Balancing on estimated terrain

Last time, I described my approach for estimating the terrain under the robot based on the inertial measurement unit and proprioceptive foot feedback. Now, I’ll cover how that is used to balance.

“R” Frame

First, let me explain the “R” or “robot” frame and how it is used. The frames I’ve discussed in this series so far are the “B” frame, which is rigidly attached to the center of the robot body, the “M” frame, which is located at the center of mass and level with the ground, and the “T” frame, which is under the robot and level with the current terrain.

The “R” frame, by contrast, is a purely invented frame that is a rigid transform away from the “B” frame. Its purpose is to allow for (1) the cool looking inverse kinematic demos that everyone seems so fond of, and (2) mostly global transforms, like this implementation of terrain based balancing. All of the gait algorithms operate almost exclusively in the R frame, which means that offsets and rotations applied there will affect the balance of the robot during its normal operation.

Using the R frame to balance

Here the algorithm is relatively straightforward. The center of the T frame is taken, transformed into the M frame and then moved up by the current average leg height. In 2D, that looks like:

Then, the point p_0 as measured in the B frame gives the desired RB transform offset. It is that simple! That formulation keeps the center of mass over the 0, 0 R frame point accounting for offsets in the center of mass and for non-level terrain.

Simulation results

Here’s the robot walking up a relatively steep slope in simulation using the above technique. The purple disc shows the estimated terrain value, while the gray disc shows the gravity normal plane.

Final steps

In the final post for this work, we’ll test it on the real robot!

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