Mobile Robots Current Trends Part 9 doc

Construction of a Vertical Displacement Service Robot with Vacuum Cups 229 Fig.. Construction of a Vertical Displacement Service Robot with Vacuum Cups 231 Fig.. Construction of a Vert

Construction of a Vertical Displacement Service Robot with Vacuum Cups 229

Fig 17 Pseudo circular movement a the positions of the platforms PLE and PLI during

translation; b The polygon of the trajectory

The radius of the circle inscribed in the travelled polygon is given by (1):

5 Modelling and simulation of the robot displacement

The displacement of the robot was modelled and simulated using Cosmos Motion software

(Alexandrescu, 2010a), (Apostolescu, 2010)

In order to simulate the robot translation, for the relative movement between platforms the

interior platform was considered to be fixed A parabolic variation was imposed for the

Figures 18, 19 and 20 present the simulation results

The simulations allowed the computation of the value of the maximum instantaneous

The needed power at the exit of the driving motor resulted equal to 1.42W

The orienting rotation of the robot was simulated for rotation cycle of 30º Figures 21, 22 and

23 present the simulation results

In the transitory areas, it can be noticed that the variation of the angular acceleration

presents deviations relatively to its theoretical shape This phenomenon can be explained by

the variation of the static charges during platform rotation

The computed maximum value of the couple was equal to 0.204 Nm The computed

maximum power at the level of the platform was equal to Prot = 0.13 W

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Fig 18 Variation of translation speed

Fig 19 Variation of translation acceleration

Fig 20 Displacement during translation

Construction of a Vertical Displacement Service Robot with Vacuum Cups 231

Fig 21 Variation of angular speed during platform rotation

Fig 22 Variation of angular acceleration during platform rotation

Fig 23 Angle variation during rotation

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6 Robot control

The robot can be controlled with a data acquisition board 7344 National Instruments and LabVIEW programming or with microcontrollers The microcontroller BS2 (Parallax) is used, easy to program but with a number of limitations concerning the control of motor speeds

Using a data acquisition board allows introducing home switches for each of four servo axes

in order to find the reference position For axis 1 (robot translation) and axis 4 (orienting rotation), home switches are mounted between the limiting micro switches For axes 2 and 3, representing cup translations for PLE and PLI, respectively, micro switches are used only as stroke limit The reference position is found with the help of a photoelectric system, as shown in Figure 24 The system consists of a light stop 6 fixed on the mobile plate 4 whose

displacement s gives the position of the cups The light stop moves between the sides of the

photoelectric sensor 2 (of type OPB 916)

Fig 24 Photoelectric system used in order to establish the reference position of axes 2 and 3

1 – corner support; 2 – photoelectric sensor; 3 – rod for movement obstruction; 4 – plate attached to the mobile rod; 5 – mobile rod; 6 – light stop; 8 – microswitch

Construction of a Vertical Displacement Service Robot with Vacuum Cups 233 Figure 25 presents the scheme of the photoelectric system used to determine the reference position When the light stop reaches the optical axis of the sensor, the state of its output

the transistor during its disconnection Connection to the data acquisition board is made through the NO contact of the relay Rel

The LabVIEW software program that allows founding the home switch is shown in Figure

26 The activation of limit switches is also needed during the search After the reference is found, the position counter is reset The program is applied for each of four axes of the acquisition board

The programs consists of two sequences introduced by the cycle 10 The first one searches the reference position and the second resets the position counter (subVI 9)

The subVI 1 loads the maximum search speed and performs axis selection The subVIs 2 and

3 load the maximum acceleration and deceleration The subVI 4 defines the movement

kinematics (S curve of the speed) A while type cycle is introduced The subVI 7 reads the

state of the search The subVI 12 seizes various interruption cases The subVI 13 stops the cycle

In order to clean glass surfaces, the robot must cover the whole window area, paying especial attention to corners The main control program of the robot controls the travel on the vitrified surface by horizontal and vertical movements, as well as by rotations that allow changing the direction An ultrasonic PING sensor (Parallax) was introduced as decision element for changing the direction and stopping The sensor is mounted on the PLI platform using the corner 3 and the jointed holder 2, as shown in Figure 27

