: Theory and Applications, vol. 24(3), pp Miyoshi, T., & Terashima, K. 24. Development of vertical power-assisted crane system to redce the operators' brden. 24 IEEE International Conference on ystems, Man and Cybernetics. Osamra, K., Kobayashi,., Hirata, M., & Okamoto, H. 27. Power assist control for slide doors. ICE Annal Conference 7, pp Ott, C., Mkherjee, R., & Nakamra, Y. 21. Unified Impedance and Admittance Control. IEEE International Conference on Robotics and Atomation. Wasserman, N Neral Compting Theory and Practice. New York: Van Nostrand Reinhold. 7