First steps towards more dynamic gaits

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.

My previous solution

As described here, the gait I was using previously is conceptually very similar to a static IK based gait. The sequencing works by picking up and moving opposing pairs of legs in an alternating fashion. As opposed to a purely IK based solution, the inverse dynamics are accounted for. During the motion, each servo is commanded with appropriate velocities to achieve the end foot velocity profile and appropriate forces are commanded to result in a ground reaction force that matches the mass of the robot.

However, there are many things this doesn’t take into account. Among them are the linear and rotational inertia of the overall machine, the torque that the gravity vector exerts on the center of mass, and the dynamics of the legs themselves, which are assumed massless. It also only uses the high rate feedback from the servos in a very limited way, only to apply a 3D force and velocity command. Thus it completely ignores if a leg strikes the ground early either because of an obstacle or because the machine tipped, or if it strikes the ground late/never because of a depression or hole. Because of all this, it also requires periods where all four legs are on the ground simultaneously in order to maintain stability.

In this simple gait on flat ground, most problems manifest as the robot tipping during the flight phase, resulting in one flight leg striking early, which then results in a high angular rate correction as the controller tries to jam it back to the desired position. This can end up with uncontrolled oscillation of the robot in a wide range of hard to define operating conditions. Note, this is roughly the same problems that most IK based gait engines have, such as on the original Super Mega Microbot.

You can make this gait work passably if you carefully tune things and stick within a limited acceleration and terrain operational envelope, but overall it is rather fragile.

Plan

I’m not planning on tackling all of these problems in one go, or just out and out copying another solution, but intend to take small documentable steps towards a more capable machine. Up next I’ll describe my first baby steps towards this, where I look to manage the gravity torque during the flight phase to keep the machine stable even under acceleration.

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