first term report-1

8/2/2019 First Term Report-1

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Hexapod Robot

Dalhousie Mechanical Engineering

Senior Year Design Team 2

To

Dalhousie University

Mechanical Engineering Department

December 1, 2008

Rene dEntremont

Brett MacDonald

Leslie Ssebazza

Seth Stoddart


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Abstract

The Hexapod Walking Robot designed by Group#2 is in the end stages of design. A final iteration

of chassis and leg design has been selected, and is such that walking speed is maximized. Prior

designs have been discarded based on complexity or physical motion limitations. Prototypes

have been both physically and virtually (Matlab Simulink) constructed with success in order to

demonstrate proof of concept. Current programming is able to produce a single step, using the

desired tripod gait, for one leg only. This program has been used to make the physical prototype

move in the stepping motion. Aspects of the project still to be completed include manufacturing

and assembly as well as communication between the full driving programs and the Hexapod.

These will be finished in the coming term.


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Table of Contents

Abstract ...................................................................................................................................... ii

Table of Contents ....................................................................................................................... iii

List of Figures .............................................................................................................................. v

List of Tables ............................................................................................................................... v

1 Introduction ............................... ........................ ................................ ........................... ...... 1

1.1 Background ............................ ......................... ................................ ...................... ....... 1

1.2 Project Description ........................... ............................... ...................... ....................... 1

2 Design Requirements ............................. ................................ ...................... ....................... 3

2.1 Primary ............................. ......................... ................................ ...................... ............ 3

2.1.1 Design ............................ ......................... ................................ ...................... ....... 3

2.1.2 Mobility ............................... ........................ ................................ ........................ 3

2.2 Secondary .............................. ......................... ................................ ...................... ....... 4

3 Design Alternatives ........................... ........................... .......................... ............................ . 5

3.1 Alternative 1: Mobility - Spider, Outboard Rotate ............................. ....................... ..... 5

3.2 Alternative 2: Smooth- Central Suspension Pivot .............................. ....................... ..... 5

3.3 Alternative 3: Fast- Central Rotation, No Suspension ............................. ....................... 6

3.4 Design Selection .............................. ................................ ...................... ....................... 7

4 Design Refinements .............................. ............................ ....................... ........................... 9

4.1 Securing Servo Motors ......................... ............................... ...................... ................... 9

4.2 Suspension and Grip......................... ......................... ............................. .................... 10

4.3 Rapid Prototype ............................... ............................... ...................... ..................... 11

5 Final Design ................................ ........................ ............................... ............................ .... 12

5.1 Overview........................... ......................... ................................ ...................... .......... 12

5.2 Frame ................................ ........................ ................................ ...................... .......... 12

5.2.1 Description .............................. ......................... ............................. .................... 12

5.2.2 Fabrication ............................... ......................... ............................ ..................... 13

5.2.3 To Be Determined ............................ ................................ ...................... ............ 13

5.3 Legs .............................. ........................ ................................ ...................... ............... 14

5.3.1 Description .............................. ......................... ............................. .................... 14


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5.3.2 Fabrication ............................... ......................... ............................ ..................... 15

5.3.3 To Be Determined ............................ ................................ ...................... ............ 15

5.4 Control Hardware............................... ............................ ....................... ..................... 15

5.4.1 Description .............................. ......................... ............................. .................... 15

5.4.2 Fabrication ............................... ......................... ............................ ..................... 16

5.4.3 To Be Determined ............................ ................................ ...................... ............ 16

5.5 Control Software .............................. ............................... ...................... ..................... 17

5.5.1 Motion Planning ............................. ............................ ....................... ................ 17

5.5.2 Conversion ............................... ......................... ............................. .................... 18

5.5.3 Communication ........................... ......................... .............................. ............... 19

6 Testing ............................. ........................ ................................ ...................... ................... 20

6.1 Finite Element Analysis (FEA) ........................ ................................ ....................... ...... 20

6.1.1 Model Description ........................... ................................ ...................... ............ 20

6.1.2 Results ........................... ......................... ................................ ...................... ..... 20

6.2 Hexapod Motion Simulations ........................ ................................ ...................... ....... 21

6.2.1 Simulink ............................... ........................ ................................ ...................... 22

6.2.2 Virtual Reality Toolbox .......................... ................................ ...................... ....... 22

6.3 Working Leg ................................ ......................... ............................. ......................... 23

6.3.1 Mechanical .............................. ........................ ............................... ................... 23

6.3.2 Hardware ................................ .......................... ............................. .................... 23

6.3.3 Software ............................. ......................... ............................... ....................... 24

7 Project Status ........................... .......................... ................................ ........................... .... 25

7.1 Progress ............................ ......................... ................................ ...................... .......... 25

7.2 Technician Time ............................... ............................... ...................... ..................... 25

8 Budget ............................. ....................... ................................ ....................... ................... 27

9 Conclusion and Recommendations ....................... ................................ ...................... ....... 28

10 Acknowledgements ........................... ........................... ............................ ..................... 29

Appendix A: 2 DOF Inverse Kinematic MATLAB program ........................................................... 30

Appendix B: Angles to Registry Format Converter Code ............................................................ 32

Appendix C: Winter Term Gantt Chart ....................................................................................... 33

Appendix D: Simulink Gait ......................................................................................................... 35

