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Hindawi Publishing CorporationJournal of RoboticsVolume 2010, Article ID 984823, 10 pagesdoi:10.1155/2010/984823

Research Article A Geometric Approach for Robotic Arm Kinematics withHardware Design, Electrical Design, and Implementation

Kurt E. Clothier and Ying Shang

Department of Electrical & Computer Engineering, Southern Illinois University Edwardsville,Campus Box 1801, Edwardsville, IL 62026, USA

Correspondence should be addressed to Ying Shang, [email protected]

Received 24 May 2010; Accepted 18 August 2010

Academic Editor: Huosheng Hu

Copyright © 2010 K. E. Clothier and Y. Shang. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper presents a geometric approach to solve the unknown joint angles required for the autonomous positioning of a roboticarm. A plethora of complex mathematical processes is reduced using basic trigonometric in the modeling of the robotic arm.This modeling and analysis approach is tested using a ve-degree-of-freedom arm with a gripper style end e ff ector mounted to aniRobot Create mobile platform. The geometric method is easily modiable for similar robotic system architectures and providesthe capability of local autonomy to a system which is very di fficult to manually control.

1. Introduction

As technology increases, robots not only become self-sufficient through autonomous behavior but actually manip-ulate the world around them. Robots are capable of amazingfeats of strength, speed, and seemingly intelligent decisions;however, this last ability is entirely dependent upon thecontinuing development of machine intelligence and logicalroutines [ 1]. A crucial part in any robotic systems is the mod-eling and analysis of the robot kinematics. This paper aimsto create a straightforward and repeatable process to solvethe problem of robotic arm positioning for local autonomy.There have been many methods presented to allow this func-tionality ([ 2–4]). However, themajority of these methods useincredibly complex mathematical procedures to achieve thegoals. Using a few basic assumptions regarding the workingenvironment of the robot and the type of manipulation totake place, this paper proposes an easier solution which reliessolely on the designation of a point in the three-dimensionalspace within the physical reach of the robotic arm. Thissolution has been achieved using a strictly trigonometricanalysis in relation to a geometric representation of an armmounted to a mobile robot platform.

In addition to the ability of robustly reaching for anobject in space, it is also vital that the robot has some way of autonomously discovering such objects, determiningwhether they are capable of manipulation, and relaying thecoordinates to the arm for positioning. There has been workdone in the area of manipulating objects without the ability of autonomously determining their position ([ 5, 6]). Theapproach in this paper is similar to that used by Xu et al.[6], in which an end e ff ector is capable of retrieving variousobjects from the oor. The robot is assumed to have already located an object through various means and positioneditself in the correct orientation in front of the object. Thisrobust grasping algorithm can then be combined with otherwork involving path planning, obstacle avoidance, andobject tracking in order to produce a more capable robot.

The paper is organized as follows. Section 2 introducesthe hardware components needed in this project. Section 3describes the geometric approach in the modeling andanalysis of the robot arm kinematics. Section 4 presents theobject detection strategies for a moving robot. Sections 5and 6 are the mechanical design and the electrical designof the robot arm, respectively. Section 7 illustrates theimplementation of the robotic arm system, which can detect



2 Journal of Robotics

Mountingpoints

IR receiver

Cargo bay

Tailgate

Handle

Cargo bay connector

Figure 1: iRobot Create from iRobot, Inc. [ 5].

Figure 2: The iRobot command module.

and grasp random objects in the sensing eld. Section 8concludes this paper with future research direction.

2. Hardware

The robot used for modeling and test purposes is the iRobotCreate shown in Figure 1. This machine is the developmentalversion of the popular Roomba vacuum cleaners by iRobot,Inc. [5]. It can be controlled by the use of small computerscripts sent wirelessly or through a data cable from acomputer or can become completely autonomous by addinga controller to the cargo bay connection port giving completeaccess to all onboard sensors, actuators, and preprogrammedroutines.

