Collision Detection for a Mobile Robot using Logistic Regression

Felix Becker and Marc Ebner

Ernst Moritz Arndt Universit

at Greifswald, Institut f

ur Mathematik und Informatik,

Walther-Rathenau-Str. 47, 17487 Greifswald, Germany

Keywords:

Collision Detection, Autonomous Mobile Robots, Acceleration Sensor.

Abstract:

Collisions cannot be entirely avoided during normal operation of an autonomous mobile robot. Therefore,

mobile robots need to detect collisions and react appropriately when they happen. We investigate whether

logistic regression on acceleration data can be used for collision detection. We have collected training data

from an acceleration sensor during normal driving behavior of a small mobile robot. Collisions were manually

marked by a human operator. Accelerations occurring in a direction opposite to the current direction of motion

are more likely to be actual collisions. Hence, we combine accelerometer data and motor commands in the

logistic regression model. The trained model was able to detect 13 out of 14 collisions on a separate test set

with no false positives.

1 INTRODUCTION

A mobile robot can be equipped with a number of dif-

ferent sensors, e.g. infrared, sonar, laser range sensors

or a camera, which allow him to move around in ar-

bitrary environments (Corke, 2011; Jones and Flynn,

1993; McKerrow, 1991). Irrespective of the type of

sensor used, collisions may occur for a number of

different reasons: sensors may not fully cover the en-

tire environment of the robot, some obstacles may be

invisible to a sensor or sensor data processing may

be too slow such that the data is already outdated by

the time the collision occurs. It may also happen that

the robot collides with an obstacle and then becomes

stuck. If a robot becomes stuck, high stall currents

may be applied to the motors. These high currents

may cause damage to the robot if applied for long time

periods. Detection and handling of different types of

collisions is essential for a mobile robot in a real life

environment.

With this contribution we use logistic regression

(Hosmer Jr. et al., 2013) to predict collisions from

data measured by an accelerometer on a mobile robot.

Logistic regression and perceptron like neural net-

works are quite similar and both can be used for clas-

siﬁcation tasks. Dreiseitl and Ohno-Machado (2002)

have compared both methods in the context of med-

ical data classiﬁcation. However, logistic regres-

sion can of course also be used for various tasks

in robotics. Dorigo and Schnepf (1993) have used

genetics-based machine learning for behavior-based

robotics. They trained a robot to follow a light point

and to avoid hot or dangerous objects.

Several researchers have used an accelerometer

for collision detection. Na et al. (2005) have used

acceleration sensor data for collision recognition for

small scale ﬁsh robots. They have used fuzzy logic

to estimate collision angles. He et al. (2007) apply

a median ﬁlter to a running window of consecutive

acceleration data and then compute the standard de-

viation. Finally a threshold is used to detect colli-

sions. Nadarajan and Sridharan (2010) used accel-

eration and gyroscope data to detect instability in a

NAO robot. They have used a support vector ma-

chine for classiﬁcation. Moorits and Usk (2012) used

accelerometer data for collision detection in naviga-

tional marine buoys.

Vail and Veloso (2004) have used decision trees

for surface identiﬁcation with a legged robot. McMa-

han et al. (2012) have shown that it is possible to use

accelerometer data for localization of contact points

on a robot arm. A multi class support vector machine

was used for classiﬁcation. Wisanuvej et al. (2014)

use multiple accelerometers distributed along a multi-

jointed robot arm for localization of collisions. They

also propose to use this data for identiﬁcation of ma-

terials the arm collided with and even for environment

mapping. Speleers and Ebner (2019) have evaluated

three different methods for collision detection using

an acceleration sensor on a mobile robot: a simple

threshold on the acceleration signal, a running median

ﬁlter and a frequency based averaging ﬁlter.

Becker, F. and Ebner, M.

Collision Detection for a Mobile Robot using Logistic Regression.

