work in progress - hex walker

Yes, lots of math, but lots of control. Almost like having 6 robotic arms all doing inverse kinematics. In my math, I inclluded the ability to configure the legs for any rotation relitive to the body, so it would also work on an inline hex as well. It is basicly like a synchro in it's ability to simply re vector, though a bit more flexable in that it can jump vectors in 90 degree increments a lot faster, though there is little utility there.

As far as what a "usual " leg attachment is, I do not pay enough attention to R/C servo hexapods to know. His design is similar to Lynx's and if I recall, Colin Mackenzie's as well. It differs from Crust Crawler's in that the hip of the crust crawler uses a linkake and cantilever arrangement.

Mike

No I haven't but thanks for the info.

Thanks.

Regards Sergio Masci

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Hi Gordon,

The spacers are white nylon threaded rod with nylon washers interspersed with nylon nuts. This gives a very rigid assembly. Originally I used just washers but this allowed the assembly to twist slightly under load. I figured this would not be good for the servos. I was going to put bracing between the spacers to increase the rigidity but accidentally found that this configuration of nuts and washers did the job.

Originally I was planning to use a lot of extruded aluminium and steel threaded rods. I decided to try polycarbonate and nylon after reading the "Robot Builder's Bonanza*". The polycarb has allowed me to greatly simplify the design.

*For anyone that doesn't know, the author of the book is "Gordon McComb".

Regards Sergio Masci

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Hi Dan,

Yes as you say "most" hexapod walkers need to expend energy just holding themselves up. However if you look carefully at

you will see that it is standing on its legs (not slumped) without any power applied. This is possible here because the weight of the robot is directed straight through the servo while it is in this stance. If you consider the horizontal bar extending from the body to be a strange looking hip joint (this is the way I look at it) then the knee and leg is in fact under the robot and behaving like that of a vertebrate skeleton as you suggest above.

Regards Sergio Masci

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arrangement.

Regards "usual" leg attachment, it wasn't clear, but I was actually referring to the usual scheme of attaching the front and rear legs on the sides of the beast, inline with the middles, rather than at equal angles around the perimeter, as in EH3 and Sergio's. With the inline arrangement, it's easy to get straight-ahead walking. With the equal angle perimeter arrangement, you have to solve a lot of trig to get straightline walking, although turning is highly versatile. I also noted Colin's Twitchie/etc several years ago.

It's a nice challenge to do all the maths, but I was wondering whether you think you really gain much by going to the trouble, as compared to using the simple inline leg arrangement, where the maths is relatively trivial?

Also, when you get to more complicated gait movements, it seems the computational complexity would keep increasing. Eg, if the bot is on a sideways slope, and attempting to maintain the body level, all of the foot trajectories will be different, etc. In the same situation with the inline arrangement, pretty much all the legs do exactly the same thing, one after the other, so once you figure out what to do with the front leg, all the others follow. Randy Dumse recently commented on the complexity of doing the inverse kinematics over on yahoo TRaCy. I think he was referring to EH3, also.

Mike and I have gone back and forth on the walkers. He'll do a revision, then I will, and so on. Yes, I probably was talking about the EH-3, but specifically the EH-3I inline (as opposed to the EH-3R the round body). The extra trouble of doing all the math allows articulated movement of each leg. For instance see the movie of the inline walking at 45 degree angle:

It can also walk forward

and sideways crab style. What I'm working on now is getting it to rotate while walking. Eventually, I should be able to get it to circle something while pointing at it, a sort of stalker manuever.

You can't get these kinds of life like motion without dealing with each leg as an independent entity.

Gary Parker and his students at Connecticut College have been doing some interesting work using Genetic Algorithms to evolve efficient gaits for hexapods. They've also looked at adaptive learning for systems in which, for example, one leg is damaged or otherwise subparr. Perhaps you can find some useful information at the following URL:

What language do you program that math in?

m

Thank you I will take a look.

Regards Sergio Masci

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The math isn't that bad, in that once you solve for one leg, you solve for all. Once I have an active sensor on there, I may go to something more reflexive. As it stands, any walker without feedback is walking only because the surface it is on accidentally happens to match its expectations. Reflexive walking would require an "ingrained" sense of matching desired direction and leg sensor feedback to an appropriate servo response. While inverse kinematics is clearly over processing, it does allow one to make precise motions and could be an interesting training tool for a more sophisticated learning algorithm, representing an ideal fitness function.

In my maths, I have ground height in the calcs, so it is one step away for setting individual ground heights for each leg. I wanted to build a software package that was extensable to inline or odd leg arrangements. I eventually plan to do a 10 legged scorpion, with each leg on a side being of different length and orientation to the body. Again, my maths are not far off. When I do the scorpion, i will likely implement one smaller processor per leg, like an TiniARM or Plug A Pod, and link them via CANbus. At this time, I will start considering the neural calcs and feedback sensors, where I will need a lot more munber crunching. I will also be doing it with DC servo motors, not RC servos.

My maths are ground track accurate, with very little scrub. To do the maths for an inline or a straight line walker is no different. I got impacted at work, so I handed further development off to Randy Dumse of NMI, since it is a great showcase for the capabilities of the ServoPod. He is building in rotation tangental to a point on a plane. This will require the legs to follow an arc or psuedo arc of different radii depending on leg position relitive to the body and the center of the arc.

One feature of the math is the gait waveform tappinge different legs into the same waveform, but at different phases allows expansion of the gait. By amplifying the height of the gait, I can make the legs more or less scary looking as they cycle through. It can mince or stomp.

The thing here is that I did a lot of this simply because I could. I wasn't putting an undue burden onthe ServoPod. I didn't have to resort to serial comms ro some servo accessory, and I could do 20K plus floating point operations per second without having to get clever with my code. Since then, Randy has optimized my code, because that is the sort of thing that bugs him, but I wasn't against hasing 20% of my processor cycles in the interest of getting things done.

Yes, with your design this is correct. When it stands up by extending the lower leg segments straight downwards, the weight will still be held by the structure and not the motor energy. This is not true for EH3 or Symapod, however. In those cases, the legs are cantilevered outwards and the body weight is held by motor activation.

If you compare the 2 different situations, you'll see that the EH3 and Symapod designs actually have capability for better ground clearance. This seems to be one of the main disadvantages of the vertebrate design. With the legs rotated under the body, they cannot be lifted as much, so travel over rough terrain is more of a problem. You'll see this if you compare the potential ground clearance for your leg designs versus the other 2 cases.

So there's a tradeoff between the 2 designs. The one uses energy more efficiently, and is also capable of holding enormous body loads, like the case of the dinosaurs, while the other is more versatile with better ground clearance over rough surfaces, but uses more energy to hold the body up, and because of this apparently cannot handle really large body weights.

challenges. (or a way to develop artificial neural networks)

I am working is IsoMax, a superset of FORTH.

It is pretty easy. It uses postfix notation, which takes a bit of getting used to, but it is worth it. The ServoPod has 26 register based PWM channels which makes things easy too.

cantilevered

Aha. By virtue of someone else's post, I found the turtle that slides on its belly .... Quad 4L1.