The controller to be used for autonomous operationis the iRobot Command Module shown in Figure 2. Thisdevice is built around the Atmega168 microcontroller andhas 14336 bytes of available space for programs [ 7]. Thiscontroller can be used to read any of the iRobot Create’sinternal sensors, control its drive wheels, LEDs, and speaker,and interface with other external hardware.

A prefabricated robotic arm has been selected for use tominimize the time spent on mechanical design. The chosenarm is the AL5C robotic arm model by Lynxmotion, Inc. [ 8]shown in Figure 3. Also displayed in this image is the SSC-32 servo driver, the secondary controller used to drive each

Figure 3: AL5C arm from Lynxmotion, Inc. [ 8].

of the servo motors used by the robot. This controller willreceive operation commands from the Command Modulefrom the iRobot Create.

3. Arm Kinematics: A Geometric Approach

One of the central objectives of this venture is solvingthe autopositioning of the arm using as straightforwardof mathematic equations as possible. Using the standardDenavit-Hartenberg convention [ 9], a free body diagram of this arm can be created by representing each of the jointsas a translational symbol and showing the links connectingeach joint as a line in Figure 4. To model this system, it isnecessary to know how many degrees of freedom (DOF) areassociatedwith the arm. To determine the DOF, it is su fficientto count the number of controllable joints [ 2]. As shownin the free body diagram, there are ve degrees of freedomassociated with the arm, including base, shoulder, elbow,wrist, and wrist rotate. Each of these joints is constructedof a controllable servo motor with the movements. For allpractical purposes, the wrist rotate can be excluded fromthe majority of the calculations as it does not a ff ect actualpositioning of the gripper, only whether it opens vertically or horizontally. Without the need to calculate this joint’spositioning, only four degrees of freedom remain whichmust be accounted for in the calculations.

This physical robotic arm is illustrated in Figure 5(a) .Each angle is found in reference to the plane perpendicularto the continuation of the previous link. Each of three jointangles to be initially solved—shoulder, elbow, and wrist—will be represented as θx where x = 1, 2, 3 denotes theidentication number for that particular joint, respectively.The links connecting these joints are labeled as Lx and are of known values. Thegripperhasbeen removed from this initialrepresentation in accordance with the free body diagramstatements. The geometric representation of the robotic armis shown in Figure 5(b) . The capital D and H are used toshow the position of a point in the two-dimensional space inrelation to the ground directly beneath the arm base. Adding



Journal of Robotics 3

160mm

Gripper

175mm

Wrist

Wrist rotateShoulder

Elbow

Base

150mm70mm

40mm

100mm

Figure 4: Arm free body diagram with the end e ff ector.

h0 to show the known elevation of the base over the groundplane allows the end point to be represented as ( D, H -h0)in the two-dimensional space relative to the arm base asopposed to the ground below the arm base.

There are two scenarios of the robotic arm system. Therst scenario is that the gripper will approach the objectin a ground parallel fashion shown in Figure 6(a) . Thismeans that link L3 would always be parallel to the groundplane; therefore, this link can be entirely omitted from thecalculations as well. The height of the point is not dependentupon L3 at all, and the distance of the base to the point couldbe reduced by the known length of this link. The secondscenario which will be considered is if thegripper approachesan object directly from above such that that link L3 would beperpendicular to the ground plane shown in Figure 6(b) . Inthis case, the changes to the calculated position of the pointare somewhat reversed from what they were in the rst case.Now, the distance of the base to the point is unchanged by L3;however, the length of L3 must be added to the point heightH -h0. The coordinates ( D A, H A) will represent the respectivedistance and height of the arm needed to be positioned at thetranslatedpoints. These coordinate pairs satisfy the followingequations:

(D A, H A)par = (D − L3, H − h0),

(D A, H A)perp = (D, H − h0 + L3).(1)

The simplied system is showed in Figure 7, where theknown variables are L1, L2, H A, and D A. Point P consists of coordinates ( D A, H A). The unknown angles θ1 and θ2 are thesystem solutions. If a line is drawn from the origin to point P ,two triangles are created. The lower is a standard right angletriangle consisting of legs L, H A, and D A, which is

φ1 = arc tan H AD A

, L =D A

H A. (2)

The nal solutions of the angles θ1 and θ2 are

θ1 =arc cos L2

1 + L2 − L22

2L1L+ φ1,

θ2=

arc cos L21 − L2 + L2

2

2L1L2−

π 2 .

