This document covers the process of working out x-y positions for
feet. it is intended that the y profile of the legs lift phase is a
sinusoidal curve with arbitrarily determined height. The alorythm shall
be applicable for all straight, rotary, and straved motion. It shall
further be assumed that the bodies yaw pitch and roll match the plane
being traveled (the ground). The goal of the algorthm is to create foot
positions for an input stream of positional data. This approach allows
for continious motion.


The idea here is to use one of about three methods to generate a walking
sequence for robots with leg counts greater than 4 (no suspension
state).


The three methods can be broken down into two sets:



   Rotary update
     Legs are updated in a rotary sequence clockwise around the robot.


   Wave update
     Legs are updated in waves along the robot. Where applicable,
     the phase between sides should be out by 180 degrees. This 
     takes two forms:
     
     Single updates
       In this method, only one leg is updates on the robot at a time.      

     Multiple updates
       In this method, multiple legs are updates along the 
         robot simotaniously. This works better as the leg 
         count of the robot goes up.  


The process of updating a leg consists of moving it to a new position
composed of the 'comfort' position of the leg mixed with a component of
its velocity and acceleration.     

The input data for the motion comes in the form of the following
variables:

position     x, y
yaw          i

Where X and Y are in meters, and I is in degrees. The maximum amount a
leg can be changed is a function of the update speed, and the stroke the
legs are capable of.


----------------

we need a variable that states what the ultimate state of the leg movements
 is at, from this it is determined what leg(s) are flying.
 
 things to be worked out:
 
  - what the step-state is
  - what legs are flying
  - what the destination of a leg is
  - how far flying legs are to their destination



fly tables derived from  http://www.oricomtech.com/projects/leg-time.htm

4 legs:

  4 time:
  State   Flying
   1        L1
   2        R2
   3        R1
   4        L2

  rotary:
  State     Flying
    1         R1
    2         L1
    3         R2
    4         L2
    
  diagonal:
  State     Flying  

6 legs:

  L1    R1
  L2    R2
  L3    R3


TriPod:
   State    Flying
     1        R2, L1, L3
     2        R1, R3, L2

Single Wave:
   State   Flying    
     1       L3
     2       L2
     3       L1
     4       R3
     5       R2
     6       R1

Double Wave:
   State   Flying
     1       L3, R1
     2       R1, L2
     3       L2, R3
     4       R3, L1
     5       L1, R2
     6       R2, L3 

Tripple Wave:
   State   Flying     
     1        L3, L2, R1  
     2        L2, L1, R3
     3        L1, R3, R2
     4        L3, R2, R1
    
     
8 Legs:


 'scorpion'
   State    Flying
     1         L4, R3, L2, R1
     2         R3, L2, R1, R4
     3         L2, R1, R4, L3
     4         R1, R4, L3, R2
     5         R4, L3, R2, L1
     6         L3, R2, L1, L4
     7         R2, L1, L4, R3
     8         L1, L4, R3, L2
     
     
     
     beat: number of feet down at once
     gait-style: lateral or rotary
     leg state:  swing or stance
     
     
     The timing of the legs has to be based on the amount of travel 
     to maintian a continious stride.
     
     Within any given distance to travel, a miniumum number of beats
     must occur.