- Email: [email protected]
Mechatronical Systems of Adaptive Robot Hand
Copyright © IFAC New Trends in Design of Control Systems, Smolenice, Slovak Republic, 1997
MECHATRONICAL SYSTEMS OF ADAPTIVE ROBOT HAND
Vaclav Kalas, Eduard Gers
Faculty of Electrical Engineering and Information Technology STU Department ofAutomation and Control Ilkovicova 3, 812 19 Bratislava, Slovakia E-mail: [email protected]
Abstract: The contribution demonstrates the robot gripper, whose compressive force is automatically controlled to inevitable minimal value, also namely in dynamic modes, when besides gravity force also a rank of other forces and torques affect to the manipulated object. Keywords: compressive force controller, variable force controller, sensoric systems of slip, tangential forces sensors, six-component force-torque sensors
The motion systems of the gripper are synthesized in cascade structures with the current, basic compressive force, variable compressive force control circuits as well as the speed and position control circuits.
1. INTRODUCTION The recent period in robotics signalizes the remarkable improvement also in the area of the robot hands improving. The new kinematic structures, control and sensor systems are being developed, adaptivity and artificial intelligence are being applied. This fact could be presented e.g. by the grippers established on the basis of SMA (Shape Memory Alloys). Encouraging results in the field of artificial muscles were achieved, grippers with sensibility close to the human hand, such as Th e belgrade USC Robot hand, resp. Salisbury Hand can be also mentioned, where the biomechanical principles, artificial reflexes control, teaching principles, neural nets and many other are applied.
The gripper is also able to identify the static friction coefficient by itself and is able to respect the alterations of this value in dynamic modes. It can also ensure the invariance of the system to the manipulated object mass within the certain bounds. The gripper contains the force sensoric system, relative acceleration, speed and position sensoric system as well as the six-component force-torque sensors to obtain the information about tangential forces .
This contribution is oriented to computer synthesis of the robot gripper with the ability of automatic jaws compressive force control, also in dynamic modes, when the manipulated object is affected besides the gravity force also by acceleration force , the environment resistance force, centrifugal force, Coriolis force, rotative torques trying to turn the object in the gripper, and others. Compressive force of the jaws is automatically controlled to inevitable minimal value to avoid object damaging or hurting, but to ensure the manipulated object not to shift, even not to drop out from the gripper.
The implementation of such type of grippers can be found for example in the following areas: robotized manipulation in glass industry, microelectronic technologies, robotized laboratory operations, robotized fruits collection and sorting, robotized vaccination and manipulation with broilers, human robotics in extremities operations and robotized reconvalescent acts, and others.
227
sensors 9, where v, represents contingent relative slip velocity between the object MO and sensors 9. In order to achieve soft grasp, the gripper disposes of critically dumped flexible elements 10.
G.
A
For the gripper activity, the following torque relationship is established, based on the motor features, as it can be seen from Figure 2:
L
(1) Fig. 1. Basic structure of gripper control systems. where
T" represents the internal motor rotary torque,
0,,, - friction
torque of the motor, i-transmission ratio of the gear with transmission efficiencies T] I' T] 2' Rp is the contact radius of the pinion 5, F compressive force of the gripper jaws, J, - moment of inertia reduced to the motor shaft and ro '" represents the motor angular velocity.
2. BASIC STRUCTURE OF GRIPPER CONTROL SYSTEMS Let us consider the manipulated object MO with the mass m to be grasped in the robot hand. An aggregate of actuating signals G l generated by the actuator A affects to the object, like grasp compressive forces F, generated velocity of the gripper motion, its position, orientation etc. - Fig. 1. Further, also gravity force F g , disturbance forces F. and torques T k from the acceleration, i.e. an aggregate of signals G 2 affects to the object, then the forces from Coriolis acceleration F Col' the resistance of environment Fp , centrifugal forces Fern ' Also rotary torques and the forces from technological operations can affect. In addition to mentioned influences, the internal forces and torques from the activity of manipulated object can cause slip, especially when manipulating biological objects.
For D.e. motor 1 with the torque-voltage constant C. and the armature current I from (1) results 1=
2FRp+Tfr{)iT]IT]2+Jr~ iT] IT] 2 C u
(2)
For the most unfavourable time progress of the force F(t) and velocity ro ,/t) according to this relationship appropriate parameters of the motor 1 can be established.
