- Email: [email protected]
Obstacle Avoidance Using Tactile Sensing for an Autonomous Mobile Robot
eopyrigth e IFAC Motion Control for Intelligent AUlOmalion Perugia. Italy. October 27 ·29. 1992
OBSTACLE AVOIDANCE USING TACTILE SENSING FOR AN AUTONOMOUS MOBILE ROBOT E. BADREDDlN ETH Swiss Federal Institute of Tcchnology Zurich Physicstrasse 3, ETH-Zcntrum / ETL I 29, CH 8092 Zurich, Switzerland Abstract. A tactile sensor-ring is built around an autonomous mobile robot to measure the force and torque acting on the robots body. The computed force/torque are then used to aid the colJjsion avoidance behaviour. This behaviour can be described as follows: Push the obstacles away if it is light enough. Repel-away from the obstacle if it acts aggressively such that the force felt by th e robot exceeds a given threshold . Finally, if the obstacle is neither movable nor aggressive , round-about it when a prescribed time has elapsed . The implementation of this strategy is described and experiments are documented which demonstrate the fruitfulness of this design. Keywords. Tactile sensing, Collision-avoidance, Mobile robots.
INTRODUCTION RAMSIS has been built at our laboratory for research purposes. One research topic is to verify a behaviourbased control structure, called the Recursive Nested Behaviour Control (RN BC) (fig. 1). A repertoire of
"0 '"
.'
.. .
EnCOde,. . lTadlo
Fig. 1. The control structure of RAMSIS behaviors are so nested such that reflexive ones occupy the inner levels overlaid by the intellectual be-
haviors in the outer levels. Th e RNBC possesses several desirable properties for autonomous robots, such as recursiveness, robustness and distributed modeling (Badreddin 1991a), (Badreddin 1991b). The collision avoidance behaviour overlays the level which implements the robot-velocity control. This means that the robot is seen from the collision-avoidance level as a velocity-servo . Therefore , collision-avoidance is realized as a reflexive behaviour which can deal with both moving and reflexive obstacles in real-time without the need for a detailed model of the environment or the obstacle. To fulfil! these requirements, a new approach has been taken to implement an adaptive potential-field about the robot itself in contrast to the conventional approach where it is built about the obstacles (Badreddin and Holenstein 1991). Significant performance improvement and cut in the implementation complexity has been, thus, achieved . Ultrasonic sensors are employed for this purpose. Some obstacles, however, may remain undetected by these sensors, e.g. slim obstacles may leak-through the ultrasonic shield . Further, their close-in performance is hampered by the limited resolution in both range and angle. In addition, tactile sensors being passive, have an inherent ad vantage over active ultrasonic sensors concerning its interference-free operation . For these reasons as well as for increased reliability and safety, tactile sensing can be advantageous especially to complement longer range sensors. In this paper we briefly describe the construction of a compliant tactile sensor-ring. Its application in avoiding obstacles is discussed in more details. The tactile obstacle-avoidance behaviour is tailored such that an obstacle is chased-away, repelledfrom or rounded-about according to the force it exerts on the robot body. Implementation details as well as experiments using the actual robot are also discussed.
325
8ADREDDIl\' E.
2
PROBLEM FORMULATION
Consider a cylindrical robot with two driven unsteerable wheels mounted on a platform. In addition, a driven turret rotating about the vertical axis of this platform provides a third degree of freedom (fig. 3). The initial position and wheel-orientation of the robot with respect to the inertial frame can be taken equal to zero without 1055 of generality. A force, F, is exerted by an obstacle, 0, on a point, P, on the robots circumference, at a distance Po and direction 0'0 (fig. 2). The force, F, acting on the robot can be decomposed into its Cartesian components, Fz and F y , at P, or at the robots origin together with a torque M •. The robot has two control inputs U y and U.p. Find a feedback control such that the robot: a) remains stationary if IFI = 0 (no contact) or IFI = Fo (constant force) c) chases 0 away, if 0 < IFI < Fo b) repels from 0 to escape the force if Fo < IFI <
Fmaz
d) rounds-about the obstacle 0 if (IFI ;::: Fma:z v(IFI = Fo /\ Y = 0 /\ t ;::: T» , i.e., y and a are such that P moves on the boundary of O. P does not have to slide along the boundary of 0 all the time, but may, instead, bounce on the boundary. 0 < Fo < Fmaz and T are prescribed force and time thresholds respectively. Case d) is obviously required to avoid endlessly sticking to an obstacle. Please notice that switching back from case d) has to be controlled from higher level commands.
