**Some examples of complex physical computing applied to an omnidirectional hexapod.**

**The hexapod featured here has 3 degree-of-freedom legs thus giving the robot omnidirectional walking capabilities. Each leg has one microcomputer that controls 3 Futaba servomechanisms and carries out real-time inverse kinematics at an update rate of 50Hz, i.e. a new set of calculations is carried out every 20ms. A set of five bytes is received by each leg microcomputer every 20ms. Each set is different for each leg. Each byte is, of course, an integer ranging from 0 to 255. The five bytes represent, for each leg, the following;**

**(i) the position, “n”, of the walking step in its digital locus cycle whose shape is a rectangle, ****(ii)the leg plan angle, “plangle”, i.e. the walking step direction, (iii) the amplitude of the walking step, “amp”, (iv) the height of the rectangle, “zag” and (v) the height bias of the rectangle, “zbias”.**

**1. Figure of eight sequence**

## Here the hexapod rotates in partial circles or arcs about two points that are separated. These points are called “Instantaneous centres of rotation”. “ICofR” and are specified as x-y coordinates with respect to the hexapod body. The +ve x-axis is to the right side of the body and the +ve y-axis is to the front of the body. |

**n varies from 0 to 255 where n=0 is the leg tip positioned at its origin, n=63 is the leg tip positioned at the end of its walking-on-the-ground stroke and just beginning its walking-in-the-air stroke, n=127 is the leg tip half way through its cycle and directly above the origin in the air, n=191 is the end of the walking-in-the-airstroke and just at the point of the leg tip placing its tip back on the ground, n=255 is just short of being back at the origin with the leg ****tip on the ground. Note that there are two values of n called bp1 and bp2, (bp=”breakpoint”), where bp1 is ****a computed value dependent on the height of the locus walking rectangle called “zag”, (Z air-to-gr****ound value). For example, if the step amplitude, “amp” is amp=40 mm, (i.e. step length of 80 mm), and the height, zag=40mm then bp1=95 and bp2=223; and if zag=0 (not practical) then bp1 merges to 63 and bp2 merges to 191. The purpose of this number design is to ensure that the leg tip spends the same amount of time in the air as on the ground. Remember, that for a double tripod gait that this is the case, i.e. equal time in air as on the ground; but zag will always be greater than zero in order to walk so the path length through the air will be greater than on the ground, thus, the speed of the leg tip through the air has to be greater (and constant) than on the ground. Tricky eh! to compute in real-time. Anyway Frank has worked out a technique where you can still walk in all the other gaits other than double-tripod gait (=3-leg-support-3-swinging), i.e 4-leg support-2-swinging which has numerous variations and 5-leg-support-1-swinging which also has numerous variations.**

**2. Hexapod as an inside epicyclic gear**

**Here the hexapod has its rotation about an IC of R updated to a new location at every step**

**3. Hexapod as an outside epicyclic gear**

## Similarly the ICofR is being update at each step |

**4. Rotating about 4 points**

## ..and once again the hexapod is rotating about 4 ICofR’s but the locaction of each ICofR is respecified after a few steps rather than after each step. Thus it can be seen that an infinite range of behaviour patterns can be programmed using the concept of rotating about an ICofR |

**Mechatronic omni-directional hexapod**

## ..a demonstration programme carried out back in 2000 outside the Singapore NTU library |

**Fast retreat in corridor**

## ..another example of playing around with the location of ICofR’s. Here the location of the ICofR is at infinity distance to the left of the universe which is equal to infinity distance to the right of the universe, i.e. the hexapod walks in a straight line; then the hexapod rotates about an ICofR that is located at the point of touching of an imaginary horizontal line that is tangential to an imaginary circle passing through the outer perimeter of the leg tips. |