DOI: 10.5220/0007768601670173

In Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2019), pages 167-173

ISBN: 978-989-758-380-3

167

Apart from mobile robotics, acceleration sensors

are also used in the car industry to deploy airbags

(Chan, 2000). Today, ordinary smartphones also con-

tain acceleration sensors. Hence, these phones can

also be used for vehicular collision detection (Lunds-

gaard and Grivas, 2006). Once a collision has been

detected, they can also be used to notify emergency

responders (Barﬁeld, Jr. and Welch, 2016; Mane and

Rana, 2014; Thompson et al., 2010).

2 COLLISION DETECTION

A simple yet efﬁcient method for collision detection

using acceleration data is to simply compare the ac-

celeration data provided by the sensor with a thresh-

old. If the acceleration is larger than a certain thresh-

old and does not occur in the direction the robot is

moving to then a collision has been detected. How-

ever, in practice it is quite difﬁcult to use this method

if the acceleration data occurring due to normal move-

ment of the robot has a similar magnitude. This is

especially the case for small robots which may be de-

ployed in peoples homes. Also, small objects on the

ground may also cause peaks in the acceleration data.

However, if the objects are small enough for the robot

to drive over then we would like to ignore such small

“collisions”. If the robot is driving over rough ter-

rain, we may obtain an oscillating signal which may

make it difﬁcult to extract obvious peaks for collision

detection.

Apart from collision detection we may also want

to classify the type of collision which occurred. A

collision against a table leg, human foot or a small

object on the ground will result in different accelera-

tion data. This data could be used to classify the type

of collision. However, a simple threshold will not be

sufﬁcient for this kind of classiﬁcation task. Learning

algorithms allow for automatic classiﬁcation of col-

lision data. No manual tuning of parameters is re-

quired.

3 ROBOT ARCHITECTURE

For our experiments, we have used the Dagu Robot

(dagurobot.com) T’Rex Tank chassis (Fig. 1). The

tracked tank chassis is driven by two motors via a

Sabertooth 2x12 motor controller. The robot is pow-

ered by 11.1V LiPo battery. An Arduino Mega 256

micro controller was used to control the robot. The

robot was equipped with three Sharp analog infrared

sensors. One was oriented towards the front, the other

two at an angle of approximately 30

◦

pointing slightly

sideways. The two sideway sensors (GP2Y0A21)

could measure distances within the range 10 − 80

cm. The frontally oriented sensor (GP2Y0A60) could

measure distances within the range 10 − 150cm. A

2x20 LCD was used to display debug information. A

BNO055 sensor (Bosch Sensortec GmbH, 2006) was

used to provide 3-axis acceleration data. This sensor

was mounted approximately at the center of the robot.

The sharp infrared distance sensor provides ana-

log output. This output is read at a rate of approx-

imately 40Hz by the Arduino micro controller. The

two lateral sensors are used to implement a corridor

following behavior which allows the robot to wander

around. The frontally oriented sensor is used to detect

obstacles in the robot’s path. If the distance measured

by the frontally oriented sensor is less than 15cm, then

we stop the robot, drive backwards for 1000ms, turn

the robot by 180

◦

and then continue with normal driv-

ing behavior.

4 CENTERING BEHAVIOR

Normal driving behavior uses the data from the left

and right sensors to center the robot inside a corridor.

This behavior is similar to the way honeybees pro-

cess optical from their left and right eye (Lehrer et al.,

1988; Srinivasan, 1992a,b). Behavior-based control

algorithms have been shown to be very effective for

robot control (Arkin, 1998). Several researchers have

built robot behaviors based on this type of processing

using optical ﬂow (Coombs et al., 1998; Coombs and

Roberts, 1992; Santos-Victor et al., 1993, 1995). If

the optical ﬂow on the left hand side is larger com-

pared to the right hand side, then the robot will turn

to the right. If the optical ﬂow on the right hand side

is larger compared to the left hand side, then the robot

will turn to the left.

Instead of working with laterally oriented cam-

eras it is also possible to process optical ﬂow from

a monocular camera. Ebner and Zell (2000) have

used a foveated camera and extracted optical ﬂow

from the left and right peripheral visual areas. Op-

tical ﬂow was computed in ego motion complex log-

arithmic space. The ego motion complex logarithmic

mapping is taken around the focus of expansion in-

stead of the center if the image. Hence, optical ﬂow

due to the angular velocity of the robot is compen-

sated for. Once this compensation is done, the optical

ﬂow from the peripheral areas on the left and right

hand side is proportional to the inverse distance of the

viewed objects. Again, this distance information can

be used for a centering behavior as described above.