(3)

The angle θ3 for the parallel and perpendicular cases isθ3par = θ1 + θ2 and θ3perp = θ1 + θ2 + π/ 2. The last of theangles to be considered is the rotation of the base, θ0. To ndthis angle, the system is represented as a plane parallel to theground where the arm base is the origin containing x and y coordinates (0, 0). The solution to θ0 is given as

θ0 = arc tan ybase

xbase,

θ0 = arc tan ybase

xbase + π , when the tangent value is negative .(4)

The variable D in Figure 5 represents the distance topoint P and is solved by D = | ybase / sin(θ0) | .

4. Object Detection

From the discussions in Section 3, the arm is capable of positioning itself at any given three-dimensional coordinatesatisfying a format of ( xbase, ybase, θ0) within its area of reachability. However, this analysis has not specied how

such a position is determined. For this to be achievable, atype of sensor must be used. Two infrared range nders areneeded at the front of the robot for scanning purposes. Afterlinearization, these sensors return a distance in millimetersto anything blocking their line of sight within the specieddistance range. These distances are then used to determinethe position of an object in relationship to the robot armbase.

A simple trigonometric process is used to solve thecoordinates of some object at point P . Once sensors havedetected an object at point P , the known distance to theobject in combination with the known angle of eitherscanning servo can be used to determine the Cartesian

coordinates of the object with respect to either sensor. Thesensor used as this origin is dependent upon which sensordetects the stable object rst. In the diagram shown inFigure 8, the distance values of the sensors are representedas DL and DR. The corresponding servo angles are seen as Φ Land Φ R. The unknown values of this gure are the Cartesiancoordinates of the point P with respect to the left or rightsensor ( xLET, yLET) and ( xRET, yRET). The solutions to theseunknowns are found in the following equations:

xLET = DL cos(Φ L), yLET = DL sin(Φ L),

xRET = DR cos(Φ R), yRET = DR sin(Φ R).(5)




iRobot create

L1

L2

L3Robotic arm

without gripper

θ3

θ1

θ2

(a)

H -ho

H

ho

D

D

L3

L2

L1

θ3

θ2

θ1

(b)

Figure 5: Arm joint angles (a) and arm joint geometric representation (b).

H -ho

H ho

D

D

L3

L2

L1

θ3

θ2

θ1

Translated point(D-L3, H -ho)

Original point(D, H -ho)

(a)

H -ho

H ho

D

D

L3

L2

L1

θ3θ2

θ1

Translated point(D-L3, H -ho)

Original point(D, H -ho)

(b)

Figure 6: The link L3 is parallel to ground (a) and perpendicular to ground (b).

H A

D A

L

P

L2

L1

θ2

θ1φ1

Figure 7: Simplied system geometry.

With these coordinates found, the position of the objectwith respect to the base can be solved, and the resultingcoordinates can be used to position the arm. The values of the Cartesian coordinates ( xbase, ybase) in Figure 9 are foundby adding the coordinates found in the various equations tothe known distances between the base and the sensors. Thevalue of xdiff is the distance from either sensor to the arm basealong the x axis, and the value of ydiff is the distance fromeither sensor to the arm base along the y axis. The solutions

to the coordinates xbase and ybase with respect to the arm baseas the origin are

X base = X LET − X diff ,

Y base = Y diff + Y LET,

X base = X diff − X RET,

Y base = Y diff + Y RET.

(6)

Inserting these results into ( 4) results in the arm distance Dand the base angle θ0 used throughout the autopositioningsolution process.