Fig. 3. Robot with a compliant tactile sensor ring
tion accuracy is not a prerequisite for this behaviour. A light-weight, stiff ring made of carbon fiber is suspended around the robots turret by means of twelve circularly-shaped spring sheets (fig. 3) . This suspension allows for three degrees of freedom . When a force is applied to the ring, the displacement from the initial position can be measured by means of four linearstroke sensors. Although three sensors would have been enough, four were mounted for construction reasons and to avoid the, time-consuming, computat.ion of trigonometric functions. From fig. 4 it can be read-
}llIIF----Fx
Fig. 2. Force/torque configuration
3
SOLUTION APPROACH
Our solut.ion approach covers the questions of force/torque measurements, of kinematic modeling and of designing a feedback controller. x
3.1
Force/Torque Measurement Fig. 4. Compliant force/torque mea.surement
Principally, one can choose between force/torque measurement with and without compliance. Compliant force measurement is advantageous in our case due to the large mass and inertia of the robot and since posi-
ily seen that the displacement in the Cartesian and rotational directions respe<:tivcl), can be written in
326
OBSTACLE A VOIDA~a; USING TACTII.E SE~SI'G FOR
3.3
terms of the chlUlges in the linear-sensor readings as: ~x, ..
c,
:::::
~!I' .. cI
:::::
~tP, ..c'
:::::
~12
~14
-
F"
M.
= = =
2 ~IJ
+ ~12 + ~13 + ~14 This results in the closed-loop system
4Po
C%~XIQCI
C.;~tPltJCI
Let us assume that the effect of the torque M z is almost nulled-out by a proportional command to the turret. As a consequent, the change in the angle-ofattack of the force F can be assumed small enough to be neglected and the turret control will be dropped from the following treatment. Now, let the polar displacement be p at an angle a :::= ao (fig . 5). The kine-
./
.--------- "-
.......
/
y
/
-kppcos n
a
-kaa + -kpsin
Q
""-\
\
\
I I
-kpp
a
-(ka - kp)a
Case b): For the case b) in which the obstacle is to be chasedaway, one is interested in another equilibrium point for some p = po f:. 0 and a = O. This can principally be done by shifting the feedback control-line of p to give U y = 0 at p = Po. Below this value, a control is required which drives the system to the new equilibrium. A combination of the feedback control characteristics required for the cases a), b) and c) would then look like fig. 6. Thereby, et may lie in the interval ±f and p < 0 is, therefore, possible. The non-linear
\
/
P
Cases a) and c) : It can be immediately seen that the origin p = a = o is asymptotically stable for k,. > 0 and ka > O. In other words. this stabilizing linear, static feedback brings the displacement from the origill to zero and, therefore, solves the cases a) and c) of the problem formulation.
Simplified Kinematic Model
./
p
The linearized system about tile origin is written as:
C,,~!I'QCI
where C z , c", and C.; are the spring coefficients in x, y, IUId tP respectively.
3.2
Feedback Control
~13
-
Hence, the tactile force and torques are:
F.
MOBlU; ROBOT
Now, consider the feedback law,
2 ~ll
A~ Al~ro~OMOLS
)
\
I
\
t:y
/
\
\
/
"-
I
"-
"- "-
./
/
/
a
....... ----"""
Fig. 5. Displacement due to compliance (exaggerated )
Fig. 6. Feedback control:
matic equations in the robot frame-of-reference can be written as:
characteristic of the ii-gai n can be appnhi lIJaled by, e.g.,
[~ ]=[ where a - arctan (
-cosa sin
kp
Q
i>
=f: ) and p --- (F
z
sin a
=1-
lin~ar
-i~
ke -;;r, k
>
in a, nOli-linear in
p
0,0' E R
case cl): This case is different from the others in t hat wc have to find a. force equilibrium point. in the x-direction instead of the direction of motion (fig. 7). We therefore propose a procedure that first rotates the robot abou t f and then tries to hold a. constant force Fr against the obstacle whilst moving along its boundary. The algorithm is:
+ F)I cos a)
with the coefficients of proportionality depending on the inverse spring stiffness in both Cartesian directions. The derivation is omitted here for space reasons and can be found in (Badreddin and Mansour 1993). The kinema.tic of the wheel-axis orientation with respect to the inertial frame are irrelevant in this treatment a.nd is, therefore, omitted.
