Author Topic: Heap 'o Questions  (Read 3567 times)

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Offline BrandonTopic starter

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Heap 'o Questions
« on: October 23, 2009, 11:01:32 AM »
Hey everyone,

Surprise, surprise, I'm new to robotics. I am however a software developer by profession. Sadly though my knowledge of electronics is limited to what I learned in high school some time ago...which I have since forgotten anyway. :-\

I've been researching the subject intensely for a little over a week now and trying to form a "plan of attack" for my project. I've come up with a number of different questions I'm hoping you guys can help me out with.

First let me explain what I'm trying to accomplish. I'm majoring in computational intelligence for my BSc. Hence my focus is primarily on developing the AI. That being said, please bear in mind I have no desire to build my own components at this time. While I realise I can do this with my PC already, the end goal is getting a robot to exhibit said intelligence and that's what I want to learn (besides, robots are element 53 on the periodic table of awesome). I want to create a simple robot that does nothing more than randomly roam, avoiding obstacles, avoid plunging to it's death off an elevated surface, basic things like that. Once I'm more familiar with the hardware and how it all fits together and how the software goes about controlling things I'm hoping to make it do more advanced things like mapping, pathfinding and so on.

I've been reading alot from various sources (including SoR), watched many youtube vids and have decided i want my robot to based on the following criteria:
  • Arduino based
  • Use tracks (yes I know what you're thinking, humor me please)
  • Needs to run for at least several hours before needing a recharge
  • Must be idiot proof (myself being the idiot)

Now the questions:
  • To limit complexity I would like to get a microcontroller with a built in motor driver. I like the look of the DFRobot RoMeo. What are your thoughts on it? One reservation I have is the only manual I can find is in Chinese. Is it safe to assume that I would still be able to get support from the community because it's Arduino based despite it being a different kind of Arduino? The description is contradictory with regards to what chip it's using ATMega328 or ATMega168. Anyone know for certain what it is?
  • Would the Arduino MEGA be a good investment. I realise it doesn't have onboard motor drivers but given the plethora of I/O I'm sure a few could be sacrificed for a motor driver or two? Is there really any tangible benefit as far as the chip is concerned (speed and mem wise)? Would this start to become more beneficial when processing large amounts of data?
  • I suppose in relation to the above to posts, what are the limitations of robots controlled using microcontrollers like the Arduino? Can they perform things like speech recognition or real-time image analysis from a camera?
  • There are several tracked chassis I've been looking at:
    Lynxmotion Tri-Track Chassis
    • + Good size
    • + Good quality
    • + Powerful motors
    • + Coolness factor
    • - Cost
    Surveyor Treaded Quad Motor Base
    • + Good size
    • + Enclosable
    • + AWD
    • + Simple
    • - 4 motors
    RP5 Tracked Chassis
    • + Plastic
    • + Enclosable
    • + Cheap
    • + Simple
    • - Small
    • - Cheap quality
    • - Looks like crap

    So my question is, which to get?
    I like the Lynxmotion alot. It looks like it would make a good investment. I'm concerned about the power required to drive the motors (12V). I don't really need such powerful motors (nor do I forsee me needing them in the future), so would it be possible to give them 6-9V and just have them run at 1/2-3/4 speed or would the motors cough and splutter before throwing their arms up and surrendering to my stupidity?
    The Surveyor I actually added to my basket I was so keen. Then I tried to figure out how I would power and control the 4 motors. I saw the Adafruit motor driver but unfortunately it's a BIY solution and as I mentioned earlier I'm not really interested in that at the moment. Is there an easy way of doing this that would avoid needing to get more motor drivers? I'm hoping because I just need differential drive I can connect the signal wires to each side together and just issue commands to the one lot of pins to control both motors. How would the power setup work?
    The RP5 is my fallback if the other two don't work out. Besides being small and looking like a turd and poor quality it looks like it should suit my immediate needs. I'm not however sure if it comes with a cover for the top?
  • Do motor drivers require programming of their own or is that handled via the microcontroller anyway?
  • Power! I would just like some clarification on a few points:
    • I should power the microcontroller along with sensors and servos from one battery pack and power the motors from another? If so, why?
    • Am I correct in assuming I can send more than 5V to the microcontroller and the microcontoller will regulate it itself?
    • If 2 motors are 6V each, they still run off a 6V power supply but current is just drawn twice as fast (so battery dies twice as fast)?
  • Do you have any opinions on the Liquidware Lithium Backpack for Arduinos?
  • I don't think I've fully grasped all the benefits of shields. From my understanding they plug into the microntroller's pins and provide functionality of their own? Does that mean one forgoes the use of all the pins on the original microcontroller? I've seen expansion board type things but havent been able to work out how they can take the limited number of IOs on the microcontroller and allow one to plug a seeminly endless array of gadgets into it. Could anyone explain shields to me more clearly?
  • Is it still possible to programmatically determine the position of a servo that is modified to rotate continuously?
  • Is processing power related to reaction time? Say the robot is moving towards someone who is also moving towards it and once close enough the robot needs to get out of the way (or be trampled on), would a faster microcontroller mean (noticeably) quicker reaction?
  • I've noticed that no IR sensors seem to extend further than 150cm. Why is that? Does this mean that long range is left up to sonar for rough guesstimations and short range is left for the precision of IR?
  • Are sensors generally microcontroller agnostic? Or are they typically made to work with a certain microcontroller?