Manipulated object MO is further influenced by the signals G., that consist of the gravity field, magnetic field, vibrations, and also climatic parameters. Real behaviour of the object is given by the aggregate of signals H , while some of them are sensed and processed by the sensoric system SES. On the basis of certain control strategy the control computer CC processes signals I and the reference states signals K of the manipulated object MO . By means of the signals L and actuators A the signals G l are generated.
6
3. BASIC STRUCTURE OF GRIPPER KINEMA TIC SYSTEMS Let the manipulated object MO to be grasped in the robot gripper and affected by the mentioned forces and torques according to Figure 2. In Figure 2, 1 means electric servomotor with the incremental position sensor 2, with the gear 3-4, cog pinion 5, cog racks 6 that are kinematic component parts of the jaws 7. The gripper disposes of compressive slabs 8, on which from the side of the object MO the sensoric systems 9 are mounted. In the real conditions adynamic friction Jl(v) can occure between the object MO and the active surface of
Fig. 2. Simplified kinematic structure of the robot hand with linear motion of jaws.
228
4. MOTION EQUATIONS FOR THE SYSTEM
The relative object motion is described as follows:
Considering general motion of the robot hand and regarding all forces and torques mentioned above, it is very difficult to express the relationship for the compressive force F. The force control circuits have to automatically manage the effects of all kinds of forces and torques. For better understanding, let us reduce only to the case of vertical motion of the gripper.
tlFmet) + Fe(v - vs)-[Fg + 2~(vs)Fo + 2~(vs)vFo + 2~(vs)FJ = dvs d 2s =ma =m-=m--s s dt dt2
5. THE GRIPPER COMPRESSIVE FORCE GENERATOR
Following the previous denotations for a symetric object, the compressive force F should satisfy the condition
Requesting automatic control of the compressive force to inevitable minimal value in dynamic modes, the compressive force generator has to be designed to reach extremely high dynamic parameters. To satisfy this condition, a torque servosystem was designed for the force 2F=40N and m=2kg with the motor ALSTHOM RS120 whose parameters are: P,,=30W, Mn=0.095Nm, n,, =3000 r.p.m., [J,,=22V, I,,=J.53A, Mf ,o=O.OlNm, C. =0.042NmIA.
(3) means the acceleration of the gripper where a = 11:. dt and object MO together, when the relative slip velocity v ,=O. The force Fc(v) is the resistance of environment that affects to the object MO with the velocity v.
The actuator consists of the "H" scheme with PWM with the switching frequency of transistors 20kHz. The mass of the gripper jaws is mg=0.42kg. The moment of inertia reduced to the motor shaft is J =0.4948 .10.5 kgm 2 • The transmission ratio i of the g~ar with efficiencies 11 /=0.92, 112=0. 9 is close to its optimal value, i=4. The pinion radius is Rp=5.10·3m . Other parameters are: R",=2.65W, K/=J.78VIA, ~=0. 786ms, Kf =l, K ac =2.5VIV, Tuc =O. l~, Tc=0.415ms.
Let us consider the moving complex of the gripper with the mass md to be affected by the motoric force . F..(t). Moving upwards, since there is not any relatIve object movement in the gripper, it holds: (mch +m) a
= Fm(t)
(4)
The forces trying to shift the object in the gripper, are Fg + ma + Fe(v) . Against these forces the friction forces 2~FIJ + 2~vFo affect to the object, where 2~Fo is the boundary friction force needful to ideally compensate the gravity force Fg and 2~vFo is ~e reserve force, i.e. over-compensation of the graVIty force F. Boundary, i.e. not-slipping acceleration of the system, ideally compensating the gravity force Fg, is acr =(2~vFo- Fc(v»lm.
The discrete time-optimal armature current controller with constrained control signal was designed using algebraic theory (fourth order discrete system). The global spring constant of the flexible elements in the gripper is Kp=20.10'Nlm and the time constants are Ta = 1.434. ]O"'s, Tb =2.395.10·'s. To reduce the disturbance influence (especially the changes of efficiencies 11/' 11), the system involves in cascade structure the superior force control loop - the analog PID controller whose parameters was experimentally tuned up . Parameters of this control loop are: KFs =0.15VIN, TFs =T,=O.Ols. Then, for comparison, also the . discrete force controller was designed by the algebraic theory and is of sixth order. Control signal is constrained.