Appendix E: Fabrication Drawings ............................................................................................. 37


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List of Figures

FIGURE 1:OUTBOARD MOUNTED LEG ASSEMBLY.................................................................................................. 5

FIGURE 2:CENTRAL PIVOTING LEGS ASSEMBLY..................................................................................................... 5

FIGURE 3:LEG OF THE INBOARD MOUNTED CONFIGURATION ................................................................................... 6

FIGURE 4:INBOARD MOUNTED LEG ASSEMBLY..................................................................................................... 7

FIGURE 5:SELECTED DESIGN WITH BODY WEIGHT CONSIDERATIONS ........................................................................... 9

FIGURE 6:REFINED LEG ASSEMBLY, USING ALL FOUR BOLT HOLES. ........................................................................... 10

FIGURE 7:SPRING RATED SHOCK ABSORBERS...................................................................................................... 10

FIGURE 8:NEOPRENE BUMPER (HTTP://WWW.MCMASTER.COM) ........................................................................... 11

FIGURE 9:FINAL DESIGN OF HEXAPOD ROBOT ................................................................................................... 12

FIGURE 10:BOTTOM VIEW OF FRAME ASSEMBLY............................................................................................... 13

FIGURE 11:LEG ASSEMBLY ........................................................................................................................... 14

FIGURE 12:THREE LEG SECTIONS, NAMED AS THE FIRST,SECOND AND THIRD LEG SECTIONS(LEFT TO RIGHT) ................. 15

FIGURE 13:VON-MISES STRESS OF THE FIRST BAR LINKAGE .................................................................................. 21

FIGURE 14:BLOCK DIAGRAM REPRESENTATION OF A DIFFERENTIAL MECHANICAL SYSTEM .............................................. 22

List of Tables

TABLE 1: WEIGHTED COMPARISON TABLE .......................................................................................................... 7

TABLE 2:SERVO SPECIFICATIONS SUMMARY ........................................................................................................ 8

TABLE 3:ESTIMATED MACHINING TIME REQUIRED FROM DEPARTMENT ................................................................... 25

TABLE 4:PROPOSED BUDGET ......................................................................................................................... 27


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1 Introduction

1.1

Background

The Hexapod Remotely Operated Vehicle (ROV) was first proposed as a project by Dr. Pan

of Dalhousie University as an idea for the Mechanical Engineering Senior Design Project.

The idea of building robots and ROVs for design project is not new, as tracked, wheeled,

and water based ROVs have all been produced in the past, but leg based ROVs have yet to

be attempted. The challenges are obvious as walking is a complicated method of

travelling that required a complex control system to coordinate the movements.

However, the benefits are numerous. Legs offer more freedom of movement to the

chassis of the ROV; it may level itself on uneven terrain, tackle obstacles that wheels (of a

proportionate size) may not, and move in all directions without changing the orientation

of the body. Legs can also be used to manipulate objects with some precision or adjust

the height of the body for increased stability or travel into restricted spaces. Overall, the

freedom of motion provided by legs is extremely useful, with few drawbacks (beyond the

complex programming). One such drawback is the low forward speed that most walking

robots are able to accomplish. The group has identified this as a challenge and an area for

improvement over traditional hexapod designs. The project will be unique from other

hexapods since it is intended to be a platform onto which additional sensors can be

mounted, making it capable of doing many different tasks. In comparison, other hexapods

tend to be simply a body and legs and are designed onto to move around. The group will

design a chassis and legs, and initial and final control systems. The intent is that the

finished product be mechanically capable and upgrade friendly, so future iterations can

accomplish increasingly complex tasks and motions.

1.2 Project Description

The ROV will have 18 degrees of freedom (DOF) as stated in the design requirements. To

be as mechanically sound as possible, the robot will use a modular design, where a small

list of spare parts may be kept on hand to repair the robot in the case of failure. These


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parts may be swapped in and out easily. Leg parts will be the same for both sides, with

only assembly of the parts differing. All 18 servos (1 DOF each) will be the same type and

are low cost and highly available. The body will contain a large surface to mount

electronics for this project, and future iterations.

Electronic hardware used on the robot will be purchased with development in mind;

additional ports for servos will be available, analog and digital inputs and outputs on the

microcontroller will be available (for sensors and upgraded controls), and should it be

desired, the ROV could accept a battery pack and onboard programming to become

completely autonomous. Some of these goals are outside of the project scope for this

year, but the ROV will not be limited in its capabilities.


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2 Design RequirementsUsing our objective of creating an instrument and development platform we developed a set of

design requirements for the hexapod robot. The requirements were separated into primary and

secondary items. The primary requirements included aspects that dealt with hexapod design,

motion control and future considerations. The secondary requirements are those that deal with

appearance and ease of use.

2.1 PrimaryInformation related to the design geometry and size had to be determined based on the

tasks the hexapod has to achieve and the scale of the robot.

2.1.1 Design

The body size (not including legs) is to be smaller than 15x12 and the total length of

the legs should be between 4 and 10. The legs will be of a modular leg design which

allows easy maintenance and repair when needed. The robot weight should be no more

than 12lbs. It will be a tethered design but should be of such a size and mass that one

person will be able to manually maneuver and transport the entire assembly. The

materials that will be used will include strong, light, low cost aluminum and plastic

(PVC). Additional requirements are that the hexapod will have a load carrying capacity

of at least 2lbs. It should also include mounting positions where additional sensory

components could be added.