I think that's all for today. If you've read this far I commend you. And if you answer my questions I'll give you a cookie!*

Thanks everyone.  :)

*There is no cookie!
Success is the ability to go from one failure to another with no loss of enthusiasm.
Sir Winston Churchill

Offline pomprocker

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Re: Heap 'o Questions
« Reply #1 on: October 23, 2009, 11:16:17 AM »
keep it simple

don't get ahead of yourself

buy a complete kit and focus on your AI.
-depends on what language you want to program in
-how much you want to spend
-what features you want (arms, vision, etc...)

Offline BrandonTopic starter

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Re: Heap 'o Questions
« Reply #2 on: October 23, 2009, 08:57:31 PM »
But where's the fun in that?! :P

Seriously though, I'm not getting ahead of myself. Trying to build it all my self one resistor at a time would be getting ahead of myself (I can count the number of times I've soldered on one hand). I want something that will suit my immediate needs but also be scalable in the long term (I don't want to complete this project in a couple of weeks and have to order a plethora of new parts again). If I can reuse components or build onto the existing fairly easily then that's justification enough for me to spend the extra money and accept the high learning curve. Afterall, with a forum full of robot boffins I'm merely a mouse click away from help, no?  ;D

With regards to your question:
C/C++
Whatever is required (within reason)
Short term I just want the capabilities I listed. Longer term however I would like to include vision and speech-recognition. Once I've got all that I'll have enough applications to develop for to keep me busy for some time.
Success is the ability to go from one failure to another with no loss of enthusiasm.
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Offline blackbeard

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Re: Heap 'o Questions
« Reply #3 on: October 23, 2009, 09:23:22 PM »
contrary to other posts i think your using too much off the shelf components expecting it to all work together like lego. also all that stuff is really expensive and you could probably build it (yes even with tracks) for allot cheaper. since you say you don't need any real power try looking at toys with tracks. most robot chassis you can buy are super over priced. robotshop.ca is expensive in general as well. that arduino based microcontroller is very overpriced for what amounts to being basicly the same thing as a regular arduino. if you can find a tracked toy (i.e. tank) then you can make an H bridge to control the existing motors or use hacked servos after you modify the hub to drive the tracks. it's pretty easy to make your own servo connections with protoboard and terminal and that way if you change microcontrollers you can just plug it in and go.
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Offline BrandonTopic starter

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Re: Heap 'o Questions
« Reply #4 on: October 24, 2009, 02:14:25 AM »
contrary to other posts i think your using too much off the shelf components expecting it to all work together like lego.

How so? I've asked about a chassis and microcontroller. The only thing with fewer components is a fully assembled robot I would imagine?

also all that stuff is really expensive and you could probably build it (yes even with tracks) for allot cheaper. since you say you don't need any real power try looking at toys with tracks. most robot chassis you can buy are super over priced. robotshop.ca is expensive in general as well.

I realise I can make it all myself and save money. But I have neither the time nor the inclination to do that. I also realise robotshop.ca is more expensive but they stock a far greater variety of stuff than other stores and judging by the site and what people have said about them they are reliable and helpful. Because of the wide variety I save on shipping, this is then balanced out by the slightly higher cost of components. But in the end the good service is worth the additional cost. Then again, not all of the options I posted were expensive, the RP5 is only AU$50 (I spend more than that on groceries ever week!).

that arduino based microcontroller is very overpriced for what amounts to being basicly the same thing as a regular arduino.