Moving upwards, following equation for the relative object movement in the gripper jaws is established: tlFmet) + Fg + Fe(v - vs)-[ 2~(vs)Fo + 2~(vs)vFo + 2~(vs)FJ dv s d 2s s =ma =m-=m-s dt dt2
=
(5)
The jaws positioning structure is not mentioned in this paper.
while tlFm(t) = m(a-aMP), where aMP is the object MO acceleration in the stationary reference frame. 2~(vs)F representing the variable compressive force will be considered later.
Global block diagram of the force generator using classic current and force control can be seen in Figure 3. The transfer function of the flexible element is considered in the case of contact between the object MO and gripper jaws. While the object and jaws are not in contact, this transfer function becomes a double integrator. So the force generator represents a variable structure system here (Kalas, et al.,1994).
Moving the gripper downwards, perfectly compensating the gravity force effect, the critical acceleration a, described by the following relationship, is ;~nsiderably higher: a cr
=
4~Fo
+ 2~vFo - F e(v) m
(7)
(6)
229
Fig. 3. The force generator block diagram. Figure 4 shows the response of the force generator with classic and algebraic force controller to reference signal UFR step change. It can be seen that the algebraic system is nearly two times faster than the classic system, and in both cases it can be said that the system reaches very good dynamics.
linear system and let /l{vJ=/l=const. Following the denotations in Figure 5, the relationship for the variable force control loop is established as follows : 2/lF(s) M~(s)
(8)
Ks(1 + Tss)MJ (S)KFNJ (s)/l 20
_
15
From (8), it results that when the relative velocity sensoric system is applied (when i=l) and considering non-persisting elements, i.e. M/s)=Mls) =N/s) =Nls)=J , then
~
u....:
I
10
o
- - - - .. -
~~
0.00
r
I
-
-
-
-
..
-
__- L__- L_ _ 0 .02
r
-
~
0.04
-
-
H
-ClaSSicoontrol -Algebraic control
- - - .
_ _~_ _L-- J__- L__~~
0.06
0.06
2/lF(s)
0 .1(
time Is)
M~(s)
KsKF/l ms + K sKF/l
(9)
Fig. 4. Response of the gripper compressive force generator at the contact between jaws and the manipulated object.
6. AUTOMATIC CONTROL OF THE GRIPPER COMPRESSIVE FORCE WITH LITTLE SLIP OF THE MANIPULATED OBJECT One of the ways to control the compressive force automatically and maintain it to its minimal value, is to apply the relative acceleration a, (AS), velocity v, (VS), or position s, sensoric system (PS) that senses the relative movement of the object - Figure 5.
KFN,(s) N,(s)
Fig. 5. Structure of the system with the minimal compressive force automatic control on the basis of slip variables.
In the structure shown in Figure 5, there is a correcting block CB that ensures the required global control process quality, and nonlinear block NB with dead band for the movement upwards and downwards that results from the upper relationships. The compressive force generator FG shown in Figure 5 generates the constant component of the force 2/lFo(l +v) that consists of the gravity force Fg compensation and the gravity force partial safety ovp.r-compensation 2/lvFo. Besides these forces the generator produces also the variable compressive force 2F that figures in equations (5), (7).
Evidently, for high gain of the control loop, the system can be invariant to the changes of the object mass m. Further, from (8) results that applying the position sensoric system, without any additional arrangements, the control loop becomes structural unstable. Using the relationship (8), appropriate correcting block CB can be designed, substituting the force generator by the second order system (from the response in Figure 4).
Let us consider the force generator FG working in a little neighborhood of the operating point to be a
230
Figure 6 shows the progress of each state variable. The transfer function of the correcting block CB is 1+Ts, where T=0.1 . 10 3s (PD type) . The global gain of the control loop is K=8000, object mass is m=2kg, T, ~O and ll{vJ=1l =const=2. The motoric force impulse to the system F,.(t) has sinusoidal shape upward and downward as well (Fig. 6), the amplitude is 60N, and the duration is Is with the 0.5s pause. The reserve force 21lvFo was chosen as 10% of ideal compensating force 21lFo' Figure 6 also shows the progress of compensating variable force 21lF that can be notably smaller at downward movement. The force generator FG was substituted by the second order system here.
To eliminate this effect, the sensoric system with tangential forces (Hlisnikovsky, 1987b) sensor can be applied, that senses the forces F, between the gripper and the manipulated object MO (labelled 9 in Figure 2). In this case, the force generator initiates at the change of tangential forces, without any need to slip of the object MO. So the dynamics of such system can be considerably higher.