Here, we are not using optical ﬂow for the center-

ICINCO 2019 - 16th International Conference on Informatics in Control, Automation and Robotics

168

(a) (b) (c)

Figure 1: Dagu Robot T’Rex Tank chassis with Sabertooth 2x12 motor controller. The robot is equipped with three frontal IR

sensors. The three ultrasonic range sensors are not used. (a) front (b) side (c) rear.

ing behavior. Distances are readily available from the

Sharp distance sensors. Let s

and s

be the distance

measurement from the two sensors facing towards the

left and right side respectively. The difference be-

tween the two sensors is used to set the angular ve-

locity

α of the robot.

α = τ(s

− s

) (1)

where τ is a scaling parameter. For our experiments,

we have used τ = 0.05.

To drive our robot, we need to specify the power

applied to the left and right motors through the Saber-

tooth motor controller. Let m

be the power applied

to the left motor and let m

be the power applied to

the right motor via the motor controller. Let m

the power applied to both motors to achieve a desired

forward velocity. The desired rotational velocity is

simply added to the left motor value and subtracted

from the right motor value.

= m

α (2)

= m

−

α (3)

A positive angular velocity will make the robot turn

right while a small angular velocity will make the

robot turn left. This simple method will center the

robot inside a corridor. If an obstacle is sensed to-

wards the left side of the robot then the robot will turn

to the right side and vice versa.

5 LOGISTIC REGRESSION FOR

COLLISION DETECTION

We use logistic regression for collision detection. Lo-

gistic regression is a statistical model for dependent

binary variables (Dreiseitl and Ohno-Machado, 2002;

Hosmer Jr. et al., 2013). Our binary output variable

will take on the value 0 if no collision has occurred

and 1 if a collision has occurred. We would like to

estimate the probability that a collision has occurred

based on acceleration sensor data.

Let a

(t), a

(t) and a

(t) be the acceleration data

in cm/s measured by the accelerometer (the compo-

nent due to gravity is automatically removed by the

sensor). It is assumed that we have a

(t) = a

(t) =

(t) = 0 at rest. The sensor was mounted such that

the x axis points to the left and the y axis points back-

wards. Let m

(t) and m

(t) be the power applied to the

two motors. This data is obtained with a frequency of

approximately 125 Hz. Each data point p(t)

p(t) = (a

(t),a

(t),m

(t)) (4)

consists of the data measured by the accelerometer as

well as the power applied to the motors.

The deceleration due to a collision usually spans

multiple data points. Using more than a single data

point allows for more reliable collision detection. Let

be n consecutive data points obtained during time

i+n−1

−t

= (p(t

),..., p(t

i+n−1

)) (5)

Let o

be our binary output value with o = 1 if a col-

lision has occurred during the time period from t

i+n−1

. We want to estimate the probability P(o =

1|W). According to our logistic regression model, we

have

P(o = 1|W ) = σ(θ

+ θW) (6)

for a sigmoid function σ(x) =

1−e

−x

and parameters

θ and θ

. The vector W contains 5n values. Logistic

regression essentially tries to compute a hyperplane

Collision Detection for a Mobile Robot using Logistic Regression

169

to separate areas inside this vector space where a col-

lision has occurred from areas where a collision has

not occurred. We need to compute the weight vec-

tor θ and bias θ

from the available training data.

The software package R (The R Development Core

Team, 2008) was used to obtain the logistic regres-

sion model. We have used the function glm (general-

ized linear model) with default parameters except for

the parameter family which was set to binomial.

The training data is recorded via the serial Ar-

duino interface during normal operation of the robot.

The data points p(t

) are obtained at a rate of 125 Hz.

