first steps towards emotionally expressive motion control for … · domestic applications...

First Steps Towards Emotionally Expressive Motion Control ForWheeled Robots∗

Steffen Muller, Thanh Q. Trinh and Horst-Michael Gross

Abstract— During social interaction between humans androbots, body language can contribute to communicate mutualemotional states. In this paper, a method is presented, thatenables wheeled robots with differential drive to express variousemotional states by means of different movement styles duringgoal-directed motion. The motion control of the robot utilizesan objective-based motion planner optimizing the control com-mands in a high-dimensional search space by means of anevolutionary algorithm. The main contribution in this paper isan objective function that uses human feedback on the perceivedrobot emotion in order to evaluate the possible robot controlsequences. First group experiments have been conducted inorder to demonstrate the system and find suitable movementstyles for possible emotional states.

I. INTRODUCTION

In continuation of [1], [2], the aim of our current researchproject SYMPARTNER (SYMbiosis of PAul and RoboTcompanion for Emotion sensitive caRe) [3] is the devel-opment of a social robot companion that is intended fordomestic applications especially in one person households.One focus of the project is the emotion awareness of thesystem. On the one hand, we try to recognize the moods andemotional states of the user by means of on-board sensingcapabilities and incorporation of a smart home installation,on the other hand, the emotion aware design of the systemtries to evoke positive feelings in the user. Futhermore,the intended long-term interaction benefits from a strongemotional binding between human and robot. To this end,we give the robot a character with own emotional states,that are to be expressed to the user by means of differentmodalities. Among animated eyes, head gestures, and voicemodulation, the body language of the robot seems to be apromising instrument for that.

In contrast to humanoid robots, our system is designed asa low cost platform and, therefore, has only five degrees offreedom (see Fig. 1). Besides the movable ears and a tiltservo for the head, the robot is equipped with a differentialdrive consisting of two driven wheels on the front side anda castor wheel in the rear. The maximum velocity of thatrobot is about 1 m/s. For obstacle and people detection, thereare two ASUS Xtion depth cameras (one in the head facingdownwards and one in the rear) as well as a Kinect 2 RGB-Dcamera in the head facing horizontally forward.

*This work has received funding from the German Federal Ministryof Education and Research (BMBF) to the project SYMPARTNER (grantagreement no. 16SV7218).

The authors are with the Neuroinformatics and CognitiveRobotics Lab, Ilmenau University of Technology, Germanywww.tu-ilmenau.de/neurob

Tiltable head including:- movable ears- eye-display- Kinect 2- ASUS Xtion

Storage tray for personal items including:

- stroke sensor

Moving base including:- touch display- ASUS Xtion facing backwards

- contact sensitive cover- dif ferential drive (inside)- battery for 6h operation- charging contacts for docking station

1.4m

, 25k

g

Fig. 1. Robot Alfred with its main sensors, actuators, and interactiondevices; conceptual design by Hassenzahl and Welge, University of Siegen;construction and implementation by MetraLabs GmbH Ilmenau

This paper is focussed on the expression of robot internalemotions by means of specific movement patterns that areto be shown during the normal operation of the robot. Thatmeans, the already challenging navigation to goals in narrowhome environments is to be augmented by different motionstyles.

Heider and Simmel [4] already showed that people doassociate emotions to abstract objects based on a two dimen-sional movement pattern. Here relations to the environmentand other objects (actors) over time seem to play an impor-tant role in addition to the velocity and acceleration profile.Correlation of perceived emotions to shape and velocity ofrobot movements has also been investigated by Dang et al.[5]. In a Wizard of Oz experiment, they tested round vs.sharp angled shapes of movement trajectories at differentvelocities.

This shows that the movement patterns should not bedisregarded in designing of an emotional robot. Also ifmainly other modalities are used for expression of emotions,the actual movement behavior should not evoke conflictingemotions to achieve a natural and consistent impression.

Studies like the aforementioned one have a general draw-back. They lack in optimality of the robots movementpatterns with respect to the recognizable emotion. Usually,

in: IEEE Int. Symp. on Robot and Human Interactive Communication (RO-MAN), Lisbon, Portugal, pp. 1351-56, IEEE 2017

the effect can only be as good as the wizard controls therobot. For future work in assistive mobile robots, the aimshould be to have a system available which can generatemovement patterns on its own and gets the feedback on theperceived emotion from observing people in order to improvethe own motion patterns.