2.1.2 Mobility

The main mobility criterion is to have a full 18 Degrees of Freedom (DOF): Each leg will

be capable of 3 independent DOF and have a range of motion so that it can extend its

legs parallel to the ground. This will ensure that future iterations of the robot will not be

limited in performable motions.


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The minimum mobility requirements for the robot include walking forward, backwards

and turning. More motions, or complex methods of performing the listed motions, may

be within the project scope depending on time constraints. Forward and backward

walking speeds must be at least 3 in/sec. The turning speed must be ninety degrees of

rotation in less than 10 seconds. The robot body will be able to operate with ground

clearances ranging from 2-10 cm.

2.2 SecondaryThe secondary requirements deal with ease of use and appearance. They include

programming considerations, life cycle, safety, and operation instructions. Program

coding will be simplified and compartmentalized with consistent notarization for easy

comprehension. An open source approach will allow easy modification of the

programming for future iterations. The program used should be universal to the

engineering community. A users manual will also be supplied, detailing how to operate

and maintain the hexapod robot to ensure smooth and reliable operation.

All electronics will be bundled and guarded to avoid electrocution hazards. All wear parts

will be contained in the modular leg design. The legs are considered replaceable, so

simple leg replacement will mean that the robot will have no finite lifespan. Servo motors

contained within the legs will be the limiting factor in leg lifespan. Our group desires 100

operational hours of use from servos in this application. Finally, the hexapod robot should

have a clean and uncluttered appearance.


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3 Design Alternatives3.1 Alternative 1: Mobility - Spider, Outboard Rotate

As shown in Figure 1, this design has

the legs mounted at equal distances

on each side of a platform body. It is

the simplest option, where the pivot

servos are mounted closely together.

The result of this configuration is

shorter legs which can rotate through

a larger angle without colliding with

other legs, therefore providing higher

angular rotation speeds. This design

also incorporates the use of large (42

kg/cm) servo motors to allow for a

higher weight capacity load on the platform. The outboard mounting design means that

the modular legs are simply mounted to the outer perimeter of any body shape desired.

However, this layout has a limited forward walking speed (as speed is directly related to

the angular rotational speed and radius to the leg tip). While investigating the large servo

motors, it was noted that when powered, under no torque loading, each servo drew

approximately two amps of current. Therefore a combination of high torque servos would

require a very large power supply.

3.2 Alternative 2: Smooth- Central Suspension Pivot

The distinguishing feature of design 2 is

that all of the legs are mounted on, and

pivot about, two long rods located in the

center of the body, shown in Figure 2.

This gives all of the legs the freedom to

Figure 1: Outboard Mounted Leg Assembly

Figure 2: Central Pivoting Legs Assembly


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rotate in the vertical plane. With the use of compression springs connected between the

body and the first motor mount position (not shown in drawing), this design would

provide a level of shock absorption. The benefit of this is that the robot could handle

rough or demanding use better than the other designs which are rigidly connected. The

drawback is the complexity associated with adding the compression springs since twelve

of them would be needed. Another feature is the ease of assembly and disassembly. Once

the end piece (holding the end of the rods) is removed and the wires are disconnected

the motors would slide out easily. This design uses that same small servo motors that will

be discussed in design alternative 3. It also has the same benefits associated with inboard

mounted motors that will be discussed in design 3.

3.3 Alternative 3: Fast- Central Rotation, No SuspensionTo provide the highest possible forward walking speed

and higher rotational speeds, a larger leg tip radius is

required, shown in Figure 3. In order to achieve the

highest speeds without adding additional torque to the

legs, a longer arc length is created using an extended

member between the leg swing servo and the first

knuckle servo. Extending this leg member would increase

the footprint size of the robot. So to avoid this, the

extended member that pivots the leg will be mounted

inboard of the body, as seen in Figure 4. Additionally, this design uses smaller servo

motors (9.6 kg/cm) that draw much less current (0.76A at stall torque) than the larger

ones used in design 1. This allows all of the motors to be run using a smaller power supply

and tether.

Figure 3: Leg of the Inboard Mounted

Configuration


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Figure 4: Inboard Mounted Leg Assembly

3.4 Design SelectionA comparison of the three designs is given in Table 1 below. Each design requirement is

rated according to relative importance then each design is assigned a grade. A higher

value represents better performance in all cases. Design alternative number three

emerged as the clear winner.

Table 1: Weighted Comparison Table

Weight Design 1 Design 2 Design 3

Forward/Backward Walking Speed 5 3 5 5

Rotational Speed 3 3 2 2

Ground Clearance Range 3 1 3 3

Load Carrying Capacity 3 3 2 2

Ease of Assembly/Disassembly 3 3 1 2

Durability 3 2 3 3

Complexity 5 5 2 5

Cost 4 2 4 4Total (29) 22 22 26

As well, the performance of servo motors varies greatly with respect to size, torque and

power consumption. A comparison of several servo motors is shown in Table 2. It can be


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seen that as the servo torque increases, so does the required power. Since the hexapod

will require a total of 16 servos, the correct selection of servo motors is necessary to build

a safe functional robot. The design selection took into consideration the servo

characteristics as well.