5. Mechanical Design

After theoretical modeling and analysis, the next step of thisresearch is to integrate each of these components such thatthey work together in an e ffi cient manner in order to achievethe project goals. This process involves with the mechanicaldesign and the electrical design. The AL5C Robotic Armfrom Lynxmotion Inc . [8] comes standard with four degreesof freedom not counting the end e ff ector. The suppliedgripper uses a type of servo-controlled linear actuation to




xLETP

xRET

yLET yRET

φL

DR

DL

y

x

φR

Figure 8: Object polar coordinates.

xLETP

xRET

yLET yRET

ydiff

ybasexdiff

xbase

y

x

Figure 9: Object Cartesian coordinates.

grasp an object. There is an optional wrist rotate upgradewhich would allow for a fth degree of freedom; however,this part has been custom created for the project in order tocut down on costs.

To build the arm, the assembly guide obtained fromthe company’s website was followed with a few slightmodications. The two arm pipes have been switched tomore evenly distribute segment lengths, and the load springshave been arranged slightly di ff erent than described in theguide to increase the maximum lift as well as force the arminto a specic position when not in use. To accommodatethis change in load spring positioning, the joint hardwareand servo connections have been altered as well. To attach

Usedmounting

points

Armbase

Customframe

(a) (b)

Figure 10: Custom frame design (a) and the robotic arm mounting(b).

external components, the iRobot Create comes equipped

with mounting points—four within the cargo bay and twoon either side of the top layer. These holes t a 6–32 sizemachine bolt andhave been used to connect a customcreatedupper frame to the Create base. A general design of the frameis shown in Figure 10(a) while the completed frame joiningthe arm to Create is displayed in Figure 10(b) .

6. Electrical Design

There are many facets which compose the electrical designof any given electro-mechanical system, such as the powerscheme, component interfacing, sensing, and control. Ablock diagram of the various known and projected com-

ponents along with their respective power and data owis given in Figure 11. The main components seen are theiRobot Create, the mobile robot platform, the CommandModule (CM), the main controller, and SSC-32-the serialservo controller. The other various components includemotors, sensors, batteries, and circuitry. Data ows fromsensors to controllers, while commands owfrom controllersto actuators.

6.1. Power Systems. One of the largest factors prohibitingrobots from being completely autonomous is the necessity for large power supplies. The longer a robot is to remainactive, the more power needs to be available. However,

adding more batteries adds more weight which requiresthe robot to apply more force to move itself, which inturn requires more power for operation. This cycle willcontinue until the proper balance between necessary powerand available power is met.

One way to reduce the power necessary as well as reducetotal weight is to use as few components as needed. TheiRobot Create comes equipped with an internal battery casewhich holds twelve non-rechargeable alkaline batteries. Therobot should remain powered for up to 1.5 hours of constantmovement as long as there are no external attachments orpayload [ 5]. For recharging capabilities, the recommendedrechargeable battery pack was purchased. With this 3Ah




Createinternalbattery

iRobotcreate Internal

sensors

Drive wheels

Command moduleServo motors

Command modulebreak out

SSC-32controller

External servo power

LCD

LegendPowerDataCommand

Externalsensors

Figure 11: The robotic electrical systems overview.

battery fully charged, the robot should remain powered forup to 3.5 hours under the previous conditions [ 5].

All of the external sensors are expected to need a5 V DC supply. This voltage level is actually generated withinthe iRobot Create and is available on a few pins of thecargo bay connector and subsequently on select pins of thecommand module. The only caution in using this sourceis not exceeding the current limitations of the internalregulator, although this is not an expected problem. Thepower required for the servo motors and controller is not aseasily obtained, and some design will be necessary.

The voltage requirement for the SSC-32 servo controlleris a stable DC voltage between six and nine volts [ 8]. Itis also highly recommended to separate logic and servosupply voltage to keep the microcontroller from resetting orbecoming damaged during power spikes. This means thattwo additional power sources are needed—a low currentsupply within the specied range for the controller and ahighcurrent sixvolt supply for the servo motors. Ideally, only one battery pack should be used for all of the various voltagesupplies to reduce maintenance, charging components, andoverall complexity; however, this requires that a highervoltage source is regulated to a much lower one. This canbe incredibly ine ffi cient for large current draws over great

voltage diff erences. For this reason, a separate six-volt battery pack is used to power the servo motors, while an eight-voltsupply is created for the controller by regulating the iRobotCreate main battery voltage.

