xiii simp osio brasileiro de automac a~o inteligente porto alegre … · the path planning method...

A COMPARISON BETWEEN A SIMULATED AND A REAL MOBILE ROBOT PATHTRACKING APPLICATION USING V-REP

Kenny A. Q. Caldas∗, Junior A. R. Silva∗, Felix M. Escalante∗, Valdir Grassi Jr∗, MarcoH. Terra∗, Adriano A. G. Siqueira†

∗Electrical Engineering Department - University of Sao Paulo at Sao CarlosAvenida Trabalhador Sao-Carlense, 400, Sao Carlos, SP, Brazil. CEP 13566-590

†Mechanical Engineering Department - University of Sao Paulo at Sao CarlosAvenida Trabalhador Sao-Carlense, 400, Sao Carlos, SP, Brazil. CEP 13566-590

Emails: [email protected], [email protected], [email protected],

[email protected], [email protected], [email protected]

Abstract— The focus of this work is the validation of the Virtual Robot Experimentation Platform, V-REP,as a reliable and resourceful simulator for robotics applications. For this purpose, a simulated and a real mobilerobot path tracking application are compared under the same conditions. A genetic path planning algorithmis used for generating the reference path for the mobile robot. A kinematic controller was implemented usingKanayma’s method. Simulated and experimental results are shown using a mobile robot e-Puck and the highprecision Vicon camera system.

Keywords— Mobile robots, Robots control, Path planning, Simulation.

1 Introduction

Study of the robotic systems has become a versa-tile and open field in all education levels, fromelementary school (Bers et al., 2002), (Churchet al., 2010) to postgraduate courses (Mirheydaret al., 2009). In large part, this is due to advancesin control systems, computer science, and commu-nications systems, which have made robotics moreaccessible. Nowadays, there is a variety of robotshapes, sizes, prices, and functionalities that allowfor a broad array of individuals, not necessarily re-searchers, to become interested in robotics. How-ever, depending on the cost and complexity of theproject, it is convenient to make use of simulationsoftware/environment beforehand.

Simulators play an important role in most re-search fields, especially in robotic systems. Ac-cording to Torres-Torriti et al. (2016), they be-came increasingly popular due to the progress incomputer technology, which allowed the develop-ment of tools to improve some pioneer simulators,such as those developed by Corke (1996), and byMarhefka and Orin (1996). Currently, there aresimulators widely used for different specific areasof robotics, such as for manipulators (Ferragutiet al., 2013) or mobile robotics (Michel, 2004).A few years ago, The Coppelia Robotics devel-oped the Virtual Robot Experimentation Plat-form (V-REPr) (Rohmer et al., 2013b), (Peraltaet al., 2016) , (Fabregas et al., 2016) . The simula-tor has a wide range of commercially known robots(manipulators and mobile), including the possibil-ity of constructing any other robot, as well as thesimulation environment. Additionally, it allowsthe versatility of communication with other soft-wares, making it possible to command and receiveinformation externally of the robotic project.

This paper focus on the comparison of arobotic application in a simulated environment inV-REP with a real world scenario. To this pur-pose, a kinematic control (Kanayama et al., 1990)of a mobile robot with differential traction is con-sidered. Initially, the control problem is repro-duced in simulated environment through the com-bination of V-REPr and MATLABr. After-wards, the same problem is applied in real timeexperiment using an e-Puck robot and a high pre-cision localization system composed by four Viconcameras. In both scenarios the reference path forthe mobile robot is generated by a genetic algo-rithm approach, according to Kala (2014). Thisway, the main contribution of this paper is thevalidation of the results obtained in V-REP as areliable and resourceful software for fast prototyp-ing of robotics systems.

The sections of this paper are organized inthe following way: in Section 2, the implemen-tation of the genetic algorithm for path planningproblems is discussed; in Section 3, the kinematicmodel of a differential mobile robot and the pro-posed controller are detailed. Section 6 covers themain results obtained in simulations and exper-iments and Section 7 approaches the discussionand conclusion of this work.

