- Email: [email protected]
Force sensing for advanced robot control
139
Force Sensing for Advanced Robot Control P r o f . H . V a n B r u s s e l , Ir. H . B e l i e n a n d Ir. H . T h i e l e m a n s
1. Introduction
Katholieke Unioersiteit Leuoen, Mechanical Engineering Department, Celestijnenlaan 300 B, B.3030 Leuven, Belgium
I n the e n d e a v o u r to i n t r o d u c e real flexibility i n t o the b e h a v i o u r o f i n d u s t r i a l robots, the conc e p t of force f e e d b a c k is n o w generally recognized to b e essential. In the recent past, several research a n d industrial l a b o r a t o r i e s have been s u p p o r t i n g this s t a t e m e n t b y designing a p p r o p r i a t e force sensors a n d force f e e d b a c k strategies. Nevertheless, t o d a y ' s reality reveals that ind u s t r i a l a p p l i c a t i o n s involving force f e e d b a c k are rare. This is in sharp c o n t r a s t with the growing p e n e t r a t i o n of vision systems. T h e m a i n reasons b e h i n d this d i s c r e p a n c y are twofold. First, force sensors are difficult to incorp o r a t e into c o m m e r c i a l l y available r o b o t controllers. A l t h o u g h a vision system is m o r e c o m p l e x t h a n a force sensor, its in.teraction with the r o b o t controller is m a i n l y geometrical. It o n l y influences target coordinates. These d a t a are easily u n d e r s t o o d b y t r a d i t i o n a l controllers p r o v i d e d with suit a b l e digital inputs. F o r c e sensor data, however, influence the d y n a m i c s of the j o i n t servo loops. M o s t available controllers d o n o t allow such low level i n t e r a c t i o n with the robot. Moreover, the i n t e r p r e t a t i o n of force sensor d a t a is m u c h less s t r a i g h t f o r w a r d t h a n the processing of vision data. A second reason can be f o u n d in the force sensor itself. N o r m a l l y , it is a fragile i n s t r u m e n t a n d thus very p r o n e to overloading. M e c h a n i c a l o v e r l o a d p r o t e c t i o n is a must, b u t very difficult to achieve p r o p e r l y . T h e m a i n p u r p o s e of this p a p e r is to p r o v e that force sensors can b e e x t r e m e l y useful even in i n d u s t r i a l environments. This will be d o n e b y highlighting some p r o v e n designs of reliable force sensors, d e v e l o p e d over the years at the M e c h a n i cal Engineering D e p a r t m e n t of K . U . Leuven. F u r ther, the usefulness will be shown b y d e s c r i b i n g s o m e successful c o n t r o l strategies a n d a p p l i c a t i o n examples.
Although several force sensing devices have been developed recently, industrial applications of these devices are rarely found. This is in severe contradiction to the growing success of vision systems. In many application domains however, tactile perception may be as important as vision. This paper discusses the design aspects of multi-degree of freedom force sensors. Some well-proven mechanical concepts developed at K.U. Leuven are presented. Further, the consequences of using force feedback upon the robot control structure will be discussed. Keywords: Force sensing, Robot control
Prof. H. Van Brussel is mechanical engineer (HTI-Oostende, 1965) and electronics engineer (K.U. Leuven, 1968). He received a Ph.D. Degree in applied Sciences in 1971 from K.U. Leuven. From 1971 until 1973 he was ABOS-expert at the Metal Industries Development Center in Bandung, Indonesia and associate professor at ITB, Bandung. In 1973 he became lecturer at K.U. Leuven and is now full professor in automation and Head of the Production Engineering Division. He published some 70 papers on subjects as structural dynamics, chatter vibrations of machine tools, control of drive systems, design, programming and control of robots.
N0rth-Holland Robotics 2 (1986) 139-148 0167-8493/86/$3.50 © 1986, Elsevier Science Pubhshers B.V. (North-Holland)
140 2. Force
H. van Brussel et al. / Force Sensing for Advanced Robot Control Sensor
Design
Principles
With respect to force sensing in robots, force can be measured at different locations. The purpose of using force sensors is always to know the interaction forces at the interface between the robot gripper and the environment. Typical applications are assembly, deburring, contour tracking, etc. The different measuring locations are: - in the joints or the actuators. This method is mainly used in master-slave manipulators. It can only be applied when reversible or direct drives are used. - in the interface between the robot arm and the gripper. This is the application domain of multi-component force-torque wrist sensors, to be discussed in this paper. - in the gripper fingers, mainly by means of strain-gauges applied to the fingers. - in the contact area between the fingers and the grasped object, by means of tactile sensors or so-called artificial skin sensors. - in the robot environment, e.g. in the table or in the mounting fixture. The closer to the object, the more accurate is the measurement. Each of the above levels requires another type of sensor. Reliable tactile sensors are still in their early development stage. Finger sensors are less flexible in use as the fingers are often exchangeable in such a way that interfacing becomes a problem. Providing sensors in the robot environment deteriorates the flexibility of the overall system as it requires a specially instrumented periphery. Therefore, in this paper our z
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attention goes to multi-component force-torque wrist sensors. In general, a six-component sensor is able to measure the interaction force vector, consisting of three force components Fx, Fy, Fz and three torque components M x, My, M s in the sensor reference point with respect to an orthogonal reference frame X Y Z defined in that point. Generally, a force sensor consists of an elastic body deforming under the applied force. Measurement of these elastic deformations by appropriate transducers yields electrical signals from which the force vector components can be derived. Different measuring principles exist, like displacement transducers (LVDT, inductive, capacitive), piezoelectrical crystals, magneto-elastic devices, strain gauges, etc. Strain-gauges have proven to be the smallest, easiest to use, cheapest reliable transducers for use in robot force sensors and are therefore used in the sensors described hereafter. Consider an elastic body (Fig. 1) on which a resultant force vector F( FX Fy Fz M X My M z ) is acting in a predetermined reference point A. On this body, n strain gauge bridges measure n different strain components yielding the measuring signal vector S ( S 1. . . . . S,,). Vectors F and S are related by: S=[AI.F,
(1)
where [A] is the (n × 6) When the signal vector elements, pseudo-inverse used to extract F from contains six components, F= [AI-'-S=
sensor coupling matrix.
