Safe Predictive Mobile Robot Navigation in Aware Environments

Michael Arndt and Karsten Berns

Robotics Research Lab, Dept. of Computer Sciences, University of Kaiserslautern, Kaiserslautern, Germany

Keywords:

Mobile Robot Path Planning, Safety, Human Motion Prediction, Human Aware Planning, Ambient Intelli-

gence, Smart Environment

Abstract:

It is a common goal to improve safety and performance of mobile indoor robots by predicting the movements

of people in the surroundings. In contrast to many related works which exclusively employ sensors mounted on

mobile robots, this work shows a method to achieve this goal in a smart environment where external sensors are

used to sense people’s positions. By using probabilistic models and ﬁlters, the evolution of the environment’s

state is predicted and optimal paths with respect to safety and performance are planned. Experiments in

reality and in a simulation environment show the applicability in real-world scenarios and the advantages over

classical path planning approaches.

1 INTRODUCTION

It has been acknowledged by many researchers that

safety and human awareness are important topics for

mobile robots employed in human environments. As

(Alami et al., 2006, sec. I) state, safety is an impor-

tant key to successfully introduce robots into such do-

mains. The concept of human aware motion planning

has been researched a lot in the past (Sisbot et al.,

2005; Sisbot et al., 2007; Bennewitz et al., 2005;

Guzzi et al., 2013) to achieve robot motion that does

interfere with human motion as little as possible.

At the same time, so called smart, aware, am-

bient or ubiquitous technologies are becoming more

and more important and present in everyday life (Au-

gusto et al., 2010; Lukowicz et al., 2012) and also

the ﬁeld of robotics tries to make use of that tech-

nology (Safﬁotti and Broxvall, 2005; Coradeschi and

Safﬁotti, 2006; Sanfeliu et al., 2008; Amato et al.,

2012).

Previous work by the authors has already shown

that the risk, a mobile robot imposes on human in-

habitants of smart environments, can be decreased by

making use of environmental sensor information. By

assessing the current situation, as perceived by wire-

less sensor nodes, distributed in the environment, the

path planner of a mobile robot is able to ﬁnd paths that

are safe according so a safety metric, but also efﬁcient

subject to the length of the path (Arndt and Berns,

2014). However, the previous method yields subopti-

mal results, as it only evaluates possible paths accord-

ing to the current situation at the time of planning.

While it provides good results for setups that remain

static after the path has been planned, this assump-

tion is of course not true in general, as environments

inhabited by people are typically highly dynamic.

In reality, people frequently change their loca-

tions, thus the environments evolve during the traver-

sal of a path of the mobile robot (i.e. while it is driv-

ing), thus the environment is time variant. This fact

will now be taken into account within this work by

making use of prediction.

When planning with respect to time, the dimen-

sionality of the planning problem increases. This

leads to an increase in complexity, which makes the

search for exact solutions often unfeasible (Linde-

mann and LaValle, 2005). However, the method pre-

sented later in this work is able to ﬁnd exact solutions

in typical application scenarios with acceptable com-

putation times.

The rest of the paper is structured in the following

way: First, work related to this one is introduced in

the next section. Afterwards, a brief overview about

the probabilistic state estimation methods that are em-

ployed, is given, followed by a description of the

essence of this work, the prediction of future states

and the planning using the outcome. Section 5 de-

scribes the experiments that have been conducted in

reality as well as in a simulation environment to val-

idate the proposed algorithms in detail. The exper-

imental results are followed by a conclusion and an

outlook over possible future works.

Arndt M. and Berns K..

Safe Predictive Mobile Robot Navigation in Aware Environments.

DOI: 10.5220/0005509500150023

In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), pages 15-23

ISBN: 978-989-758-123-6

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

2 RELATED WORK

Path planning in time variant, or dynamic environ-

ments has been known for quite a while and has al-

ready been researched in different domains. This sec-

tion aims to give an overview about some techniques

and algorithms that can be found in the literature.