6.2. Controllers and Communication. The primary robotcontroller will be the iRobot Command Model which isbuilt around the Atmega168 microcontroller and has fourePorts for additional hardware. Each of these ports containsI/O lines, a regulated ve-volt pin, ground, Create battery voltage pin, and a low side driver. One major drawbackto this conguration is that an attached device which may only require the use of one I/O line will subsequently block

the use to any other unused I/O lines available on thatparticular ePort. Although this layout can be used e ff ectively for many situations, an additional circuit has been createdto redistribute the I/O lines in a more typical arrangement.This circuit also quells the confusion created by the ePortsresembling a computer’s serial port but not being set up to

communication in such a manner. This circuit, named theCommand Module Re-Pin Out circuit (CMRP) in this paper,allows for more complete and easy access to every availableI/O pin on the CM. A schematic of this circuit is shownin Figure 12. Four male DB9 connectors were attached toeach of the four ePorts. The scattered I/O pins were thenregrouped by code and aligned in sequential order on CMRPcircuit board. Each pin was also stacked with a voltage andground pin to allow sensors to be easily connected. A bank of headers carrying the regulated ve volts was also producedas an access point for that voltage supply. Because of theeasy access to the internal battery voltage supply, the linearregulator circuit used to power the SSC-32 servo controllerwas placed on this circuit board as well. There are twoswitched LEDs present on the board. A red LED signies vevolts of power is present on the board while a green LEDindicates the correct operation of the eight-volt regulator.

The secondary controller used in this project is theSSC-32 servo controller, which is controlled through serialcommands received in string format. While these commandswill be sent from the CM during normal operation, it isalso useful to control this device from a computer to quickly test the capabilities of the arm. In order to e fficiently switchbetween CM and PC control, a triple-pole, double-throwswitch has been used to specify the connections for transmitand receive lines as well as the communication baud rate. Anextension to the serial port for easier access has also beenadded to the robot.

In order to preserve battery life, a power jack was addedsuch that a regulated wall pack can be used to power theservos while the robot is stationary as opposed to the six-voltbattery pack. A single-pole, double-throw switch can then beused to select between battery and wall outlet power. Whenonly one power supply is present, this switch also acts asan on/o ff switch for that supply. These various power andcontrol connections are illustrated in Figure 13.

6.3. Additional Hardware. Three sensors external to theiRobot Create are used. Two of these sensors are Sharp

GP2D12 Range Finders while the third is a Sharp GP2D120Range Finder. These devices are used to determine distanceto objects by measuring the reection angles of an infraredbeam emitted from the sensors. The GP2D12 is able to detectobjects between 10 and 80 cm away; the GP2D120 is forcloser range object and can detect objects between 4 and30 cm away. These sensors are commonly referred to as “ETs”because of their similarity to the head of the alien in the 1982movie of the same name.

The two GP2D12 sensors are mounted to the top of twoservo-motors attached to either side of the custom frame atthe front of the robot. These servo mounted sensors serveas front scanners for use in object scanning, detection, and




Left ePort Cente r ePort Right ePo rt Cargo ePortMale DB9 connecto rs

Female DB 9 connecto rs

1 2 3 4 5 6 7 8 9

C D A

7

C P

3

C D A /

3 B P

3 C C V

D N G

C / N

C / N

r w p V

D L

0

C P

5

C

D A /

5

C P

1

C

D A /

1 B P

1 C C V

D N G

C / N

C / N

r w p V

D L

0 C D A

6

C P

2

C

D A /

2 B P

2 C C V

D N G

C / N

C / N

r w p V

D L

0

C P

4

C D A /

4

C P

0

C D A /

0

B P

0 C C V

D N G

C / N

r w p

V D L

2 D L

1

Left ePort Cente r ePort

Cargo ePort

Right ePo r t

iRobot c reate command module

PC [ ]ADC [ ]

PB [ ]