In order to apply logistic regression, we also need to

obtain ground truth data when a collision has hap-

pened. We have connected an external button to the

Arduino. This button is pressed by a human operator

whenever a collision has happened. Let c(t) = 1 if

the button was pressed and c(t) = 0 otherwise. The

button press occurs approximately at the time of the

collision. However due to various reasons (operator

pressing too early to after a slight delay), this data is

only approximately correct. Hence, we ﬁrst correct all

collision data c(t) using an R-script and then compute

the time of the collision during post processing.

We take the button press as the approximate time

when a collision has happened. Some collisions may

have been marked before the actual event has hap-

pened and some have been marked after the event

has happened. Therefore, we search for a peak in the

magnitude of the acceleration data. If c(t) = 1, then

all data points within a window of b

time steps before

and b

time steps after time t are considered. If c(t) =

1 for several consecutive time steps, then we obtain a

window that will contain more than b

+ b

+ 1 data

values. Let t

be the time step where the magni-

tude of the acceleration was at a maximum. We then

set all values within [t − b

,t + b

] to 1. Let ˜c(t) be

this modiﬁed collision data. Preliminary experiments

have shown that the parameters b

= 6, b

= 6 and

= 12 work particularly well. The reason for assum-

ing that the collision is centered around the maximum

is because a collision frequently results in a quick im-

pulse followed by a slower decline.

Using all recorded data points p(t) and associated

ground truth collision data ˜c(t), we create overlapping

windows of size n = 19. Subsequent windows have an

offset of one data point. We compute the probability

that a collision has occurred during a window W as

the fraction of values ˜c = 1 to the total number of data

points, i.e.

∑

j=0

˜c

/n (7)

Using n = 19 we obtain P

= 1 if a collision event

is completely contained within this window. The re-

gression model has been trained using these windows

with associated P

. All data was recorded while the

robot was driving around in an ofﬁce environment.

Using the trained regression model, we are able to

detect collisions by processing a window of 19 con-

secutive data points. The model will compute a proba-

bility that a collision has occurred. We apply a thresh-

old of 0.95 to this probability, i.e. a collision only oc-

curs if the output of the mode is 0.95 or larger. If a

collision has been detected, we locate the data point

whose magnitude of the acceleration is at a max-

imum. We then compute the motor power by taking

the maximum acceleration during the collision. Let

max

be this maximum. Values larger than 8 are lim-

ited to 8. This limits the rotational velocity of the

robot. The motor power is set to

= −m

− sa

max

(8)

= −m

+ sa

max

(9)

using m

= 50 and s = 8. The parameters were manu-

ally set based on preliminary experiments. The setting

is maintained for a time of 1000 ms. This will result

in a motion that is opposite to the one that lead to

the collision. For example, if the robot bumped into

a chair leg with his front left corner then it will set

back by turning to the left. This will allow the robot

to avoid the chair leg when moving forward again.

6 EXPERIMENTS

Acceleration data obtained during a collision with a

chair leg is shown in Fig. 2. The collision is clearly

marked by the peak in the data along the y axis. Apart

from this peak along the y axis, we also see consider-

able accelerations occurring along the x and z axis of

the robot. This is due to the robot moving sideways

and downwards (the tracks are spring mounted to the

robot). Due to this type of behavior it is best to con-

sider all three axes when determining whether or not

a collision has occurred.

Fig. 3 shows the collision data while the robot

was moving upward on a ramp. The robot was collid-

ing with a chair leg. Peak acceleration also occurred

along the z direction. However, the peak is not as

high in the previous data. When the robot reaches

the bottom of the ramp, we also obtain large oscilla-

tions along the y direction. However, these data points

should not be interpreted as a collision.

It is quite difﬁcult to devise an algorithm which

will detect both types of collisions that we have an-

alyzed here (colliding with a chair leg on the ground

and colliding with a chair leg on a ramp). Apart from

ICINCO 2019 - 16th International Conference on Informatics in Control, Automation and Robotics

170

2800 3000 3200 3400 3600 3800

−6 −4 −2 0 2 4 6 8

cm s

●●●●●●●●●●●●●●●●●●

Collision

Figure 2: Acceleration data a

, a

and a

obtained from the

robot while bumping into a chair leg. The time of collision

was marked manually by a human operator.