contains more than 6 techniques have to be equation (1). When S then:
[BI-S ,
(2)
where [B] = [A]-1 is the decoupling matrix. The quality of a force sensor is reflected by the form of its decoupling matrix. First, when the B-matrix is diagonal, the sensor is mechanically decoupled. This means that every measuring component is proportional to only one force component, or F~=b,S~,
i = 1 . . . . . 6, b i j = O ,
j4=i.
(3)
(For notational reasons the following symbols are further used: Fx = F 1, Fy = F z, Fz = F 3, M x = F4, M y = F 5, M s = F 6 . ) If this is not the case, then each measuring signal contains contributions from each force component: 6
Si = E ai/Fj. j=l
(4)
H. van Brussel et al. / Force Sensing for Advanced Robot Control
Conversely, a force component is composed of contributions from all measuring signals: 6
(5)
F, = E b,jSj. j=l
We want the measuring signals to reach their maximum value Si, when all force components reach their nominal values simultaneously: 6
Si, = E aijFi,.
(6)
j=l
A second condition for the aij parameters stems from the requirement that, for hating the same measuring accuracy on all components, each force component should contribute equally to the measuring signal. Thus: a i l F l n = ai2F2n = . . . = ai6 Frn = 1Sin.
(7)
Conditions (6) and (7) can only be met realistically when the coupling matrix is diagonal. Of course, a perfect diagonal A-matrix can never be obtained in practice. There always remain non-zero off-diagonal elements aig resulting in cross-sensitivity of the sensor. It is expressed in a standardised way by so-called cross-sensitivity coefficients c~j, defined by:
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141
tivities of the measuring circuits in the different directions have to be matched in order to provide equal measuring accuracy and force resolution in all directions.
3.2. Dimension, Weight, Stiffness Miniaturisation is important, especially for use on light assembly robots, but difficult to achieve. In many cases, the sensor-gripper system represents more than 50% of the maximum payload. Therefore, aluminium alloys are widely used as sensor materials. Stiffness requirements, for instance against bending torques from overhanging tools subject to gravity and acceleration forces, mainly determine the diameter-to-height ratio of the sensor, rather than mere sensitivity requirements. There is always a compromise to be found between stiffness and sensitivity. Because of the high sensitivity of strain-gauges, sensors can be built stiff enough so as not to lower too much the natural frequencies, even when the sensor is loaded with a heavy tool. A certain compliance can be favourable however in contouring applications under force control, for avoiding limit cycles, as explained below. But it is preferred to provide this compliance in the tool rather than in the sensor.
3.3. Accuracy (8)
In a further section, some successful mechanically decoupled multi-component force-torque sensors, developed and built at K.U. Leuven, are described together with their signal processing circuitry.
The accuracy of a sensor system is affected by influences like cross-sensitivities, non-linearities, Z
3. Force Sensor Requirements A set of design parameters influences the final layout of a wrist sensor.
3.1. The Force Range The required range of the force components depends of course on the application at hand. Also the tool mass and the peak accelerations determine the maximum occurring forces and torques. Mechanical stops in all measuring directions have to be provided to prevent excessive strains in the sensitive sensor elements. The sensi-
Fig. 2. Six-component force-torque wrist sensor for deburring applications.
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errors in data-processing circuitry, calibration errors, etc. With typical cross-sensivity figures of around 3%, overall worst-case error figures of around 5% can be obtained. This is sufficient for virtually every application of force feedback.