In order to go in that direction, the developed motionplanner can be trained with arbitrary movement patterns. Af-terwards, the produced patterns are labeled with an emotionalstate by human observers. By means of that, for a given ordesired emotional state of the robot, the most appropriatepattern can be chosen among the available templates.

The remainder of the paper is structured as follows. First,a coarse sketch of the approach is given followed by somekey ideas of the developed local motion planner used inthe system. The main part consists of the description of theobjective function used for evaluation of the suitability ofpotential movement trajectories according to the intendedemotional impression on human observers. Finally, someresults of the user experiments used for training the systemare presented.

II. EMOTIONAL NAVIGATION APPROACH

For our purposes, the robot’s state of affect is modeledusing the ALMA model [6] considering emotions, moods,and personality. Based on external and internal events dur-ing interaction and autonomous operation, the state is de-scribed in a three-dimensional space of pleasure, arousal,and dominance. That emotional state is used by the arbitrarymodalities in order to modulate the robot’s expression.

For the modulation of the movement style, the 3D-stateis projected to a coordinate in the 2D emotion space (2D-ES), consisting of the dimensions arousal and valence (eachranging from -1 to 1) as proposed by J. A. Russell [7] inorder to make it more handy for human spectators, whichare an essential component in the approach.

The basic idea is to have a motion planner that is able topropose potential movement commands and internally ratethese according to several pre-defined objective functions.This approach is known as Dynamic Window Approach(DWA), which was introduced by Fox et al. in [8] as thefirst objective-based motion planner for differential driverobots and is now commonly used in the robotic fields.As a result, the selected control command is a compromisethat is safe and satisfies various criteria. These criteria,implemented in form of objective functions, comprise agoal orientation, collision avoidance, or social constraints topeople in the surroundings. In extension of that approach,we implemented a further objective function considering theemotional impression on potential observers.

We found that the quality of the resulting control com-mands greatly depends on the complexity of the potentialmovement trajectories considered by the planner during thesearch process. In early experiments with our DWA motionplanner we found, that the bow like trajectories consideredby the DWA are not sufficient for generation of moredifficult and expressive motion patterns. For that purpose, we

developed a local motion planner [9] using an evolutionaryoptimization process for generating proposal trajectories witha high degree of freedom.

Given that framework, the idea of making the movementsemotionally expressive can be broken down to an objectivefunction, that is able to rate potential movement trajectoriesaccording to the desired emotional impression. For thatpurpose, we had to find a model that given an emotional statemaps trajectories onto a scalar cost value. These costs haveto be low for trajectories that match the intended emotionalexpression and high for those ones that are perceived asa different emotion. At this point, data from experimentswith human observers come into play. The data are usedto train the model and enable the robot to estimate theimpression of trajectories correctly. Initially, the robot doesnot know how to modify the motion behavior due to missingtraining data. Therefore, in an initial experiment the robot ismanually controlled by different people in order to record arepresentative set of expressive movement trajectories. Theaim here is to cover the whole emotional repertory of theemotion space. Up to now, we do not know either if therobot will be able to reproduce these movement patterns,nor which emotional impression these patterns will have tospectators. Based on this set of template trajectories, therobot can generate movement patterns on its own in a seconduser experiment. Due to the restrictions of the objectivefunctions and the motion planner these trajectories are,however, slightly different from the manually driven ones.Now a group of human observers provide their impressionsas emotion labels in the 2D-ES. These labels now can be usedto select an appropriate template from the set of recordedtrajectories given a desired emotion to be expressed.

At the current stage of development, the motion plannerand a suitable model for the emotional objective functionhave been implemented, and first user experiments have beenconducted showing that the approach is promising. At thispoint, we are able to generate visibly different motion styleswith our robot, which are applied in combination with targetdirected motion and obstacle avoidance.

III. EVOLUTIONARY MOTION PLANNER

One essential step towards the emotionally expressivemovement patterns is the objective-based local motion plan-ner developed for optimizing the control command sequencein a very high-dimensional search space. The motion plannerworks in an interval of 250 ms and provides the actualvelocity target for the robot’s motor controllers for thatperiod. In order to correctly estimate the outcome of acommand for the next time step, all possible continuationshave to be considered up to a certain planning horizon intime. This is of particular importance for objectives, likethe emotional evaluation, which are looking at the exactshape rather than checking only a collision free progress inany direction. Other approaches, like the DWA, introducevast simplifications to that search space by discretizing thecommand space and reducing the considered continuations


of the sequences to a constant velocity, which results in onlybow-like trajectories to be tested.

In order to keep the flexibility of possible command se-quences, our approach utilizes an evolutionary optimizationprocess searching the set of complete control sequencesrather than only for the next command. For that purpose,we hold a population P = {Ai|i = 1, . . . ,m} of possiblefuture acceleration sequences as individuals. These individ-uals Ai = (at|t = 0, . . . , f) consist of an accelerationvector at = (atx, a

tφ) for each time step in the future

(cycle time of the motion planner itself) of a window ofa few seconds (typically 3 to 4 sec.). ax is the translationacceleration and aφ is the rotational acceleration (see Fig. 2for a visualization of that modeling). The acceleration valuesare limited to the robot’s physical capabilities. The length ofthe planning horizon is limited by the minimum stoppingdistance but also increases the capability to plan over localminima in the cost function. On the other hand, a longerplanning horizon also increases the complexity of the searchspace drastically. Although, we can benefit from reusingthe population in future time steps, real-time constraints arelimiting the manageable planning horizon.

An evolutionary algorithm works iteratively for g gener-ations and consists of the following steps: evaluation of theindividuals’ fitness, selection, and reproduction of the bestindividuals. Mutation and cross-over during the reproductionensures an exploration of the search space, and the selectionbrings the population closer to the optimum. At the end ofa planning cycle, the first acceleration command of the bestindividual is executed and the population is transferred tothe next time step (Fig. 2). In the following, these phasesare described in more detail.

A planning cycle starts with the initialization of thepopulation. Here, we can cope with the weaknesses of therandom search in our algorithm, which can not guarantee,that a safe trajectory can be found. In order to enforceconsideration of safe trajectories, one part of the initial pop-ulation is generated deterministically, consisting of stoppingtrajectories of different length and direction. The remainingpart is reusing knowledge from the last cycle. The bestsequences from the preceding population are transfered intothe current time step by cutting off the first command andfilling up with af = (0, 0), resulting in a shift in time. Totake into account the deviation of the real robot velocityto the planned acceleration, the new first element a0 iscorrected by the deviation of the actual velocity vodometryto the planned one divided by the cycle interval ∆t.a0 = a1old + (v1

old − vodometry)/∆tOnce a population has been set up, the loop starts with

the fitness evaluation for the individuals. Thereto, by meansof a forward model of the robot’s physics, the accelerationsequence Ai can be converted to a velocity sequence Vi =(vt|t = 0, . . . , f) with vt = (vtx, v

tφ). These velocity

sequences in turn are limited to the robot’s maximum speedparameters and integrated to a movement path in worldcoordinates.

The resulting movement trajectories are then used for

Fig. 2. Encoding of individuals as sequences of acceleration vectorswhich are optimized for g generations in each planner cycle, propagationof the final population of one planner cycle to the next helps reusing theoptimization effort from past cycles and reduces number of generationsneeded in each planner cycle.

evaluating the fitness of the individuals. This is done by theset of objective functions, each yielding a cost value or a harddeny (in case of potential collisions). These individual costvalues are summed up and can be compared to the costsof other individuals later on. In our setup, the followingobjective-functions are used:

1) A path and heading objective is responsible fornavigating towards a given target position in worldcoordinates. This is done by evaluating a globallyplanned navigation function (using E* planner [10]) atthe trajectory’s end point and additionally evaluatingthe deviation of the orientation at the end point to thewanted goal orientation in proximity to the goal posi-tion. The navigation function is replanned periodicallyon a cost-map that incorporates the current obstaclesituation as recognized by the robot’s distance sensors.

2) A distance objective for avoiding collisions withstatic and dynamic obstacles. Trajectories are checkedconsidering the robot’s exact footprint for collisions ina static occupancy map as well as in the local mapcontaining the sensed obstacles.

3) A direction objective preferring forward motion of therobot to account for the limited sensor capabilities inthe rear.

4) A personal space objective to keep distance to peoplein the close proximity of the robot. For detected people,their future movements are predicted using a linearmotion model, and the distances to the robot’s potentialmovement path along the resulting trajectories is eval-uated using a Gaussian-shaped model of the personalspace.

5) The emotional objective that is comparing the es-timated impression on the human observers to thecurrent emotional state of the robot. Further details onthis follow in the next section.

Based on the cost value, the individuals of the populationare sorted in ascending order. This allows to prefer thebest individuals over weaker ones during the generationof offsprings for the next population. The next generationis built up from the n best individuals of the last one


(selection), and the remaining individuals are generated eachby combining two randomly drawn individuals from the lastgeneration. The index in the sorted list thereby is drawnfrom a normal distribution with mean 0 and a fixed variance,which defines the selection pressure. The at of the two parentindividuals are mixed into one new sequence, while the valueis taken either form the first or the second parent randomly.Last step is mutation of the at values by means of a normaldistributed random offset. After that, the loop starts overwith the new generation of individuals, while over all ngenerations the best rated sequence is stored for executionof its first command at the end of the planning cycle.

The evolutionary motion planner has already proven itsbetter performance compared to the DWA in a social navi-gation scenario. See [9] for comparative results.

IV. EMOTIONAL OBJECTIVE FUNCTION

In order to make the selection of the individuals dependingon the intended emotional impression on human spectators,we developed a new objective function taking the velocitysequences Vi of the unrolled individuals and a desiredemotional state in the 2D-ES and mapping it to a cost value.

The emotional impression of a robot’s movement trajec-tory depends on various factors of influence. Besides theactual velocity profile (translation and rotation), distancesand orientations to people in the surroundings seem to havean influence. Moving frontally towards people may evokeassociation to a curious mood, while avoiding people cansupport the impression of fear. Also the geometry of theenvironment and the robot’s position in the environment maymake a difference. If there is a free space, and the robotmoves close to the walls, it may appear shy compared toa movement in the center of the room. Also the movingdirection in relation to the robot’s destination has an influ-ence. Very goal-oriented movements indicate attention andcuriosity, while undirected patterns can express boredom.

All these factors make a data-driven model more complex.When designing a model, one has to consider the amount ofdata that is available for training. If the model is too complex,it might not be able to generalize in unseen situations. Dueto this, we decided to concentrate on the velocity profilesonly. Spatial relations to people and obstacles are plannedfor a second version of the approach, when more trainingdata will be available.

Therefore, as a data base for the model, we have a setT = {(Vj , {Epj })} of labeled template velocity profilescovering about 10m of robot movement each. Vj = (vt|t =0, . . . , tmax) are the velocity sequences and Epj ∈ 2D−ESare the labeled emotional impressions of observer p, whenthe robot performed the pattern Vj . Fig. 3 shows the velocityprofiles of three exemplary templates on the right side, whilethe emotional labels {Epj } are illustrated in the emotionspace on the left.

An additional essential aspect is the efficiency for evaluat-ing the model. The motion planner runs at 4 Hz, and in eachcycle it processes 5 generations with 60 individuals each.This results in 1200 fitness evaluations per second. This is

the same amount of trajectories as the DWA has to evaluate,if the 2d velocity space is discretized in 15x20 bins.

Furthermore, in contrast to the other objective functions itis necessary to consider also a historic context when decidingon the suitability of future trajectories. For example, this isessential to continue a sinusoidal movement pattern in thecorrect direction rather than starting a new sinus pattern inan arbitrary direction in each time step. To that end, weadded a history part (v−h, . . . ,v−1) to the velocity profileVi, before the voting takes place. This v consists of the realodometry values measured in the past. The length h has beenchosen between 2 and 4 seconds, which corresponds to 8 to16 velocity samples in the interval of the planner cycle.

The first idea for realizing the cost function was to traina predictive model that maps the input velocity profiles Viinto the 2D-ES. Then the distance in the 2D-ES to thedesired emotion yields the costs we are looking for – highcosts for undesired emotional impressions and low onesfor a good match. Attempts for realizing such a mappingbased on the training trajectories generated during the userexperiments was unsuccessful, since the space of possibletrajectories is so huge that the little amount of training datais not representative. So, the evolutionary optimization inthe planner each time found completely different trajectoriesthat were mapped exactly onto the desired emotion state and,therefore, got low costs. However, the resulting movementpatterns did not look like the training data at all.

The actual realization of the objective function, in contrastto the mapping attempt mentioned before, operates the otherway around. First, the emotional labels Epj are used to find aset of suitable template trajectories in the training data. Then,the actual velocity profile to be rated is matched against thesepatterns, and low costs are generated if the trajectory matchesthe training profiles at any position. If no matching positioncan be found, the costs returned are high.

In more details, for each template sequence j the densityof the labels {Epj } at the current desired emotion Ed isevaluated (step one in Fig. 3). A high density of labelsindicates a good match of the j-th template in emotionspace. These matches in the second step are converted intoa template specific prior cost value

Cj = 1− 1

|p|∑p

e−(Epj−Ed)

2/σ (1)

used as a constant cost offset for the matching process (cyanbars in Fig. 3).

After this computation, which has to be done only once perplanner cycle, the input velocity profile Vi is shifted alongthe templates (step three in Fig. 3), and a distance to thevelocities in the templates is computed and added as coststo the Cj (cyan curves in the diagrams of Fig. 3). Overall templates Tj and all time offsets in the templates, theminimum yields the final costs

C = minj,t

{Cj +

(1− 1

h+ f

f∑w=−h

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Fig. 3. Illustration of cost computation in the emotional objective function, for a given proposal trajectory and a desired emotional expression (input).First, the suitability of the templates (T1 red, T2 green, and T3 blue) in the emotion space is evaluated. The colored samples in the 2D-ES on the left arethe labels given by human observers during the training experiment. The sample density in a second step leads to template-specific prior costs, which areadded to correlation results during step three. The training velocity profiles on the right (only three are shown) are used to compute the costs by matchingthe input velocity profiles to the templates resulting in the cyan curves. The global minimum of these over all time offsets and templates yields the output.T1 is a slow, curved forward motion with occasional hesitation (perceived as fear or boredom), T2 is a slow motion with stops to look left and right (fearand anger), T3 is forward motion in narrow sine like pattern (excited, happy).

for the input trajectory with ρ defining the sensitivity fordeviations in the velocity space. In order to speed up theevaluation, dynamic programming is used for the minimumsearch. Additionally, the velocity samples from the historyof the trajectory have to be matched only once per plannercycle since they are the same for all proposal trajectoriescoming from the evolutionary motion planner. Therefore,increasing the context does not increase the computationaleffort drastically.

In future work, we plan to further investigate the forwardmapping approach, which failed so far, due to the badgeneralization properties in the high-dimensional input space.For consideration of additional context information, likespatial relations to people and objects along the movementpath, the template matching approach used so far seems tobe unusable. We plan to apply artificial neural networks asa predictive model, which maps the input trajectory and thecontext information into the 2D-ES. The approach of Leibigand Wahl [11] is promising, since it enables a network toknow if the input is close to the training data or not, whichhelps to identify those inputs for which the network stillgeneralizes insufficiently.

V. HUMAN LABELING EXPERIMENTS

As already mentioned, the proposed emotional navigationsystem is based on a dataset of emotional labels for distinctmovement templates presented by the robot to human spec-tators.

Two different group experiments have been conductedin order to get these data. Initially, there are no distinctmovement patterns that could be autonomously performedby the robot. Therefore, a first group experiment with 12 par-ticipants provided a spectrum of possible movement patternsand additionally aimed to prove the existence of a commonsense of emotional interpretation among the participants.For recording the manually driven template trajectories, aneasy to use control mechanism is required, since steeringthe robot with the keyboard is not that handy and onlyuseful for smooth straight trajectories. A remote controlby means of a 13 cm small model of the robot has beenimplemented for that purpose. The model can be moved ona small glass table and is tracked by means of a webcamcapturing a QR-code like pattern from below. The velocityobservations of that model are sent to the real robot, where


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Fig. 4. Emotion labels of the autonomous navigation experiment (blue- male, red - female). The robot performed emotional movement patternswhile targeting a goal in the hallway of our institute building while 11participants observed and rated their impression in the 2D-ES.

the velocity commands are directly relayed to the motorcontrollers resulting in a relatively direct replication of themodel robot’s movements.

During the experiment, in each case, one of the partici-pants controlled the robot along a hallway of our institutebuilding, while the remaining audience observed it and had tonote their impression by means of a cross in the 2D emotioncircle on a form. During the runs, the actual movementtrajectory of the robot was recorded. The group consistedof staff members and students of our lab in age between 24and 50 with 5 female and 7 male participants.

The visual analysis of the label data showed, that there arepatterns that make a similar impression on the observers, butothers are ambivalent (also visible in the data of the secondexperiment shown in Fig. 4). Since the ”puppeteer” had acertain emotion in mind for each trial, for most of the partsof the 2D-ES a significant pattern could be generated at theend. Only the lower right quadrant representing the relaxedmood is not covered sufficiently.

After the velocity patterns were recorded, the robot wasable to perform the movement patterns autonomously. There-fore, the recorded velocity profiles have been trimmed man-ually to only contain the desired pattern going in a straightdirection, and the emotional objective function was used asdescribed above but only one template Tj was active ata time. Finally, 19 patterns have been generated using theearlier recorded velocity profiles.

In a second experiment, the participants had to label theperceived emotion again while the robot drove autonomously,resulting in the data shown in Fig. 4. During trial 20, theemotional objective function was disabled as a reference,which results in the ”normal” navigation behavior. The labeldata shows that the impression is slightly biased towards theactive side of the 2D-ES in that particular case, which isdue to the faster and goal-directed motion compared to thepatterns with the activated emotion objective.

An analysis of the emotion labels showed, that the au-tonomously generated movement patterns are of a similarquality as the manually driven patterns with respect toperceivable emotions. A comparison of the average standarddeviation of the emotion labels given by the observers formanually driven trajectories (0.471) and the autonomouslydriven (0.493) shows that there is no significant differencein the interpretability of the patterns. The concentration oflabels in different sectors of the 2D-ES shows that there is acommon sense of emotional interpretation of movements inthe group as supposed in the beginning.

VI. CONCLUSIONS

We could show that it is possible to realize an autonomousmotion controller for a mobile robot, that is able to combinesafe, goal directed navigation with emotionally expressivemovement patterns. In order to overcome arbitrariness inthe design of emotional expressive patterns, we suggested toinvolve opinions of a group of people voting the performedmovement patterns directly in a real-valued emotion spaceand demonstrated the feasibility of such an approach. Openissues to be considered in future developments are alternativemodels for the emotional objective function also taking intoaccount further context information (e.g. spatial distances tousers and obstacles). Nevertheless, the approach of usingonly the velocity profiles without any context informationshowed a good performance in our user experiments.

REFERENCES

[1] C. Schroter, S. Muller, M. Volkhardt, E. Einhorn, C. Huijnen,H. van den Heuvel, A. van Berlo, A. Bley, and H.-M. Gross, “Re-alization and user evaluation of a companion robot for people withmild cognitive impairments,” in IEEE Int. Conf. on Robotics andAutomation (ICRA). IEEE, 2013, pp. 1145–1151.

[2] H.-M. Gross, S. Muller, C. Schroter, M. Volkhardt, A. Scheidig,K. Debes, K. Richter, and N. Doring, “Robot companion for domestichealth assistance: Implementation, test and case study under everydayconditions in private apartments,” in IEEE/RSJ Int. Conf. on IntelligentRobots and Systems (IROS). IEEE, 2015, pp. 5992–5999.

[3] Sympartner project page. [Online]. Available:http://www.sympartner.de

[4] F. Heider and M. Simmel, “An experimental study of apparent behav-ior,” The American Journal of Psychology, vol. 57, no. 2, pp. 243–259,1944.

[5] T. H. H. Dang, G. Hutzler, and P. Hoppenot, “Mobile robot emotionexpression with motion based on mace-grace model,” in 2011 15thInternational Conference on Advanced Robotics (ICAR), June 2011,pp. 137–142.

[6] P. Gebhard, “Alma: A layered model of affect,” in Proceedings ofthe Fourth International Joint Conference on Autonomous Agents andMultiagent Systems. ACM, 2005, pp. 29–36.

[7] J. A. Russell, “A circumplex model of affect,” Journal of Personalityand Social Psychology, vol. 39, pp. 1161–1178, Dec. 1980.

[8] D. Fox, W. Burgard, and S. Thrun, “The dynamic window approachto collision avoidance,” IEEE Robotics Automation Magazine, vol. 4,no. 1, pp. 23–33, Mar 1997.

[9] S. Muller, T. Q. Trinh, and H.-M. Gross, “Local real-time motionplanning using evolutionary optimization,” in Proceedings of TowardsAutonomous Robotic Systems (TAROS), 2017.

[10] R. Philippsen and R. Siegwart, “An interpolated dynamic navigationfunction,” in Robotics and Automation, 2005. ICRA 2005. Proceedingsof the 2005 IEEE International Conference on. IEEE, 2005, pp.3782–3789.

[11] C. Leibig and S. Wahl, “Discriminative bayesian neural networksknow what they do not know,” in NIPS Workshop: Deep Learningand Representation Learning, 2016.


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