Fig 25 Scheme of the photoelectric circuit

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Fig 26 LabVIEW program for founding the home switch: 1 – maximum speed load; 2 – acceleration load; 3 – deceleration load; 4 – elements of curve S (kinematics without jerk); 5 –

home switch use; 6 –while type cycle; 7 – reading of search state; 8 – delay producing; 9 –

position counter reset; 10 – sequential cycle with two sequences; 11 – search settings; 12 – reading of different interrupt situations; 13 –end cycle condition; possible errors indication

of possible errors

Construction of a Vertical Displacement Service Robot with Vacuum Cups 235

Fig 27 The ultrasonic sensor mounted on the interior platform: 1 – sensor; 2 – sensor holder;

3 – corner; 4 – interior platform PLI of the robot

Figure 28 presents a sequential cycle of travel The cycle consists of the following sequences: sequential translation from left to right (this sequence ends when the proximity of the right side rim is sensed); 90º clockwise rotation; lowering with a step; 90º clockwise rotation; sequential translation from right to left (this sequence ends when the proximity of the left side rim is sensed); 90º counterclockwise rotation; lowering with a step; 90º counterclockwise rotation

Fig 28 Travel cycle of the robot

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The robot covers the whole window area by repeating the travel cycle The robot stops if the

sensor S sends the signal of proximity of the bottom rim of the vitrified surface

The block diagram of the program is shown in Figure 29

Fig 29 Block diagram of main control program of the robot: 1 - setting port 1 as output; 2 -

setting port 2 as input; 3 - initialization of local variable; 4 - boolean local variable; 5 – while cycle of the travel program; 6 – travel stop; 7 – first order while cycles; 8 – sequences of the

first order cycles; 9 – sequences of the first order cycles

Construction of a Vertical Displacement Service Robot with Vacuum Cups 237 The program uses the ports 1 and 2 of the acquisition board The port 1 is used as program output, sending the commands towards the electro valves The port 2 is used as

input, receiving the signal from the sensor S The control 3 initializes the boolean local

variable as “False” The variable changes its state to “True” during vertical displacement

The signal from the sensor S is used also for stopping the horizontal translation

sequences

7 Conclusion

The chapter reports a number of very important results regarding the design and control of

a prototype of climbing autonomous robot with vacuum attachment cups

The robot construction is able to perform its intended function: the efficient cleaning of glass surfaces The vacuum attachment system ensures good contact with the support surface, is simple and reliable The modelling and simulation of the robot functioning, developed for platform translation as well as for relative rotation of the platforms, certifies that its performances are comparable to similar solutions conceived worldwide

The overall size of the robot, 350mm x 350mm x 220mm, proves an optimal degree of robot miniaturization

8 References

Alexandrescu, N.; Apostolescu, T.C.; Udrea, C.; Duminică, D.; Cartal, L.A (2010)

Autonomous mobile robots with displacements in a vertical plane and applications

in cleaning services Proc 2010 IEEE International Conference on Automation, Quality

and Testing, Robotics, Cluj-Napoca, Romania, 28-30 May 2010, Tome I, IEEE Catalog

Number CFP10AQT-PRT, ISBN 978-1-4244-6722-8, pp 265-270

Alexandrescu, N., Udrea, C., Duminică, D., & Apostolescu, T.C (2010), Research of the

Vacuum System of a Cleaning Robot with Vertical Displacement, Proc 2010

International Conference on Mechanical Engineering, Robotics and Aerospace ICMERA

2010, Bucharest, Romania,2-4 December 2010, IEEE Catalog Number

CFP1057L-ART, ISBN 978-1-4244-8867-4, pp 279-283

Apostolescu, T.C (2010) Autonomous robot with vertical displacement and vacuummetric

attachment system (I Romanian), Ph.D Thesis, POLITEHNICA University of Bucharest, 2010

