I am interested in biped locomotion since 14 years. After lots of physics, mechanics, internship in Delft Biorobotic Laboratory, listening courses about underactuated robotics and conception of my own biped robot, I made a first draft for a method to make a biped robot. I think it can be useful to sum up this method here. Poppy is the robot the most compatible with this method.

The aim of this method is different since the objective is to make the robot walk and then standstill (by absorption of mechanical energy). The method is divided in four parts:

- understand limit cycle method and biped geometry
- definition of necessary conditions to have a stable walk
- tuning the 5 protections of the walking robot
- exploring all the possible gaits inside the protections

1

The biped robot can be seen as a very heavy beam (the upper body) linked with two others light beams (legs) with a variable length (thanks to knees). During walking, one leg is on the ground (the stance leg) and the other is free (the swing leg). Even if this model seems simple, it helps to understand all physics here.

We can say a system is in a limit cycle when its behaviour has an event which is recurrent. All the angles, angle rates, lengthsâ€¦ named state of the system can be taken like a photo at this event. if X is the state of the system, we can measure this state when the event occurs X[n], X[n+1]â€¦ A limit cycle is said stable if after a while, X[n+1]=X[n].

For a biped robot, the event is the state just after heel strike. Imagine a camera which make a photo at each hell strike. If the photos are the same, the gait is stable.

So the question is what happens between two photos so that X[n+1] is different from X[n] and make the system unstable ? It depends on the physics of the system. For a biped robot, I think there are 5 physical phenomenons which lead to fall:

- Falling forward stability : the swing leg of the robot is not fast enough to prevent falling forward
- Stumble stability : the swing leg touches the ground when it goes forward
- Falling backward stability : the upper body has not enough kinetic energy to go above the stance leg
- Falling sideward stability : the lateral kinetic is too high to be damped by the heel strike
- Twist stability : the swing leg gives an inertia moment on the stance foot. If the stance foot slides, the robot falls

The necessary conditions are the mechanical, electronic and software parameters to get the five index of stability

To be followedâ€¦