4.Some Realised Sensor Types 4.1. Sensor 1
The nominal force values for this sensor are: N, M~,,=My.=IO0 Nm, M z = 20 Nm. It is intended for deburring applications on a Cincinnati T3-hydraulic robot. It consists of two rigid rings connected by four flexural strips (Fig. 2). The construction is monolithic, obtained by machining a solid block of special Al-alloy, to avoid non-linearities (hysteresis, friction) normally present in bolted joints or glued interfaces. This high-diameter (O 170 mm), small height (60 mm) configuration gives rise to a high resistance to bending torques (except around
Fx.=Fy.=F~.=200 3.4. Resolution
Resolution is difficult to define for analog sensors. Theoretically it is infinitely small. In sensor systems with digital output, it depends of course on the resolution of the AD-convertor. For the sensors to be discussed further, typical figures for the resolution are between 0,2% and 0,1% f.s. Thus for a force range of 200 N, the resolution would be between 0,4 N and 0,2 N.
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H. van Brussel et al. / Force Sensing for Adoanced Robot Control
the Z-axis), but good sensitivity to lateral forces. The total sensor mass is 2 kg. By appropriate connection of six strain-gauge bridges, a mechanically decoupled sensor could be obtained, with a m a x i m u m cross-sensitivity of less than 3%. Force components Fx, Fy and M z are obtained through the measurement of shear strains in the appropriate flexural strips, while M x , M y and F~ are obtained by measuring normal bending and compression strains. Fig. 3 illustrates a typical calibration chart. The main disadvantage of this sensor is its low sensitivity of the F~-component, due to the fact that compression strains are measured for F~. A n alternative is provided in the design of Fig. 4, where the flexures are bended such that bending strains can be measured for obtaining F z, resulting in a higher sensitivity. Experiments with removable bolted flexures (Fig. 4) gave inferior but still valuable results due to hysteresis p h e n o m e n a in the bolted joints.
Fig.
5.
Improved design of six-component force-torque wrist
sensor.
made mechanically decoupled by appropriately locating the strain-gauge bridges. A similar sensor was built for use as a 6D-joy-
4.2. Sensor 2
The sensor consists of a central square block with four cantilevered radial spokes with square cross-section. The outer ends of the spokes are freely supported by means of thin flexures, dimensioned in such a way as to simulate a ball-hinge behaviour (Fig. 5). This configuration allows similar sensitivities for the three force-components and for the three torques. A CAD-program has been developed, which, given the force and torque ranges and the m a x i m u m overall sensor diameter, yields all dimensions of the critical sensor elements (spokes and flexures). Table 1 gives the cross-sensitivity matrix for this sensor. The lowest natural frequency without external load on the sensor was 296 Hz. Stiffness of the order of 6000 N / m m and 500 N m / d e g was obtained. The sensor has been
Fig. 6. Use of force-torque sensor as teaching aid.
Table 1. Cross-sensitivity matrix for sensor 2.
-
1.0000 0.0219 0.0029 0.0006 0.0019 0.0053
0.0012 1.0000 - 0.0098 0.0031 - 0.0035 - 0.0079
0.0052 0.0026 1.0000 0.0014 - 0.0070 - 0.0036
0.0162 - 0.0143 0.0111 1.0000 0.0177 0.0006
0.0038 - 0.0557 - 0.0078 - 0.0190 1.0000 - 0.0074
0.0136 - 0.0062 0.0153 - 0.0013 0.0040 1.0000
145
H. van Brussel et al. / Force Sensing for Advanced Robot Control
SENSOR
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Fig. 7. Signal processing scheme for multi-component force-torque sensors.
stick for teaching purposes (Fig. 6). The ranges are 20 N for the forces and 1 N m for the torques. It is built into a ball-shaped handle fitting in the palm of the hand. By exerting forces and torques one can, by using specially developed software, generate displacements of the robot in the corresponding directions of a predefined coordinate system (e.g. a predefined task frame).
4.3. Signal Processing Circuitry Because the sensor coupling matrices are diagonal, no subsequent arithmetic processing is required to separate the force component signals. Fig. 7 illustrates the adopted signal processing scheme. The strain gauge bridges are excited by a o c voltage source. Instrumentation amplifiers built
into the sensor increase the level of the bridge output signals before transmission to the controller where the rest of the circuitry is located. The amplified bridge output signals are multiplexed and via a sample/hold amplifier converted into 12 bit digital words. Consequently these six digital words are stored in a 6 × 12 bit ~ l - m e m ory, which can be read at any moment by the control computer. The forces are measured at a sampling frequency of 20 kHz, which implies a total acquisition time for the complete force vector of 300 #s. In this way, a real snap-shot of the force at a given moment is obtained. The robot controller only reads the information every 5 ms. A detailed error analysis revealed an overall error of 0.3% in the signal processing circuitry, including long-term drift phenomena.