Table 2: Servo Specifications Summary

Servo Name Torque (kg*cm) Weight (g) Power Consumption

HS-805BB Giant Scale 24.7 152 1.7A No Load

HS-765HB "Sail Arm" Servo Motor 13.2 110 1A No Load

HS-645MG Servo Motor 9.6 55.2 0.75A Stall torque

GWS Heavy Duty S777 6BB Servo Motor 42 190 2A No Load


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4 Design RefinementsThe selected design went through several modifications during the term. The leg design was

altered to ensure a more secure servo motor connection and a good floor contact during

operation. A hexapod leg was then prototyped and from it evolved some further design changes

that will be in our final hexapod design.

4.1 Securing Servo MotorsIn the initial design for the leg, the servo motors were mounted to the leg sections using

only two connection bolts. It was determined that this configuration, shown in Figure 5,

would concentrate the majority of the weight on the two servo contact points.

Although the overall load would not be of a large magnitude the servo motors would

need to be secured tightly to eliminate any unnecessary movement of the servo motor. If

not secured tightly, the moment and shear force created at these two servo contact

points will loosen the fasteners that hold the servo and leg sections together. The design

was therefore changed to better secure the servos as shown in Figure 6. This design uses

all four connection bolts of the servo mounting flange.

Figure 5: Selected Design with body weight considerations

W (body)

2 sets of

fastening

contact points


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Figure 6: Refined Leg Assembly, using all four bolt holes.

4.2 Suspension and Grip

The hexapod feet were modified after the design selection to provide the hexapod with

some suspension and better grip during operation. The initial selected design shown in

Figure 5, included soft rubber padding at the ends of the legs that would act as a cushion

with some spring characteristics. Unfortunately after doing some research into possible

materials it was found that for the scale of the robot most rubber materials would be too

stiff to be effective. The next idea was to use a set of shock absorbers shown in Figure 7

that would be fastened into the leg ends as shown in Figure 6.

Figure 7: Spring rated Shock absorbers

(http://www.mcmaster.com/catalog/114/gfx/large/3740kc1l.gif)

The issue with this idea was that the Delrin material used at the end of the shocks was

very slippery and would not provide adequate grip for walking. Since grip is very


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important for motion and each absorber costs $28.13, which is high, we chose to use a

contact bumper, shown in Figure 8.

Figure 8: Neoprene Bumper (http://www.mcmaster.com)

This bumper is made from neoprene, a material that provides better grip, and should

provide some spring like characteristics for a smoother walk during operation.

4.3 Rapid Prototype

After receiving some suggestions from the technicians, the team decided to build a

prototype leg for control and possible destructive testing purposes. The hexapod leg

prototype was built using the rapid prototyping machine of the Dalhousie University

Mechanical Engineering Department. The process took a total of three hours to complete

and cost an approximately $14 to build. With the leg prototype built, we reassessed the

design and found that the end leg section, with the threaded hole, would be better if it

was altered so that the threaded hole was centered on the mid-plane of the piece.

Another design suggestion that came from the prototype leg was to drill a hole in the

second section of the leg section which would make it easier to assemble.


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5 Final Design5.1 Overview

The final design of the robot was arrived at after the improvements from the design refinement

stage were incorporated into the original selected design. This final design is depicted in Figure

9. There are six modular legs that connect to the bottom part of the frame and there is plenty of

space available on the top plate for mounting electronic equipment. All fastening details have

been worked out and the parts are ready to be fabricated. The major components of the robot,

including mechanical and programming aspects, will now be presented in detail.

Figure 9 : Final Design of Hexapod Robot

5.2 Frame5.2.1 Description

The frame of the robot consists of two 1/8 aluminum plates that are bolted together

using six commercially available standoffs, as illustrated in Figure 10. The smaller plate is

used for mounting the legs, while the larger plate is used for mounting electronic

equipment such as the microcontroller boards. As well, there is extra space on the large


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plate so additional electronic equipment and sensors could be added to the robot in the

future, in accordance with the design requirements.

Figure 10 : Bottom View of Frame Assembly

5.2.2 Fabrication

The two aluminum plates will be machined and drilled by the department technician.

The standoffs are a purchased part and come threaded at both ends. Assembly is simple

and will be done by the team.

5.2.3 To Be Determined

The large plate is used for mounting the electronic equipment. This includes the two

microcontrollers as well as any additional sensors that might be added later on in the

project. Cutouts will need to be made in the large plate to allow wires to pass through.

The layout of the electronic equipment and associated cutouts has not been finalized

yet. However, this is not a pressing issue.


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5.3 Legs5.3.1 Description

Each of the six legs will contain three servomotors that are connected by three leg

sections as shown in Figure 11. For a better view of the individual leg sections, see

Figure 12. The leg sections are named as the first, second and third leg sections, with the

first leg section being the one joined to the frame. They are simple pieces and are

shaped in a manner that allows simple connections with the servomotors. Additionally,

there are small neoprene feet (commercially available) that thread into the third leg

section. These will provide adequate traction as well as shock absorption to reduce the

stress within the joints.

Each leg section will be machined from 1/4 or 1/2 PVC plate. The inner leg section will

require two pieces to be separately machined then bonded together using plastic

cement. The inner and outer leg sections will come in a left and right handed variety

while the middle leg section will be the same on both sides. The leg sections will be

bolted to the servomotors using small #2 bolts at the servo mounting flanges and at the

servos mounting disk (attached to output shaft).