Belforte G., Mattiazzo G., & Grassi R (2005) Innovative solution for climbing and cleaning

on smooth surfaces Proceedings of the 6th JFPS International Symposium on Fluid

Power, pp 251-255,Tsukuba, Japan

Cepolina, F.; Michelini, R.; Razzoli, R.; Zoppi, M (2003) Gecko, a climbing robot for wall

cleaning 1 st Int Workshop on Advances in service Robotics ASER03, March 13-15,

Bardolino, Italia, 2003, Available from http://www.dimec.unige.it/PMAR/ Miyake, T.; Ishihara, H.; Yoshimura, M (2007) Basic studies on wet adhesion system for

wall climbing robots Proc 2007 IEEE/RSJ International Conference on Intelligent

Robots and Systems, San Diego, CA, USA, Oct.29-Nov.2, 2007, pp 1920-1925

Novotny F.; Horak, M (2009) Computer Modelling of Suction Cups Used for Window

Cleaning Robot and Automatic Handling of Glass Sheets In: MM Science Journal,

June, 2009, pp 113-116

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Sun D., Zhu J., & Tso S K (2007), A climbing robot for cleaning glass surface with motion

planning and visual sensing, In: Climbing & walking robots: towards new applications,

pp.219-234, Hao Xiang Zhang (ed.), InTech, Retrieved from

<http://www.intechopen.com/books/show/title/climbing_and_walking_robots_towards_new_applications>

A Kinematical and Dynamical Analysis

of a Quadruped Robot

Alain Segundo Potts and José Jaime da Cruz

University of São Paulo

Brazil

1 Introduction

In general, legged locomotion requires higher degrees of freedom and therefore greatermechanical complexity than wheeled locomotion Wheeled robots are simple in general, andmore efficient than legged locomotion on flat surfaces Yet as the surface turns softer, wheeledlocomotion becomes inefficient due to rolling friction Furthermore, in some cases, wheeledrobots are unable to overcome small obstacles On the other hand, legged robots are moreeasily adaptable to different kinds of terrains due to the fact that only a set of point contacts isrequired; thus, the quality of the ground between those points does not matter as long as therobot can maintain appropriate ground clearance

Legged robots appear as the sole means of providing locomotion in highly unstructuredenvironments However, they cannot traverse every type of uneven terrain because they are

of limited dimensions Hence, if there are terrain irregularities such as a crevasse wider thanthe maximum horizontal leg reach or a cliff of depth greater than the maximum vertical legreach, then the machine is prevented from making any progress This limitation, however, can

be overcome by providing the machine with the capability of attaching its feet to the terrain.Moreover, machine functionality is limited not only by the topography of the terrain, but also

by the terrain constitution Whereas hard rock poses no serious problem to legged robots,muddy terrain can hamper its operation to the point of jamming the machine Still, under suchadverse conditions, legged robots offer a better maneuverability than other vehicles (Angeles,2007; Siegwart & Nourbakhsh, 2004)

The main disadvantages of legged locomotion include power and mechanical complexity Theleg, which may include several degrees of freedom, must be capable of sustaining part of therobotŠs total weight and, in many robots, must be capable of lifting and lowering the robot.Additionally, high maneuverability will only be achieved if the legs have a sufficient number

of degrees of freedom to impart forces in a number of different directions

In the last few years, this feature has given rise to a number of research activities on thesubject Despite all these efforts, the performance of legged robots is still far from what could

be expected from them This is true particularly because the robots performance depends onseveral factors, including the mechanical design, which sometimes may not be changed by thecontrol designer (Estremera & Waldron, 2008)

Legged robots present some problems that are not usual in wheeled robots For example,problems such as trajectory planning and stability analysis need a good kinematics anddynamics model of the system

12

2 Will-be-set-by-IN-TECH

Fig 1 Kamambaré I robot

Herein will be presented a kinematical and dynamical analysis of a quadruped robot namedKamambaré I (Bernardi & Da Cruz, 2007)

Like all the mobile robots with legs the topology of Kamambaré is time variant Deu to hisown gait, we have two different problems to solve First when there is at least one closedkinematic chain between the support surface and the platform, the robot’s behavior will besimilar to a parallel robot On the other hand, when a leg of the robot is in the air looking for

a new point of grasping, the model that best describes it is an open kinematic chain model,similar to the models of a serial industrial manipulator Through this work we will refer tothese two topological model as the platform for the parallel case of modeling and model ofthe leg for the second case reviewed like in (Potts & Da Cruz, 2010)