H. van Brussel et aL / Force Sensing for Advanced Robot Control
146
Xd FORCE CONTROLLER
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thus avoiding more severe requirements on the positioning accuracy of the robot and the peripheral equipment. In [1] a survey is given of the force control concepts that can be used for both types of problems. It turns out that for the application of force feedback using off-the-shelf robots, force loop closure around the existing robot position loop is the most straightforward method to apply. The problem with practical applications of force controlled robots is that positions as well as forces have to be controlled simultaneously. In a deburring operation, for instance, the velocity tangential to the surface has to be controlled as well as the contact force perpendicular to the surface. In the force loop around position loop approach, force errors are transformed into position commands,
5. Force Control C o n c e p t s
Force feedback applications can be divided into two types: - Applications whereby the contact force is an essential part of the process itself (grinding, polishing, deburring, et.). Both the position of the end effector and the force exerted by the end effector on the environment have to be controlled simultaneously. - Applications whereby the contact forces can be used as a source of information on the actual position of the endpoint (gripper) of the robot relative to the environment. Most operations during the assembly process belong to this category. Force feedback offers an important means to enlarge the allowed region of uncertainty,
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H. van Brussel et al. / Force Sensing f o r A d v a n c e d Robot Control
such that the robot essentially remains a position controlled device. A typical robot axis in contact with the e n vironment can be modeled as in Fig. 8. The interaction with the environment is modeled by a contact stiffness K o being the parallel connection of the sensor stiffness K s and the stiffness K e of the environment. The position controller normally consists of a high bandwidth (digital) P(I)D-controller; the force controller is a PI-controller, the gain of which is inversely proportional with the contact stiffness g o•
Two factors, the contact stiffness K o and the finite resolution of the position encoder influence the behaviour of this control system. The behaviour of the original positioning system is not influenced very much by changing K o for positioning in contact with the environment when compared with positioning in free space. However, in applications where a constant contact force is to be maintained, too high contact stiffness K o
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147
leads to unstable behaviour. On the other hand, the response of the force control loop becomes slower with lower Ko-values. The finite encoder resolution leads to fluctuations in the contact force as shown in Fig. 9. These force fluctuations will be smaller for lower contact stiffness and for finer encoder resolutions. The influence of the sensor dynamics on the stability of the force feedback system is negligible when the lowest natural frequency of the combination sensor-tool remains well above the "force feedback loop bandwidth. The above conclusions, made for a single robot axis, remain valid for a multi-degree of freedom robot, provided that the different degrees of freedom can be considered uncoupled and that their dynamic behaviour is almost identical. Identification experiments on existing robots, even of the anthropomorphic type, have shown that these assumptions are not so unrealistic as they might seem. Consider, as an illustration, a task consisting of
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H. van Brussel et al. / Force Sensing for Advanced Robot Control
148
tracking a plane contour with a constant tangential velocity o2, and a constant perpendicular contact force (Fig. 10). A task frame X t is chosen so that the contact force to be controlled always points along the xu-axis. The contact force is measured in a sensor frame X s, which is easily transformed to this task frame with transformation Ts,. A one-axis force controller with control law R t c a n be defined in this task frame along the x~,-axis, relating the desired position correction Axl, needed to correct for the force error AFar:
ax,,=R,. AF,
(9)
This xl, has to be transformed into desired position corrections Aqa in robot coordinates with the general relation: Aqa= [ j ] - i
.Ax,,
(10)
where [J] is the Jacobian relating position corrections in task and robot coordinates. Input of Aqa to the robot position controller results in actually obtained position corrections zIG: aqo = [ G ] - a q a.
(11)
Provided the system is uncoupled, the transfer function matrix [G] of the positioning system is diagonal. The resulting position corrections Ax,o in task coordinates are: A x , o = [ J ] .Aqo.
(12)
This gives rise to a contact force change A F t in task coordinates:
aF,=[Kl.ax,o,
(13)
where [K] is the stiffness matrix in task coordinates. Because there is in this example only one force component in the task frame, along the x~-axis, combinaton of the above relations results in: AFar = GO• K ° • A x , , ,
(14)
where GO is the transfer function of the position loop for one axis and K o the contact stiffness along xl,.
It is thus possible to realize force feedback in an arbitrary direction by means of one single force controller defined in the task frame. A generalised theory of compliant motion has been developed at K.U. Leuven [2] and will be published soon. It provides a general methodology for programming and control of tasks involving contact with the environment. With this method, successful applications of force control for deburring, 3D-contour tracking, assembly, palletizing, opening and closing a door, etc. have been worked out and demonstrated. A video film illustrating the method in the applications mentioned and using the above described sensors has been produced.
6. Conclusion Force sensors are valuable aids for enhancing the autonomy of robots in industrial environments. Their design and manufacture requires however considerable skill and expertise. Successful application further requires special control strategies. The most viable control method for use with off-the-shelf robots is the closure of the force loops around the existing positioning loops.
Acknowledgements This study was partly undertaken in the framework of an R and D-program in Robotics sponsored by IWONL (Institute for the Promotion of Scientific Research in Industry and Agriculture) and a consortium of Belgian companies.
References [1] Simons, J. and Van Brussel, H. (1985) "Force control schemes for robot assembly", in Robotic Assembly (Ed.: Prof. K. Rathmili), IFS-SpringerVerlag, pp. 253-265. [2] De Schutter, J. (1985) "'Programmingand control of compliant motion". Ph. D. Thesis, K.U. Leuven.
Force Sensing for Advanced Robot Control P r o f . H . V a n B r u s s e l , Ir. H . B e l i e n a n d Ir. H . T h i e l e m a n s
1. Introduction
Katholieke Unioersiteit Leuoen, Mechanical Engineering Department, Celestijnenlaan 300 B, B.3030 Leuven, Belgium
I n the e n d e a v o u r to i n t r o d u c e real flexibility i n t o the b e h a v i o u r o f i n d u s t r i a l robots, the conc e p t of force f e e d b a c k is n o w generally recognized to b e essential. In the recent past, several research a n d industrial l a b o r a t o r i e s have been s u p p o r t i n g this s t a t e m e n t b y designing a p p r o p r i a t e force sensors a n d force f e e d b a c k strategies. Nevertheless, t o d a y ' s reality reveals that ind u s t r i a l a p p l i c a t i o n s involving force f e e d b a c k are rare. This is in sharp c o n t r a s t with the growing p e n e t r a t i o n of vision systems. T h e m a i n reasons b e h i n d this d i s c r e p a n c y are twofold. First, force sensors are difficult to incorp o r a t e into c o m m e r c i a l l y available r o b o t controllers. A l t h o u g h a vision system is m o r e c o m p l e x t h a n a force sensor, its in.teraction with the r o b o t controller is m a i n l y geometrical. It o n l y influences target coordinates. These d a t a are easily u n d e r s t o o d b y t r a d i t i o n a l controllers p r o v i d e d with suit a b l e digital inputs. F o r c e sensor data, however, influence the d y n a m i c s of the j o i n t servo loops. M o s t available controllers d o n o t allow such low level i n t e r a c t i o n with the robot. Moreover, the i n t e r p r e t a t i o n of force sensor d a t a is m u c h less s t r a i g h t f o r w a r d t h a n the processing of vision data. A second reason can be f o u n d in the force sensor itself. N o r m a l l y , it is a fragile i n s t r u m e n t a n d thus very p r o n e to overloading. M e c h a n i c a l o v e r l o a d p r o t e c t i o n is a must, b u t very difficult to achieve p r o p e r l y . T h e m a i n p u r p o s e of this p a p e r is to p r o v e that force sensors can b e e x t r e m e l y useful even in i n d u s t r i a l environments. This will be d o n e b y highlighting some p r o v e n designs of reliable force sensors, d e v e l o p e d over the years at the M e c h a n i cal Engineering D e p a r t m e n t of K . U . Leuven. F u r ther, the usefulness will be shown b y d e s c r i b i n g s o m e successful c o n t r o l strategies a n d a p p l i c a t i o n examples.
Although several force sensing devices have been developed recently, industrial applications of these devices are rarely found. This is in severe contradiction to the growing success of vision systems. In many application domains however, tactile perception may be as important as vision. This paper discusses the design aspects of multi-degree of freedom force sensors. Some well-proven mechanical concepts developed at K.U. Leuven are presented. Further, the consequences of using force feedback upon the robot control structure will be discussed. Keywords: Force sensing, Robot control
Prof. H. Van Brussel is mechanical engineer (HTI-Oostende, 1965) and electronics engineer (K.U. Leuven, 1968). He received a Ph.D. Degree in applied Sciences in 1971 from K.U. Leuven. From 1971 until 1973 he was ABOS-expert at the Metal Industries Development Center in Bandung, Indonesia and associate professor at ITB, Bandung. In 1973 he became lecturer at K.U. Leuven and is now full professor in automation and Head of the Production Engineering Division. He published some 70 papers on subjects as structural dynamics, chatter vibrations of machine tools, control of drive systems, design, programming and control of robots.
N0rth-Holland Robotics 2 (1986) 139-148 0167-8493/86/$3.50 © 1986, Elsevier Science Pubhshers B.V. (North-Holland)
140 2. Force
H. van Brussel et al. / Force Sensing for Advanced Robot Control Sensor
Design
Principles
With respect to force sensing in robots, force can be measured at different locations. The purpose of using force sensors is always to know the interaction forces at the interface between the robot gripper and the environment. Typical applications are assembly, deburring, contour tracking, etc. The different measuring locations are: - in the joints or the actuators. This method is mainly used in master-slave manipulators. It can only be applied when reversible or direct drives are used. - in the interface between the robot arm and the gripper. This is the application domain of multi-component force-torque wrist sensors, to be discussed in this paper. - in the gripper fingers, mainly by means of strain-gauges applied to the fingers. - in the contact area between the fingers and the grasped object, by means of tactile sensors or so-called artificial skin sensors. - in the robot environment, e.g. in the table or in the mounting fixture. The closer to the object, the more accurate is the measurement. Each of the above levels requires another type of sensor. Reliable tactile sensors are still in their early development stage. Finger sensors are less flexible in use as the fingers are often exchangeable in such a way that interfacing becomes a problem. Providing sensors in the robot environment deteriorates the flexibility of the overall system as it requires a specially instrumented periphery. Therefore, in this paper our z
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attention goes to multi-component force-torque wrist sensors. In general, a six-component sensor is able to measure the interaction force vector, consisting of three force components Fx, Fy, Fz and three torque components M x, My, M s in the sensor reference point with respect to an orthogonal reference frame X Y Z defined in that point. Generally, a force sensor consists of an elastic body deforming under the applied force. Measurement of these elastic deformations by appropriate transducers yields electrical signals from which the force vector components can be derived. Different measuring principles exist, like displacement transducers (LVDT, inductive, capacitive), piezoelectrical crystals, magneto-elastic devices, strain gauges, etc. Strain-gauges have proven to be the smallest, easiest to use, cheapest reliable transducers for use in robot force sensors and are therefore used in the sensors described hereafter. Consider an elastic body (Fig. 1) on which a resultant force vector F( FX Fy Fz M X My M z ) is acting in a predetermined reference point A. On this body, n strain gauge bridges measure n different strain components yielding the measuring signal vector S ( S 1. . . . . S,,). Vectors F and S are related by: S=[AI.F,
(1)
where [A] is the (n × 6) When the signal vector elements, pseudo-inverse used to extract F from contains six components, F= [AI-'-S=
sensor coupling matrix.
contains more than 6 techniques have to be equation (1). When S then:
[BI-S ,
(2)
where [B] = [A]-1 is the decoupling matrix. The quality of a force sensor is reflected by the form of its decoupling matrix. First, when the B-matrix is diagonal, the sensor is mechanically decoupled. This means that every measuring component is proportional to only one force component, or F~=b,S~,
i = 1 . . . . . 6, b i j = O ,
j4=i.
(3)
(For notational reasons the following symbols are further used: Fx = F 1, Fy = F z, Fz = F 3, M x = F4, M y = F 5, M s = F 6 . ) If this is not the case, then each measuring signal contains contributions from each force component: 6
Si = E ai/Fj. j=l
(4)
H. van Brussel et al. / Force Sensing for Advanced Robot Control
Conversely, a force component is composed of contributions from all measuring signals: 6
(5)
F, = E b,jSj. j=l
We want the measuring signals to reach their maximum value Si, when all force components reach their nominal values simultaneously: 6
Si, = E aijFi,.
(6)
j=l
A second condition for the aij parameters stems from the requirement that, for hating the same measuring accuracy on all components, each force component should contribute equally to the measuring signal. Thus: a i l F l n = ai2F2n = . . . = ai6 Frn = 1Sin.
(7)
Conditions (6) and (7) can only be met realistically when the coupling matrix is diagonal. Of course, a perfect diagonal A-matrix can never be obtained in practice. There always remain non-zero off-diagonal elements aig resulting in cross-sensitivity of the sensor. It is expressed in a standardised way by so-called cross-sensitivity coefficients c~j, defined by:
s, raijFgn Sin j=lZ~
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Fj
6
Fj
" FJ n = j=xE c i j ~jn "
141
tivities of the measuring circuits in the different directions have to be matched in order to provide equal measuring accuracy and force resolution in all directions.
3.2. Dimension, Weight, Stiffness Miniaturisation is important, especially for use on light assembly robots, but difficult to achieve. In many cases, the sensor-gripper system represents more than 50% of the maximum payload. Therefore, aluminium alloys are widely used as sensor materials. Stiffness requirements, for instance against bending torques from overhanging tools subject to gravity and acceleration forces, mainly determine the diameter-to-height ratio of the sensor, rather than mere sensitivity requirements. There is always a compromise to be found between stiffness and sensitivity. Because of the high sensitivity of strain-gauges, sensors can be built stiff enough so as not to lower too much the natural frequencies, even when the sensor is loaded with a heavy tool. A certain compliance can be favourable however in contouring applications under force control, for avoiding limit cycles, as explained below. But it is preferred to provide this compliance in the tool rather than in the sensor.
3.3. Accuracy (8)
In a further section, some successful mechanically decoupled multi-component force-torque sensors, developed and built at K.U. Leuven, are described together with their signal processing circuitry.
The accuracy of a sensor system is affected by influences like cross-sensitivities, non-linearities, Z
3. Force Sensor Requirements A set of design parameters influences the final layout of a wrist sensor.
3.1. The Force Range The required range of the force components depends of course on the application at hand. Also the tool mass and the peak accelerations determine the maximum occurring forces and torques. Mechanical stops in all measuring directions have to be provided to prevent excessive strains in the sensitive sensor elements. The sensi-
Fig. 2. Six-component force-torque wrist sensor for deburring applications.
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errors in data-processing circuitry, calibration errors, etc. With typical cross-sensivity figures of around 3%, overall worst-case error figures of around 5% can be obtained. This is sufficient for virtually every application of force feedback.
4.Some Realised Sensor Types 4.1. Sensor 1
The nominal force values for this sensor are: N, M~,,=My.=IO0 Nm, M z = 20 Nm. It is intended for deburring applications on a Cincinnati T3-hydraulic robot. It consists of two rigid rings connected by four flexural strips (Fig. 2). The construction is monolithic, obtained by machining a solid block of special Al-alloy, to avoid non-linearities (hysteresis, friction) normally present in bolted joints or glued interfaces. This high-diameter (O 170 mm), small height (60 mm) configuration gives rise to a high resistance to bending torques (except around
Fx.=Fy.=F~.=200 3.4. Resolution
Resolution is difficult to define for analog sensors. Theoretically it is infinitely small. In sensor systems with digital output, it depends of course on the resolution of the AD-convertor. For the sensors to be discussed further, typical figures for the resolution are between 0,2% and 0,1% f.s. Thus for a force range of 200 N, the resolution would be between 0,4 N and 0,2 N.