2 Path planning with Genetic Algorithm

The path planning method with obstacle avoid-ance uses a camera positioned above the path re-gion where the mobile robot will move, in a waythat it will cover all possible free and occupiedspaces, as shown in Figure 1. Based on this con-figuration, it is possible to implement a geneticalgorithm to find a collision-free path from a start-ing point to a target position.

XIII Simposio Brasileiro de Automacao Inteligente

Porto Alegre – RS, 1o – 4 de Outubro de 2017

ISSN 2175 8905 2026

The first step is to take a picture of the mapwith the positioned camera. This image is con-verted to a binary matrix by thresholding usingthe function im2bw from MATLABr, where eachpixel will have a value assigned: 0 for detectedobstacles (black) and 1 for free spaces (white).

Figure 1: Position of the camera and resultingpicture of the map. Source: Modified from (Kala,2014).

The representation of the coordinate systemof the map is also shown in Figure 1. The userchooses the starting position and the desired goalbased on the map dimensions. If the genetic algo-rithm detects that the chosen points are inside anobstacle or outside the map dimensions, an errormessage is shown.

The next step is to determine the amount ofturning points the resulting path will have. Figure2 illustrates a representation of a path generatedby the genetic algorithm. The amount of pointsin the path is the maximum number of turns it isexpected the robot to make in the map. If thisnumber is too high, it could result in very largecomputational burden and may generate a pathwith useless turns, increasings its length. On theother hand, if there are not enough points to con-nect the origin to the goal coordinates, it may leadto a non feasible solution or a collision-prone path(Kala, 2014).

Figure 2: Path generated by a set of points.Source: Modified from (Kala, 2014).

The initialization of the genetic algorithm isgiven by an initial population with a predefinednumber of individuals. An individual represents apossible solution to the considered problem. Forthe path planning case, it represents a reference

path composed of a set of points from the startingposition and the desired goal. The initial popula-tion is given by (Ismail et al., 2008)

InitialPopulation = [Ind1, Ind2, ..., Indn] , (1)

where Indn represents an individual and n thepopulation size. The structure of Indn is given by

Ind = [P0, P1, ..., PN+1] , (2)

where P is the (x, y) coordinates of the path, P0

is the starting position, N is the amount of turn-ing points chosen by the user and PN+1 the goalcoordinates.

One of the main elements of the genetic al-gorithm is the definition of the fitness function.The efficiency of an individual to solve the pathplanning problem is measured by the sum of thedistances traveled from the starting position to thegoal, evaluating each line segment individually. Ahigh penalty value is assigned to segments wherethere is an obstacle. The best individuals are theones with the lowest fitness values. The fitnessfunction is defined by

fitness = d0 ∗ p+ d1 ∗ p+ ...dn ∗ p, (3)

where p is a penalty multiplier for paths resultingin collisions and dn is the distance between twoset of points and is calculated by

d =√

(xn+1 − xn)2 + (yn+1 − yn)2. (4)

The next population generation is createdby using two functions: selection and crossover.The selection function chooses the parents of thenew population based on their fitness value. Thecrossover function is responsible to determine howthe genetic algorithm creates the new individuals,called children, for the next generation. The func-tions used in this works are the stochastic uniformmethod and scattered crossover, respectively. Adetailed description of these functions can be seenin the documentation of MATLABr optimizationtoolbox 2015.

The stopping criteria adopted is a predefinednumber of generations, in order to reduce the com-putational time required for the algorithm geneticto run. In case none solution is found under aset of parameters, an output error message willbe shown.

3 Mobile robot kinematic

A differential mobile robot is used in this work,meaning that each motor of the actuated wheelshas an independent actuation. The geometryanalysis of the robot is based on Figure 3. Theaxes (X,Y ) represent the inertial coordinates sys-tem; (X0, Y0) the local coordinates system; d thedistance between the center of the wheels axis P0



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and the center of mass Pc; b the distance betweenthe actuated wheel and the symmetry axis of therobot; r the wheel radius; α the clockwise anglebetween the inertial reference axis x and the sym-metry axis of the robot and θr and θl are the an-gular displacement for the right and left wheels.

Figure 3: Unicycle model.