NB
60 40 20
v,
Yl
'----"-o-04>+-'--
Z
- - - -- - - - - - - - - - . - , v .
;;:' 0
$.
·20 ·40
Fig. 7. Principal structure of the gripper with tangential forces sensoric system.
·60 0,0
0,5
1.0
2,0
1.5
2,5
3,0
lime rsl
The principal structure of the control circuit for this case is shown in Figure 7, where TFS means six-component force-torque sensor, that can be used to sense both tangential forces and compressive force F. Nonlinear block is the same as in Figure 5. In this structure also a contingent slip caused by the friction of the environment resistance (represented by the non linearity N) is considered, but this can be ignored when the dynamics of the generator FG is sufficient.
E E
:;:.
0
E
.§. · 1 ~
~
·2
.§. <0"
.3
0, 5
1,0
1,5
2,0
2,5
3,0
time Is)
Figure 8 shows the behaviour of such system using the tangential forces sensor, with the correcting block CB of PID type (P=0.0625, I=0.0045s, D=0.015s). All of the other variables are the same as in the previous case. The force generator was considered in the full structure shown in Fig. 3, but using discrete algebraic current and force control.
Fig. 6. The progress of input, output and selected state variables with little slip of the manipulated object The lower part of Figure 6 shows the object slip acceleration, velocity and position progress. It is evident that the object MO has shifted about Imm. Since it is technically difficult to sense the slip acceleration a" miniature double-axes IRC sensoric position systems can be used, with the differentiation of the signal. More about sensoric systems that can be applied in this conception, is discussed by Havlik (1988), Hlisnikovsky (1987a), Ryasuke, et aI. , (1981) and in the prospects of Canon, USA.
40
-
Mocoriefoc'ce Cornpen.ating force
-
Deviation btlfWMn motorlc .-.cl compen. .ting fore.
- R....... upw.d RtI.....,.do¥mw.d
20
0,0
7. GRIPPER COMPRESSIVE FORCE AUTOMATIC CONTROL WITH TANGENTIAL FORCES SENSING
0,5
1,0
1,5
time(s)
2,0
2,5
3,0
Fig. 8. The variables response in the adaptive system of the gripper with tangential forces sensors. In this case, the object MO have not shifted in the robot gripper at all, and the compressive force F was as small as possible.
One of disadvantages of the system that uses a slip of the manipulated object is that it may worsen the robot positioning in some technologies. It is caused by little slip that must rise to activate the force generator.
231
Using this philosophy, the system is invariant to the changes of the object mass m in wide range. When the gain of the variable force F control loop is sufficient, the system is also invariant to the changes of the friction coefficient.
The global gripper operation program flow chart in Figure 9.
To automatically identify the friction coefficient Il at nought velocity, combination of both system can be used. While gradually increasing the compressive force, when the object MO stops slipping, the value 21lFo is remembered and following the relationship
The contribution has demonstrated some basic questions concerned with the robot hand that is able to work with minimal compressive force affecting to the manipulated object, also in dynamic modes, when a number of miscellaneous forces and torques affects. Two kinds of conceptions have been offered. One with some little slip required and the second one that does not need any slip.
(11 ) the value of the friction coefficient Il can be calculated. It is also possible to arrange a nonlinear block 1l=Il(vJ to the force generator circuit.
IS
expressed by the
8. CONCLUSION
The quality criterion of each conception can be represented by the time integral of global compressive force F(t) affecting to the manipulated object. In these conceptions the value of this integral can be multiple times lower than in conventional types of robot hands.
REFERENCES Havlik, S. (1988). Snimac sklzu predmetov, CSSR invention N° 256190 from 15. November, (Slovak). Hlisnikovsky, I. (1987a). Met6dya sp6soby snimania sklzu predmetu v chapadle, In: Adaptivne roboticke systemy, p.39, DT CSVTS, Banskli Bystrica (Slovak). Hlisnikovsky, I. (1987b). Snimac tangencialnych si! chapadla robota, kandidatska dizertacna praca, Faculty of Mechanical Enginering SUT, Bratislava (Slovak). Kalas, V., J. Polakovicova (1994). Inteligenme chapadlo robota, In: Kybernetika a umela inteligencia, pp.75-84, TU Kosice (Slovak). Ryasuke - Masuda (1981). Global Sensoric System for the Direct Robot Control and its Construction Approach, Proc. of the 11th Int. Symp. on Industrial Robots, pp. 159 - 166, Tokyo. The prospects of Canon USA. Laser Rotary Encoder, New York Office, New York.
generate variable force
Fig. 9. Possible algorithm of the gripper operation. When necessary, the information of the object mass could be automatically acquired from: 21lF o
m =g- -
(12)
232
MECHATRONICAL SYSTEMS OF ADAPTIVE ROBOT HAND
Vaclav Kalas, Eduard Gers
Faculty of Electrical Engineering and Information Technology STU Department ofAutomation and Control Ilkovicova 3, 812 19 Bratislava, Slovakia E-mail: [email protected]
Abstract: The contribution demonstrates the robot gripper, whose compressive force is automatically controlled to inevitable minimal value, also namely in dynamic modes, when besides gravity force also a rank of other forces and torques affect to the manipulated object. Keywords: compressive force controller, variable force controller, sensoric systems of slip, tangential forces sensors, six-component force-torque sensors
The motion systems of the gripper are synthesized in cascade structures with the current, basic compressive force, variable compressive force control circuits as well as the speed and position control circuits.
1. INTRODUCTION The recent period in robotics signalizes the remarkable improvement also in the area of the robot hands improving. The new kinematic structures, control and sensor systems are being developed, adaptivity and artificial intelligence are being applied. This fact could be presented e.g. by the grippers established on the basis of SMA (Shape Memory Alloys). Encouraging results in the field of artificial muscles were achieved, grippers with sensibility close to the human hand, such as Th e belgrade USC Robot hand, resp. Salisbury Hand can be also mentioned, where the biomechanical principles, artificial reflexes control, teaching principles, neural nets and many other are applied.
The gripper is also able to identify the static friction coefficient by itself and is able to respect the alterations of this value in dynamic modes. It can also ensure the invariance of the system to the manipulated object mass within the certain bounds. The gripper contains the force sensoric system, relative acceleration, speed and position sensoric system as well as the six-component force-torque sensors to obtain the information about tangential forces .
This contribution is oriented to computer synthesis of the robot gripper with the ability of automatic jaws compressive force control, also in dynamic modes, when the manipulated object is affected besides the gravity force also by acceleration force , the environment resistance force, centrifugal force, Coriolis force, rotative torques trying to turn the object in the gripper, and others. Compressive force of the jaws is automatically controlled to inevitable minimal value to avoid object damaging or hurting, but to ensure the manipulated object not to shift, even not to drop out from the gripper.
The implementation of such type of grippers can be found for example in the following areas: robotized manipulation in glass industry, microelectronic technologies, robotized laboratory operations, robotized fruits collection and sorting, robotized vaccination and manipulation with broilers, human robotics in extremities operations and robotized reconvalescent acts, and others.
227
sensors 9, where v, represents contingent relative slip velocity between the object MO and sensors 9. In order to achieve soft grasp, the gripper disposes of critically dumped flexible elements 10.
G.
A
For the gripper activity, the following torque relationship is established, based on the motor features, as it can be seen from Figure 2:
L
(1) Fig. 1. Basic structure of gripper control systems. where
T" represents the internal motor rotary torque,
0,,, - friction
torque of the motor, i-transmission ratio of the gear with transmission efficiencies T] I' T] 2' Rp is the contact radius of the pinion 5, F compressive force of the gripper jaws, J, - moment of inertia reduced to the motor shaft and ro '" represents the motor angular velocity.
2. BASIC STRUCTURE OF GRIPPER CONTROL SYSTEMS Let us consider the manipulated object MO with the mass m to be grasped in the robot hand. An aggregate of actuating signals G l generated by the actuator A affects to the object, like grasp compressive forces F, generated velocity of the gripper motion, its position, orientation etc. - Fig. 1. Further, also gravity force F g , disturbance forces F. and torques T k from the acceleration, i.e. an aggregate of signals G 2 affects to the object, then the forces from Coriolis acceleration F Col' the resistance of environment Fp , centrifugal forces Fern ' Also rotary torques and the forces from technological operations can affect. In addition to mentioned influences, the internal forces and torques from the activity of manipulated object can cause slip, especially when manipulating biological objects.
For D.e. motor 1 with the torque-voltage constant C. and the armature current I from (1) results 1=
2FRp+Tfr{)iT]IT]2+Jr~ iT] IT] 2 C u
(2)
For the most unfavourable time progress of the force F(t) and velocity ro ,/t) according to this relationship appropriate parameters of the motor 1 can be established.
