Algorithm for 6-legged walk

This page explains about algorithm for 6-legged walk of the robot. The robot is using the control wave that is calculated on PC and it is repeated when the robot walks. In case the robot changes the direction of progress, the control wave is changed to the proper one. The control waves are calculated with inverse kinematics in following steps.

1.Generate the orbit that the foot follows.
2.Divide the orbit with proper unit and get the points.
3.Calculate the angles of each joint for the points. (Inverse kinematics)
4.Calculate the output data for the servomotors at the joint angles.
(This set of data consists of control waves.)


[How to move the legs] [Control of direction speed] [Control of direction]

The robot is using oval and rectangle orbit. Oval orbit is used, when the robot walks first on flat terrain. And rectangle orbit is used, when the robot walks on rough terrain.



Oval orbit

How to move the legs

Leg number 0, 2, 4 (the set "A") and 1,3,5 (the set "B") are always move in the same time. While the feet of the set "A" is moving along the points "F -> A -> B", the set "B" is moving along the points "B->C->D->E->F". Figure of oval orbit shows that the distance from the point "B" to "F" is longer than the distance from the point "F" to "B". So the foot must be moved faster when it is not touching to the ground.

Control of direction speed

The progress of the robot is governed by adjusting the pitch of the unit to split the orbit. The PC sends data to decide the angle of the joints as first as signal generator can receive. So the speed of data sending is fixed.

The length of part of the orbit " F->A->B" is around 70mm and the unit is about 6mm. The maximum force to downward that each leg can generate is depending on the coordinate where the foots can reach. When PC controls the robot, the total weight of the robot is about 1900g. And when the robot is in "tether-less field-testing mode", the total weight of the robot is about 2600g. You can see in movies on the top page that the robot is walking faster in "PC control mode" than "tether-less field-testing mode".

Control of direction

Walking strait:
When the robot walks strait for every direction, the robot is using the control wave that is calculated from the oval orbit. The control waves that the leg set "A" and "B" is different from each other in phase. The difference of phase is half a wavelength.


------Strait forward------------Strait diagonally------

Turning:
The orbit that foots follow is calculated as following steps. The result of the calculation is an oval on a cylinder.


1.Decide the "center of turning"
(It is outside of the triangle which is consists from footprint.)
2.Rotate the triangle around the "center of turning"
(Locus that each of the apices follows consists the part of the orbit that the feet are touching on the ground.)
3.Calculate the part of the orbit that the feet are not touching on the ground.


At the figure below, the green lines are the part of the orbit that the feet are touching on the ground. And the red line is the locus that the center of the robot follows.


Turn

Turning at the point:
The orbit that foots follow is calculated as following steps. The result of the calculation is an oval on a cylinder as described above. But the direction that the foot follows is different with each other.

1.Decide the "center of turning"
(It is inside of the triangle which is consists from footprint.)
2.Rotate the triangle around the "center of turning"
(Locus that each of the apices follows consists the part of the orbit that the feet are touching on the ground.)
3.Calculate the part of the orbit that the feet are not touching on the ground.


At the figure below, the green lines are the part of the orbit that the feet are touching on the ground. The "center of the robot" and the "center of turning" is the same point at this example. So the robot dose not change the place but just change the direction at the place. It is like a kind of tank that is moving its each tracks towards opposite direction.


Turn at the place

Changing a course:
The robot can change its course with changing the control wave. Each of the control waves that before and after must have the same speed at the center of the robot to change direction smoothly.