The work by (Alvarez et al., 2004) has presented a

solution for a predictive path planner for autonomous

underwater vehicles in ocean environments. Due to

the fact that littoral waters are highly variable and

routes for the underwater vehicles should be energy

efﬁcient, forecasts are used to predict the conditions

of the ocean in advance (Alvarez et al., 2004, sec. I)

to achieve better plans. In their work, the authors

acknowledge the high dimensionality of the tempo-

ral planning problem and thus the difﬁculty of ﬁnding

computationally feasible exact solutions. Instead, in

their work, they make use of genetic algorithms and

accept possibly non-optimal solutions.

Regarding mobile robots in indoor environments,

the tracking of people (by the robot itself) is an im-

portant foundation of planning in general (Bruce and

Gordon, 2004) and human aware planning in particu-

lar. The authors acknowledge that people usually fol-

low trajectories between points of interest and do not

just walk randomly (Brownian motion) or with a con-

stant velocity through the environment. In that work,

they have used training data (trajectories of people in

the environment) to learn goal locations of people in

the environment. Later, in their motion model, they

calculate paths from people’s current locations to the

possible goal locations to be able to predict their mo-

tion and improve their tracking, compared to a simple

Brownian motion model.

The work by (Bennewitz et al., 2005) has simi-

lar goals as the one by Bruce et al. and is also highly

related to this work. It describes a way to learn mo-

tion patterns of people from laser scanner data and to

derive hidden Markov models (HMMs) from the pat-

terns. They later use the HMMs to estimate current

as well as also future positions of people. The authors

evaluated their approach in different settings. Exper-

imental results show that the HMMs can be used to

estimate the position of a single person and also mul-

tiple persons in the environment, even during times of

occlusions (Bennewitz et al., 2005, 5.2.1 - 5.2.2).

Especially related to this work is their experiment

to improve the navigation behavior of the robot using

the motion patterns (Bennewitz et al., 2005, 5.3). An

∗

search is performed for the least-cost path in the

time-space conﬁgurations of the robot with predicted

people trajectories, leading to a signiﬁcant reduction

in the time needed for the robot to perform a naviga-

tion task with prediction enabled.

An approach with a two-step prediction method

was presented by (Foka and Trahanias, 2010). They

describe an approach to enhance the path planning ca-

pabilities of a mobile indoor robot by trying to predict

future motion of humans in the environment. Their

solution makes predictions on two levels. The short-

term prediction only tries to predict the position of a

sensed human in the next time step. More interesting

in the context of this work is the long-term predic-

tion, which works with the help of having deﬁned so-

called hot points in the environment. Those are points

where people will most likely end their paths through

the environment, e.g. stairs, elevators or seats. These

points can be either manually deﬁned or automatically

learned. The connections between tracked people and

hot points in their ﬁeld of view will be interpreted as

possible paths they take and those position in the map

will be penalized for the robot, so it is less likely that

robot and person will meet.

Another very interesting work by (Luber et al.,

2010) employs the concept of social forces to predict

the future actions of people, especially in highly pop-

ulated environments. The social forces model the be-

havior of people in crowds and are used to improve

predictions during multi-target tracking in their work.

The authors have proven the concept by evaluating the

number of data association errors in their multi-target

tracker during occlusion of targets. Using the social

force model instead of just a constant velocity model

enabled them to reduce the number of data association

errors up to 50%, depending on the scenario. How-

ever, in that work, their predictions are only used for

improving the tracking (by improving the data asso-

ciation step), and not for the long-term path planning,

in contrast to this work.

3 STATE ESTIMATION

The state of the smart environment is estimated us-

ing Bayesian ﬁlters. The whole process is described

in detail in the previous work (Arndt and Berns,

2012b, Section 2), so this section will just give a brief

overview about the process and it explains modiﬁca-

tions and improvements relevant to this work. For the

full details, the reader is referred to the previous work.

People in the environment are detected using

AmICA wireless sensor nodes (Wille et al., 2010)

equipped with passive infrared (PIR) sensors. These

sensor-events are fed to a probabilistic ﬁlter which

tracks the positions of people in the environment.