+ 5V

GND

VCC LD [ ]

+5V heade rs Create batte r y headers

+ 8V regulato r + 8Vheaders

R10.125 W1 k

R20.125 W1 k

LED1green

LED2red

7808

22

1 3

C11.0 µF

C210 nF

SW1

x x x x x x x

3:05:07:0

2:0

Ω Ω

Figure 12: Command module re-pin out circuit schematics.

tracking. The GP2D120 sensor has been attached to theinside of the gripper on the robotic arm and is used formore accurate alignment of the gripper with objects whileit is attempting to manipulate them. The front mounting of the GP2D12 ETs is shown in Figure 14(a) while the grippermounted GP2D120 ET is shown in Figure 14(b) . Much likethe importance of sensors is to the robot’s autonomousabilities, an LCD screen is an invaluable tool during programtesting and trouble shooting. The screen used in this projectis the Element Direct, Inc. with four character eDisplay designed for use with the Command Module.

7. Implementation

The program to implement the geometric approach for thearm kinematics is divided into two sections. The rst issimple ashing of LEDs to alert the user that the program isready to be run. This ashing will continue to occur until theCommand Module user button hasbeen pressed or the robotbattery life expires. An attempt to add a sleep state timer wasmade to conserve battery life, but as this was not a primary focus of the project it was not completed. Thesecond portion

of this loop is the actual object detection routine and is a loopitself which is entered and exited by pressing the user button.The loop can also be exited if the iRobot Create detects acliff edge or is powered o ff . A logical ow chart of the mainprogram used to operate the iRobot Create in this simpleautonomous behavior is given as Figure 15.

As seen, a main program counter is used to establish thespeed of the LED ashing and how often the user buttonis checked. The timing of the button checks is very critical.Checking them too often will result in confusion, and theprogram will exit a mode it has just started because it stillrecognizes the button as being pressed. To counter this e ff ect,many delays are used throughout the program to aid in thetiming of everything. Once the user button is pressed, thescanning routine begins by commanding the iRobot Createto drive forward while the front scanning servos move totheir specied angles. After every scanning movement, theattached ET sensors will return the distance to the nearestobject within their range. If nothing is seen, the angle of both servos is increased or decreased, depending upon thecurrent scanning direction and object tracking status, andthe servos move to this new angle while the robot continues




Plug for servopower source

(SPDT) powerSelection switchUp: battery plugDown: external port

Port for externalpower fromregulated wall pack

SSC logic supply from 8V regulatoron CMRP

Baud rateselection jumpers

(3PDT) control &baud rate

selection switch

Serial connection forcommand module

Up: command moduleDown: computer

Serial connectionfor computer

Transmit/receiveSerial lineSource jumpers

(RX) PBx

Jack

J a c

k

P l u

g

(TX) PCx

Figure 13: SSC-32 power and control connections.

Sharp GP2D12 range nders

(a) GP2D12 front ETs

Sharp GP2D120range nder

(b) GP2D120 gripper ET

Figure 14

to drive forward. In real time, these front scanners appear tobe quickly looking back and forth as the robot slowly drivesforward.

Once an object within the specied viewing distance isdetected by either sensor, the object will begin to be trackedby the sensor which saw it, and the iRobot Create willstop moving forward. The other front sensor will continuescanning as normal unless it detects an object as well. Duringthis object tracking period, a counter will begin, and thescanner servo will change direction when it reaches the edge,ignoring its normal scanning area restrictions. The programwill remember the positions of the servo when it detectseither object edge. When the scanner detects the edge of

the object again, it will compare the current servo positionwith the previous one. If these positions are identical fortwo scanning iterations, the object is deemed stable and thearm will attempt to pick it up. Notice there is no safety mechanism here in case the object is too large. This is anadvanced line of reasoning which was not considered as allobjects within the test area will be controlled.

If the edge positions are not identical, the scanner willcontinue its attempt to track the object until the scanningtimer expires. At this point, the iRobot Create will beinstructed to rotate away from the scanner which detectedthe object—clockwise for the left scanner and counterclockwise for the right scanner. After it has rotated, the robot




Main loop

Main counter + = 1

Main counter = 50?