Bj__ _.
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Fig. 4. Alternativesensor with bended flexuresand bolted joints.
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144
H. van Brussel et al. / Force Sensing for Adoanced Robot Control
the Z-axis), but good sensitivity to lateral forces. The total sensor mass is 2 kg. By appropriate connection of six strain-gauge bridges, a mechanically decoupled sensor could be obtained, with a m a x i m u m cross-sensitivity of less than 3%. Force components Fx, Fy and M z are obtained through the measurement of shear strains in the appropriate flexural strips, while M x , M y and F~ are obtained by measuring normal bending and compression strains. Fig. 3 illustrates a typical calibration chart. The main disadvantage of this sensor is its low sensitivity of the F~-component, due to the fact that compression strains are measured for F~. A n alternative is provided in the design of Fig. 4, where the flexures are bended such that bending strains can be measured for obtaining F z, resulting in a higher sensitivity. Experiments with removable bolted flexures (Fig. 4) gave inferior but still valuable results due to hysteresis p h e n o m e n a in the bolted joints.
Fig.
5.
Improved design of six-component force-torque wrist
sensor.
made mechanically decoupled by appropriately locating the strain-gauge bridges. A similar sensor was built for use as a 6D-joy-
4.2. Sensor 2
The sensor consists of a central square block with four cantilevered radial spokes with square cross-section. The outer ends of the spokes are freely supported by means of thin flexures, dimensioned in such a way as to simulate a ball-hinge behaviour (Fig. 5). This configuration allows similar sensitivities for the three force-components and for the three torques. A CAD-program has been developed, which, given the force and torque ranges and the m a x i m u m overall sensor diameter, yields all dimensions of the critical sensor elements (spokes and flexures). Table 1 gives the cross-sensitivity matrix for this sensor. The lowest natural frequency without external load on the sensor was 296 Hz. Stiffness of the order of 6000 N / m m and 500 N m / d e g was obtained. The sensor has been
Fig. 6. Use of force-torque sensor as teaching aid.
Table 1. Cross-sensitivity matrix for sensor 2.
-
1.0000 0.0219 0.0029 0.0006 0.0019 0.0053
0.0012 1.0000 - 0.0098 0.0031 - 0.0035 - 0.0079
0.0052 0.0026 1.0000 0.0014 - 0.0070 - 0.0036
0.0162 - 0.0143 0.0111 1.0000 0.0177 0.0006
0.0038 - 0.0557 - 0.0078 - 0.0190 1.0000 - 0.0074
0.0136 - 0.0062 0.0153 - 0.0013 0.0040 1.0000
145
H. van Brussel et al. / Force Sensing for Advanced Robot Control
SENSOR
CONTROLLER +I5V OV -15V
12 BIT OUTPUT
/C)ORESS SELECT
READ READY RESET
5V I N
Fig. 7. Signal processing scheme for multi-component force-torque sensors.
stick for teaching purposes (Fig. 6). The ranges are 20 N for the forces and 1 N m for the torques. It is built into a ball-shaped handle fitting in the palm of the hand. By exerting forces and torques one can, by using specially developed software, generate displacements of the robot in the corresponding directions of a predefined coordinate system (e.g. a predefined task frame).
4.3. Signal Processing Circuitry Because the sensor coupling matrices are diagonal, no subsequent arithmetic processing is required to separate the force component signals. Fig. 7 illustrates the adopted signal processing scheme. The strain gauge bridges are excited by a o c voltage source. Instrumentation amplifiers built
into the sensor increase the level of the bridge output signals before transmission to the controller where the rest of the circuitry is located. The amplified bridge output signals are multiplexed and via a sample/hold amplifier converted into 12 bit digital words. Consequently these six digital words are stored in a 6 × 12 bit ~ l - m e m ory, which can be read at any moment by the control computer. The forces are measured at a sampling frequency of 20 kHz, which implies a total acquisition time for the complete force vector of 300 #s. In this way, a real snap-shot of the force at a given moment is obtained. The robot controller only reads the information every 5 ms. A detailed error analysis revealed an overall error of 0.3% in the signal processing circuitry, including long-term drift phenomena.