Manipulated object MO is further influenced by the signals G., that consist of the gravity field, magnetic field, vibrations, and also climatic parameters. Real behaviour of the object is given by the aggregate of signals H , while some of them are sensed and processed by the sensoric system SES. On the basis of certain control strategy the control computer CC processes signals I and the reference states signals K of the manipulated object MO . By means of the signals L and actuators A the signals G l are generated.
6
3. BASIC STRUCTURE OF GRIPPER KINEMA TIC SYSTEMS Let the manipulated object MO to be grasped in the robot gripper and affected by the mentioned forces and torques according to Figure 2. In Figure 2, 1 means electric servomotor with the incremental position sensor 2, with the gear 3-4, cog pinion 5, cog racks 6 that are kinematic component parts of the jaws 7. The gripper disposes of compressive slabs 8, on which from the side of the object MO the sensoric systems 9 are mounted. In the real conditions adynamic friction Jl(v) can occure between the object MO and the active surface of
Fig. 2. Simplified kinematic structure of the robot hand with linear motion of jaws.
228
4. MOTION EQUATIONS FOR THE SYSTEM
The relative object motion is described as follows:
Considering general motion of the robot hand and regarding all forces and torques mentioned above, it is very difficult to express the relationship for the compressive force F. The force control circuits have to automatically manage the effects of all kinds of forces and torques. For better understanding, let us reduce only to the case of vertical motion of the gripper.
tlFmet) + Fe(v - vs)-[Fg + 2~(vs)Fo + 2~(vs)vFo + 2~(vs)FJ = dvs d 2s =ma =m-=m--s s dt dt2
5. THE GRIPPER COMPRESSIVE FORCE GENERATOR
Following the previous denotations for a symetric object, the compressive force F should satisfy the condition
Requesting automatic control of the compressive force to inevitable minimal value in dynamic modes, the compressive force generator has to be designed to reach extremely high dynamic parameters. To satisfy this condition, a torque servosystem was designed for the force 2F=40N and m=2kg with the motor ALSTHOM RS120 whose parameters are: P,,=30W, Mn=0.095Nm, n,, =3000 r.p.m., [J,,=22V, I,,=J.53A, Mf ,o=O.OlNm, C. =0.042NmIA.
(3) means the acceleration of the gripper where a = 11:. dt and object MO together, when the relative slip velocity v ,=O. The force Fc(v) is the resistance of environment that affects to the object MO with the velocity v.
The actuator consists of the "H" scheme with PWM with the switching frequency of transistors 20kHz. The mass of the gripper jaws is mg=0.42kg. The moment of inertia reduced to the motor shaft is J =0.4948 .10.5 kgm 2 • The transmission ratio i of the g~ar with efficiencies 11 /=0.92, 112=0. 9 is close to its optimal value, i=4. The pinion radius is Rp=5.10·3m . Other parameters are: R",=2.65W, K/=J.78VIA, ~=0. 786ms, Kf =l, K ac =2.5VIV, Tuc =O. l~, Tc=0.415ms.
Let us consider the moving complex of the gripper with the mass md to be affected by the motoric force . F..(t). Moving upwards, since there is not any relatIve object movement in the gripper, it holds: (mch +m) a
= Fm(t)
(4)
The forces trying to shift the object in the gripper, are Fg + ma + Fe(v) . Against these forces the friction forces 2~FIJ + 2~vFo affect to the object, where 2~Fo is the boundary friction force needful to ideally compensate the gravity force Fg and 2~vFo is ~e reserve force, i.e. over-compensation of the graVIty force F. Boundary, i.e. not-slipping acceleration of the system, ideally compensating the gravity force Fg, is acr =(2~vFo- Fc(v»lm.
The discrete time-optimal armature current controller with constrained control signal was designed using algebraic theory (fourth order discrete system). The global spring constant of the flexible elements in the gripper is Kp=20.10'Nlm and the time constants are Ta = 1.434. ]O"'s, Tb =2.395.10·'s. To reduce the disturbance influence (especially the changes of efficiencies 11/' 11), the system involves in cascade structure the superior force control loop - the analog PID controller whose parameters was experimentally tuned up . Parameters of this control loop are: KFs =0.15VIN, TFs =T,=O.Ols. Then, for comparison, also the . discrete force controller was designed by the algebraic theory and is of sixth order. Control signal is constrained.