I actually thought it was well priced. The standard Duemilanove is $30. Add on another $20 for a dual motor driver and it's the same price. It does however come with a couple more IO pins which make it that little bit more appealing. DFRobot also have a wide range of shields that I'm quite impressed with and I know will work with the microcontroller. I'm certainly open to simply getting the Duemilanove and a dual motor driver if that's the recommended approach?

if you can find a tracked toy (i.e. tank) then you can make an H bridge to control the existing motors or use hacked servos after you modify the hub to drive the tracks. it's pretty easy to make your own servo connections with protoboard and terminal and that way if you change microcontrollers you can just plug it in and go.

I appreciate the suggestion, but as I mentioned, I have no interest in re-inventing the wheel. There are perfectly good solutions out there already which I'm happy to use.

Now I really do appreciate the replies, but not even the questions to help me understand more about robotics in general - like the power or reaction time or sensor questions - have been answered. I realise my first post wasn't the standard "Hi I'm new to robotics, what do I do?" kinda questions which are usually met with a link to the $50 robot tutorial but I'm well aware of what I want to achieve with this project. I'm also well aware that I can and indeed probably should just follow the tutorial and build me a cheap and cheerful little robot. But what then? Ask these same questions? Place another order for parts to build the robot I actually wanted to build?
Success is the ability to go from one failure to another with no loss of enthusiasm.
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Offline blackbeard

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Re: Heap 'o Questions
« Reply #5 on: October 24, 2009, 07:54:54 AM »
ok fair enough. i don't like tutorials either :P. lets talk about sensors. by far the most easy sensors for obstacle avoidance, line following and distance sensing are IR sensors. personally i need to brush up on ir sensors but basically all they are is a ir led and a photo transistor, both of which are fairly cheep, which pick up distance or color by bouncing ir light off things. allot of people can help with these but i'm really rusty on these (like an iron pipe soaked in salt water for 2 years rusty). for power you will need to find a balance between volatility, weight, and power. more batteries in parallel will mean that it will last longer but it will also be heavier which CAN nullify an value of sticking them on. lithium ion and lipoly are volatile if used incorrectly but if you build your circuit correctly and avoid drawing too much power or shorts then they are the absolute best hands down. reaction time is both a combination of of programming and hardware but rarely will it make a difference unless you deliberately retard the process. unless you are trying to detect and catch an arrow in mid air or something then it's almost impossible to have a bad reaction time. now IMO the best place for parts is not a robotics web site unless you REALLY want "robot" parts. ebay is a good source for things like gear motors and other things you can't usually find. dealextreme has cheep servos and leds.
« Last Edit: October 24, 2009, 08:00:58 AM by blackbeard »
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Offline billhowl

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Re: Heap 'o Questions
« Reply #6 on: October 24, 2009, 12:53:57 PM »
So my question is, which to get?

DFRobot RoMeo.  Is a good choice for a start, but for only total of 22 IO pins is limited if you need to interface to more sensors. It using ATMega168 but it may had upgraded to ATMega328, anyway 168 or 328 the only difference is the size of memory.

Flash Memory   16 KB (ATmega168) or 32 KB (ATmega328) of which 2 KB used by bootloader
SRAM       1 KB (ATmega168) or 2 KB (ATmega328)

Arduino Mega is also a good investment, it have 54 IO pins so connect to more sensors.

Flash Memory   128 KB of which 4 KB used by bootloader
SRAM      8 KB

Quote
I like the Lynxmotion alot. It looks like it would make a good investment. I'm concerned about the power required to drive the motors (12V). I don't really need such powerful motors (nor do I forsee me needing them in the future), so would it be possible to give them 6-9V and just have them run at 1/2-3/4 speed or would the motors cough and splutter before throwing their arms up and surrendering to my stupidity?
Motors can be drive with lower voltage like 9 to 10V but will draw higher currents, these is the reason why some motors use as high 24V to drive that will reduce currents.

Quote
The Surveyor I actually added to my basket I was so keen. Then I tried to figure out how I would power and control the 4 motors. I saw the Adafruit motor driver but unfortunately it's a BIY solution and as I mentioned earlier I'm not really interested in that at the moment. Is there an easy way of doing this that would avoid needing to get more motor drivers?

