This is a simple planar RR model to illustrate the differences and effects of using feed-forward force control vs. trajectory control while in contact with a surface.

The model starts at a foot (yellow rectangle in picture), that is assumed to be fixed to a vertical surface. The ankle is a simple pin joint, with no actuation. There is a rotational actuator and a small mass at the knee, and the robot's main mass is represented at the hip.

DanielSantos and AaronParness have been looking at similar force control for the actual RiSE robot, but this simple model can highlight the advantages of a feed-forward force control.

Feed-forward force control is just using for each leg where is the desired wall force and is a single leg's Jacobian. (Obviously this isn't 100% correct as it's a quasi-static assumption and ignores any compliance, but it may be good enough...)

For trajectory tracking, I ended up giving it a desired position to move to and applying simple proportional feedback to get it there. This process in itself highlighted some of the many problems of trajectory tracking when the foot is in contact with the wall. At first, I was trying to get the foot to follow a trajectory, but the under-actuation made this difficult (I probably should have added some gravity compensation in the control, but again, complicated). The results can be seen in Trajectory.mp4 (will work in Quicktime) and time histories in TrajTrack.pdf. Key thing to look at is the wall reaction forces at the bottom: peaks at about 150N and then reducing towards 0.

For the force feedback, I decided I wanted and and then calculated the required torque on the knee joint using (and ignoring the resulting desired torque for the ankle joint since there is no actuator there...). Results are in Force.mp4 and ForceCommand.pdf. The cool result is that you get very similar motion with a reduced peak wall reaction force - potentially maintaining contact if there were a limit in there somewhere.

Obviously, a multi-legged robot would need some inter-leg coordination so that a gait could result (or not get too messed up), (I'd call that thing a coxswain, but that's just me), and this could arguably be called a simple form of impedence control...

-- JonathanKarpick - 23 Aug 2005

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