Moving upwards, following equation for the relative object movement in the gripper jaws is established: tlFmet) + Fg + Fe(v - vs)-[ 2~(vs)Fo + 2~(vs)vFo + 2~(vs)FJ dv s d 2s s =ma =m-=m-s dt dt2
=
(5)
The jaws positioning structure is not mentioned in this paper.
while tlFm(t) = m(a-aMP), where aMP is the object MO acceleration in the stationary reference frame. 2~(vs)F representing the variable compressive force will be considered later.
Global block diagram of the force generator using classic current and force control can be seen in Figure 3. The transfer function of the flexible element is considered in the case of contact between the object MO and gripper jaws. While the object and jaws are not in contact, this transfer function becomes a double integrator. So the force generator represents a variable structure system here (Kalas, et al.,1994).
Moving the gripper downwards, perfectly compensating the gravity force effect, the critical acceleration a, described by the following relationship, is ;~nsiderably higher: a cr
=
4~Fo
+ 2~vFo - F e(v) m
(7)
(6)
229
Fig. 3. The force generator block diagram. Figure 4 shows the response of the force generator with classic and algebraic force controller to reference signal UFR step change. It can be seen that the algebraic system is nearly two times faster than the classic system, and in both cases it can be said that the system reaches very good dynamics.
linear system and let /l{vJ=/l=const. Following the denotations in Figure 5, the relationship for the variable force control loop is established as follows : 2/lF(s) M~(s)
(8)
Ks(1 + Tss)MJ (S)KFNJ (s)/l 20
_
15
From (8), it results that when the relative velocity sensoric system is applied (when i=l) and considering non-persisting elements, i.e. M/s)=Mls) =N/s) =Nls)=J , then
~
u....:
I
10
o
- - - - .. -
~~
0.00
r
I
-
-
-
-
..
-
__- L__- L_ _ 0 .02
r
-
~
0.04
-
-
H
-ClaSSicoontrol -Algebraic control
- - - .
_ _~_ _L-- J__- L__~~
0.06
0.06
2/lF(s)
0 .1(
time Is)
M~(s)
KsKF/l ms + K sKF/l
(9)
Fig. 4. Response of the gripper compressive force generator at the contact between jaws and the manipulated object.
6. AUTOMATIC CONTROL OF THE GRIPPER COMPRESSIVE FORCE WITH LITTLE SLIP OF THE MANIPULATED OBJECT One of the ways to control the compressive force automatically and maintain it to its minimal value, is to apply the relative acceleration a, (AS), velocity v, (VS), or position s, sensoric system (PS) that senses the relative movement of the object - Figure 5.
KFN,(s) N,(s)
Fig. 5. Structure of the system with the minimal compressive force automatic control on the basis of slip variables.
In the structure shown in Figure 5, there is a correcting block CB that ensures the required global control process quality, and nonlinear block NB with dead band for the movement upwards and downwards that results from the upper relationships. The compressive force generator FG shown in Figure 5 generates the constant component of the force 2/lFo(l +v) that consists of the gravity force Fg compensation and the gravity force partial safety ovp.r-compensation 2/lvFo. Besides these forces the generator produces also the variable compressive force 2F that figures in equations (5), (7).
Evidently, for high gain of the control loop, the system can be invariant to the changes of the object mass m. Further, from (8) results that applying the position sensoric system, without any additional arrangements, the control loop becomes structural unstable. Using the relationship (8), appropriate correcting block CB can be designed, substituting the force generator by the second order system (from the response in Figure 4).
Let us consider the force generator FG working in a little neighborhood of the operating point to be a
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Figure 6 shows the progress of each state variable. The transfer function of the correcting block CB is 1+Ts, where T=0.1 . 10 3s (PD type) . The global gain of the control loop is K=8000, object mass is m=2kg, T, ~O and ll{vJ=1l =const=2. The motoric force impulse to the system F,.(t) has sinusoidal shape upward and downward as well (Fig. 6), the amplitude is 60N, and the duration is Is with the 0.5s pause. The reserve force 21lvFo was chosen as 10% of ideal compensating force 21lFo' Figure 6 also shows the progress of compensating variable force 21lF that can be notably smaller at downward movement. The force generator FG was substituted by the second order system here.
To eliminate this effect, the sensoric system with tangential forces (Hlisnikovsky, 1987b) sensor can be applied, that senses the forces F, between the gripper and the manipulated object MO (labelled 9 in Figure 2). In this case, the force generator initiates at the change of tangential forces, without any need to slip of the object MO. So the dynamics of such system can be considerably higher.