while in case d) do measure F" and Fy
327
BADREDD/7\ E.
found that this leads, when using gains bigger than one, to unacceptable oscillations about the pitch-axis, if the controller is purely kinematically defined. A way out of this is to stabilize the tactile loop by a LAG-controller. For this, we have used the following transfer function:
yes) Ys(s) [TI/(s) yes)
=
S2
26s + 260 + 4s + 260
A LAG-controller that guarantees a ramp error of less than 0.1, a maximum overshoot of 30%, and a minimum raising time of 0.5sec is:
Fig. 7. RAMSIS moving along a wall
F = arctan ~ 6.F. = F.REF -
10 s(s + 10)
R(s)
6.t/J
= 10 1 + 3.33s 1 + 13.3s
Fr
if 16.~1 > ",or, Uy = 0 U,p = U4>O.~i9n(6.t/J) else U,p = k l 6.q, - k 2 6.F", U Y = (1 - q,maE 1A4>1)(1 - ~)U 0 Fmar Y end if F = 0, (no contact) Uy 0.5Uyo U,p = 0.5U4>O end
=
end Since we make 110 assumption about the obstacle shape, it is possible that the robot looses contact (F = 0) or has to make a full-stop (/6.
Fig. 8. RAMSIS in front of an obstacle
5 4
IMPLEMENTATION
A detailed description of the underlying implementation structure is found in (Holenstein 1991). RAMSIS has a peak velocity of 1..!!'.- . The rotation speed of the turret and the wheel ;l~tform is limited to 150 The peak acceleration is limited to 4~ . The acceleration and velocity limits of the drive wheels are to be bounded accordingly.
.:c'
The displacement of the tactile ring is measured by four linear potentiometer elements in the range of ±10Volts. These are delivered to RAMSIS' on-board computer via 12bit-AD-converters. The maximum radial displacement of the ring is about 3cm. All actions invoking the tactile ring have therefore to comply with this small margin, leaving little time to react on external forces and thus implying big acceleration values. Because of its two spring-damped castor wheels, RAMSIS then tends to bow (fig. 8). We have
EXPERIMENTS
We have done two kinds of experiments, showing RAMSIS first chasing/escaping an obstacle (cases a,b, and c) and then going around an obstacle (c'lSe d). For these experiments we have used the following parameter settings:
=
- Sampling rate 10 msecs for chasing/escaping: loa 1.0 k = 3.0 (72 0.07 for obstacle round-about: UI/O 0.15m/sec U
=
=
1.1 k2
=
1.0
=
0.05 rad/N 20° 50 N
=
"'mar
FrREF
328
OBSfACLE AVOIDANCE USING TACnI.E SE"SI1"G FOR AN AUTONOMOUS MOBll..E ROBOT
5.1
Chtuing/e$caping an obdacle
Fig. 9 shows the velocity profile of RAMSIS acting against a movable obstacle. In the first phase (O to 2$ec), there is no contact and U. and U. remain zero. Then we have pushed a movable box against the tactile ring. This led to the following reaction (2.,ec to 12.,ec): RAMSIS chased the obstacle and then pushed it, after a short acceleration time, with a slightly increasing velocity. The next phase was when the obstacle blocked (12$ec to 15.,ec). RAMSIS had then to decelerate and to find a new equilibrium (U. 0, p Po)· We then deblocked the obstacle and RAMSIS moved again. Because it started from another equilibrium point, the acceleration time was shorter. Finally, we blocked the obstacle again and then pushed it against RAMSIS with a larger force, causing RAMSIS to move back (19.,ec to 30.,ec).
=
=
Fig. 10. RAMSIS going around an obstacle
elsewhere (Badreddin and Holenstein 1991). Tactileforce sensing, being compliant, has been treated as a position control problem. The position of the robot co-ordinate frame with respect to the tactile-sensor frame of reference is controlled such that an obstacle is chased-away, repelled-from or rounded-about according to the force exerted on the sensor-ring. The fruitfulness of this design is demonstrated through experiments with the actual robot. It does not go without saying that adjusting the feedback gains to produce satisfactory results requires a good deal of experimentation effort. This effort is, however, rewarded by a reliable, fast and simple obstacle avoidance behaviour that can well be reaJized in an industrial environment using modest hardware and only little additionaJ software. The major problems are of a constructional nature concerning the suspension of the sensor-ring and the spring characteristics. Oscillations of the robots body about the Pitch-axis can also cause problems in high-dynamics situations such as abrupt jamming of an obstacle which is chased-away.