The kinematic controller proposed has toconsider the nonholonomic and holonomic con-straints. For a differential mobile robot, there arethree kinematic constraints that must be observedduring the development of the controller (Coelhoand Nunes, 2003). The first is found in relationto Pc, due the velocity at P0 being parallel to theX0 axis. This constraint is given by

yc cosα− xc sinα− dα = 0, (5)

where (xc, yc) represents the center of mass Pc po-sition in the inertial coordinates system.

The other two constraints are present on therotation of the actuated wheels, since they can notslide

xc cosα+ yc sinα+ bα− rθr = 0 (6a)

xc cosα+ yc sinα− bα− rθl = 0. (6b)

Based on these equations, it is possible torewrite the three kinematic constraints of the dif-ferential mobile robot model in the matrix formby using q1 = [xc yc α θr θl]

Tas the gener-

alized coordinate of the mobile robot

R(q1) =

− sinα cosα −d 0 0− cosα − sinα −b r 0− cosα − sinα b 0 r

. (7)

The matrix R(q1) is full rank and canbe expressed as [R(q1) R2], to ensure thatR(q1) avoids singularity and that S(q1) =[(R−11 (q1R2)T I4

]Tis in the null space of R(q1)

(Siqueira et al., 2010). This way, S(q1)T becomes

S(q1)T =c(b cosα− d sinα) c(b cosα+ d sinα)c(b cosα+ d sinα) c(b cosα− d sinα)

c −c1 00 1

, (8)

where c = r2b . The kinematic model can be ex-

pressed byq1(t) = S(q1)q2(t) (9)

or

xc = c(b cosα− d sinα)θd + c(b cosα+ d sinα)θe

yc = c(b cosα+ d sinα)θd + c(b cosα− d sinα)θe

α = c(θr − θl).

(10)

The position vectors of the right and leftwheels are defined as q2 = [θr θl]

Tand the an-

gular velocities vectors as q2 =[θr θl

]T.

The proposed kinematic controller is based onKanayama et al. (1990). The controller uses thekinematic model of the mobile robot to generatethe desired angular velocities for the left and rightwheels, in order to follow the collision-free pathreferences found by the genetic algorithm.

The mobile robot reference and current poseare defined by qr = [xr yr αr]

Tand qc =

[xc yc αc]T

, respectively, where αr is given by

αr = tan−1(yr/xr). (11)

This way, it is possible to define the error be-tween the two states as qe = [xe ye αe]

T, where

xe = cosα(xr − xc) + sinα(yr − yc)

ye = − sinα(xr − xc) + cosα(yr − yc)

αe = αr − αc.

(12)

The desired linear and angular velocities, vd

and ωd, are calculated by the kinematic controllerby using the error between the current and desiredpose based on the given references by

vr =√

(xr)2 + yr)2 ωr = αr. (13)

Based on these equations, it is possible to de-fine the kinematic controller by

vd = vr cos(αe) +Kxxe

wd = wr + vr(Kyye +Kα sin(αe)),(14)

where Kx, Ky e Kα are the controller gains.In order to correctly update the desired values

for the left and right wheels, the angular velocitiesgenerated by the controller must consider the ra-dius and distance between the wheels. Therefore,



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the relation between the angular velocities and therobot physical parameters is given by

qd2 =

[θdrθdl

]=

[1/r b/r1/r −b/r

] [vdωd

], (15)

where θdr e θdl are the angular velocities for theright and left wheel that will be updated on therobot.

4 Simulation setup

The implementation of the genetic path planningalgorithm and the kinematic controller were madeusing the V-REPr simulator. V-REPr is a plat-form for virtual experiments with a wide varietyof robots in its library , including the e-Puck, thedifferential mobile robot used in this work. Thissimulation framework allows a rapid algorithm im-plementation, system verification and quick pro-totyping, which can greatly reduce the deploy-ment complexity of robotics systems (Rohmeret al., 2013a).

The first step is to design the simulation envi-ronment where the mobile robot will be moving.The map is represented in Figure 4. It has an areaof 2 × 2m2 divided in four rooms and a main cor-ridor. Once the map is defined, the collision-freepath is obtained by implementing the genetic algo-rithm. For the simulation, the origin coordinatespoints were chosen as x0 = 0.20m, y0 = 0.25mand goal as xg = 1.50m, yg = 1.80m.