The analysis above, is important for bringing the platform or the gripper to some desiredposition in the space, but in our case it is not sufficient To move the platform or the gripperalong some desired path with a prescribed speed, the motion of the joints must be carefullycoordinated There are two types of velocity coordination problems, direct and inverse In thefirst case, the velocity of the joints is given and the objective is to find the velocity of the endeffector (platform or leg); in the other case, the velocity of the end effector is given and theinput joint rates required to produce the desired velocity are to be found

2 Kinematics model

Kamambaré I is a symmetrical quadruped robot It was developed for climbing verticalobjects such as trees, power poles, bridges, etc Each of its legs with four revolution joints.See Fig 1 At the end of each leg, there is a gripper All joints are powered by DC motors.The basic gait of the robot simulates the walking trot of a quadruped mammal In this type ofgait, the diagonals legs move in tandem While a pair of legs is fixed to the supporting surfaceand pushes the robot forward the other pair is on the air, seeking a new foothold, see Figure

2 According to that description, there are two basics stages for the legs, which will be named:

“leg on the air” to represent the leg seeking for the new foothold, and “pushing stage” whenthe leg is fixed and pushing the body to a given direction

of a Quadruped Robot 3

surface•

For a robot to move to a specific position, the location of the center of its body relative to

the base should be established first This is called by some authors position analysis problem

(Tsai, 1999) There are two types of position analysis problems: direct kinematics and inversekinematics problems In the first one, the joint variables are given and the problem is to findthe location of the body of the robot; for the inverse kinematics, the location of the body isgiven and the problem is to find the joint variables that correspond to it (Kolter et al., 2008).Two approaches will be taken herein for the complete modeling of the robot in accordancewith its topology Firstly, for the robot in the pushing stage the model will be like a parallelrobot with a closed chain between the two legs that are supporting the platform Then whenthe leg is “on the air” the model is of a serial manipulator attached at one of the corners of theplatform

2.1 Direct kinematics problem of the platform

In this section, the direct kinematics problem of the platform will be solved The system ismodeled as a parallel robot and the legs are stuck between the supporting surface and theplatform The analysis is performed using the Denavit-Hartenberg (D-H) parametrization,starting at the surface and advancing towards the platform

Table 1 Denavit-Hartenberg parameters for leg l in the pushing stage

Table 1 shows the D-H parameters for the “pushing stage” Frames{ B l },{ C l },{ D l }and{ E l }

the robotic platform The lengths of the links are L5, L4, L3, L2and L1, respectively, starting

at the pointO A l, origin of the frame{ A l } Index l,(l=1, , 4)is used to indicate the leg of

the robot, while index i,(i= 1, , 4)is used to indicate the i-th joint of the l-th leg In this

(Bernardi et al., 2009)

O T P=O T A l · A l T B l · B l T C l · C l T D l · D l T E l · E l T P (1)

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A Kinematical and Dynamical Analysis of a Quadruped Robot

4 Will-be-set-by-IN-TECH

Fig 3 Scheme of l-th leg.

Recalling that the structure ofO T A l,A l T B landB l T Pare:

2.2 Direct kinematics problem of the leg

expression to solve the direct kinematics problem for the leg on the air:

The use of 4 or 8 depends on which part of the gait is active In other words, if the leg l of the

2.3 Inverse kinematics problem for the platform

Since each leg has only four degrees of freedom, the position and orientation of the platformmust be specified in accordance with the constraints imposed by the joints

Using equations 7 and 6, it is possible to solve the inverse kinematics problem If both, clingingpointO A land the position and orientation of the platform[O P x,O P y,O P z,ψ P]are given as well

as the geometrical and mathematical constraints are respected, from equation 6 we have:

where: x PAB l= O P x − O A x l − O B x l and y PAB l= O P y − O A y l − O B y l

Equation 11 is subject to: