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.

Last time I discussed the challenges when operating the mjbots quad A1 on sloped surfaces. While there are a number of possible means of tackling this, the approach I’ve gone with for now is to estimate the slope of the terrain under the robot, and use that to determine how to position the center of mass. Here’ll I’ll cover the estimation part of this solution.

On paper, the quad A1 has plenty of information to estimate the terrain under its feet. Between the IMU with attitude estimator, the proprioceptive feedback from the joints, and the ability to move the feet around, it would be obvious to a human whether the ground under them was sloped or level. The challenge here is to devise an algorithm to do so, despite the noise in the IMU, the fact that the feet are not always on the ground, and that as the robot moves, the terrain under it changes.

Not too long ago, I ran some outdoor experiments, and while piloting the quad A1 around, realized that it wasn’t going to get very far if it was restricted to just flat ground.

Since the control algorithms are completely ignorant of slopes, the center of gravity of the machine can easily get too close to the support polygon when resting, and similarly fails to stay balanced over the support line during the trot gait.

After getting a gait which looked like it could balance across the leg support line in 1D, I needed to extend that to 2D and try it out on the robot.

Extension to 2D

Extending this to two dimensions wasn’t too bad. I just did a bunch of geometry to follow the path traced out by a given 2 dimensional velocity and rotation rate, intersected with a line segment:

• mjbots/mjmech: trajectory_line_intersect.cc

Given this function, the logic to select a swing target is basically the same as in the 1 dimensional case. We now create two “virtual legs”, which consist of two feet ganged together and produce a single support line. At each time instant when all legs are in stance, we look at the time remaining until each of the virtual legs would cross the center of mass at the current velocity. As soon as one hits the half-swing point, we start a swing.

I’m working to improve the walking gait of the mjbots quad A1. In this iteration, I wanted to tackle an incremental step towards a more fully dynamic gait, but one that will still greatly increase the capability of the machine. As mentioned last time, the current walking gait cycles between all four legs, and then alternative opposing corner legs in order to move laterally. I’d like to keep that same basic structure, but be a bit smarter about what happens during the swing phase.

Now I’ve got a machine, the mjbots quad A1, which is capable of dynamic motions, but the only gait which takes advantage of these capabilities is the pronking one. That gait has the benefit that the dynamics are very simple. The entire time that that robot is in contact with the ground, it is in contact with all 4 legs, so in that regime it is fully controllable. Since it is fully controllable up to the point of lift-off, we can ensure that there is basically zero rotational rate while the machine is mid-flight, which means that it lands with all four legs largely at the same time. Of course, pronking isn’t a very fast or efficient way of getting anywhere, so I wanted to make the first steps… I guess pun intended, towards improving the more general walking algorithm to make the machine move faster in a more robust manner.

As I am working to improve the gaits of the mjbots quad A1, one aspect I’ve wanted to tackle for a long time is improving the compliance characteristics of the whole robot. Here’s a small step in that direction.

Existing compliance strategy

The quad A1 uses qdd100 servos for each of its joints. The “qdd” in qdd100 stands for “quasi direct drive”. In a quasi direct drive actuator, a low gearing ratio is used, typically less than 10 to 1, which minimizes the amount of backlash and reflected inertia as observed at the output. Then, high rate electronic control of torque in the servo based on current and position feedback allows for dynamic manipulation of the spring and dampening of the resulting system.

Now that I finally have tplot2 working sufficiently to diagnose problems in 3D, it is time to start actually fixing those problems. The first obvious thing I noticed when watching data replay was that the legs scooted around a lot after making contact with the ground. Absent 3D visualization, I knew something was wrong, but couldn’t easily tell what.

Diagnosing the first problem

Once I was able to plot the commanded position and velocity trajectory, I could clearly see a number of problems. For one, the trajectory was not terribly achievable. The velocity jumped in a discontinuous manner between different phases of the swing cycle, which resulted in large tracking errors when moving the physical legs:

Thankfully, I’m now at the point where I’m fixing actual dynamics problems on the robot.  Doubly thankfully I have a robot which is pretty robust and keeps working!  That said, it is still, shall we say, “non-ideal”, to be testing code for the first time ever on a real robot.

Back with my HerkuleX based Super Mega MicroBot, I had a working DART based simulation which was decently accurate.  However, the actuators for that machine were so limited that it didn’t really make sense to do any work in simulation.  The only way to be effective with that machine was to tweak and tweak on the real platform and rely on exactly the right amount of bouncing and wiggling that would get it moving smoothly.

After I restructured my control laws to take advantage of high rate force feedback for the pronking experiments, I haven’t actually managed to port the walking gait yet.  Now that I have a brand new robot, it seemed like a good time!

This gait is basically the same thing as I ran on the quad A0 in principle.  The opposing feet are picked up according to a rigid schedule, and moved to a point opposite their “idle” position based on the current movement speed.  Any feet that are completely placed on the ground just move with the inverse of the robot’s velocity.