Figure 11 : Leg Assembly


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Figure 12 : Three Leg Sections, named as the First, Second and Third leg sections (left to right)

5.3.2 Fabrication

It is desired that the machining of all leg components be done by the department

technician. The bonding of the two pieces of the inner leg section will be performed by

the team, as will the fastening of all the leg assemblies.


The type of bonding agent for joining the PVC parts together has not been finalized yet.

Several options for bonding PVC to itself have been researched though, and this should

be able to be done successfully. Fastening the legs onto the disks that come with the

servos will require additional holes to be drilled in these disks. There should be

adequate room to add the two small holes that are required and this is currently a low-

level concern.

5.4 Control Hardware5.4.1 Description

To control the hexapods movements, two boards would be used: a servo control board

to send timed pulses capable of setting servo positions, and a microcontroller to send

and receive signals onboard the hexapod.


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To control servos, a Devantech SD-21 Servo Control Board was selected. In addition to

its low cost, the SD-21 has pin connections for up to 21 servos for which it can control

the position and speed through integer inputs. The board will satisfy the expandability

component of the design by allowing an additional 3 servos for an added task specific

appendage. The SD-21 is capable of receiving a basic stamp controller via one of two

standard sockets, and can communicate with an external controller through any of

three I2C connections. The latter option will be utilized in this design.

For the external microcontroller option used in this design, an Arduino Decimilla was

selected as its internal Wire library and I2C pins would allow simple interfacing with the

SD-21. In addition, the Decimilla uses an onboard serial converter so that a common

USB A to B cable can be used to interface with a computer for serial communication.

The Decimilla has the added advantage of available analog and digital in/outputs, also

satisfying the expandability requirement.

5.4.2 Fabrication

To put a polished look on the controlling hardware, interconnects that utilize headers to

connect to both the male and female I2C ports will be fabricated by the group. The

interconnect cables will be labeled, or of a design such that the hexapods electronics

cannot be incorrectly assembled.

The boards will be mounted to the robots top plate using hex standoffs and all servo

cables will be bundled and routed through the hexapods body.


Final positioning has not yet been determined. Cable routing will determine the final

position of the boards, and this cannot be finalized without a final model. Mounting isuncomplicated and will require very little fabrication making it an acceptable TBD item.


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5.5 Control SoftwareSoftware development will take place within Matlab using .m files. The programming

can be broken into 3 major components: motion planning, conversion, and

communication.

5.5.1 Motion Planning

There are two ways to control the hexapod robot. One involves having a set routine in

which every angle and timing pause are pre-defined. The second and more complex

option involves telling what you want to robot to accomplish and the software

determine the leg path along with the necessary servo angles to perform the maneuver.

The hexapod robot will use the second option which will give the robot more flexibility

and a smoother movement.

Currently ongoing work involves writing an inverse kinematics (IK) program in which the

user of a path creation program defines two points of the leg movement, the start and

end point. From the know point, IK solves for the servo angle which will move the end

effector to its new position.

The method currently developed is the Inverse Jacobian method. It will only be used for

the last two leg sections. This method involves creating the Jacobian matrix which for

two leg linkages and 2 DOF, will result in a 2x2 matrix. It is a transformation matrix

which transforms finite X or Z displacement in the required change in servo angles and

has the following form:

(1)Where J is the Jacobian, x and z are the two DOFs, and are the rotation angles ofthe servos.

To avoid the partial derivatives of complex equations for circular motion, the end

effectors motion is approximated as linear.


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Once the Jacobian has been defined, the inverse must be calculated. Most IK methods

use a pseudo inverse method since the number of actuator outnumber the DOFs, but in

this case, the Jacobian is a square matrix and can be readily inverted using a program

such as Matlab. With the inverse, the following calculation must be performed:

(2)Since the Jacobian is a linear approximation, iterations must be performed on smaller

finite divisions of the desired difference in effector position.

The first servos angular rotation can easily be determined using trigonometry as it is the

only servo capable of rotating the leg in the y direction. The servo must point the leg

from the base point directly towards the wanted position of the end effector.

5.5.2 Conversion

The resulting output of the Motion Planning software will be in degrees and time

intervals. This data will need to be converted to be understood by the SD-21 servo

control board. The SD-21s internal register stores four numbers pertaining to each

servo: a servo call, speed, and two positioning numbers. The servo call is a number given

to each servos registry spaces. When the servo call is sent to the SD-21, the following 3

numbers will be assigned to the speed and position spaces. The speed number is set to 0

for full speed, or numbers 1 through 9 for slower movement. Finally, the position

numbers are the low and high bytes of the desired pulse width integer. Testing has

revealed that for the selected servos, the pulse widths used from lock to lock are in the

700-2500 (micro-second) range. The pulse width steps correspond to degrees

proportionally using the following formula:

(3)Where: = Desired change in degrees = Change in pulse-width


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The output of the conversion from degrees will be an integer within the pulse width

range. The integer needs to be split into integer representations of the high and low

bytes of this number. These parts may be found by converting to hexadecimal: the high

byte will be the first integer value, while the low byte will be the remainder once the

high byte has been multiplied by 256 and subtracted from the original value. A

converting algorithm has been written and is incorporated in the preliminary software

appendix package.