15r-----~----_r----~----_,------r_--__,
10 .
O~~·--··-----~---·~~
·5
· 10 .
· 15~----~----~----~----~-----
o
W
15
___-----'
W
~
.....[10<1)
Fig. 9. Velocity profile of RAMSIS attacking an obstacle.
5.2
Round-about an obdacle
Fig. 10 demonstrates how RAMSIS goes around an obstacle. It starts at the position (0,0), from where RAMSIS is steered against a non-movable obstacle. As soon as the contact force exceeds FmQ%, the surrounding begins. Fig. 10 shows the following: the shape of the non-movable obstacle, RAMSIS with its tactile ring in intervals of 10 seconds, and RAMSIS' wheel axis every 0.5 seconds. The midpoint trajectory of RAMSIS is indicated by o's, in case of contact, and by points in case of no contact.
REFERENCES Badreddin, E. (1991 a) . 'Recursive behaviour-based architecture for mobile robots'. Robotics and Autonomous Systems 8(4). Badreddin, E. (1991 b). Tailoring the behaviour of a mobile robot. In 'Int. Conf. on Robotics & Automation'. IEEE. pp. 2556-2561. Badreddin, E. and A. Holenstein (1991). 'Reflexive collision-avoidance in a recursive architecture'. Robotics and Autonomous Systems 8(4), 177186.
6
DISCUSSIONS AND FINAL REMARKS
In this work we developed and implemented a method for avoiding obstacles using tactile sensing. This method complements the collision avoidance strategy using an ultrasonic sensor-array which is described
Badreddin, E. and M. Mansour (1993). Stability analysis of a fuzzy-tuned controller for a nonholonomic mobile robot. Invited paper for the IFAC World Congress. Holenstein, A. (1991). 'RAMSIS: Software description'. Internal Report, Automatic Control Lab. of Swiss Federal Institute of Technology.
329
OBSTACLE AVOIDANCE USING TACTILE SENSING FOR AN AUTONOMOUS MOBILE ROBOT E. BADREDDlN ETH Swiss Federal Institute of Tcchnology Zurich Physicstrasse 3, ETH-Zcntrum / ETL I 29, CH 8092 Zurich, Switzerland Abstract. A tactile sensor-ring is built around an autonomous mobile robot to measure the force and torque acting on the robots body. The computed force/torque are then used to aid the colJjsion avoidance behaviour. This behaviour can be described as follows: Push the obstacles away if it is light enough. Repel-away from the obstacle if it acts aggressively such that the force felt by th e robot exceeds a given threshold . Finally, if the obstacle is neither movable nor aggressive , round-about it when a prescribed time has elapsed . The implementation of this strategy is described and experiments are documented which demonstrate the fruitfulness of this design. Keywords. Tactile sensing, Collision-avoidance, Mobile robots.
INTRODUCTION RAMSIS has been built at our laboratory for research purposes. One research topic is to verify a behaviourbased control structure, called the Recursive Nested Behaviour Control (RN BC) (fig. 1). A repertoire of
"0 '"
.'
.. .
EnCOde,. . lTadlo
Fig. 1. The control structure of RAMSIS behaviors are so nested such that reflexive ones occupy the inner levels overlaid by the intellectual be-
haviors in the outer levels. Th e RNBC possesses several desirable properties for autonomous robots, such as recursiveness, robustness and distributed modeling (Badreddin 1991a), (Badreddin 1991b). The collision avoidance behaviour overlays the level which implements the robot-velocity control. This means that the robot is seen from the collision-avoidance level as a velocity-servo . Therefore , collision-avoidance is realized as a reflexive behaviour which can deal with both moving and reflexive obstacles in real-time without the need for a detailed model of the environment or the obstacle. To fulfil! these requirements, a new approach has been taken to implement an adaptive potential-field about the robot itself in contrast to the conventional approach where it is built about the obstacles (Badreddin and Holenstein 1991). Significant performance improvement and cut in the implementation complexity has been, thus, achieved . Ultrasonic sensors are employed for this purpose. Some obstacles, however, may remain undetected by these sensors, e.g. slim obstacles may leak-through the ultrasonic shield . Further, their close-in performance is hampered by the limited resolution in both range and angle. In addition, tactile sensors being passive, have an inherent ad vantage over active ultrasonic sensors concerning its interference-free operation . For these reasons as well as for increased reliability and safety, tactile sensing can be advantageous especially to complement longer range sensors. In this paper we briefly describe the construction of a compliant tactile sensor-ring. Its application in avoiding obstacles is discussed in more details. The tactile obstacle-avoidance behaviour is tailored such that an obstacle is chased-away, repelledfrom or rounded-about according to the force it exerts on the robot body. Implementation details as well as experiments using the actual robot are also discussed.