The internal state space of the probabilistic ﬁlter

is an undirected graph G(V,E) similar to the one used

ICINCO2015-12thInternationalConferenceonInformaticsinControl,AutomationandRobotics

by (Liao et al., 2003). Let the vertices of this graph

be v

∈ V and the edges e

i j

∈ E. The people that

are tracked are assumed to be moving on these edges

(edge e

i j

is the one connecting vertices v

and v

While the possibility of having complex models to

describe people’s movements in the environment has

been mentioned previously (Arndt and Berns, 2012b),

the authors have only used simple ones until recently.

For this work, the probabilities for moving from one

edge to another edge have been speciﬁed for interest-

ing vertices of the motion graph. Formally, the prob-

abilities p(e

i j

) for transferring from edge e

i j

edge e

are now initialized non-uniformly for some

vertices. This allows to model paths that are much

less likely to be traversed by humans as others.

For the experiments in this work, the graphs as

well as the transition probabilities have been manu-

ally deﬁned. However, it should be noted, that there

are various methods available in the literature to infer

the layout of such a graph and the respective transi-

tion probabilities from observations of the environ-

ment. For example, (Bennewitz et al., 2005) deﬁne

resting places between which trajectories are learned

and (Ikeda et al., 2012) use a very similar sub-goal

concept to learn positions at which people take deci-

sions on their further paths.

4 PREDICTIVE PATH PLANNING

4.1 State Prediction

To understand how the evolution of the environment is

predicted, it should ﬁrst be recapped how probabilis-

tic ﬁlters are used to track objects. They generally

work in two steps: ﬁrst, the current state is predicted

using models for motion and afterwards the belief is

updated with new incoming sensor information.

This separation into two steps is the reason why

these ﬁlters are very well suited for the long term pre-

diction of the evolution of the environment. If the

update step is simply skipped, the ﬁlter will contin-

uously predict the state of the environment. For this

case, the well-known recursive Bayesian update rule

can then be re-written as in (1). In the formula, η is

the normalizing constant while x

t−1

and x

represent

the previous and the current state of the environment,

respectively.

belief(x

) = η

p(x

t−1

) belief(x

t−1

)dx

t−1

(1)

In the implementation of this work, this process

is decoupled from the on-line tracking of the people.

When a new path has to be planned, a copy of the cur-

rent belief of the on-line tracker is created and only

this copy is then iteratively updated to “see” into the

future, leaving the rest of the tracking framework un-

affected.

4.2 Evaluation of Risk

To ﬁnd safe paths in the environment, the notion of

safety is important. This work will deﬁne the risk im-

posed on a human being by the robot exactly as in

(Arndt and Berns, 2014, sec. 3.1), as it has shown to

be a useful metric. To recap, the function that gives

the cost in terms of risk is a parameterized piecewise

polynomial according to (2).

a,b

: [0;∞] → [0;1]

a,b

(d) =

(

1 − (a

−1

d ≤ a

0 d > a.

(2)

The function assigns a risk-cost for each distance

d between the human and the robot. It will be max-

imal at d = 0, i.e. when robot and person coincide

and monotonically decrease till zero. The parame-

ters a and b are used to control the exact shape of the

curve. Parameter a reﬂects the distance from which

on the cost will be zero, i.e. it deﬁnes which distance

is assumed to be perfectly safe. The second parame-

ter b > 0 deﬁnes the steepness of the cost curve. For

the experiments later in this work, the cost function

8,2

(d) has been used. An illustration of that instance

of the function is given in Figure 1.

0 2 4

8 10

0.5

Distance [m]

Cost

8,2

(d)

Figure 1: Plot of the cost function for a = 8 and b = 2.

As outlined in Section 3, the state estimation of

people’s positions is done on a graph structure. The

risk function is thus applied to the belief (e.g. rep-

resented by particles) and the outcome is a separate

graph structure, the cost graph, with edge weights

representing the risks associated with driving along

the corresponding edge (Arndt and Berns, 2014, sec.

