Ground Reaction Force Constrained Position Control
Fixed base manipulators are nice to deal with because the motion designer is free to perform any type of motion without having the base move. Biped robots on the other hand don’t have this benefit because they suffer from under-actuation of the foot. This means that the robot can only sustain certain motions before the forces at the base will make it either slide, twist or tip.
It is difficult to stabilize a robot once the feet slide, twist or tip, usually ends with the robot having fallen over. Therefore these situations should be avoided as much as possible. It would be ideal if the motion designer could treat the biped robot like a fixed base manipulator. Ideally the system would accept any arbitrary torques and it would limit the torques such that tipping sliding and twisting doesn’t happen.
One could design the motions carefully so as to keep the base firmly on the ground however external disturbances such as unexpected bumps would still make the foot tip, slide or twist. Tipping is the biggest problem and occurs often during walking, Zero Moment Point(ZMP) feedback can be used to minimize this problem. However since the motion of the center of mass(COM) depends on the ZMP trajectory, using ZMP feedback can lead to steady state error of the COM position tracking. Besides the positioning error, the ZMP feedback approach also requires a ZMP trajectory which can be difficult to generate accurately(Simple models like LIPM aren’t very accurate) and this approach does not prevent sliding and twisting of the foot.
A better way to prevent loosing foot-ground contact would be to use force control and indeed there are several works which propose a system based on such a approach. Some shortcomings with the methods proposed so far however, is that its difficult and almost impossible to move individual joints. It would be ideal to use conventional position control but figure out the relationship between joint torques and ground reaction forces so that the joint torques can be limited such that foot can’t loose contact with the ground.
The proposed solution is to let the position controller become a reference force generator for a force control block. In so doing the ground reaction forces can be limited before being sent to the force controller. Doing so guarantees that the foot will stick to the ground while guaranteeing that the positioning performance is equivalent to pure position control(as long as no force limiting is occurring) . The way in which such a scheme can be realized is by using the virtual work principle and a structure resembling a workspace disturbance force observer.
The reader is invited to read my Masters Thesis for a more detailed explanation.
Here is a video of the experiment:
embedded by Embedded Video
This method can also be applied to stabilizing a walking trajectory so as to prevent the ZMP from going to the edge of the foot as this would make the foot tip over.
Here is a video of walking on a slope with a trajectory which was made with Preview Control. Since Preview control considers a one mass model, the trajectory generated with this method is usually inappropriate for practical, multi-mass, robots and thus requires stabilization. The proposed method managed to stabilize this trajectory for both flat and inclined(up to 8.5 degrees) floors.
embedded by Embedded Video