Parallel the front and  back motors and drive by the same motors driver because both should move the same direction and speed.

Quote
I'm hoping because I just need differential drive I can connect the signal wires to each side together and just issue commands to the one lot of pins to control both motors. How would the power setup work?

No, each motor will drive by two pins, one for on/off speed control and the other for direction, clockwise / counterclockwise.

Quote
The RP5 is my fallback if the other two don't work out. Besides being small and looking like a turd and poor quality it looks like it should suit my immediate needs. I'm not however sure if it comes with a cover for the top?

No, it don't come with top cover.

Quote
Do motor drivers require programming of their own or is that handled via the microcontroller anyway?

Motor drivers will be handled via the microcontroller.

Quote
Power! I would just like some clarification on a few points:
I should power the microcontroller along with sensors and servos from one battery pack and power the motors from another? If so, why?

Is good to power with two battery pack, if power it with only one battery pack and when to motors stalled  and draw very high current, the voltage will drop too low there cause the microcontoller to keep resetting.

Quote
Am I correct in assuming I can send more than 5V to the microcontroller and the microcontoller will regulate it itself?

If you using the on-board Regulator then you need to supply 6-7V or higher.

Quote
If 2 motors are 6V each, they still run off a 6V power supply but current is just drawn twice as fast (so battery dies twice as fast)?
Yes.

Quote
Do you have any opinions on the Liquidware Lithium Backpack for Arduinos?

This is for Auduino standalone usage not robotics.

Quote
I don't think I've fully grasped all the benefits of shields. From my understanding they plug into the microntroller's pins and provide functionality of their own?

Does that mean one forgoes the use of all the pins on the original microcontroller?

I've seen expansion board type things but havent been able to work out how they can take the limited number of IOs on the microcontroller and allow one to plug a seeminly endless array of gadgets into it. Could anyone explain shields to me more clearly?

One of the cool things about the Arduino is that you can add shields to it to make it do whatever you want it to do. Shield that Plug in an Arduino will replicates all of the pins and keep everything connected. No two Shields should use the same IO pin.


Quote
Is it still possible to programmatically determine the position of a servo that is modified to rotate continuously?

No.

Quote
Is processing power related to reaction time? Say the robot is moving towards someone who is also moving towards it and once close enough the robot needs to get out of the way (or be trampled on), would a faster microcontroller mean (noticeably) quicker reaction?

All these will done in the programming.

Quote
I've noticed that no IR sensors seem to extend further than 150cm. Why is that?


This is the hardware limit, most IR sensors use LED as the source.

Quote
Does this mean that long range is left up to sonar for rough guesstimations and short range is left for the precision of IR?
If you need long range IR sensors you need to get IR laser sensor but the cost will high. Sensors in the range of $1000+ and size is big.


Quote
Are sensors generally microcontroller agnostic? Or are they typically made to work with a certain microcontroller?

Most sensors can work with all microcontroller.


Offline BrandonTopic starter

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Re: Heap 'o Questions
« Reply #7 on: October 25, 2009, 12:17:55 AM »
Quote
ok fair enough. i don't like tutorials either . lets talk about sensors. by far the most easy sensors for obstacle avoidance, line following and distance sensing are IR sensors. personally i need to brush up on ir sensors but basically all they are is a ir led and a photo transistor, both of which are fairly cheep, which pick up distance or color by bouncing ir light off things. allot of people can help with these but i'm really rusty on these (like an iron pipe soaked in salt water for 2 years rusty). for power you will need to find a balance between volatility, weight, and power. more batteries in parallel will mean that it will last longer but it will also be heavier which CAN nullify an value of sticking them on. lithium ion and lipoly are volatile if used incorrectly but if you build your circuit correctly and avoid drawing too much power or shorts then they are the absolute best hands down. reaction time is both a combination of of programming and hardware but rarely will it make a difference unless you deliberately retard the process. unless you are trying to detect and catch an arrow in mid air or something then it's almost impossible to have a bad reaction time. now IMO the best place for parts is not a robotics web site unless you REALLY want "robot" parts. ebay is a good source for things like gear motors and other things you can't usually find. dealextreme has cheep servos and leds.