325
8ADREDDIl\' E.
2
PROBLEM FORMULATION
Consider a cylindrical robot with two driven unsteerable wheels mounted on a platform. In addition, a driven turret rotating about the vertical axis of this platform provides a third degree of freedom (fig. 3). The initial position and wheel-orientation of the robot with respect to the inertial frame can be taken equal to zero without 1055 of generality. A force, F, is exerted by an obstacle, 0, on a point, P, on the robots circumference, at a distance Po and direction 0'0 (fig. 2). The force, F, acting on the robot can be decomposed into its Cartesian components, Fz and F y , at P, or at the robots origin together with a torque M •. The robot has two control inputs U y and U.p. Find a feedback control such that the robot: a) remains stationary if IFI = 0 (no contact) or IFI = Fo (constant force) c) chases 0 away, if 0 < IFI < Fo b) repels from 0 to escape the force if Fo < IFI <
Fmaz
d) rounds-about the obstacle 0 if (IFI ;::: Fma:z v(IFI = Fo /\ Y = 0 /\ t ;::: T» , i.e., y and a are such that P moves on the boundary of O. P does not have to slide along the boundary of 0 all the time, but may, instead, bounce on the boundary. 0 < Fo < Fmaz and T are prescribed force and time thresholds respectively. Case d) is obviously required to avoid endlessly sticking to an obstacle. Please notice that switching back from case d) has to be controlled from higher level commands.
Fig. 3. Robot with a compliant tactile sensor ring
tion accuracy is not a prerequisite for this behaviour. A light-weight, stiff ring made of carbon fiber is suspended around the robots turret by means of twelve circularly-shaped spring sheets (fig. 3) . This suspension allows for three degrees of freedom . When a force is applied to the ring, the displacement from the initial position can be measured by means of four linearstroke sensors. Although three sensors would have been enough, four were mounted for construction reasons and to avoid the, time-consuming, computat.ion of trigonometric functions. From fig. 4 it can be read-
}llIIF----Fx
Fig. 2. Force/torque configuration
3
SOLUTION APPROACH
Our solut.ion approach covers the questions of force/torque measurements, of kinematic modeling and of designing a feedback controller. x
3.1
Force/Torque Measurement Fig. 4. Compliant force/torque mea.surement
Principally, one can choose between force/torque measurement with and without compliance. Compliant force measurement is advantageous in our case due to the large mass and inertia of the robot and since posi-
ily seen that the displacement in the Cartesian and rotational directions respe<:tivcl), can be written in
326
OBSTACLE A VOIDA~a; USING TACTII.E SE~SI'G FOR
3.3
terms of the chlUlges in the linear-sensor readings as: ~x, ..
c,
:::::
~!I' .. cI
:::::
~tP, ..c'
:::::
~12
~14
-
F"
M.
= = =
2 ~IJ
+ ~12 + ~13 + ~14 This results in the closed-loop system
4Po
C%~XIQCI
C.;~tPltJCI
Let us assume that the effect of the torque M z is almost nulled-out by a proportional command to the turret. As a consequent, the change in the angle-ofattack of the force F can be assumed small enough to be neglected and the turret control will be dropped from the following treatment. Now, let the polar displacement be p at an angle a :::= ao (fig . 5). The kine-
./
.--------- "-
.......
