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.

One of my goals with mjbots is to make building dynamic robots more accessible to researchers and enthusiasts everywhere. To make that more of a reality, I’m lowering the prices in a big way on the foundational components of brushless robotic systems, the moteus controller and qdd100 servo.

Don’t worry, if you purchased any of these in the last month, you should be getting a coupon in your email equivalent to the difference.

Last time I covered the new software library that I wrote to help use all the features of the pi3hat, in an efficient manner. This time, I’ll cover how I measured the performance of the result, and talk about how it can be integrated into a robotic control system.

Test Setup

To check out the timing, I wired up a pi3hat into the quad A1 and used the oscilloscope to probe one of the SPI clocks and CAN bus 1 and 3.

The pi3hat r4.2, now in the mjbots store, has only minor hardware changes from the r4 and r4.1 versions. What has changed in a bigger way is the firmware, and the software that is available to interface with it. The interface software for the previous versions was tightly coupled to the quad A1s overall codebase, that made it basically impossible to use with without significant rework. So, that rework is what I’ve done with the new libpi3hat library:

I’ve now got the last custom board from the quad A1 up in the mjbots store for sale, the mjbots pi3 hat for $129.

This board breaks out 4x 5Mbps CAN-FD ports, 1 low speed CAN port, a 1kHz IMU and a port for a nrf24l01. Despite its name, it works just fine with the Rasbperry Pi 4 in addition to the 3b+ I have tested with mostly to date. I also have a new user-space library for interfacing with it that I will document in some upcoming posts. That library makes it pretty easy to use in a variety of applications.

Only 1 full year after it was released, I managed to get a Raspberry Pi 4 and test it out in the quad A1. I had been delaying doing so because of reports of thermal issues. The Pi 3B+ already ran a little hot and I didn’t want to have to add active cooling into the robot chassis to get it stable.

It looks like the Raspberry Pi engineers have been hard at work because the newer firmware releases have significantly reduced the overall power consumption and thus the thermal load. In my testing so far it only seems “a little” hotter than the 3b+.

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.

Now that the mjbots.com store has qdd100 quasi direct drive servos, moteus controllers, and the new power dist board, it is time to start getting some useful accessories in stock. While each of these components comes with mating connectors, sometimes you need more or find that a cable harness you built previously needs to be scrapped. Availability of Amass connectors isn’t that great outside of the Chinese market, so I’ve now got XT30U male and female solder cup connectors up in packs of 10. Each pack is just $6.