Thanks blackbeard, that was very helpful. I'm glad to hear that reaction time won't be limited by what microcontroller I use. I don't know why I never considered eBay for parts! :)

And thank you very much billhowl, that was a fantastic reply!

I've decided to splurge and go for the MEGA. I don't want to be left needing more inputs later.

Quote
Motors can be drive with lower voltage like 9 to 10V but will draw higher currents, these is the reason why some motors use as high 24V to drive that will reduce currents.

Ah I see. Ok, if I can determine how much current is drawn at xV then I should be able to calculate how much would be drawn if I ran at a lower voltage? And given that doesn't exceed the max current supplied by the motor driver it should be fine? I've decided not to get the Lynxmotion chassis anyway, but if I do decide to go with bigger motors I would like to know how they can be worked with.

Quote
Parallel the front and  back motors and drive by the same motors driver because both should move the same direction and speed.

Yes! that's what I was hoping for (I think). I've made a diagram (attached), could you please let me know if I've understood correctly? I can't find any details on the current draw of the motors but the SRV-1 (which uses these motors) has an H-Bridge with a peak of 1A so I'm assuming if I get a similar specced motor driver it should be alright?

Quote
No, each motor will drive by two pins, one for on/off speed control and the other for direction, clockwise / counterclockwise.

Yes, sorry, I didn't word that properly. I was simplifying it to try make it clear what I was hoping for (the above scenario you confirmed!) with respect to the motors and the controllers themselves. Technically I realise that it is in fact two wires.

Quote
One of the cool things about the Arduino is that you can add shields to it to make it do whatever you want it to do. Shield that Plug in an Arduino will replicates all of the pins and keep everything connected. No two Shields should use the same IO pin.

Hmmm...I'm gonna have to try one those. :D

Quote
This is the hardware limit, most IR sensors use LED as the source.

Pity. :-[

Quote
Most sensors can work with all microcontroller.

Sweet!

Can't wait to start this project! Getting really ampped now! 8)
Success is the ability to go from one failure to another with no loss of enthusiasm.
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Offline BrandonTopic starter

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Re: Heap 'o Questions
« Reply #8 on: October 26, 2009, 01:09:51 AM »
Anyone got any input? Particularly in regards to my quad-motor setup diagram.
Success is the ability to go from one failure to another with no loss of enthusiasm.
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Offline kd5kfl

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Re: Heap 'o Questions
« Reply #9 on: October 26, 2009, 08:15:20 AM »
Quote
•Use tracks (yes I know what you're thinking, humor me please)
•Needs to run for at least several hours before needing a recharge

one or the other. massive friction with tracks.

Quote
◦I should power the microcontroller along with sensors and servos from one battery pack and power the motors from another? If so, why?

noise from the motors on your controlers
 
Quote
◦Am I correct in assuming I can send more than 5V to the microcontroller and the microcontoller will regulate it itself?

7805s are cheap. let the cheap device with the heat sink tab take the heat.

Quote
•Is it still possible to programmatically determine the position of a servo that is modified to rotate continuously?

if you can make an encoder, yes.

Offline blackbeard

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Re: Heap 'o Questions
« Reply #10 on: October 26, 2009, 01:32:03 PM »
if i may the quad motor system shouldn't be too much trouble but i've found that not all motors are created equal. it's easier to stick to 2 motors a side but 4 will work and is necessary for things like mecanum wheels. seriously if you had mecanum wheels on your robot you'd be ballin! i'm mostly concerned with the battery. i'd go with 14.4 personally. that way if you want to add a 12v camera or something of the sort it becomes a simple matter to regulate it
« Last Edit: October 26, 2009, 01:41:07 PM by blackbeard »
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Offline Soeren

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Re: Heap 'o Questions
« Reply #11 on: October 26, 2009, 06:43:10 PM »
Hi,

one or the other. massive friction with tracks.
Tracks has got a larger area than wheels, but, on a specific vehicle, that only means less weight per square area of footprint.
The same weight vehicle with tracks or wheels, assuming the same tire/track material, will have about equal friction. the only place where tracks shine, is when negotiating loose material like sand, mud or similar, where the weight of the vehicle can be distributed over a larger area, so that it doesn't dig in.
On firm ground, tracks are not really a good choice, as it will make odometry very unreliable and have a larger mechanical loss, with no gain whatsoever.
Regards,
Søren

A rather fast and fairly heavy robot with quite large wheels needs what? A lot of power?
Please remember...
Engineering is based on numbers - not adjectives

Offline blackbeard

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Re: Heap 'o Questions
« Reply #12 on: October 26, 2009, 07:28:37 PM »
oh btw if you're going for the mega would you consider the SOR axon? i
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Offline BrandonTopic starter

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Re: Heap 'o Questions
« Reply #13 on: October 26, 2009, 08:49:23 PM »
Quote
one or the other. massive friction with tracks.