/
y
/
-kppcos n
a
-kaa + -kpsin
Q
""-\
\
\
I I
-kpp
a
-(ka - kp)a
Case b): For the case b) in which the obstacle is to be chasedaway, one is interested in another equilibrium point for some p = po f:. 0 and a = O. This can principally be done by shifting the feedback control-line of p to give U y = 0 at p = Po. Below this value, a control is required which drives the system to the new equilibrium. A combination of the feedback control characteristics required for the cases a), b) and c) would then look like fig. 6. Thereby, et may lie in the interval ±f and p < 0 is, therefore, possible. The non-linear
\
/
P
Cases a) and c) : It can be immediately seen that the origin p = a = o is asymptotically stable for k,. > 0 and ka > O. In other words. this stabilizing linear, static feedback brings the displacement from the origill to zero and, therefore, solves the cases a) and c) of the problem formulation.
Simplified Kinematic Model
./
p
The linearized system about tile origin is written as:
C,,~!I'QCI
where C z , c", and C.; are the spring coefficients in x, y, IUId tP respectively.
3.2
Feedback Control
~13
-
Hence, the tactile force and torques are:
F.
MOBlU; ROBOT
Now, consider the feedback law,
2 ~ll
A~ Al~ro~OMOLS
)
\
I
\
t:y
/
\
\
/
"-
I
"-
"- "-
./
/
/
a
....... ----"""
Fig. 5. Displacement due to compliance (exaggerated )
Fig. 6. Feedback control:
matic equations in the robot frame-of-reference can be written as:
characteristic of the ii-gai n can be appnhi lIJaled by, e.g.,
[~ ]=[ where a - arctan (
-cosa sin
kp
Q
i>
=f: ) and p --- (F
z
sin a
=1-
lin~ar
-i~
ke -;;r, k
>
in a, nOli-linear in
p
0,0' E R
case cl): This case is different from the others in t hat wc have to find a. force equilibrium point. in the x-direction instead of the direction of motion (fig. 7). We therefore propose a procedure that first rotates the robot abou t f and then tries to hold a. constant force Fr against the obstacle whilst moving along its boundary. The algorithm is:
+ F)I cos a)
with the coefficients of proportionality depending on the inverse spring stiffness in both Cartesian directions. The derivation is omitted here for space reasons and can be found in (Badreddin and Mansour 1993). The kinema.tic of the wheel-axis orientation with respect to the inertial frame are irrelevant in this treatment a.nd is, therefore, omitted.
while in case d) do measure F" and Fy
327
BADREDD/7\ E.
found that this leads, when using gains bigger than one, to unacceptable oscillations about the pitch-axis, if the controller is purely kinematically defined. A way out of this is to stabilize the tactile loop by a LAG-controller. For this, we have used the following transfer function:
yes) Ys(s) [TI/(s) yes)
=
S2
26s + 260 + 4s + 260
A LAG-controller that guarantees a ramp error of less than 0.1, a maximum overshoot of 30%, and a minimum raising time of 0.5sec is:
Fig. 7. RAMSIS moving along a wall
F = arctan ~ 6.F. = F.REF -
10 s(s + 10)
R(s)
6.t/J
= 10 1 + 3.33s 1 + 13.3s
Fr
if 16.~1 > ",or, Uy = 0 U,p = U4>O.~i9n(6.t/J) else U,p = k l 6.q, - k 2 6.F", U Y = (1 - q,maE 1A4>1)(1 - ~)U 0 Fmar Y end if F = 0, (no contact) Uy 0.5Uyo U,p = 0.5U4>O end
=
end Since we make 110 assumption about the obstacle shape, it is possible that the robot looses contact (F = 0) or has to make a full-stop (/6.
Fig. 8. RAMSIS in front of an obstacle
5 4
IMPLEMENTATION
A detailed description of the underlying implementation structure is found in (Holenstein 1991). RAMSIS has a peak velocity of 1..!!'.- . The rotation speed of the turret and the wheel ;l~tform is limited to 150 The peak acceleration is limited to 4~ . The acceleration and velocity limits of the drive wheels are to be bounded accordingly.