16000 16500 17000 17500 18000

−10 −5 0 5

cm s

●●●●●●●●●●●●●

Collision

Figure 3: Acceleration data a

, a

and a

obtained from

the robot while it was moving upward on a ramp and then

bumping into a chair leg. The time of collision was marked

manually by a human operator.

these two types that we have seen so far, many differ-

ent collision types can occur in practice. A learning

algorithm has the advantage that we only need to col-

lect collision data for various situations as well as data

from normal driving behavior when no collisions oc-

cur. The learning algorithm will then optimally tune

its parameters to the given data.

Logistic regression allows us to detect collisions

by learning from a training data set. Our training data

set contains 27 collisions where the robot was level

and colliding with a chair leg (collision of type A). It

also contained 14 collisions where the robot was mov-

ing upward on a ramp and colliding with a chair leg

(collision of type B). The remaining training data was

recorded during normal driving behavior of the robot

on the ground. Sometimes the robot was also driving

over small objects. These objects provide for varia-

tions in the collision data. However, they should not

be considered as collisions. The small objects on the

ground should result in variations during normal driv-

ing behavior in order to make the collision detection

algorithm more robust. Our training set consisted of a

total number of 22105 data points (21014 for normal

driving behavior, 859 for type A collisions 232 for

type B collisions) with associated binary data (colli-

sion/no collision). Since each window contained 19

data points and we have used overlapping windows,

we obtained 20996 windows from normal driving be-

havior, 841 windows from type A collisions and 214

windows from type B collisions.

We then tested the robots ability to detect colli-

sions on a test data set shown in Fig. 4. This data set

consists of 14 collisions. It was recorded while the

robot was moving around on the ﬂoor. It collided with

a table chair (7 times, type A collision). The robot was

also moving upward on a ramp and then collided with

a table chair (7 times, type B collision). Only one of

these 14 collisions was not correctly classiﬁed as a

collision. Table 5 summarizes our results. Our model

did not recognize one collision of type A. This may

have been the case because the robot collided with

the chair leg at an angle that was not sufﬁciently well

represented by the available training data. Collision

detection results are also shown in Fig. 4. Actual col-

lisions have been marked manually by a black circle.

Whenever our model predicted a collision, a green cir-

cle is shown in the plot.

In order to further improve collision detection, it

would of course also be possible to learn collision de-

tection models separately for different types of colli-

sions. Once these separate models have been learned,

they could be combined in a ﬁnal processing stage.

However, this approach could result in over-training

of certain collision types. Collisions that do not occur

during training will probably not be detected.

7 CONCLUSION

We have used logistic regression for collision detec-

tion of a mobile robot. The robot was equipped with

an accelerometer. Our model was based on 19 suc-

cessive data points obtained at a rate of approx. 125

Hz. Each data point consisted of the acceleration val-

ues along the three axes of the robot together with

the power supplied to the robot’s motors. A training

data set was obtained by letting the robot drive around

inside an ofﬁce environment and then marking colli-

sions manually. Out of 14 collisions in the test set

Collision Detection for a Mobile Robot using Logistic Regression

171

0 10000 20000 30000 40000 50000 60000

−10 0 10 20 30

cm s

Beschl. X

Beschl. Y

Beschl. Z

Kollision

Vorhersage

Figure 4: Test data set with 14 collisions. Acceleration data a

, a

and a

together with manually marked collisions (black

circles). Predicted collisions have been marked by a green circle. Only one of the collisions has not been detected by the

model.

type A type B

collisions (training set) 27 14

collisions (test set) 7 7

recognized collisions (test set) 6 7

Figure 5: Collision data was gathered during normal driv-

ing behavior. Two types of collisions were recorded: Type

A collisions (table chair) and type B collisions (table chair

while robot was moving on a ramp).

13 were detected. Thus, logistic regression appears to

be a promising method for collision detection using

an acceleration sensor on a mobile robot. The advan-

tage of using logistic regression compared to a simple

threshold on the acceleration data is that the method

can be easily tuned to detect certain types of collision

by simply recording training data. Currently, training

has to take place off-line. Extending the method to an

on-line learning paradigm would be desirable.

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