3.3.2).

In a last step, the edge weights of this risk cost

graph must be fused with the ones of the classic dis-

SafePredictiveMobileRobotNavigationinAwareEnvironments

tance cost graph, to obtain a resulting graph that al-

lows to ﬁnd paths that have minimal costs in terms

of both safety and distance. This fusion takes two

weights α and β as arguments which can be used to

adapt the preference for safe or short paths, see (Arndt

and Berns, 2014, sec. 3.4) for details.

4.3 Planning

Path planning for the mobile robot takes place on the

same graph which is also used to constrain the human

motion and where the tracking of people takes place.

This has shown to be very convenient, as only a single

representation of the state space has to be maintained.

It was noted before, that the complexity of tem-

poral path planning is high and thus not computation-

ally feasible for all applications. However, for typical

graphs, our research has shown that it is perfectly fea-

sible to do the prediction for all simple (without hav-

ing cycles) paths from start to goal and to ﬁnally select

the one with the least predicted costs. This subsection

goes more into detail of how the candidate paths are

evaluated for the resulting cost.

For each candidate path

,..., v

) between the

start vertex v

and the goal vertex v

, the algorithm

AnalyzePath (see Figure 2) will be called with the

current belief at the time of planning. This algorithm

further needs the two parameters l

step

and v

robot

which

deﬁne the step length for discretization and the as-

sumed robot velocity, respectively. The step length

is important, because it deﬁnes the granularity of the

planning process in the time-dimension.

Roughly speaking, the algorithm will simulate the

robot driving a distance of l

step

and then predict the

future at the next point of time. Setting l

step

to a

smaller value increases the time resolution of the pre-

diction, but will of course also slow the algorithm

down. Reasonable values for the two parameters are

e.g. l

step

= 1m and v

robot

= 0.5

, leading to a time of

two seconds between predicted steps.

As long as the end of the path has not yet been

reached, the ﬁlter is advanced and the next segment

(the distance l

step

) will be analyzed with the algo-

rithm AnalyzeSegment (see Figure 3). This algo-

rithm takes the current edge e

i j

, the current linear po-

sition t on the vertex, the distance to travel d and the

current accumulated cost c as arguments. It traverses

the current edge for the speciﬁed distance d. If it can

stay on the edge, the fraction of the traversed distance

of the edge’s weight is summed up to the cost c and

the control is returned to the higher level algorithm.

If, however, the end of the current edge is reached it

Every simple path from start to goal qualiﬁes as a can-

didate path.

will ﬁrst check if the end of the path has been reached

in which case it returns and also the AnalyzePath al-

gorithm will terminate. If the path is not ending, the

algorithms calls itself recursively for the next edge till

the requested distance has been traversed or the end of

the path has been reached. At the end, when the single

costs of all candidate paths are known, the one with

the lowest overall costs (as returned in Algorithm 2

line 13) is selected as the resulting path.

To make these steps more intuitively accessible,

the rest of this section is dedicated to an example of

the algorithm applied to a real-world path-planning

task. Figure 4 shows the output of the “classic” path

planner that uses probabilistic information (as de-

scribed in (Arndt and Berns, 2014)), but does not do

any prediction about the evolution of the state.

From ﬁrst glimpse, this path does indeed look

quite reasonable, as it aims to avoid the region of high

probability for a person being present (red patches on

the heatmap). If, however, the prediction is enabled,

the path looks different and at ﬁrst “worse” (i. e. more

expensive), see Figure 5 which depicts the situation

at the time of planning. In this and the following ﬁg-

ures, the blue circle will indicate the predicted robot

position.