5.5.3 Communication

Once the appropriate conversion has taken place, the data is stored in matrices of leg

positions within Matlab. The matrices match the register on the SD-21 board and are

sent through the serial port to the Decimilla for storage to be sent to the SD-21 in a

timed sequence corresponding to the desired gait. Matlabs serial communication

commands simplify this procedure. An additional serial monitor is added to open TX and

RX pins on the Arduino board for debugging purposes.

Once the gait has been calculated and stored on the Decimilla, the register must be

updated with positions corresponding to leg points. The Arduino board is able to open aconnection with the SD-21 (using the aforementioned I2C ports), update the register,

and close the connection. This sets the servos in motion, roughly following the path

calculated in the motion planning stage.


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6 Testing6.1 Finite Element Analysis (FEA)

The strength of the leg links was a concern. A preliminary finite element analysis was

performed to ensure theses links would not fail in tension or compression. The leg section

subjected to the highest loading is the first section since it must support the load of the

robot and the torque of the servo along its axis of minimum moment of inertia. Therefore

only this link will be tested.

6.1.1 Model Description

Since only a rough stress profile was desired, it was appropriate to quickly mesh themodel using 3D tetrahedral elements. Another advantage to the tetrahedrons is the

ability to auto-mesh the solid part. An initial element size of 1.5mm was used, then

varied up to 3mm and down to 0.75mm to ensure a consistent result.

The Program used in this analysis is Unigraphics NX 5.0 which uses the Nastran NX

solver. The material model used was the pre-defined NX 5.0 model for PVC, which

include a Youngs modulus of 300 MPa and a Poissons ratio of 0.4.

The loading for the leg linkage was composed of two parts, the vertical force which

keeps the robot suspended, and the torque produced by the servo. The Vertical force

used was 9.4N which simulated the 9.8Kg*N of torque applying a force 6 cm from the

rotation axis. The torque applied was 0.981 N*mm which is the rated capacity of the

servo itself.

To simulate being attached to a servo at the body, the two smaller mounting holes seen

at the bottom right of Figure 13 where fixed in all 6 DOF.

6.1.2 Results

After running the simulation, the Von-Mises stress ( was plotted. This stress is theequivalent stress and is used to compare for failure against the yield stress ( of thematerial. In this case, failure is defined as . As seen in Figure 13 below, the


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Von-Mises stress found through-out most of the link is approximately 6MPa. This value

is much lower that the of PVC which is 40 MPa.It can also be seen that the stress peaks are around the mounting holes. The is stillonly 16.4 MPa. The team believes this value is much higher than would be seen on theactual part since the model is stiffly constrained whereas the actual link is clamped and

slight motion is allowed. Even with a moderate to low accuracy, the results conclude the

part will not fail.

Figure 13: Von-Mises Stress of the First Bar Linkage

6.2 Hexapod Motion SimulationsSimulation models are useful in refining the controlling schemes before applying them to

the real system. Simulations can also be used to check for design issues such as

interference within a model. The motions of the hexapod can be simulated in

programming software called Matlab. This is accomplished by using a combination of

Matlabs specialized Simulink and Virtual reality toolbox add-ons.


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6.2.1 Simulink

Simulink is a system modeling interface tool that can read in inputs from Matlab,

perform analysis on the inputs if necessary, and output the results for graphing and

other uses such as simulations. Simulink uses a block style structure in manipulating

data and performing calculations.

Figure 14: Block Diagram representation of a differential mechanical system

[Bauer, Robert; MECH 3900: Assignment 1; Department of Mechanical Engineering Dalhousie University, Jan15,2008]

Figure 14 shows a common block diagram representation of a system model defined in

Simulink.In this block diagram the input data is provided by the Matlab driving routine.

Values for all the blocks can be provided by the Matlab code or can be initialized in the

Simulink blocks. The output data is combined into an array using the MUX block and is

then sent to the workspace. The workspace could be anything from a graph to the

original driving routine for further manipulation.

6.2.2 Virtual Reality ToolboxVirtual Reality toolbox is a program that uses the position and angle data supplied by

Simulink to visually show the simulation of a model in the Virtual World. A solid works

model of the hexapod is inserted into the Virtual World and can be simulated using data

generated by Matlab. In the case of the hexapod robot simulation the input code into

a xv

MECHANICAL SYSTEM

ma + bv + kx = F(t)

|_________________________________________________________|

SYSTEM

|__________|

OUTPUT

|________|

INPUT

FILE: mech.mdl

(ENTER 'm')

(ENTER 'K')

To Workspace

(Store as 'y' for plotting )

y

Sum

Step input

force, F

Spring constant

K

Mux

Mux

Integrates

dx /dt

1

s

Integrates

d2x / dt2

1

s

Damping (variable )

B

Clock

1/mass

1/m


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Simulink will be a driving routine gait motion code (Appendix D) which has been

written in Matlab. The Virtual Reality Toolbox sink block connects the output Simulink

data to the Virtual object (which is the hexapod legs for our case) located in the virtual

reality world.

6.3 Working LegA working prototype leg has been manufactured and tested as of November 26, 2008.

The single leg was built as a proof of concept. A finished leg is required to proceed on

hardware testing and to set the initial positions of each servo, thus creating a need for the

model.

6.3.1 Mechanical

With an existing solid works model, a rapid prototype version of the leg joints was found

to be the timeliest method of manufacturing the needed leg sections. The plastic

material used by Dalhousies rapid prototype machine was considered strong enough

for preliminary testing, as its material properties closely matched the final design

material. The three leg sections were prototyped and assembled using three Hi-Tec

brand servos.

Some minor alterations from the original design came from assembly of the rapid

prototyped leg members. For reduction of weight, the first leg section would have a slot

cut through the center, as in the second leg section. To aid in assembly, all servo disk

mounting positions would have a through hole drilled to access the servo shaft spline

bolt that holds the mounting disk in place, making assembly and disassembly an easier

process.

6.3.2 Hardware

A power supply was procured to power the servos through a temporary power cable.

The 5V section of the supply was used to limit servo performance for initial testing. In

future testing a 9.6 volt supply will be used. The SD-21 board logic section was


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temporarily powered through a jumper from the servo supply side. However, in future

iterations the SD-21 will be powered by the Arduino which is supplied by the USB port.

The Arduino and SD-21s I2C ports were connected.

6.3.3

Software

All values of speed, low and high bytes were calculated using initial versions of the

Matlab software included in the appendix. These positions were then manually entered

into arrays in the Arduino board, as serial communication is not yet fully debugged. As

will be used in the final version, three positions were entered to form a leg path, which

is followed on each run of the Arduinos program, as seen in the appendix.

The legs performance is as expected and further testing will provide preliminary

performance numbers for speed and weight carrying capacity.


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7 Project Status7.1 Progress

The team has currently finalized its design selection. All drawings and specifications have

been completed along with some proof on concept work. This work includes the virtual

modeling of the leg kinematics and the building of a prototype leg.

The software is still currently being worked on and is showing promise. The IK program

has been successful in defining the correct angle changes to reposition the final two links

of the leg. The Matlab transmission program has also been able to give basic control to

the mock-up leg in order to perform a single crude step.

The group also believes they have completed the appropriate amount of modeling and

testing to begin production of the six legs and body in order to have a fully assembled

model early in the second term. The improvement of the software will be continual until

the end of term to achieve the best results possible within the allotted timeframe.

7.2 Technician TimeAll fabrication work will be completed by the department. This is limited to the cutting

and machining of parts. This will ensure quality fabrication of components. An estimate of

the machining time required from the department for this project is provided in Table 3.

Table 3: Estimated Machining Time Required from Department

Part Number Part Description QuantityTotal

MachiningTime (hrs)

HX-0012 Top Plate 1 1.5

HX-0013 Bottom Plate 1 4

HX-0022 First Leg Section 7 6

HX-0023 Second Leg Section 7 3

HX-0024 Third Leg Section 7 10

24.5


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All assembly work will be completed by the team. Assembly requires the use of simple hand

tools and bonding agents. Advice may be sought from the technicians during the assembly

process.


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8 BudgetWith the selected design being finalized, Team #2 has assembled the budget found in Table 4.

To date we have secured $1800 of our project cost.

Table 4: Proposed Budget

Materials Unit

cost

Amount Cost

ElectronicsHS-645MG Servos $39.02 21 $819.42

HS-765HB $43.78 1 $43.78

HS-805BB $43.36 1 $43.36

25' 22g black wire $2.62 1 $2.62

25' 22g red wire $2.62 1 $2.62

Netmedia 6" jumper Wire kit $8.49 1 $8.49

Eneloc 30 pc. Reinforced Jumper wire kit $18.91 1 $18.91

Pulse Witdh Modulator $63.15 2 $126.30

USB Cable $2.99 1 $2.99

Microcontroller $40.64 1 $40.64

Resistors (500 ohm + 2000 ohm) $1.00 2 $2.00

Potentiometer (500ohm) $7.85 1 $7.85

Rocker Switch $1.39 1 $1.39

Protoboard $15.00 1 $15.00

Sensors $75.00 1 $75.00

Raw Materials

3/8" Hex Standoff 1/8"PL $1.00 12 $12.00

1/4" ABS $13.29 3 $39.87

1/2" ABS $27.39 2 $54.78

1/8"Alluminum Plate 6061 $26.06 3 $78.18

Plastic Bonder $24.99 1 $24.99

1-1/4" AL Hex Standoff 10-32 screw $3.03 6 $18.18

Leg Bumper $6.23 7 $43.61

Fastners $20.00 1 $20.00

Rapid prototyping $7.00 3 $21.00

Overhead Boom $99.95 1 $99.95

Subtotal $1,622.93

10% SF $162.29

Tax (15%) $243.44

Shipping $100.00

Total $2,128.66


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9 Conclusion and RecommendationsHexapod robot is a relatively inexpensive and capable machine. The servo arrangement allows

the robot to maneuver with relative ease in both planar directions. The three degrees of

freedom per leg also allows the ROV to adjust its height without affecting the other

performance characteristics. The large plate forming the top of the body allows for the

mounting of circuit boards and additional sensors improving the versatility of the robot.

Several design choices were evaluated before the final design was chosen. The main differences

between the alternative designs were the positioning and design of the six legs. Increasing the

complexity of the robot was investigated but not done due to the difficulty on building the

model and the extra complexity of the motion programming. One alternative design had the six

legs spread evenly along a hexagonal body shape. This improved the rotation capabilities of the

hexapod, but since the ROV would have no front or back end, each leg has to be programmed

individually even to perform the simple tripod gait. The team selected a ROV consisting of a

rectangular body and the six legs being spread equally along both sides. This maximized both

the maneuverability and programming simplicity.

Several tests were performed to ensure the legs had appropriate range of motion and strength

to support the hexapod. These test included a FEA analysis, a virtual simulation in MATLAB

SImulink and then the construction of a prototype leg. With the validation of our design, the

group is ready to begin fabrication of the entire hexapod ROV.


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10AcknowledgementsTeam #2 would like to take this opportunity to acknowledge and thank the following sponsors

and individuals:

Shell Canada for their generous funding of Mechanical Senior Design Project

Dr. Ya-Jun Pan for proposing, as well as supervising, the Hexapod Walking Robot project

Angus MacPherson, mechanical technician

Jonathan MacDonald, electrical technician

The Mechanical Engineering department for providing additional resources (machine time,

expertise) necessary to make the project possible

As well, we would like to extend an informal thank-you to:

Dylan Scott, electronic hardware and controls support

Packiaraj Xavier, Matlab Simulink support


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Appendix A: 2 DOF Inverse Kinematic MATLAB programUser must manually input the initial leg position and wanted small displacement.

Clc

%defining constants**************************************************L1=0.1; L2=0.06; L3=0.08; % units -

angle=[0.75;3.7124]; % units - radiansdelta=[0.02;-0.02]acc=0.0005;j=1error='complete'

%Forward Kinematics***************************************************ang=angle(2)+angle(1);R1=L2*cos(angle(1))+L3*cos(ang);

pos=[R1;L2*sin(angle(1))+L3*sin(ang)]pos2=pos+delta;step=(pos-pos2)/10

%Determining the Jacobian*********************************************while abs(step(1))>acc || abs(step(2))>accj=j+1if j>5000

error='END OF ITERATIONS, POINT NOT REACHED'breakendfori=1:2if(angle(i)>=0 && angle(i)=1.570796 && angle(i)=pi && angle(i)=4.7124 && angle(i)


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phi(i)=1.570796-atan(pos(2)/R1); endifi==2

phi(i)=1.570796+ang-2*pi; endendendphiR2=sqrt((R1)^2+pos(2)^2);

J=[R2*cos(phi(1)) L3*cos(phi(2));R2*sin(phi(1)) -L3*sin(phi(2))]

Jinv=inv(J);angle=Jinv*step+angle;

%ensures new angle is always between 0 and 360deg*********************fori=1:2while (angle(i)6.2832)if angle(i)


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Appendix B: Angles to Registry Format Converter Codefunction [bytes] = LowHigh(pos)

%LOWBYTE HIGHBYTE CONVERTER

test = pos/256;

i = 0 ;while (i C(2)

B=C;

end

Register(i,(j))=B(1); Register(i,(j+1))=B(2);

i=i+1;j=1;

end

Register;


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Appendix C: Winter Term Gantt Chart


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Blank page where gantt chart will go


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Appendix D: Simulink Gait%This is a program for simulating a walking gait for the hexapod

%equivalent)

theta1_span= -32; %i.e -15 deg to +15 deg for a 30 deg spantheta2_span= -15; % i.e 0 deg to +15 deg for a 15 deg span

theta3_span= -10; %i.e 0 deg to +15 deg for a 15 deg span

tmax=10; %time to complete a step

theta1_max=theta1_span*pi/180;



seq=8; % 8 part sequence for 1 movement

i=1;

j=1;

k=1

%right (R:1,4,5) and left (L:2,3,6) gait walks

Rtheta1=[];

Rtheta2=[];

Rtheta3=[];

Ltheta1=[];

Ltheta2=[];

Ltheta3=[];

time = tmax/seq:tmax/seq:tmax; % time corresponding to each theta for 1 cycle

cycle=20; % number of tmax (i.e walking time)

total_time=tmax/seq:tmax/seq:cycle*tmax;simtime=cycle*tmax;

% assigning theta values for each sequence

while k


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Rtheta3(j)=0;

Ltheta2(j)=theta2_max;

Ltheta3(j)=theta3_max;

else

Rtheta2(j)=0;

Rtheta3(j)=0;

Ltheta2(j)=0;

Ltheta3(j)=0;

end

end

i=i+1;

j=j+1;

end

k=k+1;

end

sim('gait1',simtime);


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Appendix E: Fabrication Drawings

Drawing Number DescriptionHX-0001 GENERAL ASSEMBLY

HX-0010 FRAME ASSEMBLY

HX-0012 TOP PLATE

HX-0013 BOTTOM PLATE

HX-0020 LEFT LEG ASSEMBLY

HX-0022 FIRST LEG SECTION (LEFT)

HX-0023 SECOND LEG SECTION

HX-0024 THIRD LEG SECTION

HX-0025 FIRST LEG SECTION PART AHX-0026 FIRST LEG SECTION PART B

HX-0030 RIGHT LEG ASSEMBLY

HX-0032 FIRST LEG SECTION (RIGHT)

first term report-1

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