Controlling a Holonomic Platform

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The easiest way to control a Holonomic Platform type Omni-wheeled Robot is with an an Analogue Joystick, such as the Sony PlayStation PS2 Controller. Mindsensors produce the PSP-Nx-v3: Sony PlayStation2 Controller Interface for use with the Lego Mindstorms NXT. You can used any PS2 compatible Remote Control/Joystick Controller with the PSP-Nx-v3.

Killough Platform

I prefer the PlayStation2 Controller over other controllers, including the Lego PowerFunction Controllers, because of the flexibility you have with all the extra buttons and the two Analogue Joysticks. I picked up a suitable PlayStation2 Controller off eBay for around $15.00 which works just fine. It probably wouldn’t stand the punishment that the Sony version does, but it suffices very well for Robotics applications.

Now for Some Maths:

In a rigid body translation without rotation means that every point on the body has the same velocity as the center of mass of the whole body. Thus, for each motor we have two equations relating the velocity (e.g. V1) and the perpendicular velocity (e.g. V1′) with the projections of Omni velocity in the X and Y directions have – V sin(θ) and V cos(θ), respectively. In the following we denote these two velocity components simply as Vx and Vy.

For the first motor (the one in the forward direction) we have:

  • Vx = V1

  • Vy = –V1

For the second wheel:

  • Vx = –V2 cos(60°) – V2′ cos(30°)

  • Vy = –V2 sin(60°) + V2′ sin(30°)

And finally for the third wheel:

  • Vx = –V3 sin(30°) + V3′ cos(30°)

  • Vy = V3 cos(30°) + V3′ sin(30°)

These set of 6 unknowns (V1, V2, V3 and the three primed velocities) and 6 equations has exactly one solution:

  • V1 = Vx

  • V2  =–Vx / 2 – Sqrt(3) / 2 * Vy

  • V3 = –Vx / 2 + Sqrt(3) / 2 * Vy     {Where Sqrt(3) is just the squared root of 3.}

Using Not eXactly C (NXC) we can use the following:

NXC Source Code:

 

For a detailed explanation on the Physics and Vector Mathematics for controlling a Holonomic type Platform, I suggest you visit TechnicBRICKs. Koldo has by far the best theoretical resource on the subject I’ve came across. He saved my from dusting off my old Physics text Books and nutting most of it out. Thanks Koldo for your article:- Going to all places, in all directions: the Holonomic platform!

Listed below is an example program to control a Holonomic Platform with the Mindsensors PSP-Nx-v3 and Sony PlayStation2 Controller written in Not eXactly C (NXC).

NXC Source Code:

 

Need-More-Bricks

Rotacaster Fitted Lego Mindstorms NXT Holonomic Platform in Action!

 

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