In the subsequent ﬁgures 6 and 7, the ﬁlter is ad-

vanced as the robot (hypothetically) moves along the

planned path. Based on the motion model of the prob-

abilistic ﬁlter, the belief takes certain “paths” of the

graph. It can be easily seen that the chosen path

Require: l

step

> 0 {the step length for discretization}

Require: v

robot

> 0 {the assumed robot velocity}

Require: (v

,..., v

), n > 1 {the path to be ana-

lyzed}

Require: belief(x) {the initial belief}

Returns: Total cost of the path

1: AnalyzePath((v

,..., v

),belief(x)) :

2: InitializeFilter(belief(x)) {initialize the proba-

bilistic ﬁlter with the initial belief}

3: time delta = l

step

robot

4: {start on the beginning of ﬁrst edge of the path}

5: t ← 0

6: e ← e

7: c ← 0 {start with zero costs}

8: end reached ← false

9: while ¬end reached do

10: belief(x) ← AdvanceFilter(time delta)

{advance probabilistic ﬁlter for the simulated

amount of time}

11: (end reached,e,t,c) ←

AnalyzeSegment(e,t,l

step

,c)

12: end while

13: return c

Figure 2: Function to analyze a whole path.

ICINCO2015-12thInternationalConferenceonInformaticsinControl,AutomationandRobotics

Require: (v

,..., v

) {the whole path}

Require: d > 0 {remaining distance to travel}

Require: ∀e

i j

∈ E : w

i j

≥ 0 {all edge weights ac-

cording to the current belief}

Require: Successor(e) {function that ﬁnds the suc-

cessor of edge e on the current path}

1: AnalyzeSegment(e

i j

,t,d, c) :

2: l = EdgeLength(e

i j

)

3: t

= t + (d/l) {calculate the new position on

edge}

4: if t

> 1 then

5: {new position is beyond current edge}

6: c ← c + (1 − t) · w

i j

{sum up the fraction tra-

versed on current edge to the costs}

7: if ¬∃Successor(e

i j

) then

8: return (true, e

i j

,t,c) {there is no successor

of edge e

i j

, the path is ending}

9: end if

10: e

= Successor(e

i j

) {ﬁnd the next edge}

11: t

= 0

12: d

= d −(1−t)·l {calculate remaining length}

13: if d

< 0 then

14: return (false,e

,c) {no more distance to

travel, end recursion}

15: end if

16: return AnalyzeSegment(e

,c)

17: else

18: c ← c + (d/l) · w

i j

{sum up the fraction tra-

versed on current edge to the costs}

19: return (false,e

i j

,c) {as we are still on the

same edge e

i j

, just use new linear parameter

}

20: end if

Figure 3: Function to analyze a segment of a path.

mainly follows edges of the graph that have very little

probability of a person being present at the predicted

time in the future. If the original shortest path found

without prediction (Figure 4) is re-evaluated using the

predicted situation depicted in Figure 7, it can be real-

ized that the classic “shortest path” does not look that

good after all.

5 EXPERIMENTS

5.1 Experimental Setup

All of the conducted experiments are set in the facili-

ties of the authors’ research group, a common Univer-

sity building. It was equipped with a total of six Am-

ICA wireless sensor network nodes to provide ambi-

ent sensor data. A schematic view of the environment

Figure 4: Shortest path found by Dijkstra’s algorithm with-

out predicting the future states of the environment.

Figure 5: Evaluation of the path found with predictive path

planning at t = 0s.

Figure 6: Evaluation of the path found with predictive path

planning at t = 10s.

Figure 7: Evaluation of the path found with predictive path

planning at t = 36s (goal reached).

can be found in Figure 8. For each of the experiment

runs, the mobile indoor robot ARTOS was placed at a

ﬁxed start position and then given the instruction to

plan a path to a ﬁxed goal position with and without

enabled state prediction. The path was then traversed.

For the cost function in Equation 2, the parameters

have been set to a = 8 and b = 2.

Experiments were conducted in two sets. The ﬁrst

one was done with the real robot in the real environ-

ment to prove the applicability of the proposed ap-

proach. While these experiments are of great impor-

tance, as no simulation environment can replace the

reality, they are unfortunately unable to provide sta-

tistically relevant data, as the count of runs is limited.

For this reason, a second set of experiments was con-

ducted in a simulated version of the same environ-

SafePredictiveMobileRobotNavigationinAwareEnvironments

Figure 8: Layout of the environment within which the ex-

periments have been conducted. The graph for tracking,

prediction and path planning has been overlaid. Important

locations that are referenced in the text: A: start position of

the robot; B: goal position; C: meeting room.

ment. This simulation was based on the SimVis3D

framework (Wettach et al., 2010) and handled every-

thing from simulation of vehicle physics to the behav-

ior of the passive infrared motion sensors as well as

basic radio communication of the sensor nodes (Arndt

and Berns, 2012a).

5.2 Experimental Results

5.2.1 Reality

In this section, two experiment runs with the real

robot in the real smart environment will be presented.

During the ﬁrst run, a person (the author) was being

present in the meeting room all the time, “blocking”

the path through that room. As the models indicate

that, if someone is present in that room, the person

is unlikely to leave it soon, the robot predicts the sit-

uation and thus takes the path through the hallway.

Figure 9 shows the initial situation at the time of plan-

ning. The current belief as estimated by the particle

ﬁlter shows a high probability in the area of the meet-

ing room, which reﬂects the situation well. The posi-

tion of the robot itself, as predicted or localized by its

own localization system, respectively, is marked by a

dot and the resulting best path is visualized by arrows.

Figure 10 shows the robot while traversing the

hallway. It is important to note that the ﬁrst part of

the illustration (Subﬁgure 10(a)) represents the pre-

Figure 9: Experiment run one, initial situation at t = 0 with

resulting best path (according to the prediction).

diction at the time of planning while the second part

(Subﬁgure 10(b)) is a representation of the actual sit-

uation at the time the real robot passes that point. It

can be seen that the belief in reality differs from the

predicted belief, but this is due to the fact that the real

belief is updated using new sensor values while the

prediction does not have these information available.

Nevertheless, the similarities are clearly visible. Fig-

ure 11 shows an actual photo of the robot at approxi-

mately the marked position.

(a) Prediction

(b) Reality

Figure 10: Experiment run one, robot traversing the hall-

way.

Figure 11: ARTOS following the path through the hallway,

situation roughly corresponding to Figure 10.

Fast forwarding further, the robot can be seen

reaching its goal position in Figure 12. Again, this

ﬁgure can be consulted to evaluate the accuracy of

the prediction. By comparing it to reality, it can be

seen that both beliefs about the situation differ more

strongly than in in the previous illustration, but they

are still close to each other. In both of them, the prob-

ability for the person still being present in the meeting

room is rather large.

ICINCO2015-12thInternationalConferenceonInformaticsinControl,AutomationandRobotics

(a) Prediction

(b) Reality

Figure 12: Experiment run one, robot reaching the goal.

Figure 13: Experiment run two, initial situation at t = 0 with

resulting best path (according to the prediction).

For the second experiment run in reality, a person

was walking through the southern part of the hallway

at the time of planning (the exact ground truth is not

known and also not indicated in the ﬁgures). For this

situation, the models indicate that it is very likely that

the person will continue its path through the hallway

and consequently, the predicted evolution of the state

leads the robot’s path planner to choose a path through

the meeting room to minimize the chances of collision

and maximize the safety of the path. The initial situa-

tion shows the belief focused in the hallway, although

not as highly concentrated as for the previous run, see

Figure 13.

The situation after some time has passed is illus-

trated in Figure 14. The belief in reality has changed

compared to the initial situation, but not as drastically

as predicted by the planner. Still, the prediction is not

wrong, as it states that the person is most likely lo-

cated in the hallway.

Finally, in Figure 15 the situation when the robot

reaches the goal is depicted. Just as in the previous

run, the prediction further deviates from the reality,

(a) Prediction

(b) Reality

Figure 14: Experiment run two, robot traversing the meet-

ing room.

(a) Prediction

(b) Reality

Figure 15: Experiment run two, robot reaching the goal.

slowly evolving into a uniform distribution over the

whole state space.

Regarding the computational feasibility it should

be noted that during the experiments, everything

was

calculated on-line and on-board of the robot. A WiFi

connection to the robot was only used for visualiza-

tion and initialization purposes. The calculation of the

best path took about six seconds for the shown graph

Including the reception of frames from the wireless

sensor network, the processing of the probabilistic ﬁlters as

well as the planning with prediction

SafePredictiveMobileRobotNavigationinAwareEnvironments

on an (at the time of writing) eight-year old ultra-low

voltage processor

5.2.2 Simulation

As already outlined at the beginning of this section,

the simulation experiments were used to conduct a

large number (compared to the manually conducted

experiments in reality) of runs with prediction en-

abled and also disabled. These runs were then statis-

tically analyzed to compare the traditional path plan-

ning with the proposed temporal path planning in

terms of safety.

Due to the use of the simulation environment, the

ground truth of the person’s position was available

and thus the evaluation of the safety, computed just

as in (Arndt and Berns, 2014, sec. 4.2.2), was much

easier. Four different trajectories for people have been

simulated, two of them represent the same situations

as with the real robot: walking through the southern

hallway (situation 1) and staying in the meeting room

(2). The other two are different as they do not be-

have like modeled in the ﬁlter, but take paths that are

less likely: starting in the meeting room and leaving

it through the door at the west (3) or the door at the

east (4), respectively.

For all the classes, the mean duration of the traver-

sal d, the mean distance between robot and person x

as well as the mean risk-cost c are given in Table 1.

The standard deviations of the corresponding values

are sufﬁxed with a subscript σ. A total sum of 113

experiment runs have been used to calculate these val-

ues.

Table 1: Comparison of the effects of prediction using sim-

ulated experiment runs.

Sit. Pred. d [s] d

x [m] x

c c

1 Off 74 27.8 10.2 1.8 0.20 0.10

On 132 23.7 12.3 1.5 0.09 0.07

2 Off 64 3.4 7.8 0.8 0.27 0.06

On 63 4.6 9.9 0.6 0.16 0.04

3 Off 62 3.5 9.5 0.3 0.17 0.01

On 66 3.5 9.8 0.1 0.17 0.01

4 Off 63 5.0 8.5 1.2 0.23 0.12

On 69 4.0 10.1 0.1 0.09 0.01

In all regarded situations, the active prediction in-

creases the mean distance x between robot and per-

son and thus decreases the risk-costs c associated with

that path, although the effect is not that distinct in sit-

uation three. However, it must also be noted that the

reduced risk often comes at the cost of an increased

Intel Core Duo U2500 at 1.20GHz

duration of traversal, although not always as promi-

nent as in situation one.

6 CONCLUSIONS AND FUTURE

WORKS

Building on previous work that deﬁnes metrics for

safety and how to ﬁnd a trade-off between short and

safe paths, a method to predict the evolution of the

environment of a mobile robot, using external sensor

information from a smart environment, has been in-

troduced. The theoretical concept has been validated

with a real mobile robot in a smart environment. Re-

sults of the experiments show that (given good mod-

els) the evolution of the environment can indeed be

predicted to a degree that allows to optimize the path

planning in mobile robots. The simulation experi-

ments aim to analyze the concept in a more statistical

fashion, because one may of course argue that the ex-

periments in reality lack diversity. Nevertheless, the

results of these experiments also validate the princi-

ple.

The accuracy of the prediction could in the fu-

ture be increased using more sophisticated models

that also take into account the intentions people have

while moving through their environment, similar to

the goal-orientation described by (Bruce and Gordon,

2004). More complex models could then also be

trained using learning algorithms (as outlined by e.g.

(Foka and Trahanias, 2010)) instead of being hand-

crafted.

Additionally, it would be very interesting to de-

crease the computational complexity of the proposed

approach. While being perfectly feasible for the

examined examples, there might be situations with

much larger graphs or search-spaces in which it might

be needed to switch to heuristics or to ﬁnd more ef-

ﬁcient algorithms to be still able to plan paths in the

spatio-temporal domain.

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SafePredictiveMobileRobotNavigationinAwareEnvironments