Yes

Yes

Yes Yes

Yes

No

No

NoNo

Yes

No

No

No

Yes

NoYes

Yes

Main counter = 0

LEDs on?

Turn o ff LEDs Turn on LEDs

No

User button pressed?

Drive create forward

Move servos to scan angle

Object detected by ET sensors

Stop create movement and beginscanner count

Object stable?

Determine object center andretrieve object

Exit mode?

Still tracking an object?

Scanner count expired?

Rotate create base

Change scan angle by 50 ◦

Reached scanning zone edge?

Change scanning direction

Figure 15: Main loop program ow chart.

Starting position (1) Raising arm (2) Trying to grasp object (3)

Grasping object (4) Holding on (5) putting down (6)

Figure 16: Screen shots of the robot arm grasping object.




will once again begin to drive forward and scan as normal.This incredibly simple logic has proven to be very e ff ectivein testing the capabilities of the arm in conjunction with theGP2D12 Sharp Range Finding “ET” sensors. We carried outthe experiment for the robotic arm system, and the videotook a movie in which the robot arm can catch the object

and put it down on the left side of the iRobot. The screenshot of this movie is shown in Figure 16.

8. Conclusion

A geometric approach to solve for the unknown joint anglesrequired for the autonomous positioning of a robotic armhas been developed. This analysis is dependent upon theknown lengths of each arm joint to joint link as well asthe desired terminal position of the arm in the three-dimensional space of the arm’s workable area with respect toarm base. Theanalysis hasbeen developedarounda fewbasicassumptions regarding the functionality of the arm, and has

been created using a strictly trigonometric approach withregards to a geometric representation of the arm. For testingpurposes, an iRobot Create mobile robot platform has beenretrotted with a robotic arm from Lynxmotion possessingve degrees of freedom in addition to an end e ff ector. Thegeometric method is easily modiable for similar robotic sys-tem architectures and provides the capability of local auton-omy to a system which is very di ffi cult to manually control.

References

[1] C. C. Kemp, A. Edsinger, and E. Torres-Jara, “Challenges forrobot manipulation in human environments [Grand challengesof robotics],” IEEE Robotics and Automation Magazine, vol. 14,no. 1, pp. 20–29, 2007.

[2] C. S. G. Lee, “Robot arm kinematics, dynamics, and control,”Computer , vol. 15, no. 12, pp. 62–80, 1982.

[3] Y. Liu, T. Mei, X. Wang, and B. Liang, “Multisensory gripperand local autonomy of extravehicular mobile robot,” in Pro-ceedings of the IEEE International Conference on Robotics and Automation, vol. 3, pp. 2969–2973, New Orleans, LA, USA,April 2004.

[4] T. D. Thanh, J. Kotlarski, B. Heimann, and T. Ortmaier, “On theinverse dynamics problem of general parallel robots,” in Pro-ceedings of the IEEE International Conference on Mechatronics(ICM ’09), pp. 1–6, M alaga, Spain, April 2009.

[5] iRobot, “iRobot Create Owner’s Guide,” iRobot, Inc., 2006,http : / /www.irobot .com /hrd right rail/create rr/create fam/createFam rr manuals.html .

[6] Z. Xu, T. Deyle, and C. C. Kemp, “1000 trials: an empirically validated end e ff ector that robustly grasps objects from theoor,” in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA ’09), pp. 2160–2167, Kobe,Japan, May 2009.

[7] iRobot, “iRobot Command Module Owner’s Manual,”iRobot, Inc., 2007, http://www.irobot.com/hrd right rail/createfam/createFam rr manuals.html .

[8] J. Frye, “SSC-32 Manual,” Lynxmotion, Inc. December 2009,http://www.lynxmotion.com/images/html/build136.htm .

[9] J. Denavit and R. S. Hartenberg, “A kinematic notation forlower pair mechanisms base on matrices,” ASME Journal of Applied Mechanics, vol. 23, pp. 215–221, 1955.

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