Figure 4: Simulation environment in V-REPr.

The path generated from the genetic algo-rithm implementation can be seen in Figure 5.The function ga of MATLABr was used for thisapplication. The resulting set of points of the pathwere filtered, in order to eliminate the exceedingpoint and obtain a smooth path. In order to con-sider the robot dimension into the path planningproblem, the dimensions of the walls on the mapwere incremented by the radius of the robot body.This way, even if the generated path was very close

to one of the walls, the mobile robot would be ina safe distance.

Figure 5: Collision-free path generated by the ge-netic algorithm.

5 Experiment setup

The experiment performed to compare the resultsobtained from the simulation in V-REPr uses thee-Puck in an environment monitored by high pre-cision Vicon system.

(a) (b)

Figure 6: (a) Vicon camera model T-series T40S.(b) Reflective marker.

The Vicon cameras are positioned on thesuperior corners of the experiment environment.The tracking of the object inside a workspace isobtained by reflective markers placed on the mo-bile robot, and its identification is done throughthe distance between them. Figure 6 shows the Vi-con system and the reflective marker used in thiswork. The kinematic controller in MATLABr up-dates the control inputs and transmits them to thee-Puck through Bluetooth. The main characteris-tics of the Vicon cameras are presented in Table 1and a diagram of the experiment setup can be seenin Figure 7. Although the Vicon cameras have ahigh capture frame rate, the Bluetooth communi-cation between the computer and the e-Puck lim-its the sampling period to 0.14 seconds.

Once the experiment setup was defined, thesame map designed in the simulation on V-REPr



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Table 1: Vicon system technical characteristicsCamera T40S

Resolution 4Mp (2336 × 1728 )Camera frame rates 30 − 2000

Sensor Vicon Vegas S-4

Figure 7: Experiment setup diagram.

was built, using the same dimensions values. Fig-ure 8 shows the map used in the experiment.

Figure 8: Real map used in the experiment.

6 Results and discussion

The results obtained from the simulation and theexperiment are shown in Figure 9. The blue andred curve represent the simulated and real tra-jectories, respectively. The circles are the refer-ence path generated by the genetic algorithm. Itis possible to see that both results are very similar,which shows that using the V-REPr as a proto-typing tool is a good solution, since it is very ac-curate with the real system. The gains used in thekinematic controller are: kx = 0.1, ky = 1000 andkα = 10, based on Equation (14).

Figure 10 shows the orientation angle and Fig-ure 11 the lateral error for simulated and real sce-narios. The distance traveled by the e-Puck isused as abscissa for these graphs. Both resultsshowed that under the same conditions, V-REPr

could reproduce very closely the e-Puck behaviorduring its movement.

Figure 9: Path traveled by the e-Puck during theexperiment.

Figure 10: Orientation angle of the e-Puck duringthe experiment.

7 Conclusion

This paper presented a comparison between a sim-ulated and a real robotic system. A genetic algo-rithm was used to perform a collision-free pathplanning of a mobile robot in a structure environ-ment. This was done by positioning an overheadcamera that could capture a picture of the wholearea where the robot will move. In order to dothis, a map in V-REPr was designed to replicatea real world scenario and the genetic algorithmwas able to find a feasible path.

The control strategy was based on the kine-matic model of the e-Puck, as shown in the workof Kanayama et al. (1990), which generates thedesired angular velocities required to keep the mo-bile robot in the path by using a set of referencesfor the control inputs calculation.

The results were obtained initially in the sim-ulation environment in V-REPr and later in a realworld experiment, by using the Vicon cameras forlocalization. The comparison of the results ob-tained was satisfactory, since the simulation couldreproduce very accurately the behavior of the e-Puck in the real system, which validates the use



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Figure 11: Lateral error of the experiment andsimulation.

of V-REPr as a resourceful tool for quick proto-typing of robotics systems.

Future works involve the comparison of simu-lations in different environments and robotics sys-tems, as an alternative to reduce the time takento develop real world robotics applications.

8 Acknowledgments

This work is supported by National Council forScientific and Technological Development (CNPq)under grants 142080/2016-0 and by Coordinationfor the Improvement of Higher Education Person-nel (CAPES) under grants 1584685.

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