.:c'
The displacement of the tactile ring is measured by four linear potentiometer elements in the range of ±10Volts. These are delivered to RAMSIS' on-board computer via 12bit-AD-converters. The maximum radial displacement of the ring is about 3cm. All actions invoking the tactile ring have therefore to comply with this small margin, leaving little time to react on external forces and thus implying big acceleration values. Because of its two spring-damped castor wheels, RAMSIS then tends to bow (fig. 8). We have
EXPERIMENTS
We have done two kinds of experiments, showing RAMSIS first chasing/escaping an obstacle (cases a,b, and c) and then going around an obstacle (c'lSe d). For these experiments we have used the following parameter settings:
=
- Sampling rate 10 msecs for chasing/escaping: loa 1.0 k = 3.0 (72 0.07 for obstacle round-about: UI/O 0.15m/sec U
=
=
1.1 k2
=
1.0
=
0.05 rad/N 20° 50 N
=
"'mar
FrREF
328
OBSfACLE AVOIDANCE USING TACnI.E SE"SI1"G FOR AN AUTONOMOUS MOBll..E ROBOT
5.1
Chtuing/e$caping an obdacle
Fig. 9 shows the velocity profile of RAMSIS acting against a movable obstacle. In the first phase (O to 2$ec), there is no contact and U. and U. remain zero. Then we have pushed a movable box against the tactile ring. This led to the following reaction (2.,ec to 12.,ec): RAMSIS chased the obstacle and then pushed it, after a short acceleration time, with a slightly increasing velocity. The next phase was when the obstacle blocked (12$ec to 15.,ec). RAMSIS had then to decelerate and to find a new equilibrium (U. 0, p Po)· We then deblocked the obstacle and RAMSIS moved again. Because it started from another equilibrium point, the acceleration time was shorter. Finally, we blocked the obstacle again and then pushed it against RAMSIS with a larger force, causing RAMSIS to move back (19.,ec to 30.,ec).
=
=
Fig. 10. RAMSIS going around an obstacle
elsewhere (Badreddin and Holenstein 1991). Tactileforce sensing, being compliant, has been treated as a position control problem. The position of the robot co-ordinate frame with respect to the tactile-sensor frame of reference is controlled such that an obstacle is chased-away, repelled-from or rounded-about according to the force exerted on the sensor-ring. The fruitfulness of this design is demonstrated through experiments with the actual robot. It does not go without saying that adjusting the feedback gains to produce satisfactory results requires a good deal of experimentation effort. This effort is, however, rewarded by a reliable, fast and simple obstacle avoidance behaviour that can well be reaJized in an industrial environment using modest hardware and only little additionaJ software. The major problems are of a constructional nature concerning the suspension of the sensor-ring and the spring characteristics. Oscillations of the robots body about the Pitch-axis can also cause problems in high-dynamics situations such as abrupt jamming of an obstacle which is chased-away.
15r-----~----_r----~----_,------r_--__,
10 .
O~~·--··-----~---·~~
·5
· 10 .
· 15~----~----~----~----~-----
o
W
15
___-----'
W
~
.....[10<1)
Fig. 9. Velocity profile of RAMSIS attacking an obstacle.
5.2
Round-about an obdacle
Fig. 10 demonstrates how RAMSIS goes around an obstacle. It starts at the position (0,0), from where RAMSIS is steered against a non-movable obstacle. As soon as the contact force exceeds FmQ%, the surrounding begins. Fig. 10 shows the following: the shape of the non-movable obstacle, RAMSIS with its tactile ring in intervals of 10 seconds, and RAMSIS' wheel axis every 0.5 seconds. The midpoint trajectory of RAMSIS is indicated by o's, in case of contact, and by points in case of no contact.
REFERENCES Badreddin, E. (1991 a) . 'Recursive behaviour-based architecture for mobile robots'. Robotics and Autonomous Systems 8(4). Badreddin, E. (1991 b). Tailoring the behaviour of a mobile robot. In 'Int. Conf. on Robotics & Automation'. IEEE. pp. 2556-2561. Badreddin, E. and A. Holenstein (1991). 'Reflexive collision-avoidance in a recursive architecture'. Robotics and Autonomous Systems 8(4), 177186.
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DISCUSSIONS AND FINAL REMARKS
In this work we developed and implemented a method for avoiding obstacles using tactile sensing. This method complements the collision avoidance strategy using an ultrasonic sensor-array which is described
Badreddin, E. and M. Mansour (1993). Stability analysis of a fuzzy-tuned controller for a nonholonomic mobile robot. Invited paper for the IFAC World Congress. Holenstein, A. (1991). 'RAMSIS: Software description'. Internal Report, Automatic Control Lab. of Swiss Federal Institute of Technology.
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