You see friction, I see traction. 8)

Quote
noise from the motors on your controlers

Aaaahhh...good call Batman!

Quote
7805s are cheap. let the cheap device with the heat sink tab take the heat.

Hmmm...I'll look into that. Thanks.

Quote
if you can make an encoder, yes.

I've read a bit about these encoders. But I suppose it would be easier to just have 2 standard servos to cover 360 degrees?

Quote
if i may the quad motor system shouldn't be too much trouble but i've found that not all motors are created equal. it's easier to stick to 2 motors a side but 4 will work and is necessary for things like mecanum wheels. seriously if you had mecanum wheels on your robot you'd be ballin! i'm mostly concerned with the battery. i'd go with 14.4 personally. that way if you want to add a 12v camera or something of the sort it becomes a simple matter to regulate it

Sweet! Can I assume then that the setup in my diagram is correct? I'm not particularly keen to use 4 motors myself to be honest, but the SVR chassis comes with the 4 motors so I may as well. What's so great about mecanum wheels? Yeah, I'm still toying with various power strategies, thanks for the suggestion!

Quote
Tracks has got a larger area than wheels, but, on a specific vehicle, that only means less weight per square area of footprint.
The same weight vehicle with tracks or wheels, assuming the same tire/track material, will have about equal friction. the only place where tracks shine, is when negotiating loose material like sand, mud or similar, where the weight of the vehicle can be distributed over a larger area, so that it doesn't dig in.
On firm ground, tracks are not really a good choice, as it will make odometry very unreliable and have a larger mechanical loss, with no gain whatsoever.

Thanks for the advice Soeren! The robot will be used outdoors on grass, gravel and sand. It will also be required to negotiate fairly steep inclines. Hopefully I won't need to use odometry, eventually I hope to have the bot GPS enabled (although I'm not sure how accurate that would be on the scale of a 5" bot - more research is required).

Quote
oh btw if you're going for the mega would you consider the SOR axon? i

Good call! I'll take a look-see!
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Offline blackbeard

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Re: Heap 'o Questions
« Reply #14 on: October 27, 2009, 06:12:54 AM »
ya axon is pretty much a robot maker's dream come true. i'd get it over the mega personally and i think it's cheeper
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Offline BrandonTopic starter

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Re: Heap 'o Questions
« Reply #15 on: October 27, 2009, 09:03:28 PM »
ya axon is pretty much a robot maker's dream come true. i'd get it over the mega personally and i think it's cheeper

Hmmmm...apparently theres an Axon II coming soon? Any idea when that might be or what the specs and price might be?

One huge benefit I see the Axon having over the Arduino are the connectors! And this brings me to another (daft) question, how to Arduino uses hook up multiple components to say the 5V or GND connections? Through a breadboard? Splitter cables/device? Daisy chaining?
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Offline billhowl

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Re: Heap 'o Questions
« Reply #16 on: October 27, 2009, 10:18:02 PM »
You can connect servos to an Arduino by this servos bus without using a breadboard

Offline blackbeard

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Re: Heap 'o Questions
« Reply #17 on: October 28, 2009, 07:02:02 AM »
ya axon is pretty much a robot maker's dream come true. i'd get it over the mega personally and i think it's cheeper

Hmmmm...apparently theres an Axon II coming soon? Any idea when that might be or what the specs and price might be?

One huge benefit I see the Axon having over the Arduino are the connectors! And this brings me to another (daft) question, how to Arduino uses hook up multiple components to say the 5V or GND connections? Through a breadboard? Splitter cables/device? Daisy chaining?

ask admin he makes them :P as for hooking up an arduino to servos the pic in the last post shows an easy way.
"sure, you can test your combat robot on kittens... But all your going to do is make kitten juice"

First step: Build androids with AI
Next step: Give them vaginas

 


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