H. van Brussel et aL / Force Sensing for Advanced Robot Control
146
Xd FORCE CONTROLLER
POSITION CONTROLLER
J
ENVIRONMENT ~ I IsTIFFNESS K o
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IPosIrloNi ! I ENcODER I
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FILTER Fig. 8. Force control scheme for one robot axis.
thus avoiding more severe requirements on the positioning accuracy of the robot and the peripheral equipment. In [1] a survey is given of the force control concepts that can be used for both types of problems. It turns out that for the application of force feedback using off-the-shelf robots, force loop closure around the existing robot position loop is the most straightforward method to apply. The problem with practical applications of force controlled robots is that positions as well as forces have to be controlled simultaneously. In a deburring operation, for instance, the velocity tangential to the surface has to be controlled as well as the contact force perpendicular to the surface. In the force loop around position loop approach, force errors are transformed into position commands,
5. Force Control C o n c e p t s
Force feedback applications can be divided into two types: - Applications whereby the contact force is an essential part of the process itself (grinding, polishing, deburring, et.). Both the position of the end effector and the force exerted by the end effector on the environment have to be controlled simultaneously. - Applications whereby the contact forces can be used as a source of information on the actual position of the endpoint (gripper) of the robot relative to the environment. Most operations during the assembly process belong to this category. Force feedback offers an important means to enlarge the allowed region of uncertainty,
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H. van Brussel et al. / Force Sensing f o r A d v a n c e d Robot Control
such that the robot essentially remains a position controlled device. A typical robot axis in contact with the e n vironment can be modeled as in Fig. 8. The interaction with the environment is modeled by a contact stiffness K o being the parallel connection of the sensor stiffness K s and the stiffness K e of the environment. The position controller normally consists of a high bandwidth (digital) P(I)D-controller; the force controller is a PI-controller, the gain of which is inversely proportional with the contact stiffness g o•
Two factors, the contact stiffness K o and the finite resolution of the position encoder influence the behaviour of this control system. The behaviour of the original positioning system is not influenced very much by changing K o for positioning in contact with the environment when compared with positioning in free space. However, in applications where a constant contact force is to be maintained, too high contact stiffness K o
'~or"ce
147
leads to unstable behaviour. On the other hand, the response of the force control loop becomes slower with lower Ko-values. The finite encoder resolution leads to fluctuations in the contact force as shown in Fig. 9. These force fluctuations will be smaller for lower contact stiffness and for finer encoder resolutions. The influence of the sensor dynamics on the stability of the force feedback system is negligible when the lowest natural frequency of the combination sensor-tool remains well above the "force feedback loop bandwidth. The above conclusions, made for a single robot axis, remain valid for a multi-degree of freedom robot, provided that the different degrees of freedom can be considered uncoupled and that their dynamic behaviour is almost identical. Identification experiments on existing robots, even of the anthropomorphic type, have shown that these assumptions are not so unrealistic as they might seem. Consider, as an illustration, a task consisting of
Sensor',
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(3 Q Fig. 10. Force control scheme for multi-dimensional case with force controller specified in task coordinates.
H. van Brussel et al. / Force Sensing for Advanced Robot Control
148
tracking a plane contour with a constant tangential velocity o2, and a constant perpendicular contact force (Fig. 10). A task frame X t is chosen so that the contact force to be controlled always points along the xu-axis. The contact force is measured in a sensor frame X s, which is easily transformed to this task frame with transformation Ts,. A one-axis force controller with control law R t c a n be defined in this task frame along the x~,-axis, relating the desired position correction Axl, needed to correct for the force error AFar:
ax,,=R,. AF,
(9)
This xl, has to be transformed into desired position corrections Aqa in robot coordinates with the general relation: Aqa= [ j ] - i
.Ax,,
(10)
where [J] is the Jacobian relating position corrections in task and robot coordinates. Input of Aqa to the robot position controller results in actually obtained position corrections zIG: aqo = [ G ] - a q a.
(11)
Provided the system is uncoupled, the transfer function matrix [G] of the positioning system is diagonal. The resulting position corrections Ax,o in task coordinates are: A x , o = [ J ] .Aqo.
(12)
This gives rise to a contact force change A F t in task coordinates:
aF,=[Kl.ax,o,
(13)
where [K] is the stiffness matrix in task coordinates. Because there is in this example only one force component in the task frame, along the x~-axis, combinaton of the above relations results in: AFar = GO• K ° • A x , , ,
(14)
where GO is the transfer function of the position loop for one axis and K o the contact stiffness along xl,.
It is thus possible to realize force feedback in an arbitrary direction by means of one single force controller defined in the task frame. A generalised theory of compliant motion has been developed at K.U. Leuven [2] and will be published soon. It provides a general methodology for programming and control of tasks involving contact with the environment. With this method, successful applications of force control for deburring, 3D-contour tracking, assembly, palletizing, opening and closing a door, etc. have been worked out and demonstrated. A video film illustrating the method in the applications mentioned and using the above described sensors has been produced.
6. Conclusion Force sensors are valuable aids for enhancing the autonomy of robots in industrial environments. Their design and manufacture requires however considerable skill and expertise. Successful application further requires special control strategies. The most viable control method for use with off-the-shelf robots is the closure of the force loops around the existing positioning loops.
Acknowledgements This study was partly undertaken in the framework of an R and D-program in Robotics sponsored by IWONL (Institute for the Promotion of Scientific Research in Industry and Agriculture) and a consortium of Belgian companies.
References [1] Simons, J. and Van Brussel, H. (1985) "Force control schemes for robot assembly", in Robotic Assembly (Ed.: Prof. K. Rathmili), IFS-SpringerVerlag, pp. 253-265. [2] De Schutter, J. (1985) "'Programmingand control of compliant motion". Ph. D. Thesis, K.U. Leuven.