NB
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v,
Yl
'----"-o-04>+-'--
Z
- - - -- - - - - - - - - - . - , v .
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Fig. 7. Principal structure of the gripper with tangential forces sensoric system.
·60 0,0
0,5
1.0
2,0
1.5
2,5
3,0
lime rsl
The principal structure of the control circuit for this case is shown in Figure 7, where TFS means six-component force-torque sensor, that can be used to sense both tangential forces and compressive force F. Nonlinear block is the same as in Figure 5. In this structure also a contingent slip caused by the friction of the environment resistance (represented by the non linearity N) is considered, but this can be ignored when the dynamics of the generator FG is sufficient.
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~
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.§. <0"
.3
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time Is)
Figure 8 shows the behaviour of such system using the tangential forces sensor, with the correcting block CB of PID type (P=0.0625, I=0.0045s, D=0.015s). All of the other variables are the same as in the previous case. The force generator was considered in the full structure shown in Fig. 3, but using discrete algebraic current and force control.
Fig. 6. The progress of input, output and selected state variables with little slip of the manipulated object The lower part of Figure 6 shows the object slip acceleration, velocity and position progress. It is evident that the object MO has shifted about Imm. Since it is technically difficult to sense the slip acceleration a" miniature double-axes IRC sensoric position systems can be used, with the differentiation of the signal. More about sensoric systems that can be applied in this conception, is discussed by Havlik (1988), Hlisnikovsky (1987a), Ryasuke, et aI. , (1981) and in the prospects of Canon, USA.
40
-
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-
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7. GRIPPER COMPRESSIVE FORCE AUTOMATIC CONTROL WITH TANGENTIAL FORCES SENSING
0,5
1,0
1,5
time(s)
2,0
2,5
3,0
Fig. 8. The variables response in the adaptive system of the gripper with tangential forces sensors. In this case, the object MO have not shifted in the robot gripper at all, and the compressive force F was as small as possible.
One of disadvantages of the system that uses a slip of the manipulated object is that it may worsen the robot positioning in some technologies. It is caused by little slip that must rise to activate the force generator.
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Using this philosophy, the system is invariant to the changes of the object mass m in wide range. When the gain of the variable force F control loop is sufficient, the system is also invariant to the changes of the friction coefficient.
The global gripper operation program flow chart in Figure 9.
To automatically identify the friction coefficient Il at nought velocity, combination of both system can be used. While gradually increasing the compressive force, when the object MO stops slipping, the value 21lFo is remembered and following the relationship
The contribution has demonstrated some basic questions concerned with the robot hand that is able to work with minimal compressive force affecting to the manipulated object, also in dynamic modes, when a number of miscellaneous forces and torques affects. Two kinds of conceptions have been offered. One with some little slip required and the second one that does not need any slip.
(11 ) the value of the friction coefficient Il can be calculated. It is also possible to arrange a nonlinear block 1l=Il(vJ to the force generator circuit.
IS
expressed by the
8. CONCLUSION
The quality criterion of each conception can be represented by the time integral of global compressive force F(t) affecting to the manipulated object. In these conceptions the value of this integral can be multiple times lower than in conventional types of robot hands.
REFERENCES Havlik, S. (1988). Snimac sklzu predmetov, CSSR invention N° 256190 from 15. November, (Slovak). Hlisnikovsky, I. (1987a). Met6dya sp6soby snimania sklzu predmetu v chapadle, In: Adaptivne roboticke systemy, p.39, DT CSVTS, Banskli Bystrica (Slovak). Hlisnikovsky, I. (1987b). Snimac tangencialnych si! chapadla robota, kandidatska dizertacna praca, Faculty of Mechanical Enginering SUT, Bratislava (Slovak). Kalas, V., J. Polakovicova (1994). Inteligenme chapadlo robota, In: Kybernetika a umela inteligencia, pp.75-84, TU Kosice (Slovak). Ryasuke - Masuda (1981). Global Sensoric System for the Direct Robot Control and its Construction Approach, Proc. of the 11th Int. Symp. on Industrial Robots, pp. 159 - 166, Tokyo. The prospects of Canon USA. Laser Rotary Encoder, New York Office, New York.
generate variable force
Fig. 9. Possible algorithm of the gripper operation. When necessary, the information of the object mass could be automatically acquired from: 21lF o
m =g- -
(12)
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